TSTP Solution File: SYN488-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN488-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:55:52 EDT 2022
% Result : Unsatisfiable 1.63s 1.33s
% Output : Proof 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN488-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:40:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 1.63/1.33 % SZS status Unsatisfiable
% 1.63/1.33 % SZS output start Proof
% 1.63/1.33 tff(c1_1_type, type, (
% 1.63/1.33 c1_1: $i > $o)).
% 1.63/1.33 tff(a2455_type, type, (
% 1.63/1.33 a2455: $i)).
% 1.63/1.33 tff(a2425_type, type, (
% 1.63/1.33 a2425: $i)).
% 1.63/1.33 tff(a2408_type, type, (
% 1.63/1.33 a2408: $i)).
% 1.63/1.33 tff(a2409_type, type, (
% 1.63/1.33 a2409: $i)).
% 1.63/1.33 tff(c0_1_type, type, (
% 1.63/1.33 c0_1: $i > $o)).
% 1.63/1.33 tff(a2403_type, type, (
% 1.63/1.33 a2403: $i)).
% 1.63/1.33 tff(a2435_type, type, (
% 1.63/1.33 a2435: $i)).
% 1.63/1.33 tff(c2_1_type, type, (
% 1.63/1.33 c2_1: $i > $o)).
% 1.63/1.33 tff(c3_1_type, type, (
% 1.63/1.33 c3_1: $i > $o)).
% 1.63/1.33 tff(ndr1_0_type, type, (
% 1.63/1.33 ndr1_0: $o)).
% 1.63/1.33 tff(hskp1_type, type, (
% 1.63/1.33 hskp1: $o)).
% 1.63/1.33 tff(a2413_type, type, (
% 1.63/1.33 a2413: $i)).
% 1.63/1.33 tff(hskp9_type, type, (
% 1.63/1.33 hskp9: $o)).
% 1.63/1.33 tff(a2432_type, type, (
% 1.63/1.33 a2432: $i)).
% 1.63/1.33 tff(hskp19_type, type, (
% 1.63/1.33 hskp19: $o)).
% 1.63/1.33 tff(hskp14_type, type, (
% 1.63/1.33 hskp14: $o)).
% 1.63/1.33 tff(hskp23_type, type, (
% 1.63/1.33 hskp23: $o)).
% 1.63/1.33 tff(hskp29_type, type, (
% 1.63/1.33 hskp29: $o)).
% 1.63/1.33 tff(hskp5_type, type, (
% 1.63/1.33 hskp5: $o)).
% 1.63/1.33 tff(hskp16_type, type, (
% 1.63/1.33 hskp16: $o)).
% 1.63/1.33 tff(a2414_type, type, (
% 1.63/1.33 a2414: $i)).
% 1.63/1.33 tff(a2417_type, type, (
% 1.63/1.33 a2417: $i)).
% 1.63/1.33 tff(a2422_type, type, (
% 1.63/1.33 a2422: $i)).
% 1.63/1.33 tff(hskp15_type, type, (
% 1.63/1.33 hskp15: $o)).
% 1.63/1.33 tff(a2418_type, type, (
% 1.63/1.33 a2418: $i)).
% 1.63/1.33 tff(hskp13_type, type, (
% 1.63/1.33 hskp13: $o)).
% 1.63/1.33 tff(a2404_type, type, (
% 1.63/1.33 a2404: $i)).
% 1.63/1.33 tff(hskp20_type, type, (
% 1.63/1.33 hskp20: $o)).
% 1.63/1.33 tff(hskp12_type, type, (
% 1.63/1.33 hskp12: $o)).
% 1.63/1.33 tff(a2478_type, type, (
% 1.63/1.33 a2478: $i)).
% 1.63/1.33 tff(hskp10_type, type, (
% 1.63/1.33 hskp10: $o)).
% 1.63/1.33 tff(hskp25_type, type, (
% 1.63/1.33 hskp25: $o)).
% 1.63/1.33 tff(hskp11_type, type, (
% 1.63/1.33 hskp11: $o)).
% 1.63/1.33 tff(a2416_type, type, (
% 1.63/1.33 a2416: $i)).
% 1.63/1.33 tff(hskp31_type, type, (
% 1.63/1.33 hskp31: $o)).
% 1.63/1.33 tff(hskp27_type, type, (
% 1.63/1.33 hskp27: $o)).
% 1.63/1.33 tff(a2450_type, type, (
% 1.63/1.33 a2450: $i)).
% 1.63/1.33 tff(hskp30_type, type, (
% 1.63/1.33 hskp30: $o)).
% 1.63/1.33 tff(a2420_type, type, (
% 1.63/1.33 a2420: $i)).
% 1.63/1.33 tff(hskp6_type, type, (
% 1.63/1.33 hskp6: $o)).
% 1.63/1.33 tff(a2410_type, type, (
% 1.63/1.33 a2410: $i)).
% 1.63/1.33 tff(a2498_type, type, (
% 1.63/1.33 a2498: $i)).
% 1.63/1.33 tff(a2500_type, type, (
% 1.63/1.33 a2500: $i)).
% 1.63/1.33 tff(a2407_type, type, (
% 1.63/1.33 a2407: $i)).
% 1.63/1.33 tff(hskp4_type, type, (
% 1.63/1.33 hskp4: $o)).
% 1.63/1.33 tff(a2405_type, type, (
% 1.63/1.33 a2405: $i)).
% 1.63/1.33 tff(a2484_type, type, (
% 1.63/1.33 a2484: $i)).
% 1.63/1.33 tff(hskp26_type, type, (
% 1.63/1.33 hskp26: $o)).
% 1.63/1.33 tff(hskp3_type, type, (
% 1.63/1.33 hskp3: $o)).
% 1.63/1.33 tff(hskp24_type, type, (
% 1.63/1.33 hskp24: $o)).
% 1.63/1.33 tff(a2468_type, type, (
% 1.63/1.33 a2468: $i)).
% 1.63/1.33 tff(hskp2_type, type, (
% 1.63/1.33 hskp2: $o)).
% 1.63/1.33 tff(hskp22_type, type, (
% 1.63/1.33 hskp22: $o)).
% 1.63/1.33 tff(a2453_type, type, (
% 1.63/1.33 a2453: $i)).
% 1.63/1.33 tff(hskp0_type, type, (
% 1.63/1.33 hskp0: $o)).
% 1.63/1.33 tff(a2402_type, type, (
% 1.63/1.33 a2402: $i)).
% 1.63/1.33 tff(a2427_type, type, (
% 1.63/1.33 a2427: $i)).
% 1.63/1.33 tff(hskp17_type, type, (
% 1.63/1.33 hskp17: $o)).
% 1.63/1.33 tff(hskp21_type, type, (
% 1.63/1.33 hskp21: $o)).
% 1.63/1.33 tff(a2406_type, type, (
% 1.63/1.33 a2406: $i)).
% 1.63/1.33 tff(hskp28_type, type, (
% 1.63/1.33 hskp28: $o)).
% 1.63/1.33 tff(a2437_type, type, (
% 1.63/1.33 a2437: $i)).
% 1.63/1.33 tff(a2411_type, type, (
% 1.63/1.33 a2411: $i)).
% 1.63/1.33 tff(hskp7_type, type, (
% 1.63/1.33 hskp7: $o)).
% 1.63/1.33 tff(hskp18_type, type, (
% 1.63/1.33 hskp18: $o)).
% 1.63/1.33 tff(a2428_type, type, (
% 1.63/1.33 a2428: $i)).
% 1.63/1.33 tff(1,assumption,(~c1_1(a2408)), introduced(assumption)).
% 1.63/1.33 tff(2,plain,
% 1.63/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(3,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2])).
% 1.63/1.33 tff(4,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(5,plain,
% 1.63/1.33 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(6,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[5])).
% 1.63/1.33 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.63/1.33 tff(8,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.63/1.33 tff(9,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.63/1.33 tff(10,plain,(
% 1.63/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(skolemize,[status(sab)],[9])).
% 1.63/1.33 tff(11,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.63/1.33 tff(12,plain,
% 1.63/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(13,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[12])).
% 1.63/1.33 tff(14,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(15,plain,
% 1.63/1.33 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(16,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[15])).
% 1.63/1.33 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.63/1.33 tff(18,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.63/1.33 tff(19,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.63/1.33 tff(20,plain,(
% 1.63/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(skolemize,[status(sab)],[19])).
% 1.63/1.33 tff(21,plain,
% 1.63/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.63/1.33 tff(22,assumption,(~hskp1), introduced(assumption)).
% 1.63/1.33 tff(23,plain,
% 1.63/1.33 (^[U: $i] : refl((hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(24,plain,
% 1.63/1.33 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[23])).
% 1.63/1.33 tff(25,plain,
% 1.63/1.33 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(26,plain,
% 1.63/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(27,plain,
% 1.63/1.33 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[26])).
% 1.63/1.33 tff(28,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.63/1.33 tff(29,plain,
% 1.63/1.33 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.63/1.33 tff(30,plain,
% 1.63/1.33 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.63/1.33 tff(31,plain,(
% 1.63/1.33 ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(skolemize,[status(sab)],[30])).
% 1.63/1.33 tff(32,plain,
% 1.63/1.33 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.63/1.33 tff(33,plain,
% 1.63/1.33 (^[U: $i] : refl((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(34,plain,
% 1.63/1.33 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[33])).
% 1.63/1.33 tff(35,plain,
% 1.63/1.33 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(36,plain,
% 1.63/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> ((hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(37,plain,
% 1.63/1.33 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[36])).
% 1.63/1.33 tff(38,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.63/1.33 tff(39,plain,
% 1.63/1.33 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.63/1.33 tff(40,plain,
% 1.63/1.33 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.63/1.33 tff(41,plain,(
% 1.63/1.33 ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(skolemize,[status(sab)],[40])).
% 1.63/1.33 tff(42,plain,
% 1.63/1.33 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.63/1.33 tff(43,assumption,(~hskp19), introduced(assumption)).
% 1.63/1.33 tff(44,plain,
% 1.63/1.33 (^[U: $i] : refl((hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(45,plain,
% 1.63/1.33 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[44])).
% 1.63/1.33 tff(46,plain,
% 1.63/1.33 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(47,plain,
% 1.63/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> ((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(48,plain,
% 1.63/1.33 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[47])).
% 1.63/1.33 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.63/1.33 tff(50,plain,
% 1.63/1.33 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.63/1.33 tff(51,plain,
% 1.63/1.33 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.63/1.33 tff(52,plain,(
% 1.63/1.33 ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(skolemize,[status(sab)],[51])).
% 1.63/1.33 tff(53,plain,
% 1.63/1.33 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.63/1.33 tff(54,plain,
% 1.63/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(55,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[54])).
% 1.63/1.34 tff(56,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(57,plain,
% 1.63/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(58,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[57])).
% 1.63/1.34 tff(59,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.63/1.34 tff(60,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.63/1.34 tff(61,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.63/1.34 tff(62,plain,(
% 1.63/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(skolemize,[status(sab)],[61])).
% 1.63/1.34 tff(63,plain,
% 1.63/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.63/1.34 tff(64,assumption,(~hskp16), introduced(assumption)).
% 1.63/1.34 tff(65,assumption,(~hskp13), introduced(assumption)).
% 1.63/1.34 tff(66,plain,
% 1.63/1.34 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(67,plain,
% 1.63/1.34 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[66])).
% 1.63/1.34 tff(68,plain,
% 1.63/1.34 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(69,plain,
% 1.63/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(70,plain,
% 1.73/1.34 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[69])).
% 1.73/1.34 tff(71,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.73/1.34 tff(72,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.73/1.34 tff(73,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.73/1.34 tff(74,plain,(
% 1.73/1.34 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.73/1.34 inference(skolemize,[status(sab)],[73])).
% 1.73/1.34 tff(75,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.73/1.34 tff(76,plain,
% 1.73/1.34 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(77,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[76])).
% 1.73/1.34 tff(78,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(79,plain,
% 1.73/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(80,plain,
% 1.73/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[79])).
% 1.73/1.34 tff(81,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.73/1.34 tff(82,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.73/1.34 tff(83,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.73/1.34 tff(84,plain,(
% 1.73/1.34 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(skolemize,[status(sab)],[83])).
% 1.73/1.34 tff(85,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.73/1.34 tff(86,plain,
% 1.73/1.34 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(87,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[86])).
% 1.73/1.34 tff(88,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(89,plain,
% 1.73/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(90,plain,
% 1.73/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[89])).
% 1.73/1.34 tff(91,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.73/1.34 tff(92,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.73/1.34 tff(93,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.73/1.34 tff(94,plain,(
% 1.73/1.34 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(skolemize,[status(sab)],[93])).
% 1.73/1.34 tff(95,plain,
% 1.73/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[94, 87])).
% 1.73/1.34 tff(96,assumption,(~hskp10), introduced(assumption)).
% 1.73/1.34 tff(97,plain,
% 1.73/1.34 (^[U: $i] : refl((hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(98,plain,
% 1.73/1.34 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[97])).
% 1.73/1.34 tff(99,plain,
% 1.73/1.34 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(100,plain,
% 1.73/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(101,plain,
% 1.73/1.34 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[100])).
% 1.73/1.34 tff(102,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.73/1.34 tff(103,plain,
% 1.73/1.34 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.73/1.34 tff(104,plain,
% 1.73/1.34 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.73/1.34 tff(105,plain,(
% 1.73/1.34 ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(skolemize,[status(sab)],[104])).
% 1.73/1.34 tff(106,plain,
% 1.73/1.34 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.73/1.34 tff(107,assumption,(hskp25), introduced(assumption)).
% 1.73/1.34 tff(108,plain,
% 1.73/1.34 (((~hskp25) | c2_1(a2478)) <=> ((~hskp25) | c2_1(a2478))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(109,axiom,((~hskp25) | c2_1(a2478)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.73/1.34 tff(110,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.73/1.34 tff(111,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[110, 108])).
% 1.73/1.34 tff(112,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[111, 108])).
% 1.73/1.34 tff(113,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.73/1.34 tff(114,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[113, 108])).
% 1.73/1.34 tff(115,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[114, 108])).
% 1.73/1.34 tff(116,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[115, 108])).
% 1.73/1.34 tff(117,plain,
% 1.73/1.34 ((~hskp25) | c2_1(a2478)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[116, 108])).
% 1.73/1.34 tff(118,plain,
% 1.73/1.34 (c2_1(a2478)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[117, 107])).
% 1.73/1.34 tff(119,plain,
% 1.73/1.34 (((~hskp25) | (~c0_1(a2478))) <=> ((~hskp25) | (~c0_1(a2478)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(120,plain,
% 1.73/1.34 (((~c0_1(a2478)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a2478)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(121,axiom,((~c0_1(a2478)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.73/1.34 tff(122,plain,
% 1.73/1.34 ((~hskp25) | (~c0_1(a2478))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.73/1.34 tff(123,plain,
% 1.73/1.34 ((~hskp25) | (~c0_1(a2478))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[122, 119])).
% 1.73/1.34 tff(124,plain,
% 1.73/1.34 (~c0_1(a2478)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[123, 107])).
% 1.73/1.34 tff(125,plain,
% 1.73/1.34 (((~hskp25) | (~c3_1(a2478))) <=> ((~hskp25) | (~c3_1(a2478)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(126,plain,
% 1.73/1.34 (((~c3_1(a2478)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a2478)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(127,axiom,((~c3_1(a2478)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.73/1.34 tff(128,plain,
% 1.73/1.34 ((~hskp25) | (~c3_1(a2478))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.73/1.34 tff(129,plain,
% 1.73/1.34 ((~hskp25) | (~c3_1(a2478))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[128, 125])).
% 1.73/1.34 tff(130,plain,
% 1.73/1.34 (~c3_1(a2478)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[129, 107])).
% 1.73/1.34 tff(131,plain,
% 1.73/1.34 (^[U: $i] : refl((hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(132,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[131])).
% 1.73/1.34 tff(133,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(134,plain,
% 1.73/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp16))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))))),
% 1.73/1.34 inference(bind,[status(th)],[])).
% 1.73/1.34 tff(135,plain,
% 1.73/1.34 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(quant_intro,[status(thm)],[134])).
% 1.73/1.34 tff(136,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.73/1.34 tff(137,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.73/1.34 tff(138,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.73/1.34 tff(139,plain,(
% 1.73/1.34 ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(skolemize,[status(sab)],[138])).
% 1.73/1.34 tff(140,plain,
% 1.73/1.34 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.73/1.34 tff(141,assumption,(hskp11), introduced(assumption)).
% 1.73/1.34 tff(142,plain,
% 1.73/1.34 (((~hskp11) | (~c2_1(a2416))) <=> ((~hskp11) | (~c2_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(143,plain,
% 1.73/1.34 (((~c2_1(a2416)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(144,axiom,((~c2_1(a2416)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.73/1.34 tff(145,plain,
% 1.73/1.34 ((~hskp11) | (~c2_1(a2416))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.73/1.34 tff(146,plain,
% 1.73/1.34 ((~hskp11) | (~c2_1(a2416))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[145, 142])).
% 1.73/1.34 tff(147,plain,
% 1.73/1.34 (~c2_1(a2416)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[146, 141])).
% 1.73/1.34 tff(148,plain,
% 1.73/1.34 (((~hskp11) | (~c1_1(a2416))) <=> ((~hskp11) | (~c1_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(149,plain,
% 1.73/1.34 (((~c1_1(a2416)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(150,axiom,((~c1_1(a2416)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.73/1.34 tff(151,plain,
% 1.73/1.34 ((~hskp11) | (~c1_1(a2416))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.73/1.34 tff(152,plain,
% 1.73/1.34 ((~hskp11) | (~c1_1(a2416))),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[151, 148])).
% 1.73/1.34 tff(153,plain,
% 1.73/1.34 (~c1_1(a2416)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[152, 141])).
% 1.73/1.34 tff(154,plain,
% 1.73/1.34 (((~hskp11) | c3_1(a2416)) <=> ((~hskp11) | c3_1(a2416))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(155,axiom,((~hskp11) | c3_1(a2416)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.73/1.34 tff(156,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.73/1.34 tff(157,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[156, 154])).
% 1.73/1.34 tff(158,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[157, 154])).
% 1.73/1.34 tff(159,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.73/1.34 tff(160,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[159, 154])).
% 1.73/1.34 tff(161,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[160, 154])).
% 1.73/1.34 tff(162,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[161, 154])).
% 1.73/1.34 tff(163,plain,
% 1.73/1.34 ((~hskp11) | c3_1(a2416)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[162, 154])).
% 1.73/1.34 tff(164,plain,
% 1.73/1.34 (c3_1(a2416)),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[163, 141])).
% 1.73/1.34 tff(165,assumption,(~ndr1_0), introduced(assumption)).
% 1.73/1.34 tff(166,plain,
% 1.73/1.34 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(167,plain,
% 1.73/1.34 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(168,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 1.73/1.34 tff(169,plain,
% 1.73/1.34 (ndr1_0 | (~hskp25)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.73/1.34 tff(170,plain,
% 1.73/1.34 (ndr1_0 | (~hskp25)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[169, 166])).
% 1.73/1.34 tff(171,plain,
% 1.73/1.34 (~hskp25),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[170, 165])).
% 1.73/1.34 tff(172,plain,
% 1.73/1.34 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(173,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.73/1.34 tff(174,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.73/1.34 tff(175,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[174, 172])).
% 1.73/1.34 tff(176,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[175, 172])).
% 1.73/1.34 tff(177,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.73/1.34 tff(178,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[177, 172])).
% 1.73/1.34 tff(179,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[178, 172])).
% 1.73/1.34 tff(180,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[179, 172])).
% 1.73/1.34 tff(181,plain,
% 1.73/1.34 ((~hskp31) | ndr1_0),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[180, 172])).
% 1.73/1.34 tff(182,plain,
% 1.73/1.34 (~hskp31),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[181, 165])).
% 1.73/1.34 tff(183,plain,
% 1.73/1.34 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(184,plain,
% 1.73/1.34 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(185,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.73/1.34 tff(186,plain,
% 1.73/1.34 (ndr1_0 | (~hskp27)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.73/1.34 tff(187,plain,
% 1.73/1.34 (ndr1_0 | (~hskp27)),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.73/1.34 tff(188,plain,
% 1.73/1.34 (~hskp27),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[187, 165])).
% 1.73/1.34 tff(189,plain,
% 1.73/1.34 ((hskp31 | hskp27 | hskp25) <=> (hskp31 | hskp27 | hskp25)),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(190,plain,
% 1.73/1.34 (((hskp31 | hskp25) | hskp27) <=> (hskp31 | hskp27 | hskp25)),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(191,plain,
% 1.73/1.34 ((hskp31 | hskp25) <=> (hskp31 | hskp25)),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(192,plain,
% 1.73/1.34 (((hskp31 | hskp25) | hskp27) <=> ((hskp31 | hskp25) | hskp27)),
% 1.73/1.34 inference(monotonicity,[status(thm)],[191])).
% 1.73/1.34 tff(193,plain,
% 1.73/1.34 (((hskp31 | hskp25) | hskp27) <=> (hskp31 | hskp27 | hskp25)),
% 1.73/1.34 inference(transitivity,[status(thm)],[192, 190])).
% 1.73/1.34 tff(194,axiom,((hskp31 | hskp25) | hskp27), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.73/1.34 tff(195,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.73/1.34 tff(196,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[195, 189])).
% 1.73/1.34 tff(197,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.73/1.34 tff(198,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[197, 189])).
% 1.73/1.34 tff(199,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[198, 189])).
% 1.73/1.34 tff(200,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[199, 189])).
% 1.73/1.34 tff(201,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[200, 189])).
% 1.73/1.34 tff(202,plain,
% 1.73/1.34 (hskp31 | hskp27 | hskp25),
% 1.73/1.34 inference(modus_ponens,[status(thm)],[201, 189])).
% 1.73/1.34 tff(203,plain,
% 1.73/1.34 ($false),
% 1.73/1.34 inference(unit_resolution,[status(thm)],[202, 188, 182, 171])).
% 1.73/1.34 tff(204,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.73/1.34 tff(205,plain,
% 1.73/1.34 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(206,plain,
% 1.73/1.34 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416)) <=> (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.73/1.34 inference(rewrite,[status(thm)],[])).
% 1.73/1.34 tff(207,plain,
% 1.73/1.34 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416))))),
% 1.73/1.34 inference(monotonicity,[status(thm)],[206])).
% 1.73/1.35 tff(208,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[207, 205])).
% 1.73/1.35 tff(209,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(210,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.73/1.35 tff(211,plain,
% 1.73/1.35 ($false),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[210, 204, 64, 96, 164, 153, 147, 140])).
% 1.73/1.35 tff(212,plain,((~hskp11) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.73/1.35 tff(213,plain,
% 1.73/1.35 (~hskp11),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[212, 64, 96])).
% 1.73/1.35 tff(214,plain,
% 1.73/1.35 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(215,plain,
% 1.73/1.35 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[214])).
% 1.73/1.35 tff(216,plain,
% 1.73/1.35 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(217,plain,
% 1.73/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(218,plain,
% 1.73/1.35 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[217])).
% 1.73/1.35 tff(219,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.73/1.35 tff(220,plain,
% 1.73/1.35 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.73/1.35 tff(221,plain,
% 1.73/1.35 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[220, 216])).
% 1.73/1.35 tff(222,plain,(
% 1.73/1.35 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(skolemize,[status(sab)],[221])).
% 1.73/1.35 tff(223,plain,
% 1.73/1.35 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[222, 215])).
% 1.73/1.35 tff(224,assumption,(hskp12), introduced(assumption)).
% 1.73/1.35 tff(225,plain,
% 1.73/1.35 (((~hskp12) | (~c1_1(a2417))) <=> ((~hskp12) | (~c1_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(226,plain,
% 1.73/1.35 (((~c1_1(a2417)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(227,axiom,((~c1_1(a2417)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.73/1.35 tff(228,plain,
% 1.73/1.35 ((~hskp12) | (~c1_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.73/1.35 tff(229,plain,
% 1.73/1.35 ((~hskp12) | (~c1_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[228, 225])).
% 1.73/1.35 tff(230,plain,
% 1.73/1.35 (~c1_1(a2417)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[229, 224])).
% 1.73/1.35 tff(231,plain,
% 1.73/1.35 (((~hskp12) | (~c0_1(a2417))) <=> ((~hskp12) | (~c0_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(232,plain,
% 1.73/1.35 (((~c0_1(a2417)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(233,axiom,((~c0_1(a2417)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.73/1.35 tff(234,plain,
% 1.73/1.35 ((~hskp12) | (~c0_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.73/1.35 tff(235,plain,
% 1.73/1.35 ((~hskp12) | (~c0_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[234, 231])).
% 1.73/1.35 tff(236,plain,
% 1.73/1.35 (~c0_1(a2417)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[235, 224])).
% 1.73/1.35 tff(237,plain,
% 1.73/1.35 (((~hskp12) | c3_1(a2417)) <=> ((~hskp12) | c3_1(a2417))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(238,axiom,((~hskp12) | c3_1(a2417)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.73/1.35 tff(239,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[238, 237])).
% 1.73/1.35 tff(240,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[239, 237])).
% 1.73/1.35 tff(241,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[240, 237])).
% 1.73/1.35 tff(242,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[241, 237])).
% 1.73/1.35 tff(243,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[242, 237])).
% 1.73/1.35 tff(244,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[243, 237])).
% 1.73/1.35 tff(245,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[244, 237])).
% 1.73/1.35 tff(246,plain,
% 1.73/1.35 ((~hskp12) | c3_1(a2417)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[245, 237])).
% 1.73/1.35 tff(247,plain,
% 1.73/1.35 (c3_1(a2417)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[246, 224])).
% 1.73/1.35 tff(248,plain,
% 1.73/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(249,plain,
% 1.73/1.35 ((hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417))) <=> (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(250,plain,
% 1.73/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.73/1.35 inference(monotonicity,[status(thm)],[249])).
% 1.73/1.35 tff(251,plain,
% 1.73/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[250, 248])).
% 1.73/1.35 tff(252,plain,
% 1.73/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(253,plain,
% 1.73/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.73/1.35 tff(254,plain,
% 1.73/1.35 (~c2_1(a2417)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[253, 204, 96, 247, 236, 230, 223])).
% 1.73/1.35 tff(255,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(256,plain,
% 1.73/1.35 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417)) <=> (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(257,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.73/1.35 inference(monotonicity,[status(thm)],[256])).
% 1.73/1.35 tff(258,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[257, 255])).
% 1.73/1.35 tff(259,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(260,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.73/1.35 tff(261,plain,
% 1.73/1.35 ($false),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[260, 204, 64, 96, 247, 230, 140, 254])).
% 1.73/1.35 tff(262,plain,((~hskp12) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.73/1.35 tff(263,plain,
% 1.73/1.35 (~hskp12),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[262, 64, 96])).
% 1.73/1.35 tff(264,plain,
% 1.73/1.35 (^[U: $i] : refl((hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(265,plain,
% 1.73/1.35 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[264])).
% 1.73/1.35 tff(266,plain,
% 1.73/1.35 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(267,plain,
% 1.73/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(268,plain,
% 1.73/1.35 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[267])).
% 1.73/1.35 tff(269,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.73/1.35 tff(270,plain,
% 1.73/1.35 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.73/1.35 tff(271,plain,
% 1.73/1.35 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.73/1.35 tff(272,plain,(
% 1.73/1.35 ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(skolemize,[status(sab)],[271])).
% 1.73/1.35 tff(273,plain,
% 1.73/1.35 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[272, 265])).
% 1.73/1.35 tff(274,assumption,(~c3_1(a2478)), introduced(assumption)).
% 1.73/1.35 tff(275,assumption,(c2_1(a2478)), introduced(assumption)).
% 1.73/1.35 tff(276,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(277,plain,
% 1.73/1.35 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478))) <=> (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(278,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.73/1.35 inference(monotonicity,[status(thm)],[277])).
% 1.73/1.35 tff(279,plain,
% 1.73/1.35 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[278, 276])).
% 1.73/1.35 tff(280,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(281,plain,
% 1.73/1.35 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.73/1.35 tff(282,plain,
% 1.73/1.35 (hskp16 | hskp12 | c1_1(a2478)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[281, 204, 275, 274, 273])).
% 1.73/1.35 tff(283,plain,
% 1.73/1.35 (c1_1(a2478)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[282, 263, 64])).
% 1.73/1.35 tff(284,plain,
% 1.73/1.35 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(285,plain,
% 1.73/1.35 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[284])).
% 1.73/1.35 tff(286,plain,
% 1.73/1.35 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(287,plain,
% 1.73/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> ((hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.73/1.35 inference(bind,[status(th)],[])).
% 1.73/1.35 tff(288,plain,
% 1.73/1.35 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(quant_intro,[status(thm)],[287])).
% 1.73/1.35 tff(289,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.73/1.35 tff(290,plain,
% 1.73/1.35 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.73/1.35 tff(291,plain,
% 1.73/1.35 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[290, 286])).
% 1.73/1.35 tff(292,plain,(
% 1.73/1.35 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(skolemize,[status(sab)],[291])).
% 1.73/1.35 tff(293,plain,
% 1.73/1.35 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[292, 285])).
% 1.73/1.35 tff(294,assumption,(~c0_1(a2478)), introduced(assumption)).
% 1.73/1.35 tff(295,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(296,plain,
% 1.73/1.35 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478))) <=> (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(297,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.73/1.35 inference(monotonicity,[status(thm)],[296])).
% 1.73/1.35 tff(298,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[297, 295])).
% 1.73/1.35 tff(299,plain,
% 1.73/1.35 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(300,plain,
% 1.73/1.35 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.73/1.35 tff(301,plain,
% 1.73/1.35 (hskp12 | hskp11 | (~c1_1(a2478))),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[300, 204, 275, 294, 293])).
% 1.73/1.35 tff(302,plain,
% 1.73/1.35 ($false),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[301, 283, 263, 213])).
% 1.73/1.35 tff(303,plain,(hskp16 | (~c2_1(a2478)) | c0_1(a2478) | c3_1(a2478) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.73/1.35 tff(304,plain,
% 1.73/1.35 ($false),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[303, 130, 124, 96, 64, 118])).
% 1.73/1.35 tff(305,plain,((~hskp25) | hskp10 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.73/1.35 tff(306,plain,
% 1.73/1.35 (~hskp25),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[305, 64, 96])).
% 1.73/1.35 tff(307,assumption,(hskp19), introduced(assumption)).
% 1.73/1.35 tff(308,plain,
% 1.73/1.35 (((~hskp19) | (~c0_1(a2432))) <=> ((~hskp19) | (~c0_1(a2432)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(309,plain,
% 1.73/1.35 (((~c0_1(a2432)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2432)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(310,axiom,((~c0_1(a2432)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.73/1.35 tff(311,plain,
% 1.73/1.35 ((~hskp19) | (~c0_1(a2432))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.73/1.35 tff(312,plain,
% 1.73/1.35 ((~hskp19) | (~c0_1(a2432))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[311, 308])).
% 1.73/1.35 tff(313,plain,
% 1.73/1.35 (~c0_1(a2432)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[312, 307])).
% 1.73/1.35 tff(314,plain,
% 1.73/1.35 (((~hskp19) | c1_1(a2432)) <=> ((~hskp19) | c1_1(a2432))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(315,axiom,((~hskp19) | c1_1(a2432)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.73/1.35 tff(316,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[315, 314])).
% 1.73/1.35 tff(317,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[316, 314])).
% 1.73/1.35 tff(318,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[317, 314])).
% 1.73/1.35 tff(319,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[318, 314])).
% 1.73/1.35 tff(320,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[319, 314])).
% 1.73/1.35 tff(321,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[320, 314])).
% 1.73/1.35 tff(322,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[321, 314])).
% 1.73/1.35 tff(323,plain,
% 1.73/1.35 ((~hskp19) | c1_1(a2432)),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[322, 314])).
% 1.73/1.35 tff(324,plain,
% 1.73/1.35 (c1_1(a2432)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[323, 307])).
% 1.73/1.35 tff(325,assumption,(~hskp11), introduced(assumption)).
% 1.73/1.35 tff(326,assumption,(~hskp12), introduced(assumption)).
% 1.73/1.35 tff(327,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(328,plain,
% 1.73/1.35 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432))) <=> (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(329,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.73/1.35 inference(monotonicity,[status(thm)],[328])).
% 1.73/1.35 tff(330,plain,
% 1.73/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.73/1.35 inference(transitivity,[status(thm)],[329, 327])).
% 1.73/1.35 tff(331,plain,
% 1.73/1.35 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.73/1.35 inference(quant_inst,[status(thm)],[])).
% 1.73/1.35 tff(332,plain,
% 1.73/1.35 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.73/1.35 tff(333,plain,
% 1.73/1.35 (~c2_1(a2432)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[332, 204, 326, 325, 324, 313, 293])).
% 1.73/1.35 tff(334,assumption,(hskp13), introduced(assumption)).
% 1.73/1.35 tff(335,plain,
% 1.73/1.35 (((~hskp13) | (~c0_1(a2418))) <=> ((~hskp13) | (~c0_1(a2418)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(336,plain,
% 1.73/1.35 (((~c0_1(a2418)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a2418)))),
% 1.73/1.35 inference(rewrite,[status(thm)],[])).
% 1.73/1.35 tff(337,axiom,((~c0_1(a2418)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.73/1.35 tff(338,plain,
% 1.73/1.35 ((~hskp13) | (~c0_1(a2418))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.73/1.35 tff(339,plain,
% 1.73/1.35 ((~hskp13) | (~c0_1(a2418))),
% 1.73/1.35 inference(modus_ponens,[status(thm)],[338, 335])).
% 1.73/1.35 tff(340,plain,
% 1.73/1.35 (~c0_1(a2418)),
% 1.73/1.35 inference(unit_resolution,[status(thm)],[339, 334])).
% 1.73/1.35 tff(341,plain,
% 1.73/1.35 (((~hskp13) | c2_1(a2418)) <=> ((~hskp13) | c2_1(a2418))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(342,axiom,((~hskp13) | c2_1(a2418)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.73/1.36 tff(343,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.73/1.36 tff(344,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[343, 341])).
% 1.73/1.36 tff(345,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[344, 341])).
% 1.73/1.36 tff(346,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[345, 341])).
% 1.73/1.36 tff(347,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[346, 341])).
% 1.73/1.36 tff(348,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[347, 341])).
% 1.73/1.36 tff(349,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[348, 341])).
% 1.73/1.36 tff(350,plain,
% 1.73/1.36 ((~hskp13) | c2_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[349, 341])).
% 1.73/1.36 tff(351,plain,
% 1.73/1.36 (c2_1(a2418)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[350, 334])).
% 1.73/1.36 tff(352,plain,
% 1.73/1.36 (((~hskp13) | c1_1(a2418)) <=> ((~hskp13) | c1_1(a2418))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(353,axiom,((~hskp13) | c1_1(a2418)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.73/1.36 tff(354,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.73/1.36 tff(355,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[354, 352])).
% 1.73/1.36 tff(356,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[355, 352])).
% 1.73/1.36 tff(357,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[356, 352])).
% 1.73/1.36 tff(358,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[357, 352])).
% 1.73/1.36 tff(359,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[358, 352])).
% 1.73/1.36 tff(360,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[359, 352])).
% 1.73/1.36 tff(361,plain,
% 1.73/1.36 ((~hskp13) | c1_1(a2418)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[360, 352])).
% 1.73/1.36 tff(362,plain,
% 1.73/1.36 (c1_1(a2418)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[361, 334])).
% 1.73/1.36 tff(363,plain,
% 1.73/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(364,plain,
% 1.73/1.36 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418))) <=> (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(365,plain,
% 1.73/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[364])).
% 1.73/1.36 tff(366,plain,
% 1.73/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[365, 363])).
% 1.73/1.36 tff(367,plain,
% 1.73/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(368,plain,
% 1.73/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.73/1.36 tff(369,plain,
% 1.73/1.36 ($false),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[368, 204, 326, 325, 362, 351, 340, 293])).
% 1.73/1.36 tff(370,plain,((~hskp13) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.73/1.36 tff(371,plain,
% 1.73/1.36 (~hskp13),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[370, 326, 325])).
% 1.73/1.36 tff(372,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(373,plain,
% 1.73/1.36 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432))) <=> (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(374,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[373])).
% 1.73/1.36 tff(375,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[374, 372])).
% 1.73/1.36 tff(376,plain,
% 1.73/1.36 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(377,plain,
% 1.73/1.36 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.73/1.36 tff(378,plain,
% 1.73/1.36 ($false),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[377, 204, 64, 371, 324, 313, 75, 333])).
% 1.73/1.36 tff(379,plain,((~hskp19) | hskp16 | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.73/1.36 tff(380,plain,
% 1.73/1.36 (~hskp19),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[379, 64, 263, 213])).
% 1.73/1.36 tff(381,plain,
% 1.73/1.36 ((hskp25 | hskp19 | hskp5) <=> (hskp25 | hskp19 | hskp5)),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(382,plain,
% 1.73/1.36 (((hskp19 | hskp5) | hskp25) <=> (hskp25 | hskp19 | hskp5)),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(383,plain,
% 1.73/1.36 ((hskp5 | hskp19) <=> (hskp19 | hskp5)),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(384,plain,
% 1.73/1.36 (((hskp5 | hskp19) | hskp25) <=> ((hskp19 | hskp5) | hskp25)),
% 1.73/1.36 inference(monotonicity,[status(thm)],[383])).
% 1.73/1.36 tff(385,plain,
% 1.73/1.36 (((hskp5 | hskp19) | hskp25) <=> (hskp25 | hskp19 | hskp5)),
% 1.73/1.36 inference(transitivity,[status(thm)],[384, 382])).
% 1.73/1.36 tff(386,axiom,((hskp5 | hskp19) | hskp25), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.73/1.36 tff(387,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.73/1.36 tff(388,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[387, 381])).
% 1.73/1.36 tff(389,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[388, 381])).
% 1.73/1.36 tff(390,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[389, 381])).
% 1.73/1.36 tff(391,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[390, 381])).
% 1.73/1.36 tff(392,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[391, 381])).
% 1.73/1.36 tff(393,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[392, 381])).
% 1.73/1.36 tff(394,plain,
% 1.73/1.36 (hskp25 | hskp19 | hskp5),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[393, 381])).
% 1.73/1.36 tff(395,plain,
% 1.73/1.36 (hskp5),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[394, 380, 306])).
% 1.73/1.36 tff(396,plain,
% 1.73/1.36 (((~hskp5) | (~c2_1(a2408))) <=> ((~hskp5) | (~c2_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(397,plain,
% 1.73/1.36 (((~c2_1(a2408)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(398,axiom,((~c2_1(a2408)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.73/1.36 tff(399,plain,
% 1.73/1.36 ((~hskp5) | (~c2_1(a2408))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.73/1.36 tff(400,plain,
% 1.73/1.36 ((~hskp5) | (~c2_1(a2408))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[399, 396])).
% 1.73/1.36 tff(401,plain,
% 1.73/1.36 (~c2_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[400, 395])).
% 1.73/1.36 tff(402,plain,
% 1.73/1.36 (((~hskp5) | c0_1(a2408)) <=> ((~hskp5) | c0_1(a2408))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(403,axiom,((~hskp5) | c0_1(a2408)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.73/1.36 tff(404,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.73/1.36 tff(405,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[404, 402])).
% 1.73/1.36 tff(406,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[405, 402])).
% 1.73/1.36 tff(407,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[406, 402])).
% 1.73/1.36 tff(408,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[407, 402])).
% 1.73/1.36 tff(409,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[408, 402])).
% 1.73/1.36 tff(410,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[409, 402])).
% 1.73/1.36 tff(411,plain,
% 1.73/1.36 ((~hskp5) | c0_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[410, 402])).
% 1.73/1.36 tff(412,plain,
% 1.73/1.36 (c0_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[411, 395])).
% 1.73/1.36 tff(413,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(414,plain,
% 1.73/1.36 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408))) <=> (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(415,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[414])).
% 1.73/1.36 tff(416,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[415, 413])).
% 1.73/1.36 tff(417,plain,
% 1.73/1.36 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(418,plain,
% 1.73/1.36 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.73/1.36 tff(419,plain,
% 1.73/1.36 (~c1_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[418, 204, 306, 380, 412, 401, 106])).
% 1.73/1.36 tff(420,plain,
% 1.73/1.36 (((~hskp5) | c3_1(a2408)) <=> ((~hskp5) | c3_1(a2408))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(421,axiom,((~hskp5) | c3_1(a2408)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.73/1.36 tff(422,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.73/1.36 tff(423,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[422, 420])).
% 1.73/1.36 tff(424,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[423, 420])).
% 1.73/1.36 tff(425,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[424, 420])).
% 1.73/1.36 tff(426,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[425, 420])).
% 1.73/1.36 tff(427,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[426, 420])).
% 1.73/1.36 tff(428,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[427, 420])).
% 1.73/1.36 tff(429,plain,
% 1.73/1.36 ((~hskp5) | c3_1(a2408)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[428, 420])).
% 1.73/1.36 tff(430,plain,
% 1.73/1.36 (c3_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[429, 395])).
% 1.73/1.36 tff(431,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(432,plain,
% 1.73/1.36 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408)) <=> (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(433,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[432])).
% 1.73/1.36 tff(434,plain,
% 1.73/1.36 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[433, 431])).
% 1.73/1.36 tff(435,plain,
% 1.73/1.36 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(436,plain,
% 1.73/1.36 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.73/1.36 tff(437,plain,
% 1.73/1.36 ($false),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[436, 204, 64, 96, 430, 401, 140, 419])).
% 1.73/1.36 tff(438,plain,(hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.73/1.36 tff(439,plain,
% 1.73/1.36 (hskp16),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[438, 96])).
% 1.73/1.36 tff(440,plain,
% 1.73/1.36 (((~hskp16) | (~c3_1(a2425))) <=> ((~hskp16) | (~c3_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(441,plain,
% 1.73/1.36 (((~c3_1(a2425)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(442,axiom,((~c3_1(a2425)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.73/1.36 tff(443,plain,
% 1.73/1.36 ((~hskp16) | (~c3_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.73/1.36 tff(444,plain,
% 1.73/1.36 ((~hskp16) | (~c3_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[443, 440])).
% 1.73/1.36 tff(445,plain,
% 1.73/1.36 (~c3_1(a2425)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[444, 439])).
% 1.73/1.36 tff(446,plain,
% 1.73/1.36 (((~hskp16) | (~c2_1(a2425))) <=> ((~hskp16) | (~c2_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(447,plain,
% 1.73/1.36 (((~c2_1(a2425)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(448,axiom,((~c2_1(a2425)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.73/1.36 tff(449,plain,
% 1.73/1.36 ((~hskp16) | (~c2_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.73/1.36 tff(450,plain,
% 1.73/1.36 ((~hskp16) | (~c2_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[449, 446])).
% 1.73/1.36 tff(451,plain,
% 1.73/1.36 (~c2_1(a2425)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[450, 439])).
% 1.73/1.36 tff(452,plain,
% 1.73/1.36 (((~hskp16) | c0_1(a2425)) <=> ((~hskp16) | c0_1(a2425))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(453,axiom,((~hskp16) | c0_1(a2425)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.73/1.36 tff(454,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.73/1.36 tff(455,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[454, 452])).
% 1.73/1.36 tff(456,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[455, 452])).
% 1.73/1.36 tff(457,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[456, 452])).
% 1.73/1.36 tff(458,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[457, 452])).
% 1.73/1.36 tff(459,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[458, 452])).
% 1.73/1.36 tff(460,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[459, 452])).
% 1.73/1.36 tff(461,plain,
% 1.73/1.36 ((~hskp16) | c0_1(a2425)),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[460, 452])).
% 1.73/1.36 tff(462,plain,
% 1.73/1.36 (c0_1(a2425)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[461, 439])).
% 1.73/1.36 tff(463,plain,
% 1.73/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(464,plain,
% 1.73/1.36 ((hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425))) <=> (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(465,plain,
% 1.73/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[464])).
% 1.73/1.36 tff(466,plain,
% 1.73/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[465, 463])).
% 1.73/1.36 tff(467,plain,
% 1.73/1.36 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(468,plain,
% 1.73/1.36 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.73/1.36 tff(469,plain,
% 1.73/1.36 (c1_1(a2425)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[468, 204, 96, 462, 451, 445, 95])).
% 1.73/1.36 tff(470,plain,
% 1.73/1.36 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.73/1.36 inference(bind,[status(th)],[])).
% 1.73/1.36 tff(471,plain,
% 1.73/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(quant_intro,[status(thm)],[470])).
% 1.73/1.36 tff(472,plain,
% 1.73/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(473,plain,
% 1.73/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.73/1.36 inference(bind,[status(th)],[])).
% 1.73/1.36 tff(474,plain,
% 1.73/1.36 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(quant_intro,[status(thm)],[473])).
% 1.73/1.36 tff(475,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.73/1.36 tff(476,plain,
% 1.73/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.73/1.36 tff(477,plain,
% 1.73/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[476, 472])).
% 1.73/1.36 tff(478,plain,(
% 1.73/1.36 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(skolemize,[status(sab)],[477])).
% 1.73/1.36 tff(479,plain,
% 1.73/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.73/1.36 tff(480,plain,
% 1.73/1.36 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(481,plain,
% 1.73/1.36 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425))) <=> (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(482,plain,
% 1.73/1.36 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[481])).
% 1.73/1.36 tff(483,plain,
% 1.73/1.36 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[482, 480])).
% 1.73/1.36 tff(484,plain,
% 1.73/1.36 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(485,plain,
% 1.73/1.36 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.73/1.36 tff(486,plain,
% 1.73/1.36 (hskp19 | hskp5),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[485, 204, 462, 451, 445, 53])).
% 1.73/1.36 tff(487,plain,
% 1.73/1.36 (hskp5),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[486, 43])).
% 1.73/1.36 tff(488,plain,
% 1.73/1.36 (c3_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[429, 487])).
% 1.73/1.36 tff(489,plain,
% 1.73/1.36 (~c2_1(a2408)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[400, 487])).
% 1.73/1.36 tff(490,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(491,plain,
% 1.73/1.36 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.73/1.36 inference(rewrite,[status(thm)],[])).
% 1.73/1.36 tff(492,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.73/1.36 inference(monotonicity,[status(thm)],[491])).
% 1.73/1.36 tff(493,plain,
% 1.73/1.36 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.73/1.36 inference(transitivity,[status(thm)],[492, 490])).
% 1.73/1.36 tff(494,plain,
% 1.73/1.36 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.73/1.36 inference(quant_inst,[status(thm)],[])).
% 1.73/1.36 tff(495,plain,
% 1.73/1.36 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.73/1.36 inference(modus_ponens,[status(thm)],[494, 493])).
% 1.73/1.36 tff(496,plain,
% 1.73/1.36 (hskp25 | hskp19 | (~c1_1(a2425))),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[495, 204, 462, 451, 106])).
% 1.73/1.36 tff(497,plain,
% 1.73/1.36 (hskp25),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[496, 43, 469])).
% 1.73/1.36 tff(498,plain,
% 1.73/1.36 (c2_1(a2478)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[117, 497])).
% 1.73/1.36 tff(499,plain,
% 1.73/1.36 (~c3_1(a2478)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[129, 497])).
% 1.73/1.36 tff(500,plain,
% 1.73/1.36 (~c0_1(a2478)),
% 1.73/1.36 inference(unit_resolution,[status(thm)],[123, 497])).
% 1.73/1.36 tff(501,assumption,(hskp23), introduced(assumption)).
% 1.73/1.36 tff(502,plain,
% 1.73/1.36 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.73/1.36 inference(bind,[status(th)],[])).
% 1.73/1.37 tff(503,plain,
% 1.73/1.37 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(quant_intro,[status(thm)],[502])).
% 1.73/1.37 tff(504,plain,
% 1.73/1.37 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(505,plain,
% 1.73/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.73/1.37 inference(bind,[status(th)],[])).
% 1.73/1.37 tff(506,plain,
% 1.73/1.37 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(quant_intro,[status(thm)],[505])).
% 1.73/1.37 tff(507,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.73/1.37 tff(508,plain,
% 1.73/1.37 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.73/1.37 tff(509,plain,
% 1.73/1.37 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[508, 504])).
% 1.73/1.37 tff(510,plain,(
% 1.73/1.37 ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(skolemize,[status(sab)],[509])).
% 1.73/1.37 tff(511,plain,
% 1.73/1.37 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[510, 503])).
% 1.73/1.37 tff(512,plain,
% 1.73/1.37 (((~hskp23) | (~c0_1(a2455))) <=> ((~hskp23) | (~c0_1(a2455)))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(513,plain,
% 1.73/1.37 (((~c0_1(a2455)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a2455)))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(514,axiom,((~c0_1(a2455)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.73/1.37 tff(515,plain,
% 1.73/1.37 ((~hskp23) | (~c0_1(a2455))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.73/1.37 tff(516,plain,
% 1.73/1.37 ((~hskp23) | (~c0_1(a2455))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[515, 512])).
% 1.73/1.37 tff(517,plain,
% 1.73/1.37 (~c0_1(a2455)),
% 1.73/1.37 inference(unit_resolution,[status(thm)],[516, 501])).
% 1.73/1.37 tff(518,plain,
% 1.73/1.37 (((~hskp23) | c3_1(a2455)) <=> ((~hskp23) | c3_1(a2455))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(519,axiom,((~hskp23) | c3_1(a2455)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.73/1.37 tff(520,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.73/1.37 tff(521,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[520, 518])).
% 1.73/1.37 tff(522,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.73/1.37 tff(523,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.73/1.37 tff(524,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[523, 518])).
% 1.73/1.37 tff(525,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[524, 518])).
% 1.73/1.37 tff(526,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[525, 518])).
% 1.73/1.37 tff(527,plain,
% 1.73/1.37 ((~hskp23) | c3_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[526, 518])).
% 1.73/1.37 tff(528,plain,
% 1.73/1.37 (c3_1(a2455)),
% 1.73/1.37 inference(unit_resolution,[status(thm)],[527, 501])).
% 1.73/1.37 tff(529,plain,
% 1.73/1.37 (((~hskp23) | c2_1(a2455)) <=> ((~hskp23) | c2_1(a2455))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(530,axiom,((~hskp23) | c2_1(a2455)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.73/1.37 tff(531,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.73/1.37 tff(532,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[531, 529])).
% 1.73/1.37 tff(533,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[532, 529])).
% 1.73/1.37 tff(534,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[533, 529])).
% 1.73/1.37 tff(535,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[534, 529])).
% 1.73/1.37 tff(536,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[535, 529])).
% 1.73/1.37 tff(537,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[536, 529])).
% 1.73/1.37 tff(538,plain,
% 1.73/1.37 ((~hskp23) | c2_1(a2455)),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[537, 529])).
% 1.73/1.37 tff(539,plain,
% 1.73/1.37 (c2_1(a2455)),
% 1.73/1.37 inference(unit_resolution,[status(thm)],[538, 501])).
% 1.73/1.37 tff(540,assumption,(~hskp15), introduced(assumption)).
% 1.73/1.37 tff(541,plain,
% 1.73/1.37 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(542,plain,
% 1.73/1.37 ((hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455))) <=> (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.73/1.37 inference(rewrite,[status(thm)],[])).
% 1.73/1.37 tff(543,plain,
% 1.73/1.37 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.73/1.37 inference(monotonicity,[status(thm)],[542])).
% 1.73/1.37 tff(544,plain,
% 1.73/1.37 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.73/1.37 inference(transitivity,[status(thm)],[543, 541])).
% 1.73/1.37 tff(545,plain,
% 1.73/1.37 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.73/1.37 inference(quant_inst,[status(thm)],[])).
% 1.73/1.37 tff(546,plain,
% 1.73/1.37 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.73/1.37 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.73/1.37 tff(547,plain,
% 1.73/1.37 ($false),
% 1.73/1.37 inference(unit_resolution,[status(thm)],[546, 204, 540, 539, 528, 517, 511])).
% 1.73/1.37 tff(548,plain,((~hskp23) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.76/1.37 tff(549,plain,
% 1.76/1.37 (hskp15),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[548, 501])).
% 1.76/1.37 tff(550,plain,
% 1.76/1.37 (((~hskp15) | c3_1(a2422)) <=> ((~hskp15) | c3_1(a2422))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(551,axiom,((~hskp15) | c3_1(a2422)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.76/1.37 tff(552,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.76/1.37 tff(553,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[552, 550])).
% 1.76/1.37 tff(554,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[553, 550])).
% 1.76/1.37 tff(555,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[554, 550])).
% 1.76/1.37 tff(556,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[555, 550])).
% 1.76/1.37 tff(557,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[556, 550])).
% 1.76/1.37 tff(558,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[557, 550])).
% 1.76/1.37 tff(559,plain,
% 1.76/1.37 ((~hskp15) | c3_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[558, 550])).
% 1.76/1.37 tff(560,plain,
% 1.76/1.37 (c3_1(a2422)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[559, 549])).
% 1.76/1.37 tff(561,plain,
% 1.76/1.37 (((~hskp15) | c1_1(a2422)) <=> ((~hskp15) | c1_1(a2422))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(562,axiom,((~hskp15) | c1_1(a2422)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.76/1.37 tff(563,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.76/1.37 tff(564,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[563, 561])).
% 1.76/1.37 tff(565,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[564, 561])).
% 1.76/1.37 tff(566,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[565, 561])).
% 1.76/1.37 tff(567,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[566, 561])).
% 1.76/1.37 tff(568,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[567, 561])).
% 1.76/1.37 tff(569,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[568, 561])).
% 1.76/1.37 tff(570,plain,
% 1.76/1.37 ((~hskp15) | c1_1(a2422)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[569, 561])).
% 1.76/1.37 tff(571,plain,
% 1.76/1.37 (c1_1(a2422)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[570, 549])).
% 1.76/1.37 tff(572,plain,
% 1.76/1.37 (((~hskp15) | (~c2_1(a2422))) <=> ((~hskp15) | (~c2_1(a2422)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(573,plain,
% 1.76/1.37 (((~c2_1(a2422)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2422)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(574,axiom,((~c2_1(a2422)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.76/1.37 tff(575,plain,
% 1.76/1.37 ((~hskp15) | (~c2_1(a2422))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.76/1.37 tff(576,plain,
% 1.76/1.37 ((~hskp15) | (~c2_1(a2422))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[575, 572])).
% 1.76/1.37 tff(577,plain,
% 1.76/1.37 (~c2_1(a2422)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[576, 549])).
% 1.76/1.37 tff(578,plain,
% 1.76/1.37 (hskp16),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[303, 96, 294, 274, 275])).
% 1.76/1.37 tff(579,plain,
% 1.76/1.37 (~c3_1(a2425)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[444, 578])).
% 1.76/1.37 tff(580,plain,
% 1.76/1.37 (~c2_1(a2425)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[450, 578])).
% 1.76/1.37 tff(581,plain,
% 1.76/1.37 (c0_1(a2425)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[461, 578])).
% 1.76/1.37 tff(582,plain,
% 1.76/1.37 (c1_1(a2425)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[468, 204, 96, 581, 580, 579, 95])).
% 1.76/1.37 tff(583,assumption,(c3_1(a2455)), introduced(assumption)).
% 1.76/1.37 tff(584,assumption,(c2_1(a2455)), introduced(assumption)).
% 1.76/1.37 tff(585,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(586,plain,
% 1.76/1.37 ((hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(587,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.76/1.37 inference(monotonicity,[status(thm)],[586])).
% 1.76/1.37 tff(588,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.76/1.37 inference(transitivity,[status(thm)],[587, 585])).
% 1.76/1.37 tff(589,plain,
% 1.76/1.37 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.37 inference(quant_inst,[status(thm)],[])).
% 1.76/1.37 tff(590,plain,
% 1.76/1.37 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.76/1.37 tff(591,plain,
% 1.76/1.37 ((~c1_1(a2425)) | (~c1_1(a2455))),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[590, 204, 96, 584, 583, 581, 579, 479])).
% 1.76/1.37 tff(592,plain,
% 1.76/1.37 (~c1_1(a2455)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[591, 582])).
% 1.76/1.37 tff(593,plain,
% 1.76/1.37 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 1.76/1.37 inference(bind,[status(th)],[])).
% 1.76/1.37 tff(594,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(quant_intro,[status(thm)],[593])).
% 1.76/1.37 tff(595,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(596,plain,
% 1.76/1.37 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 1.76/1.37 inference(bind,[status(th)],[])).
% 1.76/1.37 tff(597,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(quant_intro,[status(thm)],[596])).
% 1.76/1.37 tff(598,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.76/1.37 tff(599,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.76/1.37 tff(600,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[599, 595])).
% 1.76/1.37 tff(601,plain,(
% 1.76/1.37 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(skolemize,[status(sab)],[600])).
% 1.76/1.37 tff(602,plain,
% 1.76/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[601, 594])).
% 1.76/1.37 tff(603,plain,
% 1.76/1.37 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.76/1.37 inference(bind,[status(th)],[])).
% 1.76/1.37 tff(604,plain,
% 1.76/1.37 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(quant_intro,[status(thm)],[603])).
% 1.76/1.37 tff(605,plain,
% 1.76/1.37 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(606,plain,
% 1.76/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.76/1.37 inference(bind,[status(th)],[])).
% 1.76/1.37 tff(607,plain,
% 1.76/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(quant_intro,[status(thm)],[606])).
% 1.76/1.37 tff(608,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.76/1.37 tff(609,plain,
% 1.76/1.37 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.76/1.37 tff(610,plain,
% 1.76/1.37 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.76/1.37 tff(611,plain,(
% 1.76/1.37 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(skolemize,[status(sab)],[610])).
% 1.76/1.37 tff(612,plain,
% 1.76/1.37 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[611, 604])).
% 1.76/1.37 tff(613,assumption,(~c2_1(a2422)), introduced(assumption)).
% 1.76/1.37 tff(614,assumption,(c3_1(a2422)), introduced(assumption)).
% 1.76/1.37 tff(615,assumption,(c1_1(a2422)), introduced(assumption)).
% 1.76/1.37 tff(616,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(617,plain,
% 1.76/1.37 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422))) <=> (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(618,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.76/1.37 inference(monotonicity,[status(thm)],[617])).
% 1.76/1.37 tff(619,plain,
% 1.76/1.37 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.37 inference(transitivity,[status(thm)],[618, 616])).
% 1.76/1.37 tff(620,plain,
% 1.76/1.37 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.76/1.37 inference(quant_inst,[status(thm)],[])).
% 1.76/1.37 tff(621,plain,
% 1.76/1.37 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[620, 619])).
% 1.76/1.37 tff(622,plain,
% 1.76/1.37 (hskp30 | (~c1_1(a2425))),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[621, 204, 581, 615, 614, 579, 613, 612])).
% 1.76/1.37 tff(623,plain,
% 1.76/1.37 (hskp30),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[622, 582])).
% 1.76/1.37 tff(624,plain,
% 1.76/1.37 (((~hskp30) | c3_1(a2450)) <=> ((~hskp30) | c3_1(a2450))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(625,axiom,((~hskp30) | c3_1(a2450)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.76/1.37 tff(626,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.76/1.37 tff(627,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[626, 624])).
% 1.76/1.37 tff(628,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[627, 624])).
% 1.76/1.37 tff(629,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[628, 624])).
% 1.76/1.37 tff(630,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[629, 624])).
% 1.76/1.37 tff(631,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[630, 624])).
% 1.76/1.37 tff(632,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[631, 624])).
% 1.76/1.37 tff(633,plain,
% 1.76/1.37 ((~hskp30) | c3_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[632, 624])).
% 1.76/1.37 tff(634,plain,
% 1.76/1.37 (c3_1(a2450)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[633, 623])).
% 1.76/1.37 tff(635,plain,
% 1.76/1.37 (((~hskp30) | c1_1(a2450)) <=> ((~hskp30) | c1_1(a2450))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(636,axiom,((~hskp30) | c1_1(a2450)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.76/1.37 tff(637,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.76/1.37 tff(638,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[637, 635])).
% 1.76/1.37 tff(639,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[638, 635])).
% 1.76/1.37 tff(640,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[639, 635])).
% 1.76/1.37 tff(641,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[640, 635])).
% 1.76/1.37 tff(642,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[641, 635])).
% 1.76/1.37 tff(643,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[642, 635])).
% 1.76/1.37 tff(644,plain,
% 1.76/1.37 ((~hskp30) | c1_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[643, 635])).
% 1.76/1.37 tff(645,plain,
% 1.76/1.37 (c1_1(a2450)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[644, 623])).
% 1.76/1.37 tff(646,plain,
% 1.76/1.37 (((~hskp30) | c0_1(a2450)) <=> ((~hskp30) | c0_1(a2450))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(647,axiom,((~hskp30) | c0_1(a2450)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.76/1.37 tff(648,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.76/1.37 tff(649,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[648, 646])).
% 1.76/1.37 tff(650,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[649, 646])).
% 1.76/1.37 tff(651,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[650, 646])).
% 1.76/1.37 tff(652,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[651, 646])).
% 1.76/1.37 tff(653,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[652, 646])).
% 1.76/1.37 tff(654,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[653, 646])).
% 1.76/1.37 tff(655,plain,
% 1.76/1.37 ((~hskp30) | c0_1(a2450)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[654, 646])).
% 1.76/1.37 tff(656,plain,
% 1.76/1.37 (c0_1(a2450)),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[655, 623])).
% 1.76/1.37 tff(657,plain,
% 1.76/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(658,plain,
% 1.76/1.37 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.76/1.37 inference(rewrite,[status(thm)],[])).
% 1.76/1.37 tff(659,plain,
% 1.76/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.76/1.37 inference(monotonicity,[status(thm)],[658])).
% 1.76/1.37 tff(660,plain,
% 1.76/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.76/1.37 inference(transitivity,[status(thm)],[659, 657])).
% 1.76/1.37 tff(661,plain,
% 1.76/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.76/1.37 inference(quant_inst,[status(thm)],[])).
% 1.76/1.37 tff(662,plain,
% 1.76/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.76/1.37 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.76/1.37 tff(663,plain,
% 1.76/1.37 ($false),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[662, 204, 656, 645, 634, 584, 583, 581, 580, 579, 602, 592])).
% 1.76/1.37 tff(664,plain,(hskp10 | (~c2_1(a2455)) | (~c3_1(a2455)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2422) | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.76/1.37 tff(665,plain,
% 1.76/1.37 ($false),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[664, 577, 571, 96, 294, 274, 539, 528, 560, 275])).
% 1.76/1.37 tff(666,plain,((~hskp23) | hskp10 | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.76/1.37 tff(667,plain,
% 1.76/1.37 (~hskp23),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[666, 500, 96, 499, 498])).
% 1.76/1.37 tff(668,assumption,(~c2_1(a2408)), introduced(assumption)).
% 1.76/1.37 tff(669,assumption,(c3_1(a2408)), introduced(assumption)).
% 1.76/1.37 tff(670,plain,
% 1.76/1.37 (hskp16 | hskp10),
% 1.76/1.37 inference(unit_resolution,[status(thm)],[436, 204, 669, 668, 140, 1])).
% 1.76/1.38 tff(671,plain,
% 1.76/1.38 (hskp16),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[670, 96])).
% 1.76/1.38 tff(672,plain,
% 1.76/1.38 (~c3_1(a2425)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[444, 671])).
% 1.76/1.38 tff(673,plain,
% 1.76/1.38 (~c2_1(a2425)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[450, 671])).
% 1.76/1.38 tff(674,plain,
% 1.76/1.38 (c0_1(a2425)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[461, 671])).
% 1.76/1.38 tff(675,plain,
% 1.76/1.38 (c1_1(a2425)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[468, 204, 96, 674, 673, 672, 95])).
% 1.76/1.38 tff(676,plain,
% 1.76/1.38 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.76/1.38 inference(bind,[status(th)],[])).
% 1.76/1.38 tff(677,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(quant_intro,[status(thm)],[676])).
% 1.76/1.38 tff(678,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(679,plain,
% 1.76/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.76/1.38 inference(bind,[status(th)],[])).
% 1.76/1.38 tff(680,plain,
% 1.76/1.38 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(quant_intro,[status(thm)],[679])).
% 1.76/1.38 tff(681,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.76/1.38 tff(682,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.76/1.38 tff(683,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[682, 678])).
% 1.76/1.38 tff(684,plain,(
% 1.76/1.38 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(skolemize,[status(sab)],[683])).
% 1.76/1.38 tff(685,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[684, 677])).
% 1.76/1.38 tff(686,assumption,(~hskp23), introduced(assumption)).
% 1.76/1.38 tff(687,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(688,plain,
% 1.76/1.38 ((hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(689,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425))))),
% 1.76/1.38 inference(monotonicity,[status(thm)],[688])).
% 1.76/1.38 tff(690,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(transitivity,[status(thm)],[689, 687])).
% 1.76/1.38 tff(691,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.38 inference(quant_inst,[status(thm)],[])).
% 1.76/1.38 tff(692,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.76/1.38 tff(693,plain,
% 1.76/1.38 ($false),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[692, 204, 686, 669, 673, 672, 668, 685, 1, 675])).
% 1.76/1.38 tff(694,plain,(hskp10 | hskp23 | (~c3_1(a2408)) | c2_1(a2408) | c1_1(a2408)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.38 tff(695,plain,
% 1.76/1.38 (c1_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[694, 667, 96, 489, 488])).
% 1.76/1.38 tff(696,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(697,plain,
% 1.76/1.38 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408))) <=> (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(698,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.76/1.38 inference(monotonicity,[status(thm)],[697])).
% 1.76/1.38 tff(699,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(transitivity,[status(thm)],[698, 696])).
% 1.76/1.38 tff(700,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.76/1.38 inference(quant_inst,[status(thm)],[])).
% 1.76/1.38 tff(701,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.76/1.38 tff(702,plain,
% 1.76/1.38 (hskp30 | (~c1_1(a2408))),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[701, 204, 462, 488, 445, 489, 612, 469])).
% 1.76/1.38 tff(703,plain,
% 1.76/1.38 (hskp30),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[702, 695])).
% 1.76/1.38 tff(704,plain,
% 1.76/1.38 (c3_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[633, 703])).
% 1.76/1.38 tff(705,plain,
% 1.76/1.38 (c1_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[644, 703])).
% 1.76/1.38 tff(706,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(707,plain,
% 1.76/1.38 ((hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(708,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.76/1.38 inference(monotonicity,[status(thm)],[707])).
% 1.76/1.38 tff(709,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(transitivity,[status(thm)],[708, 706])).
% 1.76/1.38 tff(710,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.38 inference(quant_inst,[status(thm)],[])).
% 1.76/1.38 tff(711,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.76/1.38 tff(712,plain,
% 1.76/1.38 (~c2_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[711, 204, 96, 705, 704, 462, 445, 479, 469])).
% 1.76/1.38 tff(713,plain,
% 1.76/1.38 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.76/1.38 inference(bind,[status(th)],[])).
% 1.76/1.38 tff(714,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(quant_intro,[status(thm)],[713])).
% 1.76/1.38 tff(715,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(716,plain,
% 1.76/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.76/1.38 inference(bind,[status(th)],[])).
% 1.76/1.38 tff(717,plain,
% 1.76/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(quant_intro,[status(thm)],[716])).
% 1.76/1.38 tff(718,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.76/1.38 tff(719,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.76/1.38 tff(720,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[719, 715])).
% 1.76/1.38 tff(721,plain,(
% 1.76/1.38 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(skolemize,[status(sab)],[720])).
% 1.76/1.38 tff(722,plain,
% 1.76/1.38 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[721, 714])).
% 1.76/1.38 tff(723,plain,
% 1.76/1.38 (c0_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[411, 487])).
% 1.76/1.38 tff(724,plain,
% 1.76/1.38 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(725,plain,
% 1.76/1.38 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(726,plain,
% 1.76/1.38 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408))))),
% 1.76/1.38 inference(monotonicity,[status(thm)],[725])).
% 1.76/1.38 tff(727,plain,
% 1.76/1.38 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.76/1.38 inference(transitivity,[status(thm)],[726, 724])).
% 1.76/1.38 tff(728,plain,
% 1.76/1.38 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.76/1.38 inference(quant_inst,[status(thm)],[])).
% 1.76/1.38 tff(729,plain,
% 1.76/1.38 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[728, 727])).
% 1.76/1.38 tff(730,plain,
% 1.76/1.38 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[729, 204, 723, 488, 42])).
% 1.76/1.38 tff(731,plain,
% 1.76/1.38 (hskp14),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[730, 667, 695])).
% 1.76/1.38 tff(732,plain,
% 1.76/1.38 (((~hskp14) | (~c3_1(a2420))) <=> ((~hskp14) | (~c3_1(a2420)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(733,plain,
% 1.76/1.38 (((~c3_1(a2420)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a2420)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(734,axiom,((~c3_1(a2420)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.76/1.38 tff(735,plain,
% 1.76/1.38 ((~hskp14) | (~c3_1(a2420))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.76/1.38 tff(736,plain,
% 1.76/1.38 ((~hskp14) | (~c3_1(a2420))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[735, 732])).
% 1.76/1.38 tff(737,plain,
% 1.76/1.38 (~c3_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[736, 731])).
% 1.76/1.38 tff(738,plain,
% 1.76/1.38 (((~hskp14) | c2_1(a2420)) <=> ((~hskp14) | c2_1(a2420))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(739,axiom,((~hskp14) | c2_1(a2420)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.76/1.38 tff(740,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[739, 738])).
% 1.76/1.38 tff(741,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[740, 738])).
% 1.76/1.38 tff(742,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[741, 738])).
% 1.76/1.38 tff(743,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[742, 738])).
% 1.76/1.38 tff(744,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[743, 738])).
% 1.76/1.38 tff(745,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[744, 738])).
% 1.76/1.38 tff(746,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[745, 738])).
% 1.76/1.38 tff(747,plain,
% 1.76/1.38 ((~hskp14) | c2_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[746, 738])).
% 1.76/1.38 tff(748,plain,
% 1.76/1.38 (c2_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[747, 731])).
% 1.76/1.38 tff(749,plain,
% 1.76/1.38 (((~hskp14) | c1_1(a2420)) <=> ((~hskp14) | c1_1(a2420))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(750,axiom,((~hskp14) | c1_1(a2420)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.76/1.38 tff(751,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.76/1.38 tff(752,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[751, 749])).
% 1.76/1.38 tff(753,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[752, 749])).
% 1.76/1.38 tff(754,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[753, 749])).
% 1.76/1.38 tff(755,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[754, 749])).
% 1.76/1.38 tff(756,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[755, 749])).
% 1.76/1.38 tff(757,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[756, 749])).
% 1.76/1.38 tff(758,plain,
% 1.76/1.38 ((~hskp14) | c1_1(a2420)),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[757, 749])).
% 1.76/1.38 tff(759,plain,
% 1.76/1.38 (c1_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[758, 731])).
% 1.76/1.38 tff(760,plain,
% 1.76/1.38 (hskp5),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[485, 204, 43, 581, 580, 579, 53])).
% 1.76/1.38 tff(761,plain,
% 1.76/1.38 (~c2_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[400, 760])).
% 1.76/1.38 tff(762,plain,
% 1.76/1.38 (c3_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[429, 760])).
% 1.76/1.38 tff(763,plain,
% 1.76/1.38 (c1_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[694, 762, 96, 761, 686])).
% 1.76/1.38 tff(764,plain,
% 1.76/1.38 (hskp30),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[701, 204, 581, 762, 579, 761, 612, 763, 582])).
% 1.76/1.38 tff(765,plain,
% 1.76/1.38 (c3_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[633, 764])).
% 1.76/1.38 tff(766,plain,
% 1.76/1.38 (c1_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[644, 764])).
% 1.76/1.38 tff(767,plain,
% 1.76/1.38 (~c2_1(a2450)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[711, 204, 96, 766, 765, 581, 579, 479, 582])).
% 1.76/1.38 tff(768,assumption,(c1_1(a2425)), introduced(assumption)).
% 1.76/1.38 tff(769,assumption,(~c3_1(a2425)), introduced(assumption)).
% 1.76/1.38 tff(770,assumption,(~c2_1(a2425)), introduced(assumption)).
% 1.76/1.38 tff(771,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(772,plain,
% 1.76/1.38 ((hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(rewrite,[status(thm)],[])).
% 1.76/1.38 tff(773,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425))))),
% 1.76/1.38 inference(monotonicity,[status(thm)],[772])).
% 1.76/1.38 tff(774,plain,
% 1.76/1.38 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.76/1.38 inference(transitivity,[status(thm)],[773, 771])).
% 1.76/1.38 tff(775,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.76/1.38 inference(quant_inst,[status(thm)],[])).
% 1.76/1.38 tff(776,plain,
% 1.76/1.38 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425))),
% 1.76/1.38 inference(modus_ponens,[status(thm)],[775, 774])).
% 1.76/1.38 tff(777,plain,
% 1.76/1.38 ($false),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[776, 204, 686, 164, 770, 769, 153, 147, 685, 768])).
% 1.76/1.38 tff(778,plain,((~hskp11) | hskp23 | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425))), inference(lemma,lemma(discharge,[]))).
% 1.76/1.38 tff(779,plain,
% 1.76/1.38 (~hskp11),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[778, 582, 580, 579, 686])).
% 1.76/1.38 tff(780,plain,
% 1.76/1.38 (c0_1(a2408)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[411, 760])).
% 1.76/1.38 tff(781,plain,
% 1.76/1.38 (hskp14),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[729, 204, 686, 780, 762, 42, 763])).
% 1.76/1.38 tff(782,plain,
% 1.76/1.38 (~c3_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[736, 781])).
% 1.76/1.38 tff(783,plain,
% 1.76/1.38 (c2_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[747, 781])).
% 1.76/1.38 tff(784,plain,
% 1.76/1.38 (c1_1(a2420)),
% 1.76/1.38 inference(unit_resolution,[status(thm)],[758, 781])).
% 1.76/1.38 tff(785,assumption,(~c2_1(a2435)), introduced(assumption)).
% 1.76/1.38 tff(786,assumption,(c2_1(a2420)), introduced(assumption)).
% 1.76/1.38 tff(787,assumption,(c1_1(a2420)), introduced(assumption)).
% 1.76/1.38 tff(788,plain,
% 1.76/1.38 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(789,plain,
% 1.76/1.39 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(790,plain,
% 1.76/1.39 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[789])).
% 1.76/1.39 tff(791,plain,
% 1.76/1.39 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[790, 788])).
% 1.76/1.39 tff(792,plain,
% 1.76/1.39 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(793,plain,
% 1.76/1.39 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[792, 791])).
% 1.76/1.39 tff(794,plain,
% 1.76/1.39 (hskp12 | c0_1(a2420)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[793, 204, 325, 787, 786, 293])).
% 1.76/1.39 tff(795,plain,
% 1.76/1.39 (c0_1(a2420)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[794, 326])).
% 1.76/1.39 tff(796,assumption,(~c3_1(a2420)), introduced(assumption)).
% 1.76/1.39 tff(797,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(798,plain,
% 1.76/1.39 ((hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420))) <=> (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(799,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[798])).
% 1.76/1.39 tff(800,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[799, 797])).
% 1.76/1.39 tff(801,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(802,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.76/1.39 tff(803,plain,
% 1.76/1.39 (hskp20 | (~c0_1(a2420))),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[802, 204, 787, 786, 796, 722])).
% 1.76/1.39 tff(804,plain,
% 1.76/1.39 (hskp20),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[803, 795])).
% 1.76/1.39 tff(805,plain,
% 1.76/1.39 (((~hskp20) | c3_1(a2435)) <=> ((~hskp20) | c3_1(a2435))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(806,axiom,((~hskp20) | c3_1(a2435)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.76/1.39 tff(807,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.76/1.39 tff(808,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[807, 805])).
% 1.76/1.39 tff(809,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[808, 805])).
% 1.76/1.39 tff(810,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[809, 805])).
% 1.76/1.39 tff(811,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[810, 805])).
% 1.76/1.39 tff(812,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[811, 805])).
% 1.76/1.39 tff(813,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[812, 805])).
% 1.76/1.39 tff(814,plain,
% 1.76/1.39 ((~hskp20) | c3_1(a2435)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[813, 805])).
% 1.76/1.39 tff(815,plain,
% 1.76/1.39 (c3_1(a2435)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[814, 804])).
% 1.76/1.39 tff(816,plain,
% 1.76/1.39 (((~hskp20) | (~c0_1(a2435))) <=> ((~hskp20) | (~c0_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(817,plain,
% 1.76/1.39 (((~c0_1(a2435)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(818,axiom,((~c0_1(a2435)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.76/1.39 tff(819,plain,
% 1.76/1.39 ((~hskp20) | (~c0_1(a2435))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.76/1.39 tff(820,plain,
% 1.76/1.39 ((~hskp20) | (~c0_1(a2435))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[819, 816])).
% 1.76/1.39 tff(821,plain,
% 1.76/1.39 (~c0_1(a2435)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[820, 804])).
% 1.76/1.39 tff(822,assumption,(c1_1(a2408)), introduced(assumption)).
% 1.76/1.39 tff(823,plain,
% 1.76/1.39 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.76/1.39 inference(bind,[status(th)],[])).
% 1.76/1.39 tff(824,plain,
% 1.76/1.39 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(quant_intro,[status(thm)],[823])).
% 1.76/1.39 tff(825,plain,
% 1.76/1.39 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(826,plain,
% 1.76/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.76/1.39 inference(bind,[status(th)],[])).
% 1.76/1.39 tff(827,plain,
% 1.76/1.39 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(quant_intro,[status(thm)],[826])).
% 1.76/1.39 tff(828,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.76/1.39 tff(829,plain,
% 1.76/1.39 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.76/1.39 tff(830,plain,
% 1.76/1.39 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[829, 825])).
% 1.76/1.39 tff(831,plain,(
% 1.76/1.39 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(skolemize,[status(sab)],[830])).
% 1.76/1.39 tff(832,plain,
% 1.76/1.39 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[831, 824])).
% 1.76/1.39 tff(833,assumption,(c0_1(a2408)), introduced(assumption)).
% 1.76/1.39 tff(834,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(835,plain,
% 1.76/1.39 ((hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(836,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[835])).
% 1.76/1.39 tff(837,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[836, 834])).
% 1.76/1.39 tff(838,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(839,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.76/1.39 tff(840,plain,
% 1.76/1.39 (hskp12 | c0_1(a2435) | (~c3_1(a2435))),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[839, 204, 833, 669, 785, 832, 822])).
% 1.76/1.39 tff(841,plain,
% 1.76/1.39 ($false),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[840, 821, 815, 326])).
% 1.76/1.39 tff(842,plain,(hskp12 | (~c0_1(a2408)) | (~c3_1(a2408)) | c2_1(a2435) | (~c1_1(a2408)) | (~c1_1(a2420)) | (~c2_1(a2420)) | c3_1(a2420) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.76/1.39 tff(843,plain,
% 1.76/1.39 (hskp12),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[842, 780, 762, 785, 763, 784, 783, 782, 779])).
% 1.76/1.39 tff(844,plain,
% 1.76/1.39 (~c1_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[229, 843])).
% 1.76/1.39 tff(845,plain,
% 1.76/1.39 (c3_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[246, 843])).
% 1.76/1.39 tff(846,plain,
% 1.76/1.39 (c0_1(a2450)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[655, 764])).
% 1.76/1.39 tff(847,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(848,plain,
% 1.76/1.39 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(849,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[848])).
% 1.76/1.39 tff(850,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[849, 847])).
% 1.76/1.39 tff(851,plain,
% 1.76/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(852,plain,
% 1.76/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.76/1.39 tff(853,plain,
% 1.76/1.39 (~c2_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[852, 204, 846, 766, 765, 581, 845, 580, 579, 844, 602])).
% 1.76/1.39 tff(854,plain,
% 1.76/1.39 (~c0_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[235, 843])).
% 1.76/1.39 tff(855,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(856,plain,
% 1.76/1.39 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(857,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[856])).
% 1.76/1.39 tff(858,plain,
% 1.76/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[857, 855])).
% 1.76/1.39 tff(859,plain,
% 1.76/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(860,plain,
% 1.76/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.76/1.39 tff(861,plain,
% 1.76/1.39 ($false),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[860, 204, 766, 765, 580, 579, 854, 844, 11, 853, 767, 582])).
% 1.76/1.39 tff(862,plain,(hskp10 | c2_1(a2435) | hskp23 | hskp19 | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.76/1.39 tff(863,plain,
% 1.76/1.39 (c2_1(a2435)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[862, 667, 96, 43, 500, 499, 498])).
% 1.76/1.39 tff(864,plain,
% 1.76/1.39 (((~hskp20) | (~c2_1(a2435))) <=> ((~hskp20) | (~c2_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(865,plain,
% 1.76/1.39 (((~c2_1(a2435)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a2435)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(866,axiom,((~c2_1(a2435)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.76/1.39 tff(867,plain,
% 1.76/1.39 ((~hskp20) | (~c2_1(a2435))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.76/1.39 tff(868,plain,
% 1.76/1.39 ((~hskp20) | (~c2_1(a2435))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[867, 864])).
% 1.76/1.39 tff(869,plain,
% 1.76/1.39 (~hskp20),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[868, 863])).
% 1.76/1.39 tff(870,plain,
% 1.76/1.39 (~c0_1(a2420)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[802, 204, 869, 759, 748, 737, 722])).
% 1.76/1.39 tff(871,plain,
% 1.76/1.39 (~hskp11),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[778, 667, 451, 445, 469])).
% 1.76/1.39 tff(872,plain,
% 1.76/1.39 (hskp12 | c0_1(a2420)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[793, 204, 871, 759, 748, 293])).
% 1.76/1.39 tff(873,plain,
% 1.76/1.39 (hskp12),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[872, 870])).
% 1.76/1.39 tff(874,plain,
% 1.76/1.39 (~c1_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[229, 873])).
% 1.76/1.39 tff(875,plain,
% 1.76/1.39 (c3_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[246, 873])).
% 1.76/1.39 tff(876,plain,
% 1.76/1.39 (c0_1(a2450)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[655, 703])).
% 1.76/1.39 tff(877,plain,
% 1.76/1.39 (~c2_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[852, 204, 876, 705, 704, 462, 875, 451, 445, 874, 602])).
% 1.76/1.39 tff(878,plain,
% 1.76/1.39 (~c0_1(a2417)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[235, 873])).
% 1.76/1.39 tff(879,plain,
% 1.76/1.39 ($false),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[860, 204, 705, 704, 451, 445, 878, 874, 11, 877, 712, 469])).
% 1.76/1.39 tff(880,plain,(hskp19 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.76/1.39 tff(881,plain,
% 1.76/1.39 (hskp19),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[880, 96])).
% 1.76/1.39 tff(882,plain,
% 1.76/1.39 (((~hskp19) | c3_1(a2432)) <=> ((~hskp19) | c3_1(a2432))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(883,axiom,((~hskp19) | c3_1(a2432)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.76/1.39 tff(884,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.76/1.39 tff(885,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[884, 882])).
% 1.76/1.39 tff(886,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[885, 882])).
% 1.76/1.39 tff(887,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[886, 882])).
% 1.76/1.39 tff(888,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[887, 882])).
% 1.76/1.39 tff(889,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[888, 882])).
% 1.76/1.39 tff(890,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[889, 882])).
% 1.76/1.39 tff(891,plain,
% 1.76/1.39 ((~hskp19) | c3_1(a2432)),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[890, 882])).
% 1.76/1.39 tff(892,plain,
% 1.76/1.39 (c3_1(a2432)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[891, 881])).
% 1.76/1.39 tff(893,plain,
% 1.76/1.39 (c1_1(a2432)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[323, 881])).
% 1.76/1.39 tff(894,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(895,plain,
% 1.76/1.39 ((hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(896,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[895])).
% 1.76/1.39 tff(897,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[896, 894])).
% 1.76/1.39 tff(898,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(899,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.76/1.39 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.76/1.39 tff(900,plain,
% 1.76/1.39 (~c2_1(a2432)),
% 1.76/1.39 inference(unit_resolution,[status(thm)],[899, 204, 96, 893, 892, 462, 445, 479, 469])).
% 1.76/1.39 tff(901,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(902,plain,
% 1.76/1.39 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.39 inference(rewrite,[status(thm)],[])).
% 1.76/1.39 tff(903,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.76/1.39 inference(monotonicity,[status(thm)],[902])).
% 1.76/1.39 tff(904,plain,
% 1.76/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.39 inference(transitivity,[status(thm)],[903, 901])).
% 1.76/1.39 tff(905,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.76/1.39 inference(quant_inst,[status(thm)],[])).
% 1.76/1.39 tff(906,plain,
% 1.76/1.39 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.76/1.40 tff(907,plain,
% 1.76/1.40 (hskp30),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[906, 204, 893, 892, 462, 445, 612, 900, 469])).
% 1.76/1.40 tff(908,plain,
% 1.76/1.40 (c3_1(a2450)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[633, 907])).
% 1.76/1.40 tff(909,plain,
% 1.76/1.40 (c1_1(a2450)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[644, 907])).
% 1.76/1.40 tff(910,plain,
% 1.76/1.40 (~c2_1(a2450)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[711, 204, 96, 909, 908, 462, 445, 479, 469])).
% 1.76/1.40 tff(911,plain,
% 1.76/1.40 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(912,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[911])).
% 1.76/1.40 tff(913,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(914,plain,
% 1.76/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(915,plain,
% 1.76/1.40 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[914])).
% 1.76/1.40 tff(916,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.76/1.40 tff(917,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.76/1.40 tff(918,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[917, 913])).
% 1.76/1.40 tff(919,plain,(
% 1.76/1.40 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(skolemize,[status(sab)],[918])).
% 1.76/1.40 tff(920,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[919, 912])).
% 1.76/1.40 tff(921,plain,
% 1.76/1.40 (~c0_1(a2432)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[312, 881])).
% 1.76/1.40 tff(922,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(923,plain,
% 1.76/1.40 ((hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(924,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.76/1.40 inference(monotonicity,[status(thm)],[923])).
% 1.76/1.40 tff(925,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.76/1.40 inference(transitivity,[status(thm)],[924, 922])).
% 1.76/1.40 tff(926,plain,
% 1.76/1.40 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.76/1.40 inference(quant_inst,[status(thm)],[])).
% 1.76/1.40 tff(927,plain,
% 1.76/1.40 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.76/1.40 tff(928,plain,
% 1.76/1.40 (hskp20),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[927, 204, 893, 892, 921, 920, 900])).
% 1.76/1.40 tff(929,plain,
% 1.76/1.40 (~c2_1(a2435)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[868, 928])).
% 1.76/1.40 tff(930,plain,
% 1.76/1.40 (~c0_1(a2435)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[820, 928])).
% 1.76/1.40 tff(931,plain,
% 1.76/1.40 (c3_1(a2435)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[814, 928])).
% 1.76/1.40 tff(932,plain,
% 1.76/1.40 (c0_1(a2450)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[655, 907])).
% 1.76/1.40 tff(933,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(934,plain,
% 1.76/1.40 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(935,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435))))),
% 1.76/1.40 inference(monotonicity,[status(thm)],[934])).
% 1.76/1.40 tff(936,plain,
% 1.76/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.76/1.40 inference(transitivity,[status(thm)],[935, 933])).
% 1.76/1.40 tff(937,plain,
% 1.76/1.40 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.76/1.40 inference(quant_inst,[status(thm)],[])).
% 1.76/1.40 tff(938,plain,
% 1.76/1.40 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.76/1.40 tff(939,plain,
% 1.76/1.40 (hskp12),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[938, 204, 932, 909, 908, 931, 930, 929, 832])).
% 1.76/1.40 tff(940,plain,
% 1.76/1.40 (~c1_1(a2417)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[229, 939])).
% 1.76/1.40 tff(941,plain,
% 1.76/1.40 (c3_1(a2417)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[246, 939])).
% 1.76/1.40 tff(942,plain,
% 1.76/1.40 (~c2_1(a2417)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[852, 204, 932, 909, 908, 462, 941, 451, 445, 940, 602])).
% 1.76/1.40 tff(943,plain,
% 1.76/1.40 (~c0_1(a2417)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[235, 939])).
% 1.76/1.40 tff(944,plain,
% 1.76/1.40 ($false),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[860, 204, 909, 908, 451, 445, 943, 940, 11, 942, 910, 469])).
% 1.76/1.40 tff(945,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.76/1.40 tff(946,plain,
% 1.76/1.40 (((~hskp10) | (~c3_1(a2414))) <=> ((~hskp10) | (~c3_1(a2414)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(947,plain,
% 1.76/1.40 (((~c3_1(a2414)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2414)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(948,axiom,((~c3_1(a2414)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.76/1.40 tff(949,plain,
% 1.76/1.40 ((~hskp10) | (~c3_1(a2414))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.76/1.40 tff(950,plain,
% 1.76/1.40 ((~hskp10) | (~c3_1(a2414))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[949, 946])).
% 1.76/1.40 tff(951,plain,
% 1.76/1.40 (~c3_1(a2414)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[950, 945])).
% 1.76/1.40 tff(952,plain,
% 1.76/1.40 (((~hskp10) | (~c1_1(a2414))) <=> ((~hskp10) | (~c1_1(a2414)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(953,plain,
% 1.76/1.40 (((~c1_1(a2414)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2414)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(954,axiom,((~c1_1(a2414)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.76/1.40 tff(955,plain,
% 1.76/1.40 ((~hskp10) | (~c1_1(a2414))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[954, 953])).
% 1.76/1.40 tff(956,plain,
% 1.76/1.40 ((~hskp10) | (~c1_1(a2414))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[955, 952])).
% 1.76/1.40 tff(957,plain,
% 1.76/1.40 (~c1_1(a2414)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[956, 945])).
% 1.76/1.40 tff(958,assumption,(~hskp25), introduced(assumption)).
% 1.76/1.40 tff(959,assumption,(hskp6), introduced(assumption)).
% 1.76/1.40 tff(960,plain,
% 1.76/1.40 (((~hskp6) | (~c2_1(a2410))) <=> ((~hskp6) | (~c2_1(a2410)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(961,plain,
% 1.76/1.40 (((~c2_1(a2410)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a2410)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(962,axiom,((~c2_1(a2410)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.76/1.40 tff(963,plain,
% 1.76/1.40 ((~hskp6) | (~c2_1(a2410))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.76/1.40 tff(964,plain,
% 1.76/1.40 ((~hskp6) | (~c2_1(a2410))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[963, 960])).
% 1.76/1.40 tff(965,plain,
% 1.76/1.40 (~c2_1(a2410)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[964, 959])).
% 1.76/1.40 tff(966,plain,
% 1.76/1.40 (((~hskp6) | c1_1(a2410)) <=> ((~hskp6) | c1_1(a2410))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(967,axiom,((~hskp6) | c1_1(a2410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.76/1.40 tff(968,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[967, 966])).
% 1.76/1.40 tff(969,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[968, 966])).
% 1.76/1.40 tff(970,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[969, 966])).
% 1.76/1.40 tff(971,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[970, 966])).
% 1.76/1.40 tff(972,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[971, 966])).
% 1.76/1.40 tff(973,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[972, 966])).
% 1.76/1.40 tff(974,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[973, 966])).
% 1.76/1.40 tff(975,plain,
% 1.76/1.40 ((~hskp6) | c1_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[974, 966])).
% 1.76/1.40 tff(976,plain,
% 1.76/1.40 (c1_1(a2410)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[975, 959])).
% 1.76/1.40 tff(977,plain,
% 1.76/1.40 (((~hskp6) | c0_1(a2410)) <=> ((~hskp6) | c0_1(a2410))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(978,axiom,((~hskp6) | c0_1(a2410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.76/1.40 tff(979,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.76/1.40 tff(980,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[979, 977])).
% 1.76/1.40 tff(981,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[980, 977])).
% 1.76/1.40 tff(982,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[981, 977])).
% 1.76/1.40 tff(983,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[982, 977])).
% 1.76/1.40 tff(984,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[983, 977])).
% 1.76/1.40 tff(985,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[984, 977])).
% 1.76/1.40 tff(986,plain,
% 1.76/1.40 ((~hskp6) | c0_1(a2410)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[985, 977])).
% 1.76/1.40 tff(987,plain,
% 1.76/1.40 (c0_1(a2410)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[986, 959])).
% 1.76/1.40 tff(988,plain,
% 1.76/1.40 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(989,plain,
% 1.76/1.40 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(990,plain,
% 1.76/1.40 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 1.76/1.40 inference(monotonicity,[status(thm)],[989])).
% 1.76/1.40 tff(991,plain,
% 1.76/1.40 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.76/1.40 inference(transitivity,[status(thm)],[990, 988])).
% 1.76/1.40 tff(992,plain,
% 1.76/1.40 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.76/1.40 inference(quant_inst,[status(thm)],[])).
% 1.76/1.40 tff(993,plain,
% 1.76/1.40 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.76/1.40 tff(994,plain,
% 1.76/1.40 ($false),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[993, 204, 958, 43, 987, 976, 965, 106])).
% 1.76/1.40 tff(995,plain,((~hskp6) | hskp25 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.76/1.40 tff(996,plain,
% 1.76/1.40 (~hskp6),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[995, 958, 43])).
% 1.76/1.40 tff(997,assumption,(~hskp31), introduced(assumption)).
% 1.76/1.40 tff(998,plain,
% 1.76/1.40 (hskp27),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[202, 958, 997])).
% 1.76/1.40 tff(999,plain,
% 1.76/1.40 (((~hskp27) | (~c1_1(a2500))) <=> ((~hskp27) | (~c1_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1000,plain,
% 1.76/1.40 (((~c1_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c1_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1001,axiom,((~c1_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.76/1.40 tff(1002,plain,
% 1.76/1.40 ((~hskp27) | (~c1_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.76/1.40 tff(1003,plain,
% 1.76/1.40 ((~hskp27) | (~c1_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1002, 999])).
% 1.76/1.40 tff(1004,plain,
% 1.76/1.40 (~c1_1(a2500)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[1003, 998])).
% 1.76/1.40 tff(1005,plain,
% 1.76/1.40 (((~hskp27) | (~c0_1(a2500))) <=> ((~hskp27) | (~c0_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1006,plain,
% 1.76/1.40 (((~c0_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1007,axiom,((~c0_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.76/1.40 tff(1008,plain,
% 1.76/1.40 ((~hskp27) | (~c0_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.76/1.40 tff(1009,plain,
% 1.76/1.40 ((~hskp27) | (~c0_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 1.76/1.40 tff(1010,plain,
% 1.76/1.40 (~c0_1(a2500)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[1009, 998])).
% 1.76/1.40 tff(1011,plain,
% 1.76/1.40 (((~hskp27) | (~c3_1(a2500))) <=> ((~hskp27) | (~c3_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1012,plain,
% 1.76/1.40 (((~c3_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c3_1(a2500)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1013,axiom,((~c3_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.76/1.40 tff(1014,plain,
% 1.76/1.40 ((~hskp27) | (~c3_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.76/1.40 tff(1015,plain,
% 1.76/1.40 ((~hskp27) | (~c3_1(a2500))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 1.76/1.40 tff(1016,plain,
% 1.76/1.40 (~c3_1(a2500)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[1015, 998])).
% 1.76/1.40 tff(1017,plain,
% 1.76/1.40 (^[U: $i] : refl((hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(1018,plain,
% 1.76/1.40 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[1017])).
% 1.76/1.40 tff(1019,plain,
% 1.76/1.40 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1020,plain,
% 1.76/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(1021,plain,
% 1.76/1.40 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[1020])).
% 1.76/1.40 tff(1022,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.76/1.40 tff(1023,plain,
% 1.76/1.40 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.76/1.40 tff(1024,plain,
% 1.76/1.40 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 1.76/1.40 tff(1025,plain,(
% 1.76/1.40 ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(skolemize,[status(sab)],[1024])).
% 1.76/1.40 tff(1026,plain,
% 1.76/1.40 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 1.76/1.40 tff(1027,assumption,(~c3_1(a2500)), introduced(assumption)).
% 1.76/1.40 tff(1028,assumption,(~c1_1(a2500)), introduced(assumption)).
% 1.76/1.40 tff(1029,assumption,(~c0_1(a2500)), introduced(assumption)).
% 1.76/1.40 tff(1030,plain,
% 1.76/1.40 (^[U: $i] : refl((hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(1031,plain,
% 1.76/1.40 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[1030])).
% 1.76/1.40 tff(1032,plain,
% 1.76/1.40 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1033,plain,
% 1.76/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(1034,plain,
% 1.76/1.40 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[1033])).
% 1.76/1.40 tff(1035,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.76/1.40 tff(1036,plain,
% 1.76/1.40 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.76/1.40 tff(1037,plain,
% 1.76/1.40 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 1.76/1.40 tff(1038,plain,(
% 1.76/1.40 ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(skolemize,[status(sab)],[1037])).
% 1.76/1.40 tff(1039,plain,
% 1.76/1.40 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1038, 1031])).
% 1.76/1.40 tff(1040,plain,
% 1.76/1.40 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1041,plain,
% 1.76/1.40 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500)) <=> (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1042,plain,
% 1.76/1.40 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500)))),
% 1.76/1.40 inference(monotonicity,[status(thm)],[1041])).
% 1.76/1.40 tff(1043,plain,
% 1.76/1.40 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.76/1.40 inference(transitivity,[status(thm)],[1042, 1040])).
% 1.76/1.40 tff(1044,plain,
% 1.76/1.40 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))),
% 1.76/1.40 inference(quant_inst,[status(thm)],[])).
% 1.76/1.40 tff(1045,plain,
% 1.76/1.40 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500)),
% 1.76/1.40 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.76/1.40 tff(1046,plain,
% 1.76/1.40 (hskp13 | hskp1 | c2_1(a2500)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[1045, 204, 1029, 1027, 1039])).
% 1.76/1.40 tff(1047,plain,
% 1.76/1.40 (c2_1(a2500)),
% 1.76/1.40 inference(unit_resolution,[status(thm)],[1046, 65, 22])).
% 1.76/1.40 tff(1048,plain,
% 1.76/1.40 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.76/1.40 inference(bind,[status(th)],[])).
% 1.76/1.40 tff(1049,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.40 inference(quant_intro,[status(thm)],[1048])).
% 1.76/1.40 tff(1050,plain,
% 1.76/1.40 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.40 inference(rewrite,[status(thm)],[])).
% 1.76/1.40 tff(1051,plain,
% 1.76/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1052,plain,
% 1.76/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1051])).
% 1.76/1.41 tff(1053,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.76/1.41 tff(1054,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.76/1.41 tff(1055,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 1.76/1.41 tff(1056,plain,(
% 1.76/1.41 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(skolemize,[status(sab)],[1055])).
% 1.76/1.41 tff(1057,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1056, 1049])).
% 1.76/1.41 tff(1058,plain,
% 1.76/1.41 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1059,plain,
% 1.76/1.41 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500))) <=> (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1060,plain,
% 1.76/1.41 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500))))),
% 1.76/1.41 inference(monotonicity,[status(thm)],[1059])).
% 1.76/1.41 tff(1061,plain,
% 1.76/1.41 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.76/1.41 inference(transitivity,[status(thm)],[1060, 1058])).
% 1.76/1.41 tff(1062,plain,
% 1.76/1.41 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))),
% 1.76/1.41 inference(quant_inst,[status(thm)],[])).
% 1.76/1.41 tff(1063,plain,
% 1.76/1.41 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.76/1.41 tff(1064,plain,
% 1.76/1.41 (hskp16 | hskp12 | (~c2_1(a2500))),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1063, 204, 1028, 1027, 273])).
% 1.76/1.41 tff(1065,plain,
% 1.76/1.41 (hskp12),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1064, 64, 1047])).
% 1.76/1.41 tff(1066,plain,
% 1.76/1.41 (~c0_1(a2417)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[235, 1065])).
% 1.76/1.41 tff(1067,plain,
% 1.76/1.41 (~c1_1(a2417)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[229, 1065])).
% 1.76/1.41 tff(1068,plain,
% 1.76/1.41 (c3_1(a2417)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[246, 1065])).
% 1.76/1.41 tff(1069,plain,
% 1.76/1.41 (hskp5),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[394, 43, 958])).
% 1.76/1.41 tff(1070,plain,
% 1.76/1.41 (~c2_1(a2408)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[400, 1069])).
% 1.76/1.41 tff(1071,plain,
% 1.76/1.41 (c0_1(a2408)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[411, 1069])).
% 1.76/1.41 tff(1072,plain,
% 1.76/1.41 (~c1_1(a2408)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[418, 204, 958, 43, 1071, 1070, 106])).
% 1.76/1.41 tff(1073,plain,
% 1.76/1.41 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1074,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1073])).
% 1.76/1.41 tff(1075,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1076,plain,
% 1.76/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1077,plain,
% 1.76/1.41 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1076])).
% 1.76/1.41 tff(1078,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.76/1.41 tff(1079,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.76/1.41 tff(1080,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 1.76/1.41 tff(1081,plain,(
% 1.76/1.41 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(skolemize,[status(sab)],[1080])).
% 1.76/1.41 tff(1082,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1081, 1074])).
% 1.76/1.41 tff(1083,assumption,(~c1_1(a2417)), introduced(assumption)).
% 1.76/1.41 tff(1084,plain,
% 1.76/1.41 (c3_1(a2408)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[429, 1069])).
% 1.76/1.41 tff(1085,assumption,(c3_1(a2417)), introduced(assumption)).
% 1.76/1.41 tff(1086,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1087,plain,
% 1.76/1.41 ((hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1088,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.76/1.41 inference(monotonicity,[status(thm)],[1087])).
% 1.76/1.41 tff(1089,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.76/1.41 inference(transitivity,[status(thm)],[1088, 1086])).
% 1.76/1.41 tff(1090,plain,
% 1.76/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.41 inference(quant_inst,[status(thm)],[])).
% 1.76/1.41 tff(1091,plain,
% 1.76/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 1.76/1.41 tff(1092,plain,
% 1.76/1.41 (~c2_1(a2417)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1091, 204, 22, 1085, 1084, 1083, 1070, 1082, 1072])).
% 1.76/1.41 tff(1093,assumption,(c2_1(a2500)), introduced(assumption)).
% 1.76/1.41 tff(1094,assumption,(~c0_1(a2417)), introduced(assumption)).
% 1.76/1.41 tff(1095,assumption,(hskp10), introduced(assumption)).
% 1.76/1.41 tff(1096,plain,
% 1.76/1.41 (((~hskp10) | c0_1(a2414)) <=> ((~hskp10) | c0_1(a2414))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1097,axiom,((~hskp10) | c0_1(a2414)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.76/1.41 tff(1098,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 1.76/1.41 tff(1099,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1098, 1096])).
% 1.76/1.41 tff(1100,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 1.76/1.41 tff(1101,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1100, 1096])).
% 1.76/1.41 tff(1102,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1101, 1096])).
% 1.76/1.41 tff(1103,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1102, 1096])).
% 1.76/1.41 tff(1104,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1103, 1096])).
% 1.76/1.41 tff(1105,plain,
% 1.76/1.41 ((~hskp10) | c0_1(a2414)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1104, 1096])).
% 1.76/1.41 tff(1106,plain,
% 1.76/1.41 (c0_1(a2414)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1105, 1095])).
% 1.76/1.41 tff(1107,plain,
% 1.76/1.41 (~c3_1(a2414)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[950, 1095])).
% 1.76/1.41 tff(1108,plain,
% 1.76/1.41 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1109,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1108])).
% 1.76/1.41 tff(1110,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1111,plain,
% 1.76/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1112,plain,
% 1.76/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1111])).
% 1.76/1.41 tff(1113,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.76/1.41 tff(1114,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.76/1.41 tff(1115,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1114, 1110])).
% 1.76/1.41 tff(1116,plain,(
% 1.76/1.41 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(skolemize,[status(sab)],[1115])).
% 1.76/1.41 tff(1117,plain,
% 1.76/1.41 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1116, 1109])).
% 1.76/1.41 tff(1118,assumption,(~hskp29), introduced(assumption)).
% 1.76/1.41 tff(1119,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1120,plain,
% 1.76/1.41 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1121,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500))))),
% 1.76/1.41 inference(monotonicity,[status(thm)],[1120])).
% 1.76/1.41 tff(1122,plain,
% 1.76/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.76/1.41 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.76/1.41 tff(1123,plain,
% 1.76/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.76/1.41 inference(quant_inst,[status(thm)],[])).
% 1.76/1.41 tff(1124,plain,
% 1.76/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.76/1.41 tff(1125,plain,
% 1.76/1.41 ($false),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1124, 204, 1118, 1071, 1084, 1029, 1028, 1117, 1093, 1072])).
% 1.76/1.41 tff(1126,plain,(hskp19 | hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.76/1.41 tff(1127,plain,
% 1.76/1.41 (hskp29),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1126, 43, 1029, 1028, 1093, 958])).
% 1.76/1.41 tff(1128,plain,
% 1.76/1.41 (((~hskp29) | c2_1(a2409)) <=> ((~hskp29) | c2_1(a2409))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1129,axiom,((~hskp29) | c2_1(a2409)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.76/1.41 tff(1130,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 1.76/1.41 tff(1131,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1130, 1128])).
% 1.76/1.41 tff(1132,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1131, 1128])).
% 1.76/1.41 tff(1133,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1132, 1128])).
% 1.76/1.41 tff(1134,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1133, 1128])).
% 1.76/1.41 tff(1135,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1134, 1128])).
% 1.76/1.41 tff(1136,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1135, 1128])).
% 1.76/1.41 tff(1137,plain,
% 1.76/1.41 ((~hskp29) | c2_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1136, 1128])).
% 1.76/1.41 tff(1138,plain,
% 1.76/1.41 (c2_1(a2409)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1137, 1127])).
% 1.76/1.41 tff(1139,plain,
% 1.76/1.41 (((~hskp29) | c3_1(a2409)) <=> ((~hskp29) | c3_1(a2409))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1140,axiom,((~hskp29) | c3_1(a2409)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.76/1.41 tff(1141,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.76/1.41 tff(1142,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1141, 1139])).
% 1.76/1.41 tff(1143,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1142, 1139])).
% 1.76/1.41 tff(1144,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 1.76/1.41 tff(1145,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1144, 1139])).
% 1.76/1.41 tff(1146,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1145, 1139])).
% 1.76/1.41 tff(1147,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1146, 1139])).
% 1.76/1.41 tff(1148,plain,
% 1.76/1.41 ((~hskp29) | c3_1(a2409)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1147, 1139])).
% 1.76/1.41 tff(1149,plain,
% 1.76/1.41 (c3_1(a2409)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1148, 1127])).
% 1.76/1.41 tff(1150,plain,
% 1.76/1.41 (~c1_1(a2414)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[956, 1095])).
% 1.76/1.41 tff(1151,plain,
% 1.76/1.41 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1152,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1151])).
% 1.76/1.41 tff(1153,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1154,plain,
% 1.76/1.41 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.76/1.41 inference(bind,[status(th)],[])).
% 1.76/1.41 tff(1155,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(quant_intro,[status(thm)],[1154])).
% 1.76/1.41 tff(1156,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.76/1.41 tff(1157,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.76/1.41 tff(1158,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 1.76/1.41 tff(1159,plain,(
% 1.76/1.41 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(skolemize,[status(sab)],[1158])).
% 1.76/1.41 tff(1160,plain,
% 1.76/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 1.76/1.41 tff(1161,assumption,(~c3_1(a2414)), introduced(assumption)).
% 1.76/1.41 tff(1162,assumption,(~c1_1(a2414)), introduced(assumption)).
% 1.76/1.41 tff(1163,assumption,(~hskp30), introduced(assumption)).
% 1.76/1.41 tff(1164,plain,
% 1.76/1.41 ((hskp30 | hskp26 | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1165,plain,
% 1.76/1.41 (((hskp30 | hskp26) | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1166,plain,
% 1.76/1.41 ((hskp30 | hskp26) <=> (hskp30 | hskp26)),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1167,plain,
% 1.76/1.41 (((hskp30 | hskp26) | hskp19) <=> ((hskp30 | hskp26) | hskp19)),
% 1.76/1.41 inference(monotonicity,[status(thm)],[1166])).
% 1.76/1.41 tff(1168,plain,
% 1.76/1.41 (((hskp30 | hskp26) | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.76/1.41 inference(transitivity,[status(thm)],[1167, 1165])).
% 1.76/1.41 tff(1169,axiom,((hskp30 | hskp26) | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.76/1.41 tff(1170,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 1.76/1.41 tff(1171,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1170, 1164])).
% 1.76/1.41 tff(1172,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1171, 1164])).
% 1.76/1.41 tff(1173,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1172, 1164])).
% 1.76/1.41 tff(1174,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1173, 1164])).
% 1.76/1.41 tff(1175,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1174, 1164])).
% 1.76/1.41 tff(1176,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1175, 1164])).
% 1.76/1.41 tff(1177,plain,
% 1.76/1.41 (hskp30 | hskp26 | hskp19),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1176, 1164])).
% 1.76/1.41 tff(1178,plain,
% 1.76/1.41 (hskp26),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1177, 43, 1163])).
% 1.76/1.41 tff(1179,plain,
% 1.76/1.41 (((~hskp26) | (~c3_1(a2484))) <=> ((~hskp26) | (~c3_1(a2484)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1180,plain,
% 1.76/1.41 (((~c3_1(a2484)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a2484)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1181,axiom,((~c3_1(a2484)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.76/1.41 tff(1182,plain,
% 1.76/1.41 ((~hskp26) | (~c3_1(a2484))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 1.76/1.41 tff(1183,plain,
% 1.76/1.41 ((~hskp26) | (~c3_1(a2484))),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1182, 1179])).
% 1.76/1.41 tff(1184,plain,
% 1.76/1.41 (~c3_1(a2484)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1183, 1178])).
% 1.76/1.41 tff(1185,assumption,(c0_1(a2414)), introduced(assumption)).
% 1.76/1.41 tff(1186,plain,
% 1.76/1.41 (((~hskp26) | c1_1(a2484)) <=> ((~hskp26) | c1_1(a2484))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1187,axiom,((~hskp26) | c1_1(a2484)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.76/1.41 tff(1188,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.76/1.41 tff(1189,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1188, 1186])).
% 1.76/1.41 tff(1190,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1189, 1186])).
% 1.76/1.41 tff(1191,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1190, 1186])).
% 1.76/1.41 tff(1192,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1191, 1186])).
% 1.76/1.41 tff(1193,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1192, 1186])).
% 1.76/1.41 tff(1194,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1193, 1186])).
% 1.76/1.41 tff(1195,plain,
% 1.76/1.41 ((~hskp26) | c1_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1194, 1186])).
% 1.76/1.41 tff(1196,plain,
% 1.76/1.41 (c1_1(a2484)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1195, 1178])).
% 1.76/1.41 tff(1197,plain,
% 1.76/1.41 (((~hskp26) | c0_1(a2484)) <=> ((~hskp26) | c0_1(a2484))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1198,axiom,((~hskp26) | c0_1(a2484)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.76/1.41 tff(1199,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.76/1.41 tff(1200,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1199, 1197])).
% 1.76/1.41 tff(1201,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1200, 1197])).
% 1.76/1.41 tff(1202,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1201, 1197])).
% 1.76/1.41 tff(1203,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1202, 1197])).
% 1.76/1.41 tff(1204,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1203, 1197])).
% 1.76/1.41 tff(1205,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1204, 1197])).
% 1.76/1.41 tff(1206,plain,
% 1.76/1.41 ((~hskp26) | c0_1(a2484)),
% 1.76/1.41 inference(modus_ponens,[status(thm)],[1205, 1197])).
% 1.76/1.41 tff(1207,plain,
% 1.76/1.41 (c0_1(a2484)),
% 1.76/1.41 inference(unit_resolution,[status(thm)],[1206, 1178])).
% 1.76/1.41 tff(1208,assumption,(c3_1(a2409)), introduced(assumption)).
% 1.76/1.41 tff(1209,assumption,(c2_1(a2409)), introduced(assumption)).
% 1.76/1.41 tff(1210,plain,
% 1.76/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1211,plain,
% 1.76/1.41 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.76/1.41 inference(rewrite,[status(thm)],[])).
% 1.76/1.41 tff(1212,plain,
% 1.76/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1211])).
% 1.76/1.42 tff(1213,plain,
% 1.76/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1212, 1210])).
% 1.76/1.42 tff(1214,plain,
% 1.76/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1215,plain,
% 1.76/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.76/1.42 tff(1216,plain,
% 1.76/1.42 (~c1_1(a2409)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1215, 204, 1209, 1208, 1207, 1196, 1185, 1184, 1162, 1161, 1160])).
% 1.76/1.42 tff(1217,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1218,plain,
% 1.76/1.42 ((hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1219,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1218])).
% 1.76/1.42 tff(1220,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1219, 1217])).
% 1.76/1.42 tff(1221,plain,
% 1.76/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1222,plain,
% 1.76/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.76/1.42 tff(1223,plain,
% 1.76/1.42 ($false),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1222, 204, 22, 1209, 1208, 1084, 1070, 1082, 1216, 1072])).
% 1.76/1.42 tff(1224,plain,(hskp19 | hskp1 | (~c2_1(a2409)) | (~c3_1(a2409)) | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | hskp25 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.76/1.42 tff(1225,plain,
% 1.76/1.42 (hskp30),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1224, 1150, 43, 1149, 22, 1138, 1107, 958, 1106])).
% 1.76/1.42 tff(1226,plain,
% 1.76/1.42 (c1_1(a2450)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[644, 1225])).
% 1.76/1.42 tff(1227,plain,
% 1.76/1.42 (c0_1(a2450)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[655, 1225])).
% 1.76/1.42 tff(1228,plain,
% 1.76/1.42 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1229,plain,
% 1.76/1.42 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450))) <=> (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1230,plain,
% 1.76/1.42 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1229])).
% 1.76/1.42 tff(1231,plain,
% 1.76/1.42 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.76/1.42 tff(1232,plain,
% 1.76/1.42 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1233,plain,
% 1.76/1.42 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.76/1.42 tff(1234,plain,
% 1.76/1.42 (c2_1(a2450)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1233, 204, 958, 43, 1227, 1226, 106])).
% 1.76/1.42 tff(1235,plain,
% 1.76/1.42 (~hskp6),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[995, 43, 958])).
% 1.76/1.42 tff(1236,assumption,(hskp24), introduced(assumption)).
% 1.76/1.42 tff(1237,plain,
% 1.76/1.42 (((~hskp24) | (~c3_1(a2468))) <=> ((~hskp24) | (~c3_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1238,plain,
% 1.76/1.42 (((~c3_1(a2468)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1239,axiom,((~c3_1(a2468)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.76/1.42 tff(1240,plain,
% 1.76/1.42 ((~hskp24) | (~c3_1(a2468))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.76/1.42 tff(1241,plain,
% 1.76/1.42 ((~hskp24) | (~c3_1(a2468))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1240, 1237])).
% 1.76/1.42 tff(1242,plain,
% 1.76/1.42 (~c3_1(a2468)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1241, 1236])).
% 1.76/1.42 tff(1243,plain,
% 1.76/1.42 (((~hskp24) | c1_1(a2468)) <=> ((~hskp24) | c1_1(a2468))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1244,axiom,((~hskp24) | c1_1(a2468)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.76/1.42 tff(1245,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.76/1.42 tff(1246,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1245, 1243])).
% 1.76/1.42 tff(1247,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1246, 1243])).
% 1.76/1.42 tff(1248,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1247, 1243])).
% 1.76/1.42 tff(1249,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1248, 1243])).
% 1.76/1.42 tff(1250,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1249, 1243])).
% 1.76/1.42 tff(1251,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1250, 1243])).
% 1.76/1.42 tff(1252,plain,
% 1.76/1.42 ((~hskp24) | c1_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1251, 1243])).
% 1.76/1.42 tff(1253,plain,
% 1.76/1.42 (c1_1(a2468)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1252, 1236])).
% 1.76/1.42 tff(1254,assumption,(~hskp6), introduced(assumption)).
% 1.76/1.42 tff(1255,plain,
% 1.76/1.42 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1256,plain,
% 1.76/1.42 ((hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468))) <=> (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1257,plain,
% 1.76/1.42 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468)))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1256])).
% 1.76/1.42 tff(1258,plain,
% 1.76/1.42 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1257, 1255])).
% 1.76/1.42 tff(1259,plain,
% 1.76/1.42 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1260,plain,
% 1.76/1.42 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.76/1.42 tff(1261,plain,
% 1.76/1.42 (c2_1(a2468)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1260, 204, 1254, 22, 1253, 1242, 1026])).
% 1.76/1.42 tff(1262,plain,
% 1.76/1.42 (((~hskp24) | (~c0_1(a2468))) <=> ((~hskp24) | (~c0_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1263,plain,
% 1.76/1.42 (((~c0_1(a2468)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1264,axiom,((~c0_1(a2468)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.76/1.42 tff(1265,plain,
% 1.76/1.42 ((~hskp24) | (~c0_1(a2468))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.76/1.42 tff(1266,plain,
% 1.76/1.42 ((~hskp24) | (~c0_1(a2468))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1265, 1262])).
% 1.76/1.42 tff(1267,plain,
% 1.76/1.42 (~c0_1(a2468)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1266, 1236])).
% 1.76/1.42 tff(1268,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1269,plain,
% 1.76/1.42 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468))) <=> (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1270,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1269])).
% 1.76/1.42 tff(1271,plain,
% 1.76/1.42 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1270, 1268])).
% 1.76/1.42 tff(1272,plain,
% 1.76/1.42 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1273,plain,
% 1.76/1.42 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.76/1.42 tff(1274,plain,
% 1.76/1.42 ($false),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1273, 204, 43, 1253, 1185, 1267, 1162, 1161, 85, 1261])).
% 1.76/1.42 tff(1275,plain,((~hskp24) | hskp19 | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | hskp6 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.76/1.42 tff(1276,plain,
% 1.76/1.42 (~hskp24),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1275, 1106, 43, 1150, 1107, 1235, 22])).
% 1.76/1.42 tff(1277,plain,
% 1.76/1.42 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.76/1.42 inference(bind,[status(th)],[])).
% 1.76/1.42 tff(1278,plain,
% 1.76/1.42 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(quant_intro,[status(thm)],[1277])).
% 1.76/1.42 tff(1279,plain,
% 1.76/1.42 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1280,plain,
% 1.76/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.76/1.42 inference(bind,[status(th)],[])).
% 1.76/1.42 tff(1281,plain,
% 1.76/1.42 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(quant_intro,[status(thm)],[1280])).
% 1.76/1.42 tff(1282,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.76/1.42 tff(1283,plain,
% 1.76/1.42 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 1.76/1.42 tff(1284,plain,
% 1.76/1.42 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 1.76/1.42 tff(1285,plain,(
% 1.76/1.42 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(skolemize,[status(sab)],[1284])).
% 1.76/1.42 tff(1286,plain,
% 1.76/1.42 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1285, 1278])).
% 1.76/1.42 tff(1287,plain,
% 1.76/1.42 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1288,plain,
% 1.76/1.42 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1289,plain,
% 1.76/1.42 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1288])).
% 1.76/1.42 tff(1290,plain,
% 1.76/1.42 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1289, 1287])).
% 1.76/1.42 tff(1291,plain,
% 1.76/1.42 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))),
% 1.76/1.42 inference(quant_inst,[status(thm)],[])).
% 1.76/1.42 tff(1292,plain,
% 1.76/1.42 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.76/1.42 tff(1293,plain,
% 1.76/1.42 (hskp24 | hskp3 | (~c2_1(a2450))),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1292, 204, 1227, 1226, 1286])).
% 1.76/1.42 tff(1294,plain,
% 1.76/1.42 (hskp3),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1293, 1276, 1234])).
% 1.76/1.42 tff(1295,plain,
% 1.76/1.42 (((~hskp3) | (~c3_1(a2405))) <=> ((~hskp3) | (~c3_1(a2405)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1296,plain,
% 1.76/1.42 (((~c3_1(a2405)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2405)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1297,axiom,((~c3_1(a2405)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.76/1.42 tff(1298,plain,
% 1.76/1.42 ((~hskp3) | (~c3_1(a2405))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.76/1.42 tff(1299,plain,
% 1.76/1.42 ((~hskp3) | (~c3_1(a2405))),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1298, 1295])).
% 1.76/1.42 tff(1300,plain,
% 1.76/1.42 (~c3_1(a2405)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1299, 1294])).
% 1.76/1.42 tff(1301,plain,
% 1.76/1.42 (((~hskp3) | c0_1(a2405)) <=> ((~hskp3) | c0_1(a2405))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1302,axiom,((~hskp3) | c0_1(a2405)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.76/1.42 tff(1303,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.76/1.42 tff(1304,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1303, 1301])).
% 1.76/1.42 tff(1305,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1304, 1301])).
% 1.76/1.42 tff(1306,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1305, 1301])).
% 1.76/1.42 tff(1307,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1306, 1301])).
% 1.76/1.42 tff(1308,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1307, 1301])).
% 1.76/1.42 tff(1309,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1308, 1301])).
% 1.76/1.42 tff(1310,plain,
% 1.76/1.42 ((~hskp3) | c0_1(a2405)),
% 1.76/1.42 inference(modus_ponens,[status(thm)],[1309, 1301])).
% 1.76/1.42 tff(1311,plain,
% 1.76/1.42 (c0_1(a2405)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[1310, 1294])).
% 1.76/1.42 tff(1312,plain,
% 1.76/1.42 (c3_1(a2450)),
% 1.76/1.42 inference(unit_resolution,[status(thm)],[633, 1225])).
% 1.76/1.42 tff(1313,plain,
% 1.76/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1314,plain,
% 1.76/1.42 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.76/1.42 inference(rewrite,[status(thm)],[])).
% 1.76/1.42 tff(1315,plain,
% 1.76/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))))),
% 1.76/1.42 inference(monotonicity,[status(thm)],[1314])).
% 1.76/1.42 tff(1316,plain,
% 1.76/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.76/1.42 inference(transitivity,[status(thm)],[1315, 1313])).
% 1.76/1.42 tff(1317,plain,
% 1.76/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.76/1.43 inference(quant_inst,[status(thm)],[])).
% 1.76/1.43 tff(1318,plain,
% 1.76/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.76/1.43 tff(1319,plain,
% 1.76/1.43 (~c1_1(a2405)),
% 1.76/1.43 inference(unit_resolution,[status(thm)],[1318, 204, 1226, 1312, 1106, 1311, 1150, 1107, 1300, 1160, 1234])).
% 1.76/1.43 tff(1320,assumption,(~c2_1(a2417)), introduced(assumption)).
% 1.76/1.43 tff(1321,plain,
% 1.76/1.43 (((~hskp3) | c2_1(a2405)) <=> ((~hskp3) | c2_1(a2405))),
% 1.76/1.43 inference(rewrite,[status(thm)],[])).
% 1.76/1.43 tff(1322,axiom,((~hskp3) | c2_1(a2405)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.76/1.43 tff(1323,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 1.76/1.43 tff(1324,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1323, 1321])).
% 1.76/1.43 tff(1325,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1324, 1321])).
% 1.76/1.43 tff(1326,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1325, 1321])).
% 1.76/1.43 tff(1327,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1326, 1321])).
% 1.76/1.43 tff(1328,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1327, 1321])).
% 1.76/1.43 tff(1329,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1328, 1321])).
% 1.76/1.43 tff(1330,plain,
% 1.76/1.43 ((~hskp3) | c2_1(a2405)),
% 1.76/1.43 inference(modus_ponens,[status(thm)],[1329, 1321])).
% 1.76/1.43 tff(1331,plain,
% 1.76/1.43 (c2_1(a2405)),
% 1.76/1.43 inference(unit_resolution,[status(thm)],[1330, 1294])).
% 1.76/1.43 tff(1332,plain,
% 1.76/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.76/1.43 inference(rewrite,[status(thm)],[])).
% 1.76/1.43 tff(1333,plain,
% 1.76/1.43 (((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.76/1.43 inference(rewrite,[status(thm)],[])).
% 1.76/1.43 tff(1334,plain,
% 1.76/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500))))),
% 1.76/1.43 inference(monotonicity,[status(thm)],[1333])).
% 1.76/1.43 tff(1335,plain,
% 1.76/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1334, 1332])).
% 1.82/1.43 tff(1336,plain,
% 1.82/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1337,plain,
% 1.82/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 1.82/1.43 tff(1338,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1337, 204, 1311, 1331, 1029, 1028, 1094, 1083, 21, 1093, 1320, 1319])).
% 1.82/1.43 tff(1339,plain,((~hskp10) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~c2_1(a2500)) | c2_1(a2417) | hskp19 | hskp1 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.82/1.43 tff(1340,plain,
% 1.82/1.43 (~hskp10),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1339, 1092, 1028, 1094, 1083, 1093, 1029, 43, 22, 958])).
% 1.82/1.43 tff(1341,plain,
% 1.82/1.43 (hskp16 | hskp10 | c2_1(a2417)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[260, 204, 1085, 1083, 140])).
% 1.82/1.43 tff(1342,plain,
% 1.82/1.43 (hskp16),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1341, 1340, 1092])).
% 1.82/1.43 tff(1343,plain,
% 1.82/1.43 (~c2_1(a2425)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[450, 1342])).
% 1.82/1.43 tff(1344,plain,
% 1.82/1.43 (c0_1(a2425)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[461, 1342])).
% 1.82/1.43 tff(1345,plain,
% 1.82/1.43 (~c1_1(a2425)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[495, 204, 958, 43, 1344, 1343, 106])).
% 1.82/1.43 tff(1346,plain,
% 1.82/1.43 (~c3_1(a2425)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[444, 1342])).
% 1.82/1.43 tff(1347,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[468, 204, 1340, 1344, 1343, 1346, 95, 1345])).
% 1.82/1.43 tff(1348,plain,(hskp19 | hskp25 | (~c3_1(a2417)) | c1_1(a2417) | c1_1(a2500) | c0_1(a2417) | (~c2_1(a2500)) | c0_1(a2500) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.82/1.43 tff(1349,plain,
% 1.82/1.43 (hskp19),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1348, 1068, 958, 1067, 1028, 1066, 1047, 1029, 22])).
% 1.82/1.43 tff(1350,plain,
% 1.82/1.43 (~c0_1(a2432)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[312, 1349])).
% 1.82/1.43 tff(1351,plain,
% 1.82/1.43 (c1_1(a2432)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[323, 1349])).
% 1.82/1.43 tff(1352,plain,
% 1.82/1.43 (c3_1(a2432)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[891, 1349])).
% 1.82/1.43 tff(1353,assumption,(~c0_1(a2432)), introduced(assumption)).
% 1.82/1.43 tff(1354,assumption,(c1_1(a2432)), introduced(assumption)).
% 1.82/1.43 tff(1355,plain,
% 1.82/1.43 (hskp16 | c2_1(a2432)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[377, 204, 65, 1354, 1353, 75])).
% 1.82/1.43 tff(1356,plain,
% 1.82/1.43 (c2_1(a2432)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1355, 64])).
% 1.82/1.43 tff(1357,assumption,(c3_1(a2432)), introduced(assumption)).
% 1.82/1.43 tff(1358,plain,
% 1.82/1.43 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1359,plain,
% 1.82/1.43 ((hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432))) <=> (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1360,plain,
% 1.82/1.43 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1359])).
% 1.82/1.43 tff(1361,plain,
% 1.82/1.43 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1360, 1358])).
% 1.82/1.43 tff(1362,plain,
% 1.82/1.43 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1363,plain,
% 1.82/1.43 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 1.82/1.43 tff(1364,plain,
% 1.82/1.43 (hskp15 | (~c2_1(a2432))),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1363, 204, 1357, 1353, 511])).
% 1.82/1.43 tff(1365,plain,
% 1.82/1.43 (hskp15),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1364, 1356])).
% 1.82/1.43 tff(1366,plain,
% 1.82/1.43 (~c2_1(a2422)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[576, 1365])).
% 1.82/1.43 tff(1367,plain,
% 1.82/1.43 (c1_1(a2422)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[570, 1365])).
% 1.82/1.43 tff(1368,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1369,plain,
% 1.82/1.43 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422))) <=> (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1370,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1369])).
% 1.82/1.43 tff(1371,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1370, 1368])).
% 1.82/1.43 tff(1372,plain,
% 1.82/1.43 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1373,plain,
% 1.82/1.43 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 1.82/1.43 tff(1374,plain,
% 1.82/1.43 (c0_1(a2422)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1373, 204, 64, 65, 1367, 1366, 75])).
% 1.82/1.43 tff(1375,plain,
% 1.82/1.43 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(1376,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[1375])).
% 1.82/1.43 tff(1377,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1378,plain,
% 1.82/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(1379,plain,
% 1.82/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[1378])).
% 1.82/1.43 tff(1380,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.82/1.43 tff(1381,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.82/1.43 tff(1382,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1381, 1377])).
% 1.82/1.43 tff(1383,plain,(
% 1.82/1.43 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(skolemize,[status(sab)],[1382])).
% 1.82/1.43 tff(1384,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1383, 1376])).
% 1.82/1.43 tff(1385,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1386,plain,
% 1.82/1.43 ((hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1387,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1386])).
% 1.82/1.43 tff(1388,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1387, 1385])).
% 1.82/1.43 tff(1389,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1390,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.82/1.43 tff(1391,plain,
% 1.82/1.43 (hskp2 | (~c0_1(a2422))),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1390, 204, 1367, 1028, 1027, 1366, 1384, 1093])).
% 1.82/1.43 tff(1392,plain,
% 1.82/1.43 (hskp2),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1391, 1374])).
% 1.82/1.43 tff(1393,plain,
% 1.82/1.43 (((~hskp2) | (~c3_1(a2404))) <=> ((~hskp2) | (~c3_1(a2404)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1394,plain,
% 1.82/1.43 (((~c3_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2404)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1395,axiom,((~c3_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.82/1.43 tff(1396,plain,
% 1.82/1.43 ((~hskp2) | (~c3_1(a2404))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.82/1.43 tff(1397,plain,
% 1.82/1.43 ((~hskp2) | (~c3_1(a2404))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1396, 1393])).
% 1.82/1.43 tff(1398,plain,
% 1.82/1.43 (~c3_1(a2404)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1397, 1392])).
% 1.82/1.43 tff(1399,plain,
% 1.82/1.43 (((~hskp2) | (~c2_1(a2404))) <=> ((~hskp2) | (~c2_1(a2404)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1400,plain,
% 1.82/1.43 (((~c2_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2404)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1401,axiom,((~c2_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.82/1.43 tff(1402,plain,
% 1.82/1.43 ((~hskp2) | (~c2_1(a2404))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.82/1.43 tff(1403,plain,
% 1.82/1.43 ((~hskp2) | (~c2_1(a2404))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1402, 1399])).
% 1.82/1.43 tff(1404,plain,
% 1.82/1.43 (~c2_1(a2404)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1403, 1392])).
% 1.82/1.43 tff(1405,plain,
% 1.82/1.43 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1406,plain,
% 1.82/1.43 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404)) <=> (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1407,plain,
% 1.82/1.43 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404)))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1406])).
% 1.82/1.43 tff(1408,plain,
% 1.82/1.43 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1407, 1405])).
% 1.82/1.43 tff(1409,plain,
% 1.82/1.43 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1410,plain,
% 1.82/1.43 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.82/1.43 tff(1411,plain,
% 1.82/1.43 (c0_1(a2404)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1410, 204, 65, 22, 1404, 1398, 1039])).
% 1.82/1.43 tff(1412,plain,
% 1.82/1.43 (c3_1(a2422)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[559, 1365])).
% 1.82/1.43 tff(1413,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1414,plain,
% 1.82/1.43 ((hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1415,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1414])).
% 1.82/1.43 tff(1416,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.82/1.43 tff(1417,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1418,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.82/1.43 tff(1419,plain,
% 1.82/1.43 (hskp20),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1418, 204, 1354, 1357, 1367, 1412, 1353, 1366, 920])).
% 1.82/1.43 tff(1420,plain,
% 1.82/1.43 (~c2_1(a2435)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[868, 1419])).
% 1.82/1.43 tff(1421,plain,
% 1.82/1.43 (~c0_1(a2435)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[820, 1419])).
% 1.82/1.43 tff(1422,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1423,plain,
% 1.82/1.43 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))) <=> (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1424,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[1423])).
% 1.82/1.43 tff(1425,plain,
% 1.82/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[1424, 1422])).
% 1.82/1.43 tff(1426,plain,
% 1.82/1.43 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(1427,plain,
% 1.82/1.43 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.82/1.43 tff(1428,plain,
% 1.82/1.43 (~c1_1(a2435)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[1427, 204, 64, 65, 1421, 1420, 75])).
% 1.82/1.43 tff(1429,plain,
% 1.82/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(1430,plain,
% 1.82/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[1429])).
% 1.82/1.43 tff(1431,plain,
% 1.82/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(1432,plain,
% 1.82/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(1433,plain,
% 1.82/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[1432])).
% 1.82/1.44 tff(1434,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.82/1.44 tff(1435,plain,
% 1.82/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.82/1.44 tff(1436,plain,
% 1.82/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1435, 1431])).
% 1.82/1.44 tff(1437,plain,(
% 1.82/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.44 inference(skolemize,[status(sab)],[1436])).
% 1.82/1.44 tff(1438,plain,
% 1.82/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1437, 1430])).
% 1.82/1.44 tff(1439,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1440,plain,
% 1.82/1.44 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1441,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1440])).
% 1.82/1.44 tff(1442,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.82/1.44 tff(1443,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1444,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.82/1.44 tff(1445,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1444, 204, 1367, 1412, 1421, 1420, 1366, 1404, 1398, 1438, 1428, 1411])).
% 1.82/1.44 tff(1446,plain,(hskp16 | hskp13 | hskp1 | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)) | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1447,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1446, 1352, 1351, 22, 1028, 1027, 1047, 65, 64, 1350])).
% 1.82/1.44 tff(1448,plain,(hskp16 | hskp1 | c1_1(a2500) | c3_1(a2500) | hskp13 | hskp25 | c0_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1449,plain,
% 1.82/1.44 (hskp16),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1448, 65, 1028, 1027, 22, 958, 1029])).
% 1.82/1.44 tff(1450,plain,
% 1.82/1.44 (~c3_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[444, 1449])).
% 1.82/1.44 tff(1451,plain,
% 1.82/1.44 (~c2_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[450, 1449])).
% 1.82/1.44 tff(1452,plain,
% 1.82/1.44 (c0_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[461, 1449])).
% 1.82/1.44 tff(1453,assumption,(c0_1(a2425)), introduced(assumption)).
% 1.82/1.44 tff(1454,plain,
% 1.82/1.44 (hskp19 | (~c1_1(a2425))),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[495, 204, 958, 1453, 770, 106])).
% 1.82/1.44 tff(1455,plain,
% 1.82/1.44 (~c1_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1454, 43])).
% 1.82/1.44 tff(1456,plain,
% 1.82/1.44 (hskp10 | c1_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[468, 204, 1453, 770, 769, 95])).
% 1.82/1.44 tff(1457,plain,
% 1.82/1.44 (hskp10),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1456, 1455])).
% 1.82/1.44 tff(1458,plain,
% 1.82/1.44 (c0_1(a2414)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1105, 1457])).
% 1.82/1.44 tff(1459,plain,
% 1.82/1.44 (~c3_1(a2414)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[950, 1457])).
% 1.82/1.44 tff(1460,plain,
% 1.82/1.44 (~c1_1(a2414)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[956, 1457])).
% 1.82/1.44 tff(1461,plain,
% 1.82/1.44 (hskp30),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1224, 1460, 43, 1149, 22, 1138, 1459, 958, 1458])).
% 1.82/1.44 tff(1462,plain,
% 1.82/1.44 (c1_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[644, 1461])).
% 1.82/1.44 tff(1463,plain,
% 1.82/1.44 (c0_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[655, 1461])).
% 1.82/1.44 tff(1464,plain,
% 1.82/1.44 (c2_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1233, 204, 958, 43, 1463, 1462, 106])).
% 1.82/1.44 tff(1465,plain,
% 1.82/1.44 (~hskp24),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1275, 1458, 43, 1460, 1459, 1235, 22])).
% 1.82/1.44 tff(1466,plain,
% 1.82/1.44 (hskp3 | (~c2_1(a2450))),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1292, 204, 1465, 1463, 1462, 1286])).
% 1.82/1.44 tff(1467,plain,
% 1.82/1.44 (hskp3),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1466, 1464])).
% 1.82/1.44 tff(1468,plain,
% 1.82/1.44 (~c3_1(a2405)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1299, 1467])).
% 1.82/1.44 tff(1469,plain,
% 1.82/1.44 (c2_1(a2405)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1330, 1467])).
% 1.82/1.44 tff(1470,plain,
% 1.82/1.44 (c0_1(a2405)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1310, 1467])).
% 1.82/1.44 tff(1471,plain,
% 1.82/1.44 (hskp30),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1224, 1460, 1209, 1208, 22, 43, 1459, 958, 1458])).
% 1.82/1.44 tff(1472,plain,
% 1.82/1.44 (c1_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[644, 1471])).
% 1.82/1.44 tff(1473,plain,
% 1.82/1.44 (c0_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[655, 1471])).
% 1.82/1.44 tff(1474,plain,
% 1.82/1.44 (c2_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1233, 204, 958, 43, 1473, 1472, 106])).
% 1.82/1.44 tff(1475,assumption,(~c3_1(a2405)), introduced(assumption)).
% 1.82/1.44 tff(1476,assumption,(c2_1(a2405)), introduced(assumption)).
% 1.82/1.44 tff(1477,assumption,(c0_1(a2405)), introduced(assumption)).
% 1.82/1.44 tff(1478,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1479,plain,
% 1.82/1.44 ((hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405))) <=> (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1480,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1479])).
% 1.82/1.44 tff(1481,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1480, 1478])).
% 1.82/1.44 tff(1482,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1483,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.82/1.44 tff(1484,plain,
% 1.82/1.44 (hskp20),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1483, 204, 1473, 1472, 1477, 1476, 1475, 722, 1474])).
% 1.82/1.44 tff(1485,plain,
% 1.82/1.44 (~c2_1(a2435)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[868, 1484])).
% 1.82/1.44 tff(1486,plain,
% 1.82/1.44 (~c0_1(a2435)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[820, 1484])).
% 1.82/1.44 tff(1487,plain,
% 1.82/1.44 (c3_1(a2435)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[814, 1484])).
% 1.82/1.44 tff(1488,plain,
% 1.82/1.44 (c3_1(a2450)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[633, 1471])).
% 1.82/1.44 tff(1489,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[938, 204, 326, 1473, 1472, 1488, 1487, 1486, 1485, 832])).
% 1.82/1.44 tff(1490,plain,(hskp19 | hskp12 | (~c0_1(a2405)) | (~c2_1(a2405)) | c3_1(a2405) | hskp25 | (~c2_1(a2409)) | (~c3_1(a2409)) | hskp1 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1491,plain,
% 1.82/1.44 (hskp12),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1490, 1470, 43, 1469, 1468, 958, 1138, 1149, 22, 1453, 770, 769])).
% 1.82/1.44 tff(1492,plain,
% 1.82/1.44 (~c0_1(a2417)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[235, 1491])).
% 1.82/1.44 tff(1493,plain,
% 1.82/1.44 (c3_1(a2417)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[246, 1491])).
% 1.82/1.44 tff(1494,plain,
% 1.82/1.44 (~c1_1(a2417)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[229, 1491])).
% 1.82/1.44 tff(1495,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1348, 1494, 1493, 958, 43, 1028, 1492, 1093, 1029, 22])).
% 1.82/1.44 tff(1496,plain,(hskp19 | hskp25 | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | hskp1 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1497,plain,
% 1.82/1.44 (hskp19),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1496, 1047, 1028, 958, 1029, 22, 1452, 1451, 1450])).
% 1.82/1.44 tff(1498,plain,
% 1.82/1.44 (~c0_1(a2432)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[312, 1497])).
% 1.82/1.44 tff(1499,plain,
% 1.82/1.44 (c3_1(a2432)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[891, 1497])).
% 1.82/1.44 tff(1500,plain,
% 1.82/1.44 (c1_1(a2432)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[323, 1497])).
% 1.82/1.44 tff(1501,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1502,plain,
% 1.82/1.44 ((hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1503,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1502])).
% 1.82/1.44 tff(1504,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1503, 1501])).
% 1.82/1.44 tff(1505,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1506,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.82/1.44 tff(1507,plain,
% 1.82/1.44 (hskp4),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1506, 204, 1500, 1499, 1029, 1028, 1498, 1057, 1047])).
% 1.82/1.44 tff(1508,plain,
% 1.82/1.44 (((~hskp4) | (~c1_1(a2407))) <=> ((~hskp4) | (~c1_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1509,plain,
% 1.82/1.44 (((~c1_1(a2407)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1510,axiom,((~c1_1(a2407)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.82/1.44 tff(1511,plain,
% 1.82/1.44 ((~hskp4) | (~c1_1(a2407))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.82/1.44 tff(1512,plain,
% 1.82/1.44 ((~hskp4) | (~c1_1(a2407))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 1.82/1.44 tff(1513,plain,
% 1.82/1.44 (~c1_1(a2407)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1512, 1507])).
% 1.82/1.44 tff(1514,plain,
% 1.82/1.44 (((~hskp4) | (~c2_1(a2407))) <=> ((~hskp4) | (~c2_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1515,plain,
% 1.82/1.44 (((~c2_1(a2407)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1516,axiom,((~c2_1(a2407)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.82/1.44 tff(1517,plain,
% 1.82/1.44 ((~hskp4) | (~c2_1(a2407))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 1.82/1.44 tff(1518,plain,
% 1.82/1.44 ((~hskp4) | (~c2_1(a2407))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1517, 1514])).
% 1.82/1.44 tff(1519,plain,
% 1.82/1.44 (~c2_1(a2407)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1518, 1507])).
% 1.82/1.44 tff(1520,assumption,(~c2_1(a2407)), introduced(assumption)).
% 1.82/1.44 tff(1521,assumption,(~c1_1(a2407)), introduced(assumption)).
% 1.82/1.44 tff(1522,assumption,(~c0_1(a2407)), introduced(assumption)).
% 1.82/1.44 tff(1523,plain,
% 1.82/1.44 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(1524,plain,
% 1.82/1.44 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[1523])).
% 1.82/1.44 tff(1525,plain,
% 1.82/1.44 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1526,plain,
% 1.82/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(1527,plain,
% 1.82/1.44 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[1526])).
% 1.82/1.44 tff(1528,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.82/1.44 tff(1529,plain,
% 1.82/1.44 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.82/1.44 tff(1530,plain,
% 1.82/1.44 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1529, 1525])).
% 1.82/1.44 tff(1531,plain,(
% 1.82/1.44 ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(skolemize,[status(sab)],[1530])).
% 1.82/1.44 tff(1532,plain,
% 1.82/1.44 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1531, 1524])).
% 1.82/1.44 tff(1533,plain,
% 1.82/1.44 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1534,plain,
% 1.82/1.44 ((hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407))) <=> (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1535,plain,
% 1.82/1.44 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1534])).
% 1.82/1.44 tff(1536,plain,
% 1.82/1.44 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.82/1.44 tff(1537,plain,
% 1.82/1.44 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1538,plain,
% 1.82/1.44 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.82/1.44 tff(1539,plain,
% 1.82/1.44 (hskp12 | c0_1(a2407) | (~c3_1(a2407))),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1538, 204, 1521, 1532])).
% 1.82/1.44 tff(1540,plain,
% 1.82/1.44 (~c3_1(a2407)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1539, 1522, 326])).
% 1.82/1.44 tff(1541,plain,
% 1.82/1.44 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1542,plain,
% 1.82/1.44 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407)) <=> (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1543,plain,
% 1.82/1.44 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407)))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1542])).
% 1.82/1.44 tff(1544,plain,
% 1.82/1.44 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1543, 1541])).
% 1.82/1.44 tff(1545,plain,
% 1.82/1.44 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1546,plain,
% 1.82/1.44 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.82/1.44 tff(1547,plain,
% 1.82/1.44 (c0_1(a2407) | c3_1(a2407)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1546, 204, 65, 22, 1520, 1039])).
% 1.82/1.44 tff(1548,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1547, 1540, 1522])).
% 1.82/1.44 tff(1549,plain,(c0_1(a2407) | hskp13 | hskp1 | c2_1(a2407) | hskp12 | c1_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1550,plain,
% 1.82/1.44 (c0_1(a2407)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1549, 326, 22, 1520, 65, 1521])).
% 1.82/1.44 tff(1551,plain,
% 1.82/1.44 (hskp16),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1064, 326, 1047])).
% 1.82/1.44 tff(1552,plain,
% 1.82/1.44 (~c2_1(a2425)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[450, 1551])).
% 1.82/1.44 tff(1553,assumption,(hskp22), introduced(assumption)).
% 1.82/1.44 tff(1554,plain,
% 1.82/1.44 (((~hskp22) | (~c2_1(a2453))) <=> ((~hskp22) | (~c2_1(a2453)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1555,plain,
% 1.82/1.44 (((~c2_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a2453)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1556,axiom,((~c2_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.82/1.44 tff(1557,plain,
% 1.82/1.44 ((~hskp22) | (~c2_1(a2453))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.82/1.44 tff(1558,plain,
% 1.82/1.44 ((~hskp22) | (~c2_1(a2453))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1557, 1554])).
% 1.82/1.44 tff(1559,plain,
% 1.82/1.44 (~c2_1(a2453)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1558, 1553])).
% 1.82/1.44 tff(1560,plain,
% 1.82/1.44 (((~hskp22) | (~c0_1(a2453))) <=> ((~hskp22) | (~c0_1(a2453)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1561,plain,
% 1.82/1.44 (((~c0_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2453)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1562,axiom,((~c0_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.82/1.44 tff(1563,plain,
% 1.82/1.44 ((~hskp22) | (~c0_1(a2453))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.82/1.44 tff(1564,plain,
% 1.82/1.44 ((~hskp22) | (~c0_1(a2453))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1563, 1560])).
% 1.82/1.44 tff(1565,plain,
% 1.82/1.44 (~c0_1(a2453)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1564, 1553])).
% 1.82/1.44 tff(1566,plain,
% 1.82/1.44 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1567,plain,
% 1.82/1.45 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453)) <=> (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1568,plain,
% 1.82/1.45 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453)))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1567])).
% 1.82/1.45 tff(1569,plain,
% 1.82/1.45 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.82/1.45 tff(1570,plain,
% 1.82/1.45 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1571,plain,
% 1.82/1.45 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.82/1.45 tff(1572,plain,
% 1.82/1.45 (c3_1(a2453)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1571, 204, 65, 22, 1565, 1559, 1039])).
% 1.82/1.45 tff(1573,plain,
% 1.82/1.45 (((~hskp22) | (~c1_1(a2453))) <=> ((~hskp22) | (~c1_1(a2453)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1574,plain,
% 1.82/1.45 (((~c1_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2453)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1575,axiom,((~c1_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.82/1.45 tff(1576,plain,
% 1.82/1.45 ((~hskp22) | (~c1_1(a2453))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.82/1.45 tff(1577,plain,
% 1.82/1.45 ((~hskp22) | (~c1_1(a2453))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1576, 1573])).
% 1.82/1.45 tff(1578,plain,
% 1.82/1.45 (~c1_1(a2453)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1577, 1553])).
% 1.82/1.45 tff(1579,plain,
% 1.82/1.45 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1580,plain,
% 1.82/1.45 ((hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453))) <=> (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1581,plain,
% 1.82/1.45 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1580])).
% 1.82/1.45 tff(1582,plain,
% 1.82/1.45 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.82/1.45 tff(1583,plain,
% 1.82/1.45 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1584,plain,
% 1.82/1.45 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.82/1.45 tff(1585,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1584, 204, 326, 1565, 1578, 1532, 1572])).
% 1.82/1.45 tff(1586,plain,((~hskp22) | hskp12 | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1587,plain,
% 1.82/1.45 (~hskp22),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1586, 326, 65, 22])).
% 1.82/1.45 tff(1588,plain,
% 1.82/1.45 (^[U: $i] : refl((hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1589,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1588])).
% 1.82/1.45 tff(1590,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1591,plain,
% 1.82/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1592,plain,
% 1.82/1.45 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1591])).
% 1.82/1.45 tff(1593,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.82/1.45 tff(1594,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.82/1.45 tff(1595,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1594, 1590])).
% 1.82/1.45 tff(1596,plain,(
% 1.82/1.45 ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(skolemize,[status(sab)],[1595])).
% 1.82/1.45 tff(1597,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1596, 1589])).
% 1.82/1.45 tff(1598,plain,
% 1.82/1.45 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1599,plain,
% 1.82/1.45 ((hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407))) <=> (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1600,plain,
% 1.82/1.45 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1599])).
% 1.82/1.45 tff(1601,plain,
% 1.82/1.45 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.82/1.45 tff(1602,plain,
% 1.82/1.45 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1603,plain,
% 1.82/1.45 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.82/1.45 tff(1604,plain,
% 1.82/1.45 (hskp22 | hskp5 | c2_1(a2407) | (~c0_1(a2407))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1603, 204, 1521, 1597])).
% 1.82/1.45 tff(1605,plain,
% 1.82/1.45 (hskp5),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1604, 1587, 1550, 1520])).
% 1.82/1.45 tff(1606,plain,
% 1.82/1.45 (c0_1(a2408)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[411, 1605])).
% 1.82/1.45 tff(1607,plain,
% 1.82/1.45 (c0_1(a2425)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[461, 1551])).
% 1.82/1.45 tff(1608,plain,
% 1.82/1.45 (~c3_1(a2425)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[444, 1551])).
% 1.82/1.45 tff(1609,assumption,(hskp0), introduced(assumption)).
% 1.82/1.45 tff(1610,plain,
% 1.82/1.45 (((~hskp0) | (~c1_1(a2402))) <=> ((~hskp0) | (~c1_1(a2402)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1611,plain,
% 1.82/1.45 (((~c1_1(a2402)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a2402)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1612,axiom,((~c1_1(a2402)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.82/1.45 tff(1613,plain,
% 1.82/1.45 ((~hskp0) | (~c1_1(a2402))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 1.82/1.45 tff(1614,plain,
% 1.82/1.45 ((~hskp0) | (~c1_1(a2402))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1613, 1610])).
% 1.82/1.45 tff(1615,plain,
% 1.82/1.45 (~c1_1(a2402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1614, 1609])).
% 1.82/1.45 tff(1616,plain,
% 1.82/1.45 (((~hskp0) | c3_1(a2402)) <=> ((~hskp0) | c3_1(a2402))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1617,axiom,((~hskp0) | c3_1(a2402)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.82/1.45 tff(1618,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.82/1.45 tff(1619,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1618, 1616])).
% 1.82/1.45 tff(1620,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1619, 1616])).
% 1.82/1.45 tff(1621,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1620, 1616])).
% 1.82/1.45 tff(1622,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1621, 1616])).
% 1.82/1.45 tff(1623,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1622, 1616])).
% 1.82/1.45 tff(1624,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1623, 1616])).
% 1.82/1.45 tff(1625,plain,
% 1.82/1.45 ((~hskp0) | c3_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1624, 1616])).
% 1.82/1.45 tff(1626,plain,
% 1.82/1.45 (c3_1(a2402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1625, 1609])).
% 1.82/1.45 tff(1627,plain,
% 1.82/1.45 (((~hskp0) | c0_1(a2402)) <=> ((~hskp0) | c0_1(a2402))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1628,axiom,((~hskp0) | c0_1(a2402)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.82/1.45 tff(1629,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.82/1.45 tff(1630,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1629, 1627])).
% 1.82/1.45 tff(1631,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1630, 1627])).
% 1.82/1.45 tff(1632,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1631, 1627])).
% 1.82/1.45 tff(1633,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1632, 1627])).
% 1.82/1.45 tff(1634,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1633, 1627])).
% 1.82/1.45 tff(1635,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1634, 1627])).
% 1.82/1.45 tff(1636,plain,
% 1.82/1.45 ((~hskp0) | c0_1(a2402)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1635, 1627])).
% 1.82/1.45 tff(1637,plain,
% 1.82/1.45 (c0_1(a2402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1636, 1609])).
% 1.82/1.45 tff(1638,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1639,plain,
% 1.82/1.45 ((hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1640,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1639])).
% 1.82/1.45 tff(1641,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.82/1.45 tff(1642,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1643,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.82/1.45 tff(1644,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1643, 204, 1118, 1637, 1626, 1029, 1028, 1615, 1117, 1093])).
% 1.82/1.45 tff(1645,plain,((~hskp0) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1646,plain,
% 1.82/1.45 (~hskp0),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1645, 1118, 1029, 1028, 1093])).
% 1.82/1.45 tff(1647,plain,
% 1.82/1.45 (^[U: $i] : refl((hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1648,plain,
% 1.82/1.45 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1647])).
% 1.82/1.45 tff(1649,plain,
% 1.82/1.45 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1650,plain,
% 1.82/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1651,plain,
% 1.82/1.45 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1650])).
% 1.82/1.45 tff(1652,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.82/1.45 tff(1653,plain,
% 1.82/1.45 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.82/1.45 tff(1654,plain,
% 1.82/1.45 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1653, 1649])).
% 1.82/1.45 tff(1655,plain,(
% 1.82/1.45 ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(skolemize,[status(sab)],[1654])).
% 1.82/1.45 tff(1656,plain,
% 1.82/1.45 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1655, 1648])).
% 1.82/1.45 tff(1657,plain,
% 1.82/1.45 (hskp19),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1126, 1118, 1029, 1028, 1093, 958])).
% 1.82/1.45 tff(1658,plain,
% 1.82/1.45 (~c0_1(a2432)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[312, 1657])).
% 1.82/1.45 tff(1659,plain,
% 1.82/1.45 (c1_1(a2432)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[323, 1657])).
% 1.82/1.45 tff(1660,plain,
% 1.82/1.45 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1661,plain,
% 1.82/1.45 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432))) <=> (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1662,plain,
% 1.82/1.45 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1661])).
% 1.82/1.45 tff(1663,plain,
% 1.82/1.45 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.82/1.45 tff(1664,plain,
% 1.82/1.45 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1665,plain,
% 1.82/1.45 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.82/1.45 tff(1666,plain,
% 1.82/1.45 (hskp0 | c2_1(a2432)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1665, 204, 1118, 1659, 1658, 1656])).
% 1.82/1.45 tff(1667,plain,
% 1.82/1.45 (c2_1(a2432)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1666, 1646])).
% 1.82/1.45 tff(1668,plain,
% 1.82/1.45 (hskp11 | (~c2_1(a2432))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[332, 204, 326, 1659, 1658, 293])).
% 1.82/1.45 tff(1669,plain,
% 1.82/1.45 (hskp11),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1668, 1667])).
% 1.82/1.45 tff(1670,plain,
% 1.82/1.45 (~c2_1(a2416)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[146, 1669])).
% 1.82/1.45 tff(1671,plain,
% 1.82/1.45 (~c1_1(a2416)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[152, 1669])).
% 1.82/1.45 tff(1672,plain,
% 1.82/1.45 (c3_1(a2432)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[891, 1657])).
% 1.82/1.45 tff(1673,plain,
% 1.82/1.45 (hskp15 | (~c2_1(a2432))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1363, 204, 1672, 1658, 511])).
% 1.82/1.45 tff(1674,plain,
% 1.82/1.45 (hskp15),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1673, 1667])).
% 1.82/1.45 tff(1675,plain,
% 1.82/1.45 (~c2_1(a2422)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[576, 1674])).
% 1.82/1.45 tff(1676,plain,
% 1.82/1.45 (c3_1(a2422)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[559, 1674])).
% 1.82/1.45 tff(1677,plain,
% 1.82/1.45 (c1_1(a2422)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[570, 1674])).
% 1.82/1.45 tff(1678,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1679,plain,
% 1.82/1.45 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416)) <=> (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1680,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1679])).
% 1.82/1.45 tff(1681,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1680, 1678])).
% 1.82/1.45 tff(1682,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1683,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.82/1.45 tff(1684,plain,
% 1.82/1.45 (c0_1(a2416)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1683, 204, 1453, 1677, 1676, 770, 769, 1675, 1671, 1670, 1438])).
% 1.82/1.45 tff(1685,plain,
% 1.82/1.45 (c3_1(a2416)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[163, 1669])).
% 1.82/1.45 tff(1686,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1687,plain,
% 1.82/1.45 ((hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1688,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1687])).
% 1.82/1.45 tff(1689,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1688, 1686])).
% 1.82/1.45 tff(1690,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1691,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 1.82/1.45 tff(1692,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1691, 204, 1118, 1685, 1029, 1028, 1671, 1117, 1093, 1684])).
% 1.82/1.45 tff(1693,plain,(hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | hskp12 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1694,plain,
% 1.82/1.45 (hskp29),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1693, 1607, 1028, 1047, 1029, 1552, 1608, 326, 958])).
% 1.82/1.45 tff(1695,plain,
% 1.82/1.45 (c3_1(a2409)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1148, 1694])).
% 1.82/1.45 tff(1696,plain,
% 1.82/1.45 (c2_1(a2409)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1137, 1694])).
% 1.85/1.46 tff(1697,assumption,(~hskp3), introduced(assumption)).
% 1.85/1.46 tff(1698,plain,
% 1.85/1.46 (^[U: $i] : refl((hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.85/1.46 inference(bind,[status(th)],[])).
% 1.85/1.46 tff(1699,plain,
% 1.85/1.46 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(quant_intro,[status(thm)],[1698])).
% 1.85/1.46 tff(1700,plain,
% 1.85/1.46 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1701,plain,
% 1.85/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.85/1.46 inference(bind,[status(th)],[])).
% 1.85/1.46 tff(1702,plain,
% 1.85/1.46 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(quant_intro,[status(thm)],[1701])).
% 1.85/1.46 tff(1703,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.85/1.46 tff(1704,plain,
% 1.85/1.46 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.85/1.46 tff(1705,plain,
% 1.85/1.46 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1704, 1700])).
% 1.85/1.46 tff(1706,plain,(
% 1.85/1.46 ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(skolemize,[status(sab)],[1705])).
% 1.85/1.46 tff(1707,plain,
% 1.85/1.46 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1706, 1699])).
% 1.85/1.46 tff(1708,plain,
% 1.85/1.46 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1709,plain,
% 1.85/1.46 ((hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1710,plain,
% 1.85/1.46 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0)))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1709])).
% 1.85/1.46 tff(1711,plain,
% 1.85/1.46 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1710, 1708])).
% 1.85/1.46 tff(1712,plain,
% 1.85/1.46 ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1713,plain,
% 1.85/1.46 ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 1.85/1.46 tff(1714,plain,
% 1.85/1.46 (hskp28 | hskp3),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1713, 204, 1029, 1028, 1027, 1707])).
% 1.85/1.46 tff(1715,plain,
% 1.85/1.46 (hskp28),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1714, 1697])).
% 1.85/1.46 tff(1716,plain,
% 1.85/1.46 (((~hskp28) | c2_1(a2406)) <=> ((~hskp28) | c2_1(a2406))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1717,axiom,((~hskp28) | c2_1(a2406)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.85/1.46 tff(1718,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.85/1.46 tff(1719,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1718, 1716])).
% 1.85/1.46 tff(1720,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1719, 1716])).
% 1.85/1.46 tff(1721,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1720, 1716])).
% 1.85/1.46 tff(1722,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1721, 1716])).
% 1.85/1.46 tff(1723,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1722, 1716])).
% 1.85/1.46 tff(1724,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1723, 1716])).
% 1.85/1.46 tff(1725,plain,
% 1.85/1.46 ((~hskp28) | c2_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1724, 1716])).
% 1.85/1.46 tff(1726,plain,
% 1.85/1.46 (c2_1(a2406)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1725, 1715])).
% 1.85/1.46 tff(1727,plain,
% 1.85/1.46 (((~hskp28) | c1_1(a2406)) <=> ((~hskp28) | c1_1(a2406))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1728,axiom,((~hskp28) | c1_1(a2406)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.85/1.46 tff(1729,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 1.85/1.46 tff(1730,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1729, 1727])).
% 1.85/1.46 tff(1731,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1730, 1727])).
% 1.85/1.46 tff(1732,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1731, 1727])).
% 1.85/1.46 tff(1733,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1732, 1727])).
% 1.85/1.46 tff(1734,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1733, 1727])).
% 1.85/1.46 tff(1735,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1734, 1727])).
% 1.85/1.46 tff(1736,plain,
% 1.85/1.46 ((~hskp28) | c1_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1735, 1727])).
% 1.85/1.46 tff(1737,plain,
% 1.85/1.46 (c1_1(a2406)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1736, 1715])).
% 1.85/1.46 tff(1738,assumption,(c2_1(a2406)), introduced(assumption)).
% 1.85/1.46 tff(1739,assumption,(c1_1(a2406)), introduced(assumption)).
% 1.85/1.46 tff(1740,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1741,plain,
% 1.85/1.46 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1742,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406)))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1741])).
% 1.85/1.46 tff(1743,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1742, 1740])).
% 1.85/1.46 tff(1744,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1745,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.85/1.46 tff(1746,plain,
% 1.85/1.46 (hskp11 | c0_1(a2406)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1745, 204, 326, 1739, 1738, 293])).
% 1.85/1.46 tff(1747,plain,
% 1.85/1.46 (c0_1(a2406)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1746, 325])).
% 1.85/1.46 tff(1748,plain,
% 1.85/1.46 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1749,plain,
% 1.85/1.46 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1750,plain,
% 1.85/1.46 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.85/1.46 tff(1751,plain,
% 1.85/1.46 (hskp24 | (~c0_1(a2406))),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1750, 204, 1697, 1739, 1738, 1286])).
% 1.85/1.46 tff(1752,plain,
% 1.85/1.46 (hskp24),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1751, 1747])).
% 1.85/1.46 tff(1753,plain,
% 1.85/1.46 (~c0_1(a2468)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1266, 1752])).
% 1.85/1.46 tff(1754,plain,
% 1.85/1.46 (c1_1(a2468)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1252, 1752])).
% 1.85/1.46 tff(1755,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1756,plain,
% 1.85/1.46 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468))) <=> (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1757,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1756])).
% 1.85/1.46 tff(1758,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1757, 1755])).
% 1.85/1.46 tff(1759,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1760,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.85/1.46 tff(1761,plain,
% 1.85/1.46 (~c2_1(a2468)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1760, 204, 326, 325, 1754, 1753, 293])).
% 1.85/1.46 tff(1762,plain,
% 1.85/1.46 (~c3_1(a2468)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1241, 1752])).
% 1.85/1.46 tff(1763,plain,
% 1.85/1.46 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1764,plain,
% 1.85/1.46 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468)) <=> (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1765,plain,
% 1.85/1.46 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468)))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1764])).
% 1.85/1.46 tff(1766,plain,
% 1.85/1.46 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1765, 1763])).
% 1.85/1.46 tff(1767,plain,
% 1.85/1.46 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1768,plain,
% 1.85/1.46 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.85/1.46 tff(1769,plain,
% 1.85/1.46 ($false),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1768, 204, 65, 22, 1753, 1762, 1039, 1761])).
% 1.85/1.46 tff(1770,plain,(hskp11 | hskp13 | hskp1 | hskp12 | hskp3 | (~c1_1(a2406)) | (~c2_1(a2406))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.46 tff(1771,plain,
% 1.85/1.46 (hskp11),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1770, 1697, 22, 326, 65, 1737, 1726])).
% 1.85/1.46 tff(1772,plain,
% 1.85/1.46 (~c1_1(a2416)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[152, 1771])).
% 1.85/1.46 tff(1773,plain,
% 1.85/1.46 (c3_1(a2416)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[163, 1771])).
% 1.85/1.46 tff(1774,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1775,plain,
% 1.85/1.46 ((hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416))) <=> (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1776,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416))))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1775])).
% 1.85/1.46 tff(1777,plain,
% 1.85/1.46 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.85/1.46 tff(1778,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1779,plain,
% 1.85/1.46 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.85/1.46 tff(1780,plain,
% 1.85/1.46 (c0_1(a2416)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1779, 204, 326, 1773, 1772, 1532])).
% 1.85/1.46 tff(1781,plain,
% 1.85/1.46 (hskp29),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1691, 204, 1773, 1029, 1028, 1772, 1117, 1047, 1780])).
% 1.85/1.46 tff(1782,plain,
% 1.85/1.46 (c2_1(a2409)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1137, 1781])).
% 1.85/1.46 tff(1783,plain,
% 1.85/1.46 (((~hskp29) | c0_1(a2409)) <=> ((~hskp29) | c0_1(a2409))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1784,axiom,((~hskp29) | c0_1(a2409)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.85/1.46 tff(1785,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 1.85/1.46 tff(1786,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1785, 1783])).
% 1.85/1.46 tff(1787,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1786, 1783])).
% 1.85/1.46 tff(1788,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1787, 1783])).
% 1.85/1.46 tff(1789,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1788, 1783])).
% 1.85/1.46 tff(1790,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1789, 1783])).
% 1.85/1.46 tff(1791,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1790, 1783])).
% 1.85/1.46 tff(1792,plain,
% 1.85/1.46 ((~hskp29) | c0_1(a2409)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1791, 1783])).
% 1.85/1.46 tff(1793,plain,
% 1.85/1.46 (c0_1(a2409)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1792, 1781])).
% 1.85/1.46 tff(1794,assumption,(~c1_1(a2409)), introduced(assumption)).
% 1.85/1.46 tff(1795,plain,
% 1.85/1.46 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.85/1.46 inference(bind,[status(th)],[])).
% 1.85/1.46 tff(1796,plain,
% 1.85/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(quant_intro,[status(thm)],[1795])).
% 1.85/1.46 tff(1797,plain,
% 1.85/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1798,plain,
% 1.85/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.85/1.46 inference(bind,[status(th)],[])).
% 1.85/1.46 tff(1799,plain,
% 1.85/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(quant_intro,[status(thm)],[1798])).
% 1.85/1.46 tff(1800,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.85/1.46 tff(1801,plain,
% 1.85/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.85/1.46 tff(1802,plain,
% 1.85/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1801, 1797])).
% 1.85/1.46 tff(1803,plain,(
% 1.85/1.46 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(skolemize,[status(sab)],[1802])).
% 1.85/1.46 tff(1804,plain,
% 1.85/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1803, 1796])).
% 1.85/1.46 tff(1805,assumption,(c0_1(a2409)), introduced(assumption)).
% 1.85/1.46 tff(1806,plain,
% 1.85/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1807,plain,
% 1.85/1.46 ((hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1808,plain,
% 1.85/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500))))),
% 1.85/1.46 inference(monotonicity,[status(thm)],[1807])).
% 1.85/1.46 tff(1809,plain,
% 1.85/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.85/1.46 inference(transitivity,[status(thm)],[1808, 1806])).
% 1.85/1.46 tff(1810,plain,
% 1.85/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.85/1.46 inference(quant_inst,[status(thm)],[])).
% 1.85/1.46 tff(1811,plain,
% 1.85/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 1.85/1.46 tff(1812,plain,
% 1.85/1.46 ($false),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1811, 204, 1697, 1805, 1209, 1028, 1027, 1804, 1093, 1794])).
% 1.85/1.46 tff(1813,plain,(c1_1(a2409) | hskp3 | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.46 tff(1814,plain,
% 1.85/1.46 (c1_1(a2409)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1813, 1697, 1793, 1782, 1028, 1027, 1047])).
% 1.85/1.46 tff(1815,plain,
% 1.85/1.46 (c3_1(a2409)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1148, 1781])).
% 1.85/1.46 tff(1816,assumption,(c1_1(a2409)), introduced(assumption)).
% 1.85/1.46 tff(1817,assumption,(hskp21), introduced(assumption)).
% 1.85/1.46 tff(1818,plain,
% 1.85/1.46 (((~hskp21) | (~c1_1(a2437))) <=> ((~hskp21) | (~c1_1(a2437)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1819,plain,
% 1.85/1.46 (((~c1_1(a2437)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a2437)))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1820,axiom,((~c1_1(a2437)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.85/1.46 tff(1821,plain,
% 1.85/1.46 ((~hskp21) | (~c1_1(a2437))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 1.85/1.46 tff(1822,plain,
% 1.85/1.46 ((~hskp21) | (~c1_1(a2437))),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1821, 1818])).
% 1.85/1.46 tff(1823,plain,
% 1.85/1.46 (~c1_1(a2437)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1822, 1817])).
% 1.85/1.46 tff(1824,plain,
% 1.85/1.46 (((~hskp21) | c2_1(a2437)) <=> ((~hskp21) | c2_1(a2437))),
% 1.85/1.46 inference(rewrite,[status(thm)],[])).
% 1.85/1.46 tff(1825,axiom,((~hskp21) | c2_1(a2437)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.85/1.46 tff(1826,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 1.85/1.46 tff(1827,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1826, 1824])).
% 1.85/1.46 tff(1828,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1827, 1824])).
% 1.85/1.46 tff(1829,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1828, 1824])).
% 1.85/1.46 tff(1830,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1829, 1824])).
% 1.85/1.46 tff(1831,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1830, 1824])).
% 1.85/1.46 tff(1832,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1831, 1824])).
% 1.85/1.46 tff(1833,plain,
% 1.85/1.46 ((~hskp21) | c2_1(a2437)),
% 1.85/1.46 inference(modus_ponens,[status(thm)],[1832, 1824])).
% 1.85/1.46 tff(1834,plain,
% 1.85/1.46 (c2_1(a2437)),
% 1.85/1.46 inference(unit_resolution,[status(thm)],[1833, 1817])).
% 1.85/1.46 tff(1835,plain,
% 1.85/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1836,plain,
% 1.85/1.47 (((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437))) <=> (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1837,plain,
% 1.85/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437))))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1836])).
% 1.85/1.47 tff(1838,plain,
% 1.85/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.85/1.47 tff(1839,plain,
% 1.85/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1840,plain,
% 1.85/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.85/1.47 tff(1841,plain,
% 1.85/1.47 (~c3_1(a2437)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1840, 204, 1805, 1208, 1834, 1453, 1823, 770, 769, 602, 1816])).
% 1.85/1.47 tff(1842,plain,
% 1.85/1.47 (((~hskp21) | c0_1(a2437)) <=> ((~hskp21) | c0_1(a2437))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1843,axiom,((~hskp21) | c0_1(a2437)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.85/1.47 tff(1844,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.85/1.47 tff(1845,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1844, 1842])).
% 1.85/1.47 tff(1846,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1845, 1842])).
% 1.85/1.47 tff(1847,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1846, 1842])).
% 1.85/1.47 tff(1848,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1847, 1842])).
% 1.85/1.47 tff(1849,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1848, 1842])).
% 1.85/1.47 tff(1850,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1849, 1842])).
% 1.85/1.47 tff(1851,plain,
% 1.85/1.47 ((~hskp21) | c0_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1850, 1842])).
% 1.85/1.47 tff(1852,plain,
% 1.85/1.47 (c0_1(a2437)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1851, 1817])).
% 1.85/1.47 tff(1853,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1854,plain,
% 1.85/1.47 ((hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437))) <=> (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1855,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437)))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1854])).
% 1.85/1.47 tff(1856,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1855, 1853])).
% 1.85/1.47 tff(1857,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1858,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 1.85/1.47 tff(1859,plain,
% 1.85/1.47 ($false),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1858, 204, 1697, 1852, 1834, 1823, 1804, 1841])).
% 1.85/1.47 tff(1860,plain,((~hskp21) | hskp3 | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2409))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.47 tff(1861,plain,
% 1.85/1.47 (~hskp21),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1860, 1697, 1793, 1815, 1607, 1552, 1608, 1814])).
% 1.85/1.47 tff(1862,plain,
% 1.85/1.47 (^[U: $i] : refl((hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1863,plain,
% 1.85/1.47 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1862])).
% 1.85/1.47 tff(1864,plain,
% 1.85/1.47 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1865,plain,
% 1.85/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1866,plain,
% 1.85/1.47 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1865])).
% 1.85/1.47 tff(1867,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.85/1.47 tff(1868,plain,
% 1.85/1.47 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.85/1.47 tff(1869,plain,
% 1.85/1.47 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1868, 1864])).
% 1.85/1.47 tff(1870,plain,(
% 1.85/1.47 ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(skolemize,[status(sab)],[1869])).
% 1.85/1.47 tff(1871,plain,
% 1.85/1.47 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1870, 1863])).
% 1.85/1.47 tff(1872,plain,
% 1.85/1.47 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1873,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1872])).
% 1.85/1.47 tff(1874,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1875,plain,
% 1.85/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1876,plain,
% 1.85/1.47 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1875])).
% 1.85/1.47 tff(1877,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.85/1.47 tff(1878,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.85/1.47 tff(1879,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1878, 1874])).
% 1.85/1.47 tff(1880,plain,(
% 1.85/1.47 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(skolemize,[status(sab)],[1879])).
% 1.85/1.47 tff(1881,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1880, 1873])).
% 1.85/1.47 tff(1882,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1883,plain,
% 1.85/1.47 ((hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1884,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1883])).
% 1.85/1.47 tff(1885,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1884, 1882])).
% 1.85/1.47 tff(1886,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1887,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.85/1.47 tff(1888,plain,
% 1.85/1.47 (hskp2 | (~c1_1(a2409))),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1887, 204, 1793, 1782, 1029, 1028, 1027, 1881])).
% 1.85/1.47 tff(1889,plain,
% 1.85/1.47 (hskp2),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1888, 1814])).
% 1.85/1.47 tff(1890,plain,
% 1.85/1.47 (~c3_1(a2404)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1397, 1889])).
% 1.85/1.47 tff(1891,plain,
% 1.85/1.47 (~c2_1(a2404)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1403, 1889])).
% 1.85/1.47 tff(1892,plain,
% 1.85/1.47 (c0_1(a2404)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1410, 204, 65, 22, 1891, 1890, 1039])).
% 1.85/1.47 tff(1893,plain,
% 1.85/1.47 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1894,plain,
% 1.85/1.47 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1895,plain,
% 1.85/1.47 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1894])).
% 1.85/1.47 tff(1896,plain,
% 1.85/1.47 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1895, 1893])).
% 1.85/1.47 tff(1897,plain,
% 1.85/1.47 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1898,plain,
% 1.85/1.47 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.85/1.47 tff(1899,plain,
% 1.85/1.47 (hskp24 | (~c1_1(a2409))),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1898, 204, 1697, 1793, 1782, 1286])).
% 1.85/1.47 tff(1900,plain,
% 1.85/1.47 (hskp24),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1899, 1814])).
% 1.85/1.47 tff(1901,plain,
% 1.85/1.47 (~c3_1(a2468)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1241, 1900])).
% 1.85/1.47 tff(1902,plain,
% 1.85/1.47 (~c0_1(a2468)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1266, 1900])).
% 1.85/1.47 tff(1903,plain,
% 1.85/1.47 (c2_1(a2468)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1768, 204, 65, 22, 1902, 1901, 1039])).
% 1.85/1.47 tff(1904,plain,
% 1.85/1.47 (((~hskp2) | (~c1_1(a2404))) <=> ((~hskp2) | (~c1_1(a2404)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1905,plain,
% 1.85/1.47 (((~c1_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a2404)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1906,axiom,((~c1_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.85/1.47 tff(1907,plain,
% 1.85/1.47 ((~hskp2) | (~c1_1(a2404))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 1.85/1.47 tff(1908,plain,
% 1.85/1.47 ((~hskp2) | (~c1_1(a2404))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1907, 1904])).
% 1.85/1.47 tff(1909,plain,
% 1.85/1.47 (~c1_1(a2404)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1908, 1889])).
% 1.85/1.47 tff(1910,plain,
% 1.85/1.47 (c1_1(a2468)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1252, 1900])).
% 1.85/1.47 tff(1911,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1912,plain,
% 1.85/1.47 ((hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468))) <=> (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1913,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1912])).
% 1.85/1.47 tff(1914,plain,
% 1.85/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1913, 1911])).
% 1.85/1.47 tff(1915,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1916,plain,
% 1.85/1.47 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.85/1.47 tff(1917,plain,
% 1.85/1.47 (hskp19 | (~c0_1(a2404)) | (~c2_1(a2468))),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1916, 204, 1910, 1902, 1909, 1890, 85])).
% 1.85/1.47 tff(1918,plain,
% 1.85/1.47 (hskp19),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1917, 1903, 1892])).
% 1.85/1.47 tff(1919,plain,
% 1.85/1.47 (~c0_1(a2432)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[312, 1918])).
% 1.85/1.47 tff(1920,plain,
% 1.85/1.47 (c3_1(a2432)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[891, 1918])).
% 1.85/1.47 tff(1921,plain,
% 1.85/1.47 (c1_1(a2432)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[323, 1918])).
% 1.85/1.47 tff(1922,plain,
% 1.85/1.47 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1923,plain,
% 1.85/1.47 ((hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432))) <=> (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1924,plain,
% 1.85/1.47 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.85/1.47 inference(monotonicity,[status(thm)],[1923])).
% 1.85/1.47 tff(1925,plain,
% 1.85/1.47 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.85/1.47 inference(transitivity,[status(thm)],[1924, 1922])).
% 1.85/1.47 tff(1926,plain,
% 1.85/1.47 ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.85/1.47 inference(quant_inst,[status(thm)],[])).
% 1.85/1.47 tff(1927,plain,
% 1.85/1.47 ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.85/1.47 tff(1928,plain,
% 1.85/1.47 (hskp21 | hskp17),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1927, 204, 1921, 1920, 1919, 1871])).
% 1.85/1.47 tff(1929,plain,
% 1.85/1.47 (hskp17),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1928, 1861])).
% 1.85/1.47 tff(1930,plain,
% 1.85/1.47 (((~hskp17) | (~c1_1(a2427))) <=> ((~hskp17) | (~c1_1(a2427)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1931,plain,
% 1.85/1.47 (((~c1_1(a2427)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2427)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1932,axiom,((~c1_1(a2427)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.85/1.47 tff(1933,plain,
% 1.85/1.47 ((~hskp17) | (~c1_1(a2427))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.85/1.47 tff(1934,plain,
% 1.85/1.47 ((~hskp17) | (~c1_1(a2427))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1933, 1930])).
% 1.85/1.47 tff(1935,plain,
% 1.85/1.47 (~c1_1(a2427)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1934, 1929])).
% 1.85/1.47 tff(1936,plain,
% 1.85/1.47 (((~hskp17) | c3_1(a2427)) <=> ((~hskp17) | c3_1(a2427))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1937,axiom,((~hskp17) | c3_1(a2427)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.85/1.47 tff(1938,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.85/1.47 tff(1939,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1938, 1936])).
% 1.85/1.47 tff(1940,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1939, 1936])).
% 1.85/1.47 tff(1941,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1940, 1936])).
% 1.85/1.47 tff(1942,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1941, 1936])).
% 1.85/1.47 tff(1943,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1942, 1936])).
% 1.85/1.47 tff(1944,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1943, 1936])).
% 1.85/1.47 tff(1945,plain,
% 1.85/1.47 ((~hskp17) | c3_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1944, 1936])).
% 1.85/1.47 tff(1946,plain,
% 1.85/1.47 (c3_1(a2427)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1945, 1929])).
% 1.85/1.47 tff(1947,plain,
% 1.85/1.47 (((~hskp17) | c2_1(a2427)) <=> ((~hskp17) | c2_1(a2427))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1948,axiom,((~hskp17) | c2_1(a2427)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.85/1.47 tff(1949,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.85/1.47 tff(1950,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1949, 1947])).
% 1.85/1.47 tff(1951,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1950, 1947])).
% 1.85/1.47 tff(1952,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1951, 1947])).
% 1.85/1.47 tff(1953,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1952, 1947])).
% 1.85/1.47 tff(1954,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1953, 1947])).
% 1.85/1.47 tff(1955,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1954, 1947])).
% 1.85/1.47 tff(1956,plain,
% 1.85/1.47 ((~hskp17) | c2_1(a2427)),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1955, 1947])).
% 1.85/1.47 tff(1957,plain,
% 1.85/1.47 (c2_1(a2427)),
% 1.85/1.47 inference(unit_resolution,[status(thm)],[1956, 1929])).
% 1.85/1.47 tff(1958,plain,
% 1.85/1.47 (^[U: $i] : refl((hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1959,plain,
% 1.85/1.47 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1958])).
% 1.85/1.47 tff(1960,plain,
% 1.85/1.47 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1961,plain,
% 1.85/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.85/1.48 inference(bind,[status(th)],[])).
% 1.85/1.48 tff(1962,plain,
% 1.85/1.48 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(quant_intro,[status(thm)],[1961])).
% 1.85/1.48 tff(1963,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.85/1.48 tff(1964,plain,
% 1.85/1.48 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.85/1.48 tff(1965,plain,
% 1.85/1.48 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1964, 1960])).
% 1.85/1.48 tff(1966,plain,(
% 1.85/1.48 ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(skolemize,[status(sab)],[1965])).
% 1.85/1.48 tff(1967,plain,
% 1.85/1.48 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1966, 1959])).
% 1.85/1.48 tff(1968,plain,
% 1.85/1.48 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1969,plain,
% 1.85/1.48 ((hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407))) <=> (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1970,plain,
% 1.85/1.48 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1969])).
% 1.85/1.48 tff(1971,plain,
% 1.85/1.48 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.85/1.48 tff(1972,plain,
% 1.85/1.48 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1973,plain,
% 1.85/1.48 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.85/1.48 tff(1974,plain,
% 1.85/1.48 (hskp30 | hskp21 | c2_1(a2407) | (~c0_1(a2407))),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1973, 204, 1521, 1967])).
% 1.85/1.48 tff(1975,plain,
% 1.85/1.48 (hskp30),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1974, 1861, 1550, 1520])).
% 1.85/1.48 tff(1976,plain,
% 1.85/1.48 (c3_1(a2450)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[633, 1975])).
% 1.85/1.48 tff(1977,plain,
% 1.85/1.48 (c1_1(a2450)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[644, 1975])).
% 1.85/1.48 tff(1978,plain,
% 1.85/1.48 (c0_1(a2450)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[655, 1975])).
% 1.85/1.48 tff(1979,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1980,plain,
% 1.85/1.48 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427))) <=> (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1981,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1980])).
% 1.85/1.48 tff(1982,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1981, 1979])).
% 1.85/1.48 tff(1983,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1984,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.85/1.48 tff(1985,plain,
% 1.85/1.48 ($false),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1984, 204, 1978, 1977, 1976, 1957, 1946, 1607, 1935, 1552, 1608, 602])).
% 1.85/1.48 tff(1986,plain,(hskp3 | c2_1(a2407) | c1_1(a2407) | hskp13 | hskp1 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.85/1.48 tff(1987,plain,
% 1.85/1.48 (hskp3),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1986, 326, 1521, 65, 22, 1029, 1028, 1027, 1520])).
% 1.85/1.48 tff(1988,plain,
% 1.85/1.48 (~c3_1(a2405)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1299, 1987])).
% 1.85/1.48 tff(1989,plain,
% 1.85/1.48 (c2_1(a2405)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1330, 1987])).
% 1.85/1.48 tff(1990,plain,
% 1.85/1.48 (c0_1(a2405)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1310, 1987])).
% 1.85/1.48 tff(1991,plain,
% 1.85/1.48 (hskp19),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1490, 326, 1990, 1989, 1988, 958, 1696, 1695, 22, 1607, 1552, 1608])).
% 1.85/1.48 tff(1992,plain,
% 1.85/1.48 (c1_1(a2432)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[323, 1991])).
% 1.85/1.48 tff(1993,plain,
% 1.85/1.48 (~c0_1(a2432)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[312, 1991])).
% 1.85/1.48 tff(1994,plain,
% 1.85/1.48 (c3_1(a2432)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[891, 1991])).
% 1.85/1.48 tff(1995,plain,
% 1.85/1.48 (c0_1(a2409)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1792, 1694])).
% 1.85/1.48 tff(1996,plain,
% 1.85/1.48 (~c2_1(a2408)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[400, 1605])).
% 1.85/1.48 tff(1997,plain,
% 1.85/1.48 (c3_1(a2408)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[429, 1605])).
% 1.85/1.48 tff(1998,assumption,(~c2_1(a2432)), introduced(assumption)).
% 1.85/1.48 tff(1999,plain,
% 1.85/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.85/1.48 inference(bind,[status(th)],[])).
% 1.85/1.48 tff(2000,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(quant_intro,[status(thm)],[1999])).
% 1.85/1.48 tff(2001,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2002,plain,
% 1.85/1.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.85/1.48 inference(bind,[status(th)],[])).
% 1.85/1.48 tff(2003,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(quant_intro,[status(thm)],[2002])).
% 1.85/1.48 tff(2004,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 1.85/1.48 tff(2005,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.85/1.48 tff(2006,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2005, 2001])).
% 1.85/1.48 tff(2007,plain,(
% 1.85/1.48 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(skolemize,[status(sab)],[2006])).
% 1.85/1.48 tff(2008,plain,
% 1.85/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2007, 2000])).
% 1.85/1.48 tff(2009,assumption,(c0_1(a2407)), introduced(assumption)).
% 1.85/1.48 tff(2010,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2011,plain,
% 1.85/1.48 (((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2012,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[2011])).
% 1.85/1.48 tff(2013,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.85/1.48 tff(2014,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(2015,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.85/1.48 tff(2016,plain,
% 1.85/1.48 (~c1_1(a2425)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[2015, 204, 1354, 1453, 2009, 1353, 770, 1521, 1520, 2008, 1998])).
% 1.85/1.48 tff(2017,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2018,plain,
% 1.85/1.48 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2019,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[2018])).
% 1.85/1.48 tff(2020,plain,
% 1.85/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[2019, 2017])).
% 1.85/1.48 tff(2021,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(2022,plain,
% 1.85/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 1.85/1.48 tff(2023,plain,
% 1.85/1.48 (~c1_1(a2408)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[2022, 204, 1354, 1453, 833, 1353, 770, 668, 2008, 2016, 1998])).
% 1.85/1.48 tff(2024,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2025,plain,
% 1.85/1.48 ((hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432))) <=> (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(2026,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432)))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[2025])).
% 1.85/1.48 tff(2027,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.85/1.48 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.85/1.48 tff(2028,plain,
% 1.85/1.48 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(2029,plain,
% 1.85/1.48 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432)),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.85/1.48 tff(2030,plain,
% 1.85/1.48 (~c1_1(a2409)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[2029, 204, 326, 1805, 1208, 1357, 1353, 832, 1998])).
% 1.85/1.48 tff(2031,plain,
% 1.85/1.48 ($false),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1222, 204, 22, 1209, 1208, 669, 668, 1082, 2030, 2023])).
% 1.85/1.48 tff(2032,plain,(c2_1(a2432) | hskp1 | (~c2_1(a2409)) | (~c3_1(a2409)) | (~c3_1(a2408)) | c2_1(a2408) | hskp12 | (~c0_1(a2409)) | (~c3_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c0_1(a2425)) | (~c0_1(a2408)) | c2_1(a2425) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.48 tff(2033,plain,
% 1.85/1.48 (c2_1(a2432)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[2032, 1696, 22, 1695, 1997, 1996, 326, 1995, 1994, 1993, 1992, 1607, 1606, 1552, 1550, 1521, 1520])).
% 1.85/1.48 tff(2034,plain,
% 1.85/1.48 (hskp15 | (~c2_1(a2432))),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1363, 204, 1994, 1993, 511])).
% 1.85/1.48 tff(2035,plain,
% 1.85/1.48 (hskp15),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[2034, 2033])).
% 1.85/1.48 tff(2036,plain,
% 1.85/1.48 (~c2_1(a2422)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[576, 2035])).
% 1.85/1.48 tff(2037,plain,
% 1.85/1.48 (c3_1(a2422)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[559, 2035])).
% 1.85/1.48 tff(2038,plain,
% 1.85/1.48 (c1_1(a2422)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[570, 2035])).
% 1.85/1.48 tff(2039,plain,
% 1.85/1.48 (hskp20),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1418, 204, 1992, 1994, 2038, 2037, 1993, 2036, 920])).
% 1.85/1.48 tff(2040,plain,
% 1.85/1.48 (~c2_1(a2435)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[868, 2039])).
% 1.85/1.48 tff(2041,plain,
% 1.85/1.48 (~c0_1(a2435)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[820, 2039])).
% 1.85/1.48 tff(2042,plain,
% 1.85/1.48 (c3_1(a2435)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[814, 2039])).
% 1.85/1.48 tff(2043,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2044,plain,
% 1.85/1.49 ((hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2045,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2044])).
% 1.85/1.49 tff(2046,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.85/1.49 tff(2047,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2048,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.85/1.49 tff(2049,plain,
% 1.85/1.49 (~c1_1(a2409)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2048, 204, 326, 1995, 1695, 2042, 2041, 2040, 832])).
% 1.85/1.49 tff(2050,plain,
% 1.85/1.49 (hskp11 | (~c2_1(a2432))),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[332, 204, 326, 1992, 1993, 293])).
% 1.85/1.49 tff(2051,plain,
% 1.85/1.49 (hskp11),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2050, 2033])).
% 1.85/1.49 tff(2052,plain,
% 1.85/1.49 (~c2_1(a2416)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[146, 2051])).
% 1.85/1.49 tff(2053,plain,
% 1.85/1.49 (~c1_1(a2416)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[152, 2051])).
% 1.85/1.49 tff(2054,plain,
% 1.85/1.49 (c3_1(a2416)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[163, 2051])).
% 1.85/1.49 tff(2055,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2056,plain,
% 1.85/1.49 ((hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2057,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2056])).
% 1.85/1.49 tff(2058,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2057, 2055])).
% 1.85/1.49 tff(2059,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2060,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 1.85/1.49 tff(2061,plain,
% 1.85/1.49 ($false),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2060, 204, 22, 1696, 1695, 2054, 2053, 2052, 1082, 2049])).
% 1.85/1.49 tff(2062,plain,(hskp12 | hskp1 | c1_1(a2407) | c2_1(a2407) | hskp25 | hskp13 | c1_1(a2500) | c0_1(a2500) | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.49 tff(2063,plain,
% 1.85/1.49 (hskp12),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2062, 1520, 1521, 22, 958, 65, 1028, 1029, 1027])).
% 1.85/1.49 tff(2064,plain,
% 1.85/1.49 (~c0_1(a2417)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[235, 2063])).
% 1.85/1.49 tff(2065,plain,
% 1.85/1.49 (~c1_1(a2417)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[229, 2063])).
% 1.85/1.49 tff(2066,plain,
% 1.85/1.49 (c3_1(a2417)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[246, 2063])).
% 1.85/1.49 tff(2067,plain,
% 1.85/1.49 (hskp19),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1348, 2066, 958, 2065, 1028, 2064, 1047, 1029, 22])).
% 1.85/1.49 tff(2068,plain,
% 1.85/1.49 (~c0_1(a2432)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[312, 2067])).
% 1.85/1.49 tff(2069,plain,
% 1.85/1.49 (c3_1(a2432)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[891, 2067])).
% 1.85/1.49 tff(2070,plain,
% 1.85/1.49 (c1_1(a2432)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[323, 2067])).
% 1.85/1.49 tff(2071,plain,
% 1.85/1.49 (hskp4),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1506, 204, 2070, 2069, 1029, 1028, 2068, 1057, 1047])).
% 1.85/1.49 tff(2072,plain,
% 1.85/1.49 (((~hskp4) | c0_1(a2407)) <=> ((~hskp4) | c0_1(a2407))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2073,axiom,((~hskp4) | c0_1(a2407)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.85/1.49 tff(2074,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.85/1.49 tff(2075,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2074, 2072])).
% 1.85/1.49 tff(2076,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2075, 2072])).
% 1.85/1.49 tff(2077,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2076, 2072])).
% 1.85/1.49 tff(2078,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2077, 2072])).
% 1.85/1.49 tff(2079,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2078, 2072])).
% 1.85/1.49 tff(2080,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2079, 2072])).
% 1.85/1.49 tff(2081,plain,
% 1.85/1.49 ((~hskp4) | c0_1(a2407)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2080, 2072])).
% 1.85/1.49 tff(2082,plain,
% 1.85/1.49 (c0_1(a2407)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2081, 2071])).
% 1.85/1.49 tff(2083,plain,
% 1.85/1.49 (hskp16),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1446, 2070, 22, 1028, 1027, 1047, 65, 2069, 2068])).
% 1.85/1.49 tff(2084,plain,
% 1.85/1.49 (~c3_1(a2425)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[444, 2083])).
% 1.85/1.49 tff(2085,plain,
% 1.85/1.49 (~c2_1(a2425)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[450, 2083])).
% 1.85/1.49 tff(2086,plain,
% 1.85/1.49 (c0_1(a2425)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[461, 2083])).
% 1.85/1.49 tff(2087,assumption,(~hskp5), introduced(assumption)).
% 1.85/1.49 tff(2088,plain,
% 1.85/1.49 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.85/1.49 inference(bind,[status(th)],[])).
% 1.85/1.49 tff(2089,plain,
% 1.85/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(quant_intro,[status(thm)],[2088])).
% 1.85/1.49 tff(2090,plain,
% 1.85/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2091,plain,
% 1.85/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.85/1.49 inference(bind,[status(th)],[])).
% 1.85/1.49 tff(2092,plain,
% 1.85/1.49 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(quant_intro,[status(thm)],[2091])).
% 1.85/1.49 tff(2093,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.85/1.49 tff(2094,plain,
% 1.85/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.85/1.49 tff(2095,plain,
% 1.85/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2094, 2090])).
% 1.85/1.49 tff(2096,plain,(
% 1.85/1.49 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(skolemize,[status(sab)],[2095])).
% 1.85/1.49 tff(2097,plain,
% 1.85/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2096, 2089])).
% 1.85/1.49 tff(2098,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2099,plain,
% 1.85/1.49 ((hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2100,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2099])).
% 1.85/1.49 tff(2101,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.85/1.49 tff(2102,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2103,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.85/1.49 tff(2104,plain,
% 1.85/1.49 (hskp5 | (~c2_1(a2417))),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2103, 204, 1085, 1029, 1028, 1094, 2097, 1093])).
% 1.85/1.49 tff(2105,plain,
% 1.85/1.49 (~c2_1(a2417)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2104, 2087])).
% 1.85/1.49 tff(2106,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2107,plain,
% 1.85/1.49 ((hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2108,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2107])).
% 1.85/1.49 tff(2109,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2108, 2106])).
% 1.85/1.49 tff(2110,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2111,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 1.85/1.49 tff(2112,plain,
% 1.85/1.49 (hskp5 | (~c2_1(a2432))),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2111, 204, 1357, 1029, 1028, 1353, 2097, 1093])).
% 1.85/1.49 tff(2113,plain,
% 1.85/1.49 (~c2_1(a2432)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2112, 2087])).
% 1.85/1.49 tff(2114,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2115,plain,
% 1.85/1.49 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2116,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2115])).
% 1.85/1.49 tff(2117,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.85/1.49 tff(2118,plain,
% 1.85/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2119,plain,
% 1.85/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.85/1.49 tff(2120,plain,
% 1.85/1.49 ($false),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2119, 204, 1354, 1357, 1453, 770, 769, 1094, 1083, 1438, 2113, 2105])).
% 1.85/1.49 tff(2121,plain,(hskp5 | (~c1_1(a2432)) | (~c3_1(a2432)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~c2_1(a2500)) | (~c3_1(a2417))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.49 tff(2122,plain,
% 1.85/1.49 (hskp5),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2121, 2070, 2069, 2086, 2085, 2084, 2064, 2065, 1029, 1028, 2068, 1047, 2066])).
% 1.85/1.49 tff(2123,plain,
% 1.85/1.49 (c0_1(a2408)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[411, 2122])).
% 1.85/1.49 tff(2124,plain,
% 1.85/1.49 (~c2_1(a2408)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[400, 2122])).
% 1.85/1.49 tff(2125,plain,
% 1.85/1.49 (c3_1(a2408)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[429, 2122])).
% 1.85/1.49 tff(2126,plain,
% 1.85/1.49 (~c1_1(a2408)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2022, 204, 1354, 1453, 833, 1353, 770, 668, 2008, 1998, 2016])).
% 1.85/1.49 tff(2127,plain,
% 1.85/1.49 (c1_1(a2408) | (~c2_1(a2417))),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1091, 204, 22, 1085, 669, 1083, 668, 1082])).
% 1.85/1.49 tff(2128,plain,
% 1.85/1.49 (~c2_1(a2417)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2127, 2126])).
% 1.85/1.49 tff(2129,plain,
% 1.85/1.49 (hskp20 | c2_1(a2432)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[927, 204, 1354, 1357, 1353, 920])).
% 1.85/1.49 tff(2130,plain,
% 1.85/1.49 (hskp20),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2129, 1998])).
% 1.85/1.49 tff(2131,plain,
% 1.85/1.49 (~c2_1(a2435)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[868, 2130])).
% 1.85/1.49 tff(2132,plain,
% 1.85/1.49 (~c0_1(a2435)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[820, 2130])).
% 1.85/1.49 tff(2133,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2134,plain,
% 1.85/1.49 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2135,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2134])).
% 1.85/1.49 tff(2136,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2135, 2133])).
% 1.85/1.49 tff(2137,plain,
% 1.85/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(2138,plain,
% 1.85/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.85/1.49 tff(2139,plain,
% 1.85/1.49 (c1_1(a2435)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[2138, 204, 1354, 1357, 1453, 2132, 2131, 770, 769, 1438, 1998])).
% 1.85/1.49 tff(2140,plain,
% 1.85/1.49 (c3_1(a2435)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[814, 2130])).
% 1.85/1.49 tff(2141,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2142,plain,
% 1.85/1.49 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(2143,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[2142])).
% 1.85/1.49 tff(2144,plain,
% 1.85/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.85/1.49 tff(2145,plain,
% 1.85/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2146,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.85/1.50 tff(2147,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2146, 204, 2140, 1453, 2131, 770, 769, 1094, 1083, 1438, 2139, 2128])).
% 1.85/1.50 tff(2148,plain,(c2_1(a2432) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | hskp1 | (~c3_1(a2417)) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2432)) | (~c3_1(a2432)) | (~c0_1(a2408)) | c0_1(a2432) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2149,plain,
% 1.85/1.50 (c2_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2148, 2086, 2085, 2084, 2064, 2065, 22, 2066, 2125, 2124, 2070, 2069, 2123, 2068, 2082, 1521, 1520])).
% 1.85/1.50 tff(2150,plain,
% 1.85/1.50 (hskp15 | (~c2_1(a2432))),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1363, 204, 2069, 2068, 511])).
% 1.85/1.50 tff(2151,plain,
% 1.85/1.50 (hskp15),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2150, 2149])).
% 1.85/1.50 tff(2152,plain,
% 1.85/1.50 (~c2_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[576, 2151])).
% 1.85/1.50 tff(2153,plain,
% 1.85/1.50 (c3_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[559, 2151])).
% 1.85/1.50 tff(2154,plain,
% 1.85/1.50 (c1_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[570, 2151])).
% 1.85/1.50 tff(2155,plain,
% 1.85/1.50 (hskp20),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1418, 204, 2070, 2069, 2154, 2153, 2068, 2152, 920])).
% 1.85/1.50 tff(2156,plain,
% 1.85/1.50 (~c2_1(a2435)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[868, 2155])).
% 1.85/1.50 tff(2157,plain,
% 1.85/1.50 (~c0_1(a2435)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[820, 2155])).
% 1.85/1.50 tff(2158,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2159,plain,
% 1.85/1.50 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2160,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435)))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2159])).
% 1.85/1.50 tff(2161,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.85/1.50 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.85/1.50 tff(2162,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2163,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435)),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.85/1.50 tff(2164,plain,
% 1.85/1.50 (c1_1(a2435)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2163, 204, 2086, 2154, 2153, 2157, 2156, 2085, 2084, 2152, 1438])).
% 1.85/1.50 tff(2165,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2166,plain,
% 1.85/1.50 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2167,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2166])).
% 1.85/1.50 tff(2168,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.85/1.50 tff(2169,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2170,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.85/1.50 tff(2171,plain,
% 1.85/1.50 ((~c1_1(a2408)) | (~c1_1(a2435))),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2170, 204, 2123, 2082, 2157, 2156, 2124, 1521, 1520, 2008])).
% 1.85/1.50 tff(2172,plain,
% 1.85/1.50 (~c1_1(a2408)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2171, 2164])).
% 1.85/1.50 tff(2173,plain,
% 1.85/1.50 (c1_1(a2408) | (~c2_1(a2417))),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1091, 204, 22, 2066, 2125, 2065, 2124, 1082])).
% 1.85/1.50 tff(2174,plain,
% 1.85/1.50 (~c2_1(a2417)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2173, 2172])).
% 1.85/1.50 tff(2175,plain,
% 1.85/1.50 (c3_1(a2435)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[814, 2155])).
% 1.85/1.50 tff(2176,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2146, 204, 2175, 2086, 2156, 2085, 2084, 2064, 2065, 1438, 2164, 2174])).
% 1.85/1.50 tff(2177,plain,(c2_1(a2407) | hskp1 | c1_1(a2407) | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp13 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2178,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2177, 1519, 1513, 22, 1029, 1028, 1027, 65, 958])).
% 1.85/1.50 tff(2179,plain,(hskp13 | hskp1 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2180,plain,
% 1.85/1.50 (hskp13),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2179, 22, 1029, 1028, 1027, 958])).
% 1.85/1.50 tff(2181,plain,
% 1.85/1.50 (~c0_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[339, 2180])).
% 1.85/1.50 tff(2182,plain,
% 1.85/1.50 (c2_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[350, 2180])).
% 1.85/1.50 tff(2183,plain,
% 1.85/1.50 (c1_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[361, 2180])).
% 1.85/1.50 tff(2184,assumption,(c1_1(a2418)), introduced(assumption)).
% 1.85/1.50 tff(2185,assumption,(~c0_1(a2418)), introduced(assumption)).
% 1.85/1.50 tff(2186,assumption,(c2_1(a2418)), introduced(assumption)).
% 1.85/1.50 tff(2187,assumption,(~c2_1(a2500)), introduced(assumption)).
% 1.85/1.50 tff(2188,assumption,(hskp15), introduced(assumption)).
% 1.85/1.50 tff(2189,plain,
% 1.85/1.50 (~c2_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[576, 2188])).
% 1.85/1.50 tff(2190,plain,
% 1.85/1.50 (c3_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[559, 2188])).
% 1.85/1.50 tff(2191,plain,
% 1.85/1.50 (c1_1(a2422)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[570, 2188])).
% 1.85/1.50 tff(2192,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2193,plain,
% 1.85/1.50 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2194,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2193])).
% 1.85/1.50 tff(2195,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.85/1.50 inference(transitivity,[status(thm)],[2194, 2192])).
% 1.85/1.50 tff(2196,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2197,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 1.85/1.50 tff(2198,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2197, 204, 2191, 2190, 2184, 2186, 1029, 1027, 2189, 2185, 63, 2187])).
% 1.85/1.50 tff(2199,plain,((~hskp15) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | c2_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2200,plain,
% 1.85/1.50 (~hskp15),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2199, 2187, 2186, 1029, 1027, 2185, 2184])).
% 1.85/1.50 tff(2201,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2202,plain,
% 1.85/1.50 ((hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418))) <=> (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2203,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2202])).
% 1.85/1.50 tff(2204,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[2203, 2201])).
% 1.85/1.50 tff(2205,plain,
% 1.85/1.50 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2206,plain,
% 1.85/1.50 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 1.85/1.50 tff(2207,plain,
% 1.85/1.50 (hskp15 | (~c3_1(a2418))),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2206, 204, 2186, 2185, 511])).
% 1.85/1.50 tff(2208,plain,
% 1.85/1.50 (~c3_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2207, 2200])).
% 1.85/1.50 tff(2209,plain,
% 1.85/1.50 (~hskp23),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[548, 2200])).
% 1.85/1.50 tff(2210,plain,
% 1.85/1.50 (^[U: $i] : refl((hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.85/1.50 inference(bind,[status(th)],[])).
% 1.85/1.50 tff(2211,plain,
% 1.85/1.50 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(quant_intro,[status(thm)],[2210])).
% 1.85/1.50 tff(2212,plain,
% 1.85/1.50 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2213,plain,
% 1.85/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp23))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp23) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.85/1.50 inference(bind,[status(th)],[])).
% 1.85/1.50 tff(2214,plain,
% 1.85/1.50 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(quant_intro,[status(thm)],[2213])).
% 1.85/1.50 tff(2215,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.85/1.50 tff(2216,plain,
% 1.85/1.50 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.85/1.50 tff(2217,plain,
% 1.85/1.50 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2216, 2212])).
% 1.85/1.50 tff(2218,plain,(
% 1.85/1.50 ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(skolemize,[status(sab)],[2217])).
% 1.85/1.50 tff(2219,plain,
% 1.85/1.50 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2218, 2211])).
% 1.85/1.50 tff(2220,plain,
% 1.85/1.50 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2221,plain,
% 1.85/1.50 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2222,plain,
% 1.85/1.50 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.85/1.50 tff(2223,plain,
% 1.85/1.50 (hskp23 | hskp6 | c3_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2222, 204, 2184, 2186, 2219])).
% 1.85/1.50 tff(2224,plain,
% 1.85/1.50 (hskp6),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2223, 2209, 2208])).
% 1.85/1.50 tff(2225,plain,
% 1.85/1.50 (hskp19),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[995, 2224, 958])).
% 1.85/1.50 tff(2226,plain,
% 1.85/1.50 (~c0_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[312, 2225])).
% 1.85/1.50 tff(2227,plain,
% 1.85/1.50 (c3_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[891, 2225])).
% 1.85/1.50 tff(2228,plain,
% 1.85/1.50 (~c2_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1363, 204, 2200, 2227, 2226, 511])).
% 1.85/1.50 tff(2229,plain,
% 1.85/1.50 (c1_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[323, 2225])).
% 1.85/1.50 tff(2230,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2231,plain,
% 1.85/1.50 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2232,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2231])).
% 1.85/1.50 tff(2233,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.85/1.50 inference(transitivity,[status(thm)],[2232, 2230])).
% 1.85/1.50 tff(2234,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(2235,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 1.85/1.50 tff(2236,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2235, 204, 2229, 2227, 2184, 2186, 1029, 1027, 2185, 63, 2187, 2228])).
% 1.85/1.50 tff(2237,plain,(c2_1(a2500) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2238,plain,
% 1.85/1.50 (c2_1(a2500)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2237, 2183, 2182, 1029, 1027, 2181, 958])).
% 1.85/1.50 tff(2239,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1348, 230, 247, 958, 43, 1028, 236, 1093, 1029, 22])).
% 1.85/1.50 tff(2240,plain,((~hskp12) | hskp25 | hskp19 | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2241,plain,
% 1.85/1.50 (~hskp12),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2240, 43, 958, 1028, 2238, 1029, 22])).
% 1.85/1.50 tff(2242,plain,
% 1.85/1.50 (hskp16),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1064, 2241, 2238])).
% 1.85/1.50 tff(2243,plain,
% 1.85/1.50 (~c3_1(a2425)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[444, 2242])).
% 1.85/1.50 tff(2244,plain,
% 1.85/1.50 (c0_1(a2425)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[461, 2242])).
% 1.85/1.50 tff(2245,plain,
% 1.85/1.50 (~c2_1(a2425)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[450, 2242])).
% 1.85/1.50 tff(2246,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1496, 2245, 2244, 1028, 958, 1029, 22, 2238, 43, 2243])).
% 1.85/1.50 tff(2247,plain,(hskp19 | c1_1(a2500) | hskp25 | c0_1(a2500) | hskp1 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(2248,plain,
% 1.85/1.50 (hskp19),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2247, 22, 958, 1029, 1028, 1027])).
% 1.85/1.50 tff(2249,plain,
% 1.85/1.50 (c3_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[891, 2248])).
% 1.85/1.50 tff(2250,plain,
% 1.85/1.50 (~c0_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[312, 2248])).
% 1.85/1.50 tff(2251,plain,
% 1.85/1.50 (c1_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[323, 2248])).
% 1.85/1.50 tff(2252,plain,
% 1.85/1.50 (hskp4),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1506, 204, 2251, 2249, 1029, 1028, 2250, 1057, 2238])).
% 1.85/1.50 tff(2253,plain,
% 1.85/1.50 (~c2_1(a2407)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1518, 2252])).
% 1.85/1.50 tff(2254,plain,
% 1.85/1.50 (~c1_1(a2407)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1512, 2252])).
% 1.85/1.50 tff(2255,plain,
% 1.85/1.50 (c0_1(a2407)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2081, 2252])).
% 1.85/1.50 tff(2256,plain,
% 1.85/1.50 (~c2_1(a2432)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1364, 540])).
% 1.85/1.50 tff(2257,plain,
% 1.85/1.50 (~c3_1(a2418)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2207, 540])).
% 1.85/1.50 tff(2258,plain,
% 1.85/1.50 (~hskp23),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[548, 540])).
% 1.85/1.50 tff(2259,plain,
% 1.85/1.50 (hskp6),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[2223, 2258, 2257])).
% 1.85/1.50 tff(2260,plain,
% 1.85/1.50 (~c2_1(a2410)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[964, 2259])).
% 1.85/1.50 tff(2261,plain,
% 1.85/1.50 (c1_1(a2410)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[975, 2259])).
% 1.85/1.50 tff(2262,plain,
% 1.85/1.50 (c0_1(a2410)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[986, 2259])).
% 1.85/1.50 tff(2263,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2264,plain,
% 1.85/1.50 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(2265,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[2264])).
% 1.85/1.50 tff(2266,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2265, 2263])).
% 1.85/1.51 tff(2267,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2268,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 1.85/1.51 tff(2269,plain,
% 1.85/1.51 ($false),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2268, 204, 1354, 2262, 2261, 2009, 1353, 2260, 1521, 1520, 2008, 2256])).
% 1.85/1.51 tff(2270,plain,(hskp15 | (~c1_1(a2432)) | (~c0_1(a2407)) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | (~c1_1(a2418)) | (~c2_1(a2418)) | (~c3_1(a2432)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.51 tff(2271,plain,
% 1.85/1.51 (hskp15),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2270, 2251, 2255, 2250, 2254, 2253, 2183, 2182, 2249, 2181])).
% 1.85/1.51 tff(2272,plain,
% 1.85/1.51 (c1_1(a2422)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[570, 2271])).
% 1.85/1.51 tff(2273,plain,
% 1.85/1.51 (~c2_1(a2422)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[576, 2271])).
% 1.85/1.51 tff(2274,plain,
% 1.85/1.51 (c3_1(a2422)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[559, 2271])).
% 1.85/1.51 tff(2275,plain,
% 1.85/1.51 (hskp20),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1418, 204, 2251, 2249, 2272, 2274, 2250, 2273, 920])).
% 1.85/1.51 tff(2276,plain,
% 1.85/1.51 (c3_1(a2435)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[814, 2275])).
% 1.85/1.51 tff(2277,plain,
% 1.85/1.51 (~c2_1(a2435)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[868, 2275])).
% 1.85/1.51 tff(2278,plain,
% 1.85/1.51 (~c0_1(a2435)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[820, 2275])).
% 1.85/1.51 tff(2279,assumption,(~c0_1(a2435)), introduced(assumption)).
% 1.85/1.51 tff(2280,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2281,plain,
% 1.85/1.51 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2282,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2281])).
% 1.85/1.51 tff(2283,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2282, 2280])).
% 1.85/1.51 tff(2284,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2285,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 1.85/1.51 tff(2286,plain,
% 1.85/1.51 (~c1_1(a2435)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2285, 204, 987, 976, 2009, 2279, 785, 965, 1521, 1520, 2008])).
% 1.85/1.51 tff(2287,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2288,plain,
% 1.85/1.51 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2289,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2288])).
% 1.85/1.51 tff(2290,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2289, 2287])).
% 1.85/1.51 tff(2291,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2292,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 1.85/1.51 tff(2293,plain,
% 1.85/1.51 (c3_1(a2410)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2292, 204, 615, 614, 976, 2279, 785, 613, 965, 11, 2286])).
% 1.85/1.51 tff(2294,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2295,plain,
% 1.85/1.51 ((hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2296,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2295])).
% 1.85/1.51 tff(2297,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.85/1.51 tff(2298,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2299,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.85/1.51 tff(2300,plain,
% 1.85/1.51 (hskp2),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2299, 204, 987, 976, 1028, 1027, 965, 1384, 1093])).
% 1.85/1.51 tff(2301,plain,
% 1.85/1.51 (~c3_1(a2404)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1397, 2300])).
% 1.85/1.51 tff(2302,plain,
% 1.85/1.51 (~c2_1(a2404)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1403, 2300])).
% 1.85/1.51 tff(2303,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2304,plain,
% 1.85/1.51 (((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404)) <=> (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2305,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2304])).
% 1.85/1.51 tff(2306,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.85/1.51 tff(2307,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2308,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.85/1.51 tff(2309,plain,
% 1.85/1.51 (c0_1(a2404)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2308, 204, 2184, 2186, 976, 2185, 965, 2302, 2301, 63, 2293])).
% 1.85/1.51 tff(2310,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2311,plain,
% 1.85/1.51 (((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2312,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435)))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2311])).
% 1.85/1.51 tff(2313,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2312, 2310])).
% 1.85/1.51 tff(2314,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2315,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 1.85/1.51 tff(2316,plain,
% 1.85/1.51 ($false),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2315, 204, 976, 2279, 785, 965, 2302, 2301, 1438, 2286, 2293, 2309])).
% 1.85/1.51 tff(2317,plain,((~hskp6) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2422) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.51 tff(2318,plain,
% 1.85/1.51 (~hskp6),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[2317, 2278, 2277, 2183, 2182, 2181, 1028, 1027, 2238, 2272, 2274, 2273, 2255, 2254, 2253])).
% 1.85/1.51 tff(2319,plain,
% 1.85/1.51 (^[U: $i] : refl((hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.85/1.51 inference(bind,[status(th)],[])).
% 1.85/1.51 tff(2320,plain,
% 1.85/1.51 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(quant_intro,[status(thm)],[2319])).
% 1.85/1.51 tff(2321,plain,
% 1.85/1.51 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2322,plain,
% 1.85/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.85/1.51 inference(bind,[status(th)],[])).
% 1.85/1.51 tff(2323,plain,
% 1.85/1.51 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(quant_intro,[status(thm)],[2322])).
% 1.85/1.51 tff(2324,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.85/1.51 tff(2325,plain,
% 1.85/1.51 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.85/1.51 tff(2326,plain,
% 1.85/1.51 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2325, 2321])).
% 1.85/1.51 tff(2327,plain,(
% 1.85/1.51 ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(skolemize,[status(sab)],[2326])).
% 1.85/1.51 tff(2328,plain,
% 1.85/1.51 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[2327, 2320])).
% 1.85/1.51 tff(2329,plain,
% 1.85/1.51 (hskp12),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1064, 64, 1093])).
% 1.85/1.51 tff(2330,plain,
% 1.85/1.51 (~c1_1(a2417)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[229, 2329])).
% 1.85/1.51 tff(2331,plain,
% 1.85/1.51 (~c0_1(a2417)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[235, 2329])).
% 1.85/1.51 tff(2332,plain,
% 1.85/1.51 (c3_1(a2417)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[246, 2329])).
% 1.85/1.51 tff(2333,assumption,(c3_1(a2435)), introduced(assumption)).
% 1.85/1.51 tff(2334,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2335,plain,
% 1.85/1.51 ((hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(2336,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[2335])).
% 1.85/1.51 tff(2337,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[2336, 2334])).
% 1.85/1.51 tff(2338,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(2339,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.85/1.52 tff(2340,plain,
% 1.85/1.52 (~c2_1(a2417)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2339, 204, 22, 1085, 164, 1083, 153, 147, 1082])).
% 1.85/1.52 tff(2341,plain,
% 1.85/1.52 (hskp10),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[210, 204, 64, 164, 153, 147, 140])).
% 1.85/1.52 tff(2342,plain,
% 1.85/1.52 (~c1_1(a2414)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[956, 2341])).
% 1.85/1.52 tff(2343,plain,
% 1.85/1.52 (c0_1(a2414)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1105, 2341])).
% 1.85/1.52 tff(2344,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2345,plain,
% 1.85/1.52 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2346,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2345])).
% 1.85/1.52 tff(2347,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.85/1.52 tff(2348,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2349,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.85/1.52 tff(2350,plain,
% 1.85/1.52 (~c2_1(a2414)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2349, 204, 2343, 1029, 1028, 1094, 1083, 2342, 21, 1093, 2340])).
% 1.85/1.52 tff(2351,plain,
% 1.85/1.52 (~c3_1(a2414)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[950, 2341])).
% 1.85/1.52 tff(2352,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2353,plain,
% 1.85/1.52 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2354,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2353])).
% 1.85/1.52 tff(2355,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.85/1.52 tff(2356,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2357,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.85/1.52 tff(2358,plain,
% 1.85/1.52 (~c1_1(a2435)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2357, 204, 2333, 2343, 785, 1094, 1083, 2351, 1438, 2340, 2350])).
% 1.85/1.52 tff(2359,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2360,plain,
% 1.85/1.52 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2361,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2360])).
% 1.85/1.52 tff(2362,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2361, 2359])).
% 1.85/1.52 tff(2363,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2364,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 1.85/1.52 tff(2365,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2364, 204, 615, 614, 2343, 2279, 785, 613, 2351, 1438, 2358, 2350])).
% 1.85/1.52 tff(2366,plain,((~hskp11) | (~c1_1(a2422)) | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | (~c3_1(a2435)) | c0_1(a2417) | c1_1(a2417) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp16 | hskp1 | (~c3_1(a2417))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(2367,plain,
% 1.85/1.52 (~hskp11),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2366, 2331, 614, 2279, 785, 613, 2333, 615, 2330, 1029, 1028, 1093, 64, 22, 2332])).
% 1.85/1.52 tff(2368,plain,
% 1.85/1.52 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2369,plain,
% 1.85/1.52 ((hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417))) <=> (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2370,plain,
% 1.85/1.52 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2369])).
% 1.85/1.52 tff(2371,plain,
% 1.85/1.52 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2370, 2368])).
% 1.85/1.52 tff(2372,plain,
% 1.85/1.52 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2373,plain,
% 1.85/1.52 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.85/1.52 tff(2374,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2373, 204, 2367, 1254, 2332, 2331, 2330, 2328])).
% 1.85/1.52 tff(2375,plain,(hskp16 | hskp6 | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | (~c3_1(a2435)) | (~c1_1(a2422)) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp1 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(2376,plain,
% 1.85/1.52 (hskp16),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2375, 2318, 2274, 2278, 2277, 2273, 2276, 2272, 1029, 1028, 2238, 22, 1027])).
% 1.85/1.52 tff(2377,plain,
% 1.85/1.52 (~c3_1(a2425)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[444, 2376])).
% 1.85/1.52 tff(2378,plain,
% 1.85/1.52 (~c2_1(a2425)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[450, 2376])).
% 1.85/1.52 tff(2379,plain,
% 1.85/1.52 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2380,plain,
% 1.85/1.52 ((hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425))) <=> (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2381,plain,
% 1.85/1.52 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2380])).
% 1.85/1.52 tff(2382,plain,
% 1.85/1.52 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2381, 2379])).
% 1.85/1.52 tff(2383,plain,
% 1.85/1.52 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2384,plain,
% 1.85/1.52 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.85/1.52 tff(2385,plain,
% 1.85/1.52 (~c1_1(a2425)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2384, 204, 2318, 22, 2378, 2377, 1026])).
% 1.85/1.52 tff(2386,plain,
% 1.85/1.52 (c0_1(a2425)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[461, 2376])).
% 1.85/1.52 tff(2387,plain,
% 1.85/1.52 (c1_1(a2435)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2163, 204, 2386, 2272, 2274, 2278, 2277, 2378, 2377, 2273, 1438])).
% 1.85/1.52 tff(2388,plain,
% 1.85/1.52 (hskp29),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1693, 326, 1028, 1093, 1029, 770, 769, 1453, 958])).
% 1.85/1.52 tff(2389,plain,
% 1.85/1.52 (c3_1(a2409)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1148, 2388])).
% 1.85/1.52 tff(2390,plain,
% 1.85/1.52 (c0_1(a2409)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1792, 2388])).
% 1.85/1.52 tff(2391,plain,
% 1.85/1.52 (~c1_1(a2409)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2048, 204, 326, 2390, 2389, 2333, 2279, 785, 832])).
% 1.85/1.52 tff(2392,plain,
% 1.85/1.52 (hskp12 | hskp11),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[368, 204, 2184, 2186, 2185, 293])).
% 1.85/1.52 tff(2393,plain,
% 1.85/1.52 (hskp11),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2392, 326])).
% 1.85/1.52 tff(2394,plain,
% 1.85/1.52 (~c2_1(a2416)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[146, 2393])).
% 1.85/1.52 tff(2395,plain,
% 1.85/1.52 (~c1_1(a2416)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[152, 2393])).
% 1.85/1.52 tff(2396,plain,
% 1.85/1.52 (c3_1(a2416)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[163, 2393])).
% 1.85/1.52 tff(2397,plain,
% 1.85/1.52 (c2_1(a2409)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1137, 2388])).
% 1.85/1.52 tff(2398,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2060, 204, 22, 2397, 2389, 2396, 2395, 2394, 1082, 2391])).
% 1.85/1.52 tff(2399,plain,(hskp12 | hskp1 | (~c3_1(a2435)) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418) | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(2400,plain,
% 1.85/1.52 (hskp12),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2399, 22, 2276, 2278, 2277, 2183, 2182, 2181, 1028, 2238, 1029, 2378, 2377, 2386, 958])).
% 1.85/1.52 tff(2401,plain,
% 1.85/1.52 (~c1_1(a2417)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[229, 2400])).
% 1.85/1.52 tff(2402,plain,
% 1.85/1.52 (~c0_1(a2417)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[235, 2400])).
% 1.85/1.52 tff(2403,plain,
% 1.85/1.52 (c3_1(a2417)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[246, 2400])).
% 1.85/1.52 tff(2404,plain,
% 1.85/1.52 (hskp5),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2121, 2403, 2249, 2386, 2378, 2377, 2251, 2402, 1029, 1028, 2250, 2238, 2401])).
% 1.85/1.52 tff(2405,plain,
% 1.85/1.52 (~c2_1(a2408)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[400, 2404])).
% 1.85/1.52 tff(2406,plain,
% 1.85/1.52 (c0_1(a2408)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[411, 2404])).
% 1.85/1.52 tff(2407,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2408,plain,
% 1.85/1.52 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2409,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[2408])).
% 1.85/1.52 tff(2410,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[2409, 2407])).
% 1.85/1.52 tff(2411,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(2412,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.85/1.52 tff(2413,plain,
% 1.85/1.52 (~c1_1(a2408)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2412, 204, 2386, 2406, 2278, 2277, 2378, 2405, 2008, 2387, 2385])).
% 1.85/1.52 tff(2414,plain,
% 1.85/1.52 (c3_1(a2408)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[429, 2404])).
% 1.85/1.52 tff(2415,plain,
% 1.85/1.52 (~c2_1(a2417)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1091, 204, 22, 2403, 2414, 2401, 2405, 1082, 2413])).
% 1.85/1.52 tff(2416,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2146, 204, 2276, 2386, 2277, 2378, 2377, 2402, 2401, 1438, 2387, 2415])).
% 1.85/1.52 tff(2417,plain,(hskp1 | c0_1(a2500) | c1_1(a2500) | hskp25 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(2418,plain,
% 1.85/1.52 (hskp1),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2417, 1010, 1004, 958, 1016])).
% 1.85/1.52 tff(2419,plain,
% 1.85/1.52 (((~hskp1) | (~c3_1(a2403))) <=> ((~hskp1) | (~c3_1(a2403)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2420,plain,
% 1.85/1.52 (((~c3_1(a2403)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2403)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2421,axiom,((~c3_1(a2403)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.85/1.52 tff(2422,plain,
% 1.85/1.52 ((~hskp1) | (~c3_1(a2403))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 1.85/1.52 tff(2423,plain,
% 1.85/1.52 ((~hskp1) | (~c3_1(a2403))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2422, 2419])).
% 1.85/1.52 tff(2424,plain,
% 1.85/1.52 (~c3_1(a2403)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2423, 2418])).
% 1.85/1.52 tff(2425,plain,
% 1.85/1.52 (((~hskp1) | (~c2_1(a2403))) <=> ((~hskp1) | (~c2_1(a2403)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2426,plain,
% 1.85/1.52 (((~c2_1(a2403)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2403)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2427,axiom,((~c2_1(a2403)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.85/1.52 tff(2428,plain,
% 1.85/1.52 ((~hskp1) | (~c2_1(a2403))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 1.85/1.52 tff(2429,plain,
% 1.85/1.52 ((~hskp1) | (~c2_1(a2403))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2428, 2425])).
% 1.85/1.52 tff(2430,plain,
% 1.85/1.52 (~c2_1(a2403)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2429, 2418])).
% 1.85/1.52 tff(2431,plain,
% 1.85/1.52 (((~hskp1) | c1_1(a2403)) <=> ((~hskp1) | c1_1(a2403))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2432,axiom,((~hskp1) | c1_1(a2403)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.85/1.52 tff(2433,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 1.85/1.52 tff(2434,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2433, 2431])).
% 1.85/1.52 tff(2435,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2434, 2431])).
% 1.85/1.52 tff(2436,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2435, 2431])).
% 1.85/1.52 tff(2437,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2436, 2431])).
% 1.85/1.52 tff(2438,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2437, 2431])).
% 1.85/1.52 tff(2439,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2438, 2431])).
% 1.85/1.52 tff(2440,plain,
% 1.85/1.52 ((~hskp1) | c1_1(a2403)),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[2439, 2431])).
% 1.85/1.52 tff(2441,plain,
% 1.85/1.52 (c1_1(a2403)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[2440, 2418])).
% 1.85/1.52 tff(2442,plain,
% 1.85/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 1.85/1.52 inference(bind,[status(th)],[])).
% 1.85/1.52 tff(2443,plain,
% 1.85/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.85/1.52 inference(quant_intro,[status(thm)],[2442])).
% 1.85/1.52 tff(2444,plain,
% 1.85/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(2445,plain,
% 1.85/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 1.92/1.52 inference(bind,[status(th)],[])).
% 1.92/1.52 tff(2446,plain,
% 1.92/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.92/1.52 inference(quant_intro,[status(thm)],[2445])).
% 1.92/1.52 tff(2447,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.92/1.52 tff(2448,plain,
% 1.92/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.92/1.52 tff(2449,plain,
% 1.92/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[2448, 2444])).
% 1.92/1.52 tff(2450,plain,(
% 1.92/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.92/1.52 inference(skolemize,[status(sab)],[2449])).
% 1.92/1.52 tff(2451,plain,
% 1.92/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[2450, 2443])).
% 1.92/1.52 tff(2452,assumption,(~c3_1(a2403)), introduced(assumption)).
% 1.92/1.52 tff(2453,assumption,(~c2_1(a2403)), introduced(assumption)).
% 1.92/1.52 tff(2454,plain,
% 1.92/1.52 (^[U: $i] : refl((hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.92/1.52 inference(bind,[status(th)],[])).
% 1.92/1.52 tff(2455,plain,
% 1.92/1.52 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.52 inference(quant_intro,[status(thm)],[2454])).
% 1.92/1.52 tff(2456,plain,
% 1.92/1.52 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(2457,plain,
% 1.92/1.52 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.92/1.53 inference(bind,[status(th)],[])).
% 1.92/1.53 tff(2458,plain,
% 1.92/1.53 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.53 inference(quant_intro,[status(thm)],[2457])).
% 1.92/1.53 tff(2459,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.92/1.53 tff(2460,plain,
% 1.92/1.53 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 1.92/1.53 tff(2461,plain,
% 1.92/1.53 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2460, 2456])).
% 1.92/1.53 tff(2462,plain,(
% 1.92/1.53 ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.53 inference(skolemize,[status(sab)],[2461])).
% 1.92/1.53 tff(2463,plain,
% 1.92/1.53 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2462, 2455])).
% 1.92/1.53 tff(2464,assumption,(c1_1(a2403)), introduced(assumption)).
% 1.92/1.53 tff(2465,plain,
% 1.92/1.53 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2466,plain,
% 1.92/1.53 ((hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2467,plain,
% 1.92/1.53 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2466])).
% 1.92/1.53 tff(2468,plain,
% 1.92/1.53 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2467, 2465])).
% 1.92/1.53 tff(2469,plain,
% 1.92/1.53 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2470,plain,
% 1.92/1.53 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 1.92/1.53 tff(2471,plain,
% 1.92/1.53 ($false),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2470, 204, 686, 1084, 2464, 1070, 2453, 2452, 685, 1072])).
% 1.92/1.53 tff(2472,plain,(hskp19 | hskp23 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.92/1.53 tff(2473,plain,
% 1.92/1.53 (hskp23),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2472, 43, 2464, 2453, 2452, 958])).
% 1.92/1.53 tff(2474,plain,
% 1.92/1.53 (~c0_1(a2455)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[516, 2473])).
% 1.92/1.53 tff(2475,plain,
% 1.92/1.53 (c3_1(a2455)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[527, 2473])).
% 1.92/1.53 tff(2476,plain,
% 1.92/1.53 (c2_1(a2455)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[538, 2473])).
% 1.92/1.53 tff(2477,plain,
% 1.92/1.53 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2478,plain,
% 1.92/1.53 ((hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455))) <=> (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2479,plain,
% 1.92/1.53 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2478])).
% 1.92/1.53 tff(2480,plain,
% 1.92/1.53 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.92/1.53 tff(2481,plain,
% 1.92/1.53 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2482,plain,
% 1.92/1.53 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.92/1.53 tff(2483,plain,
% 1.92/1.53 (hskp21),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2482, 204, 1235, 2476, 2475, 2474, 2463])).
% 1.92/1.53 tff(2484,plain,
% 1.92/1.53 (~c1_1(a2437)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1822, 2483])).
% 1.92/1.53 tff(2485,plain,
% 1.92/1.53 (c2_1(a2437)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1833, 2483])).
% 1.92/1.53 tff(2486,plain,
% 1.92/1.53 (c0_1(a2437)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1851, 2483])).
% 1.92/1.53 tff(2487,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2488,plain,
% 1.92/1.53 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2489,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2488])).
% 1.92/1.53 tff(2490,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2489, 2487])).
% 1.92/1.53 tff(2491,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2492,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 1.92/1.53 tff(2493,plain,
% 1.92/1.53 ($false),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2492, 204, 2191, 2190, 2464, 1029, 1028, 2189, 2453, 2452, 11, 2187])).
% 1.92/1.53 tff(2494,plain,((~hskp15) | (~c1_1(a2403)) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | c2_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.53 tff(2495,plain,
% 1.92/1.53 (~hskp15),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2494, 2187, 1029, 1028, 2453, 2452, 2464])).
% 1.92/1.53 tff(2496,plain,
% 1.92/1.53 (~hskp23),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[548, 2495])).
% 1.92/1.53 tff(2497,plain,
% 1.92/1.53 (hskp19),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2472, 2496, 2464, 2453, 2452, 958])).
% 1.92/1.53 tff(2498,plain,
% 1.92/1.53 (c3_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[891, 2497])).
% 1.92/1.53 tff(2499,plain,
% 1.92/1.53 (c1_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[323, 2497])).
% 1.92/1.53 tff(2500,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2501,plain,
% 1.92/1.53 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2502,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2501])).
% 1.92/1.53 tff(2503,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2502, 2500])).
% 1.92/1.53 tff(2504,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2505,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 1.92/1.53 tff(2506,plain,
% 1.92/1.53 (c2_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2505, 204, 2499, 2498, 2464, 1029, 1028, 2453, 2452, 11, 2187])).
% 1.92/1.53 tff(2507,plain,
% 1.92/1.53 (~c0_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[312, 2497])).
% 1.92/1.53 tff(2508,plain,
% 1.92/1.53 ($false),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1363, 204, 2495, 2498, 2507, 511, 2506])).
% 1.92/1.53 tff(2509,plain,(c2_1(a2500) | (~c1_1(a2403)) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.92/1.53 tff(2510,plain,
% 1.92/1.53 (c2_1(a2500)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2509, 2464, 1029, 1028, 2453, 2452, 958])).
% 1.92/1.53 tff(2511,plain,
% 1.92/1.53 (hskp29),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1126, 43, 1029, 1028, 2510, 958])).
% 1.92/1.53 tff(2512,plain,
% 1.92/1.53 (c3_1(a2409)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1148, 2511])).
% 1.92/1.53 tff(2513,plain,
% 1.92/1.53 (c2_1(a2409)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1137, 2511])).
% 1.92/1.53 tff(2514,plain,
% 1.92/1.53 (c0_1(a2409)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1792, 2511])).
% 1.92/1.53 tff(2515,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2516,plain,
% 1.92/1.53 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437))) <=> (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2517,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2516])).
% 1.92/1.53 tff(2518,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2517, 2515])).
% 1.92/1.53 tff(2519,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2520,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.92/1.53 tff(2521,plain,
% 1.92/1.53 ($false),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2520, 204, 2514, 2513, 2512, 2486, 2485, 2464, 2484, 2453, 2452, 2451])).
% 1.92/1.53 tff(2522,plain,(hskp19 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c0_1(a2500) | c1_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.92/1.53 tff(2523,plain,
% 1.92/1.53 (hskp19),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2522, 2441, 2430, 2424, 1010, 1004, 958])).
% 1.92/1.53 tff(2524,plain,
% 1.92/1.53 (~c0_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[312, 2523])).
% 1.92/1.53 tff(2525,plain,
% 1.92/1.53 (c3_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[891, 2523])).
% 1.92/1.53 tff(2526,plain,
% 1.92/1.53 (c1_1(a2432)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[323, 2523])).
% 1.92/1.53 tff(2527,plain,
% 1.92/1.53 (c2_1(a2500)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2509, 2441, 1010, 1004, 2430, 2424, 958])).
% 1.92/1.53 tff(2528,plain,
% 1.92/1.53 (hskp4),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1506, 204, 1354, 1357, 1029, 1028, 1353, 1057, 1093])).
% 1.92/1.53 tff(2529,plain,
% 1.92/1.53 (~c2_1(a2407)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1518, 2528])).
% 1.92/1.53 tff(2530,plain,
% 1.92/1.53 (~c1_1(a2407)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[1512, 2528])).
% 1.92/1.53 tff(2531,plain,
% 1.92/1.53 (c0_1(a2407)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2081, 2528])).
% 1.92/1.53 tff(2532,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2533,plain,
% 1.92/1.53 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2534,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2533])).
% 1.92/1.53 tff(2535,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.92/1.53 inference(transitivity,[status(thm)],[2534, 2532])).
% 1.92/1.53 tff(2536,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.92/1.53 inference(quant_inst,[status(thm)],[])).
% 1.92/1.53 tff(2537,plain,
% 1.92/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.92/1.53 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 1.92/1.53 tff(2538,plain,
% 1.92/1.53 (~c0_1(a2403)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2537, 204, 1354, 2531, 2464, 1353, 2530, 2529, 2453, 2008, 2256])).
% 1.92/1.53 tff(2539,plain,
% 1.92/1.53 (hskp20),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[2129, 2256])).
% 1.92/1.53 tff(2540,plain,
% 1.92/1.53 (~c2_1(a2435)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[868, 2539])).
% 1.92/1.53 tff(2541,plain,
% 1.92/1.53 (~c0_1(a2435)),
% 1.92/1.53 inference(unit_resolution,[status(thm)],[820, 2539])).
% 1.92/1.53 tff(2542,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2543,plain,
% 1.92/1.53 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.92/1.53 inference(rewrite,[status(thm)],[])).
% 1.92/1.53 tff(2544,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)))),
% 1.92/1.53 inference(monotonicity,[status(thm)],[2543])).
% 1.92/1.53 tff(2545,plain,
% 1.92/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2544, 2542])).
% 1.92/1.54 tff(2546,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2547,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.92/1.54 tff(2548,plain,
% 1.92/1.54 (c1_1(a2435)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2547, 204, 1354, 1357, 2464, 2541, 2540, 2453, 2452, 11, 2256])).
% 1.92/1.54 tff(2549,assumption,(c1_1(a2435)), introduced(assumption)).
% 1.92/1.54 tff(2550,plain,
% 1.92/1.54 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.92/1.54 inference(bind,[status(th)],[])).
% 1.92/1.54 tff(2551,plain,
% 1.92/1.54 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(quant_intro,[status(thm)],[2550])).
% 1.92/1.54 tff(2552,plain,
% 1.92/1.54 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2553,plain,
% 1.92/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.92/1.54 inference(bind,[status(th)],[])).
% 1.92/1.54 tff(2554,plain,
% 1.92/1.54 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(quant_intro,[status(thm)],[2553])).
% 1.92/1.54 tff(2555,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.92/1.54 tff(2556,plain,
% 1.92/1.54 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2555, 2554])).
% 1.92/1.54 tff(2557,plain,
% 1.92/1.54 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2556, 2552])).
% 1.92/1.54 tff(2558,plain,(
% 1.92/1.54 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(skolemize,[status(sab)],[2557])).
% 1.92/1.54 tff(2559,plain,
% 1.92/1.54 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2558, 2551])).
% 1.92/1.54 tff(2560,assumption,(hskp29), introduced(assumption)).
% 1.92/1.54 tff(2561,plain,
% 1.92/1.54 (c2_1(a2409)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1137, 2560])).
% 1.92/1.54 tff(2562,plain,
% 1.92/1.54 (c0_1(a2409)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1792, 2560])).
% 1.92/1.54 tff(2563,plain,
% 1.92/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2564,plain,
% 1.92/1.54 ((hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2565,plain,
% 1.92/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435))))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2564])).
% 1.92/1.54 tff(2566,plain,
% 1.92/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.92/1.54 tff(2567,plain,
% 1.92/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2568,plain,
% 1.92/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435))),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.92/1.54 tff(2569,plain,
% 1.92/1.54 (~c1_1(a2409)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2568, 204, 540, 2562, 2561, 2279, 785, 2559, 2549])).
% 1.92/1.54 tff(2570,plain,
% 1.92/1.54 (c3_1(a2409)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1148, 2560])).
% 1.92/1.54 tff(2571,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2572,plain,
% 1.92/1.54 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2573,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2572])).
% 1.92/1.54 tff(2574,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2573, 2571])).
% 1.92/1.54 tff(2575,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2576,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 1.92/1.54 tff(2577,plain,
% 1.92/1.54 ($false),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2576, 204, 2562, 2561, 2570, 2464, 2453, 2452, 2451, 2569])).
% 1.92/1.54 tff(2578,plain,((~hskp29) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))), inference(lemma,lemma(discharge,[]))).
% 1.92/1.54 tff(2579,plain,
% 1.92/1.54 (~hskp29),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2578, 540, 2453, 2452, 2464, 2541, 2540, 2548])).
% 1.92/1.54 tff(2580,plain,
% 1.92/1.54 (~hskp0),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1645, 2579, 1029, 1028, 1093])).
% 1.92/1.54 tff(2581,plain,
% 1.92/1.54 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2582,plain,
% 1.92/1.54 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403))) <=> (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2583,plain,
% 1.92/1.54 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2582])).
% 1.92/1.54 tff(2584,plain,
% 1.92/1.54 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2583, 2581])).
% 1.92/1.54 tff(2585,plain,
% 1.92/1.54 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2586,plain,
% 1.92/1.54 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.92/1.54 tff(2587,plain,
% 1.92/1.54 (hskp29 | hskp0 | c0_1(a2403)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2586, 204, 2464, 2453, 1656])).
% 1.92/1.54 tff(2588,plain,
% 1.92/1.54 ($false),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2587, 2580, 2579, 2538])).
% 1.92/1.54 tff(2589,plain,(hskp15 | (~c1_1(a2403)) | c2_1(a2403) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | c3_1(a2403) | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.54 tff(2590,plain,
% 1.92/1.54 (hskp15),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2589, 2441, 2430, 1010, 1004, 2527, 2424, 2526, 2525, 2524])).
% 1.92/1.54 tff(2591,plain,
% 1.92/1.54 (~c2_1(a2422)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[576, 2590])).
% 1.92/1.54 tff(2592,plain,
% 1.92/1.54 (c3_1(a2422)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[559, 2590])).
% 1.92/1.54 tff(2593,plain,
% 1.92/1.54 (c1_1(a2422)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[570, 2590])).
% 1.92/1.54 tff(2594,plain,
% 1.92/1.54 (hskp20),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1418, 204, 2526, 2525, 2593, 2592, 2524, 2591, 920])).
% 1.92/1.54 tff(2595,plain,
% 1.92/1.54 (~c2_1(a2435)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[868, 2594])).
% 1.92/1.54 tff(2596,plain,
% 1.92/1.54 (~c0_1(a2435)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[820, 2594])).
% 1.92/1.54 tff(2597,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2598,plain,
% 1.92/1.54 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2599,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2598])).
% 1.92/1.54 tff(2600,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2599, 2597])).
% 1.92/1.54 tff(2601,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2602,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 1.92/1.54 tff(2603,plain,
% 1.92/1.54 (c1_1(a2435)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2602, 204, 2593, 2592, 2441, 2596, 2595, 2591, 2430, 2424, 11])).
% 1.92/1.54 tff(2604,plain,
% 1.92/1.54 (hskp4),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1506, 204, 2526, 2525, 1010, 1004, 2524, 1057, 2527])).
% 1.92/1.54 tff(2605,plain,
% 1.92/1.54 (~c2_1(a2407)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1518, 2604])).
% 1.92/1.54 tff(2606,plain,
% 1.92/1.54 (~c1_1(a2407)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[1512, 2604])).
% 1.92/1.54 tff(2607,plain,
% 1.92/1.54 (c0_1(a2407)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2081, 2604])).
% 1.92/1.54 tff(2608,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2609,plain,
% 1.92/1.54 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2610,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435))))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2609])).
% 1.92/1.54 tff(2611,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.92/1.54 inference(transitivity,[status(thm)],[2610, 2608])).
% 1.92/1.54 tff(2612,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.92/1.54 inference(quant_inst,[status(thm)],[])).
% 1.92/1.54 tff(2613,plain,
% 1.92/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435))),
% 1.92/1.54 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 1.92/1.54 tff(2614,plain,
% 1.92/1.54 ((~c0_1(a2403)) | (~c1_1(a2435))),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2613, 204, 2607, 2441, 2596, 2595, 2606, 2605, 2430, 2008])).
% 1.92/1.54 tff(2615,plain,
% 1.92/1.54 (~c0_1(a2403)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[2614, 2603])).
% 1.92/1.54 tff(2616,plain,
% 1.92/1.54 (c3_1(a2435)),
% 1.92/1.54 inference(unit_resolution,[status(thm)],[814, 2594])).
% 1.92/1.54 tff(2617,assumption,(~c0_1(a2403)), introduced(assumption)).
% 1.92/1.54 tff(2618,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2619,plain,
% 1.92/1.54 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.92/1.54 inference(rewrite,[status(thm)],[])).
% 1.92/1.54 tff(2620,plain,
% 1.92/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.92/1.54 inference(monotonicity,[status(thm)],[2619])).
% 1.92/1.54 tff(2621,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2620, 2618])).
% 1.92/1.55 tff(2622,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2623,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.92/1.55 tff(2624,plain,
% 1.92/1.55 ($false),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2623, 204, 2333, 362, 351, 785, 340, 2453, 2452, 63, 2549, 2617])).
% 1.92/1.55 tff(2625,plain,((~hskp13) | (~c3_1(a2435)) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2435)) | c0_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.55 tff(2626,plain,
% 1.92/1.55 (~hskp13),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2625, 2616, 2595, 2430, 2424, 2603, 2615])).
% 1.92/1.55 tff(2627,plain,
% 1.92/1.55 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2628,plain,
% 1.92/1.55 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403))) <=> (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2629,plain,
% 1.92/1.55 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)))),
% 1.92/1.55 inference(monotonicity,[status(thm)],[2628])).
% 1.92/1.55 tff(2630,plain,
% 1.92/1.55 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2629, 2627])).
% 1.92/1.55 tff(2631,plain,
% 1.92/1.55 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2632,plain,
% 1.92/1.55 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.92/1.55 tff(2633,plain,
% 1.92/1.55 (hskp16 | hskp13 | c0_1(a2403)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2632, 204, 2441, 2430, 75])).
% 1.92/1.55 tff(2634,plain,
% 1.92/1.55 (hskp16),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2633, 2626, 2615])).
% 1.92/1.55 tff(2635,plain,
% 1.92/1.55 (c0_1(a2425)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[461, 2634])).
% 1.92/1.55 tff(2636,plain,
% 1.92/1.55 (~c2_1(a2425)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[450, 2634])).
% 1.92/1.55 tff(2637,plain,
% 1.92/1.55 (~c3_1(a2425)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[444, 2634])).
% 1.92/1.55 tff(2638,plain,
% 1.92/1.55 (hskp19),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2522, 2464, 2453, 2452, 1029, 1028, 958])).
% 1.92/1.55 tff(2639,plain,
% 1.92/1.55 (~c0_1(a2432)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[312, 2638])).
% 1.92/1.55 tff(2640,plain,
% 1.92/1.55 (c3_1(a2432)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[891, 2638])).
% 1.92/1.55 tff(2641,plain,
% 1.92/1.55 (c1_1(a2432)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[323, 2638])).
% 1.92/1.55 tff(2642,plain,
% 1.92/1.55 (hskp15),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2589, 2464, 2453, 1029, 1028, 2510, 2452, 2641, 2640, 2639])).
% 1.92/1.55 tff(2643,plain,
% 1.92/1.55 (~c2_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[576, 2642])).
% 1.92/1.55 tff(2644,plain,
% 1.92/1.55 (c3_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[559, 2642])).
% 1.92/1.55 tff(2645,plain,
% 1.92/1.55 (c1_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[570, 2642])).
% 1.92/1.55 tff(2646,plain,
% 1.92/1.55 (hskp20),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1418, 204, 2641, 2640, 2645, 2644, 2639, 2643, 920])).
% 1.92/1.55 tff(2647,plain,
% 1.92/1.55 (~c2_1(a2435)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[868, 2646])).
% 1.92/1.55 tff(2648,plain,
% 1.92/1.55 (~c0_1(a2435)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[820, 2646])).
% 1.92/1.55 tff(2649,plain,
% 1.92/1.55 (c1_1(a2435)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2602, 204, 2645, 2644, 2464, 2648, 2647, 2643, 2453, 2452, 11])).
% 1.92/1.55 tff(2650,plain,
% 1.92/1.55 (hskp4),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1506, 204, 2641, 2640, 1029, 1028, 2639, 1057, 2510])).
% 1.92/1.55 tff(2651,plain,
% 1.92/1.55 (~c2_1(a2407)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1518, 2650])).
% 1.92/1.55 tff(2652,plain,
% 1.92/1.55 (~c1_1(a2407)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1512, 2650])).
% 1.92/1.55 tff(2653,plain,
% 1.92/1.55 (c0_1(a2407)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2081, 2650])).
% 1.92/1.55 tff(2654,plain,
% 1.92/1.55 ((~c0_1(a2403)) | (~c1_1(a2435))),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2613, 204, 2653, 2464, 2648, 2647, 2652, 2651, 2453, 2008])).
% 1.92/1.55 tff(2655,plain,
% 1.92/1.55 (~c0_1(a2403)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2654, 2649])).
% 1.92/1.55 tff(2656,plain,
% 1.92/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.92/1.55 inference(bind,[status(th)],[])).
% 1.92/1.55 tff(2657,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(quant_intro,[status(thm)],[2656])).
% 1.92/1.55 tff(2658,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2659,plain,
% 1.92/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.92/1.55 inference(bind,[status(th)],[])).
% 1.92/1.55 tff(2660,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(quant_intro,[status(thm)],[2659])).
% 1.92/1.55 tff(2661,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.92/1.55 tff(2662,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 1.92/1.55 tff(2663,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2662, 2658])).
% 1.92/1.55 tff(2664,plain,(
% 1.92/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(skolemize,[status(sab)],[2663])).
% 1.92/1.55 tff(2665,plain,
% 1.92/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2664, 2657])).
% 1.92/1.55 tff(2666,plain,
% 1.92/1.55 (c3_1(a2435)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[814, 2646])).
% 1.92/1.55 tff(2667,plain,
% 1.92/1.55 (hskp29),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1693, 326, 1028, 2510, 1029, 770, 769, 1453, 958])).
% 1.92/1.55 tff(2668,plain,
% 1.92/1.55 (c3_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1148, 2667])).
% 1.92/1.55 tff(2669,plain,
% 1.92/1.55 (c0_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1792, 2667])).
% 1.92/1.55 tff(2670,plain,
% 1.92/1.55 (~c1_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2048, 204, 326, 2669, 2668, 2666, 2648, 2647, 832])).
% 1.92/1.55 tff(2671,plain,
% 1.92/1.55 (c2_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1137, 2667])).
% 1.92/1.55 tff(2672,plain,
% 1.92/1.55 ($false),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2576, 204, 2669, 2671, 2668, 2464, 2453, 2452, 2451, 2670])).
% 1.92/1.55 tff(2673,plain,(hskp12 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c1_1(a2500) | c0_1(a2500) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.92/1.55 tff(2674,plain,
% 1.92/1.55 (hskp12),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2673, 769, 2453, 2452, 1028, 1029, 770, 2464, 1453, 958])).
% 1.92/1.55 tff(2675,plain,
% 1.92/1.55 (~c1_1(a2417)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[229, 2674])).
% 1.92/1.55 tff(2676,plain,
% 1.92/1.55 (~c0_1(a2417)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[235, 2674])).
% 1.92/1.55 tff(2677,plain,
% 1.92/1.55 (c3_1(a2417)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[246, 2674])).
% 1.92/1.55 tff(2678,plain,
% 1.92/1.55 (hskp29 | hskp0 | c2_1(a2432)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1665, 204, 1354, 1353, 1656])).
% 1.92/1.55 tff(2679,plain,
% 1.92/1.55 (c2_1(a2432)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2678, 1646, 1118])).
% 1.92/1.55 tff(2680,plain,
% 1.92/1.55 (hskp15),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1364, 2679])).
% 1.92/1.55 tff(2681,plain,
% 1.92/1.55 (~c2_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[576, 2680])).
% 1.92/1.55 tff(2682,plain,
% 1.92/1.55 (c1_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[570, 2680])).
% 1.92/1.55 tff(2683,plain,
% 1.92/1.55 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2684,plain,
% 1.92/1.55 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422))) <=> (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2685,plain,
% 1.92/1.55 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)))),
% 1.92/1.55 inference(monotonicity,[status(thm)],[2684])).
% 1.92/1.55 tff(2686,plain,
% 1.92/1.55 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2685, 2683])).
% 1.92/1.55 tff(2687,plain,
% 1.92/1.55 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2688,plain,
% 1.92/1.55 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2687, 2686])).
% 1.92/1.55 tff(2689,plain,
% 1.92/1.55 (c0_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2688, 204, 1118, 1646, 2682, 2681, 1656])).
% 1.92/1.55 tff(2690,plain,
% 1.92/1.55 (c3_1(a2422)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[559, 2680])).
% 1.92/1.55 tff(2691,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2692,plain,
% 1.92/1.55 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2693,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.92/1.55 inference(monotonicity,[status(thm)],[2692])).
% 1.92/1.55 tff(2694,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2693, 2691])).
% 1.92/1.55 tff(2695,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2696,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.92/1.55 tff(2697,plain,
% 1.92/1.55 (~c2_1(a2417)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2696, 204, 1453, 2682, 2690, 1085, 770, 769, 1083, 602, 2689])).
% 1.92/1.55 tff(2698,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2699,plain,
% 1.92/1.55 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2700,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.92/1.55 inference(monotonicity,[status(thm)],[2699])).
% 1.92/1.55 tff(2701,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.92/1.55 tff(2702,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2703,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.92/1.55 tff(2704,plain,
% 1.92/1.55 ($false),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2703, 204, 1453, 2682, 2690, 770, 769, 2681, 1094, 1083, 1438, 2697])).
% 1.92/1.55 tff(2705,plain,(hskp29 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~c3_1(a2417)) | (~c3_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.92/1.55 tff(2706,plain,
% 1.92/1.55 (hskp29),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2705, 2676, 770, 1453, 769, 2677, 2675, 2640, 2639, 2641, 1029, 1028, 2510])).
% 1.92/1.55 tff(2707,plain,
% 1.92/1.55 (c3_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1148, 2706])).
% 1.92/1.55 tff(2708,plain,
% 1.92/1.55 (c2_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1137, 2706])).
% 1.92/1.55 tff(2709,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2710,plain,
% 1.92/1.55 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2711,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417))))),
% 1.92/1.55 inference(monotonicity,[status(thm)],[2710])).
% 1.92/1.55 tff(2712,plain,
% 1.92/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.92/1.55 inference(transitivity,[status(thm)],[2711, 2709])).
% 1.92/1.55 tff(2713,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2714,plain,
% 1.92/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 1.92/1.55 tff(2715,plain,
% 1.92/1.55 (~c1_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2714, 204, 2708, 2707, 2677, 2676, 2675, 2453, 2452, 2665, 2655])).
% 1.92/1.55 tff(2716,plain,
% 1.92/1.55 (c0_1(a2409)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[1792, 2706])).
% 1.92/1.55 tff(2717,plain,
% 1.92/1.55 ($false),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2576, 204, 2716, 2708, 2707, 2464, 2453, 2452, 2451, 2715])).
% 1.92/1.55 tff(2718,plain,(c3_1(a2425) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c2_1(a2425) | (~c0_1(a2425)) | c0_1(a2500) | c1_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.92/1.55 tff(2719,plain,
% 1.92/1.55 ($false),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2718, 2637, 2636, 2430, 2424, 2441, 2635, 1010, 1004, 958])).
% 1.92/1.55 tff(2720,plain,(hskp25 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.92/1.55 tff(2721,plain,
% 1.92/1.55 (hskp31),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2720, 958])).
% 1.92/1.55 tff(2722,plain,
% 1.92/1.55 (((~hskp31) | c0_1(a2498)) <=> ((~hskp31) | c0_1(a2498))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2723,axiom,((~hskp31) | c0_1(a2498)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.92/1.55 tff(2724,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.92/1.55 tff(2725,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2724, 2722])).
% 1.92/1.55 tff(2726,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2725, 2722])).
% 1.92/1.55 tff(2727,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2726, 2722])).
% 1.92/1.55 tff(2728,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2727, 2722])).
% 1.92/1.55 tff(2729,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2728, 2722])).
% 1.92/1.55 tff(2730,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2729, 2722])).
% 1.92/1.55 tff(2731,plain,
% 1.92/1.55 ((~hskp31) | c0_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2730, 2722])).
% 1.92/1.55 tff(2732,plain,
% 1.92/1.55 (c0_1(a2498)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2731, 2721])).
% 1.92/1.55 tff(2733,plain,
% 1.92/1.55 (((~hskp31) | c2_1(a2498)) <=> ((~hskp31) | c2_1(a2498))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2734,axiom,((~hskp31) | c2_1(a2498)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.92/1.55 tff(2735,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.92/1.55 tff(2736,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2735, 2733])).
% 1.92/1.55 tff(2737,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2736, 2733])).
% 1.92/1.55 tff(2738,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2737, 2733])).
% 1.92/1.55 tff(2739,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2738, 2733])).
% 1.92/1.55 tff(2740,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2739, 2733])).
% 1.92/1.55 tff(2741,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2740, 2733])).
% 1.92/1.55 tff(2742,plain,
% 1.92/1.55 ((~hskp31) | c2_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2741, 2733])).
% 1.92/1.55 tff(2743,plain,
% 1.92/1.55 (c2_1(a2498)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2742, 2721])).
% 1.92/1.55 tff(2744,plain,
% 1.92/1.55 (((~hskp31) | c1_1(a2498)) <=> ((~hskp31) | c1_1(a2498))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2745,axiom,((~hskp31) | c1_1(a2498)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.92/1.55 tff(2746,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 1.92/1.55 tff(2747,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2746, 2744])).
% 1.92/1.55 tff(2748,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2747, 2744])).
% 1.92/1.55 tff(2749,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2748, 2744])).
% 1.92/1.55 tff(2750,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2749, 2744])).
% 1.92/1.55 tff(2751,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2750, 2744])).
% 1.92/1.55 tff(2752,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2751, 2744])).
% 1.92/1.55 tff(2753,plain,
% 1.92/1.55 ((~hskp31) | c1_1(a2498)),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2752, 2744])).
% 1.92/1.55 tff(2754,plain,
% 1.92/1.55 (c1_1(a2498)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2753, 2721])).
% 1.92/1.55 tff(2755,assumption,(c2_1(a2498)), introduced(assumption)).
% 1.92/1.55 tff(2756,assumption,(c1_1(a2498)), introduced(assumption)).
% 1.92/1.55 tff(2757,plain,
% 1.92/1.55 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))),
% 1.92/1.55 inference(rewrite,[status(thm)],[])).
% 1.92/1.55 tff(2758,plain,
% 1.92/1.55 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))),
% 1.92/1.55 inference(quant_inst,[status(thm)],[])).
% 1.92/1.55 tff(2759,plain,
% 1.92/1.55 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498))),
% 1.92/1.55 inference(modus_ponens,[status(thm)],[2758, 2757])).
% 1.92/1.55 tff(2760,plain,
% 1.92/1.55 (hskp23 | c3_1(a2498)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2759, 204, 1254, 2756, 2755, 2219])).
% 1.92/1.55 tff(2761,plain,
% 1.92/1.55 (c3_1(a2498)),
% 1.92/1.55 inference(unit_resolution,[status(thm)],[2760, 686])).
% 1.92/1.55 tff(2762,assumption,(c0_1(a2498)), introduced(assumption)).
% 1.92/1.55 tff(2763,plain,
% 1.92/1.55 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2764,plain,
% 1.92/1.56 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2765,plain,
% 1.92/1.56 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2764])).
% 1.92/1.56 tff(2766,plain,
% 1.92/1.56 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2765, 2763])).
% 1.92/1.56 tff(2767,plain,
% 1.92/1.56 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2768,plain,
% 1.92/1.56 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2767, 2766])).
% 1.92/1.56 tff(2769,plain,
% 1.92/1.56 (hskp23 | hskp14 | (~c3_1(a2498))),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2768, 204, 2762, 2756, 42])).
% 1.92/1.56 tff(2770,plain,
% 1.92/1.56 (hskp14),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2769, 2761, 686])).
% 1.92/1.56 tff(2771,plain,
% 1.92/1.56 (c1_1(a2420)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[758, 2770])).
% 1.92/1.56 tff(2772,plain,
% 1.92/1.56 (c0_1(a2414)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[1105, 945])).
% 1.92/1.56 tff(2773,plain,
% 1.92/1.56 (c2_1(a2420)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[747, 2770])).
% 1.92/1.56 tff(2774,assumption,(~c0_1(a2420)), introduced(assumption)).
% 1.92/1.56 tff(2775,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2776,plain,
% 1.92/1.56 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420))) <=> (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2777,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2776])).
% 1.92/1.56 tff(2778,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2777, 2775])).
% 1.92/1.56 tff(2779,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2780,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 1.92/1.56 tff(2781,plain,
% 1.92/1.56 ($false),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2780, 204, 43, 787, 786, 1185, 1162, 1161, 85, 2774])).
% 1.92/1.56 tff(2782,plain,(c0_1(a2420) | hskp19 | (~c1_1(a2420)) | (~c2_1(a2420)) | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.56 tff(2783,plain,
% 1.92/1.56 (c0_1(a2420)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2782, 2773, 2772, 951, 2771, 957, 43])).
% 1.92/1.56 tff(2784,plain,
% 1.92/1.56 (~c3_1(a2420)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[736, 2770])).
% 1.92/1.56 tff(2785,plain,
% 1.92/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2786,plain,
% 1.92/1.56 (((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2787,plain,
% 1.92/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2786])).
% 1.92/1.56 tff(2788,plain,
% 1.92/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2787, 2785])).
% 1.92/1.56 tff(2789,plain,
% 1.92/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2790,plain,
% 1.92/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2789, 2788])).
% 1.92/1.56 tff(2791,plain,
% 1.92/1.56 ($false),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2790, 204, 2756, 2755, 2771, 2772, 2784, 957, 951, 1160, 2783, 2761])).
% 1.92/1.56 tff(2792,plain,(hskp23 | (~c1_1(a2498)) | (~c2_1(a2498)) | hskp19 | (~c0_1(a2498)) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.92/1.56 tff(2793,plain,
% 1.92/1.56 (hskp23),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2792, 2754, 2743, 43, 2732, 996])).
% 1.92/1.56 tff(2794,plain,
% 1.92/1.56 (hskp15),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[548, 2793])).
% 1.92/1.56 tff(2795,plain,
% 1.92/1.56 (~c2_1(a2422)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[576, 2794])).
% 1.92/1.56 tff(2796,plain,
% 1.92/1.56 (c1_1(a2422)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[570, 2794])).
% 1.92/1.56 tff(2797,plain,
% 1.92/1.56 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2798,plain,
% 1.92/1.56 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422))) <=> (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2799,plain,
% 1.92/1.56 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2798])).
% 1.92/1.56 tff(2800,plain,
% 1.92/1.56 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.92/1.56 tff(2801,plain,
% 1.92/1.56 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2802,plain,
% 1.92/1.56 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.92/1.56 tff(2803,plain,
% 1.92/1.56 (~c0_1(a2422)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2802, 204, 958, 43, 2796, 2795, 106])).
% 1.92/1.56 tff(2804,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2805,plain,
% 1.92/1.56 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418))) <=> (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2806,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2805])).
% 1.92/1.56 tff(2807,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2806, 2804])).
% 1.92/1.56 tff(2808,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2809,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.92/1.56 tff(2810,plain,
% 1.92/1.56 ($false),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2809, 204, 43, 2184, 2186, 1106, 2185, 1150, 1107, 85])).
% 1.92/1.56 tff(2811,plain,((~hskp10) | hskp19 | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.56 tff(2812,plain,
% 1.92/1.56 ($false),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2811, 351, 362, 43, 1095, 340])).
% 1.92/1.56 tff(2813,plain,((~hskp13) | hskp19 | (~hskp10)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.56 tff(2814,plain,
% 1.92/1.56 (~hskp13),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2813, 43, 945])).
% 1.92/1.56 tff(2815,plain,
% 1.92/1.56 ($false),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[1373, 204, 64, 2814, 2796, 2795, 75, 2803])).
% 1.92/1.56 tff(2816,plain,(hskp25 | hskp16 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.56 tff(2817,plain,
% 1.92/1.56 (hskp25),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2816, 43, 64])).
% 1.92/1.56 tff(2818,plain,
% 1.92/1.56 (~c0_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[123, 2817])).
% 1.92/1.56 tff(2819,plain,
% 1.92/1.56 (c2_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[117, 2817])).
% 1.92/1.56 tff(2820,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2821,plain,
% 1.92/1.56 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2822,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2821])).
% 1.92/1.56 tff(2823,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2822, 2820])).
% 1.92/1.56 tff(2824,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2825,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 1.92/1.56 tff(2826,plain,
% 1.92/1.56 (~c1_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2825, 204, 43, 2819, 2772, 2818, 957, 951, 85])).
% 1.92/1.56 tff(2827,plain,
% 1.92/1.56 (~c3_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[129, 2817])).
% 1.92/1.56 tff(2828,plain,
% 1.92/1.56 (hskp12 | c1_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[281, 204, 64, 2819, 2827, 273])).
% 1.92/1.56 tff(2829,plain,
% 1.92/1.56 (hskp12),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2828, 2826])).
% 1.92/1.56 tff(2830,plain,
% 1.92/1.56 (c3_1(a2417)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[246, 2829])).
% 1.92/1.56 tff(2831,plain,
% 1.92/1.56 (~c1_1(a2417)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[229, 2829])).
% 1.92/1.56 tff(2832,plain,
% 1.92/1.56 (~c0_1(a2417)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[235, 2829])).
% 1.92/1.56 tff(2833,plain,
% 1.92/1.56 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2834,plain,
% 1.92/1.56 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414))) <=> (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2835,plain,
% 1.92/1.56 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414)))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2834])).
% 1.92/1.56 tff(2836,plain,
% 1.92/1.56 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2835, 2833])).
% 1.92/1.56 tff(2837,plain,
% 1.92/1.56 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2838,plain,
% 1.92/1.56 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414)),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.92/1.56 tff(2839,plain,
% 1.92/1.56 (hskp19 | hskp5 | c2_1(a2414)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2838, 204, 2772, 951, 53])).
% 1.92/1.56 tff(2840,plain,
% 1.92/1.56 (c2_1(a2414)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2839, 2087, 43])).
% 1.92/1.56 tff(2841,plain,
% 1.92/1.56 (~c1_1(a2478)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2825, 204, 43, 275, 2772, 294, 957, 951, 85])).
% 1.92/1.56 tff(2842,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2843,plain,
% 1.92/1.56 ((hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2844,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2843])).
% 1.92/1.56 tff(2845,plain,
% 1.92/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(transitivity,[status(thm)],[2844, 2842])).
% 1.92/1.56 tff(2846,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(quant_inst,[status(thm)],[])).
% 1.92/1.56 tff(2847,plain,
% 1.92/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.92/1.56 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 1.92/1.56 tff(2848,plain,
% 1.92/1.56 (hskp5 | (~c2_1(a2417))),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2847, 204, 275, 1085, 294, 1094, 2097, 2841])).
% 1.92/1.56 tff(2849,plain,
% 1.92/1.56 (~c2_1(a2417)),
% 1.92/1.56 inference(unit_resolution,[status(thm)],[2848, 2087])).
% 1.92/1.56 tff(2850,plain,
% 1.92/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2851,plain,
% 1.92/1.56 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.92/1.56 inference(rewrite,[status(thm)],[])).
% 1.92/1.56 tff(2852,plain,
% 1.92/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.92/1.56 inference(monotonicity,[status(thm)],[2851])).
% 1.92/1.56 tff(2853,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2852, 2850])).
% 1.96/1.57 tff(2854,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2855,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 1.96/1.57 tff(2856,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2855, 204, 275, 2772, 294, 1094, 1083, 957, 21, 2849, 2841, 2840])).
% 1.96/1.57 tff(2857,plain,(hskp5 | (~c2_1(a2478)) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~c3_1(a2417)) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2858,plain,
% 1.96/1.57 (hskp5),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2857, 2819, 2818, 2832, 2831, 2830, 43])).
% 1.96/1.57 tff(2859,plain,
% 1.96/1.57 (c0_1(a2408)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[411, 2858])).
% 1.96/1.57 tff(2860,plain,
% 1.96/1.57 (c3_1(a2408)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[429, 2858])).
% 1.96/1.57 tff(2861,plain,
% 1.96/1.57 (~c2_1(a2408)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[400, 2858])).
% 1.96/1.57 tff(2862,assumption,(~hskp14), introduced(assumption)).
% 1.96/1.57 tff(2863,assumption,(c1_1(a2410)), introduced(assumption)).
% 1.96/1.57 tff(2864,assumption,(c0_1(a2410)), introduced(assumption)).
% 1.96/1.57 tff(2865,plain,
% 1.96/1.57 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2866,plain,
% 1.96/1.57 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2867,plain,
% 1.96/1.57 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2866])).
% 1.96/1.57 tff(2868,plain,
% 1.96/1.57 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2867, 2865])).
% 1.96/1.57 tff(2869,plain,
% 1.96/1.57 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2870,plain,
% 1.96/1.57 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 1.96/1.57 tff(2871,plain,
% 1.96/1.57 (hskp14 | (~c3_1(a2410))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2870, 204, 686, 2864, 2863, 42])).
% 1.96/1.57 tff(2872,plain,
% 1.96/1.57 (~c3_1(a2410)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2871, 2862])).
% 1.96/1.57 tff(2873,plain,
% 1.96/1.57 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[729, 204, 833, 669, 42])).
% 1.96/1.57 tff(2874,plain,
% 1.96/1.57 (~c1_1(a2408)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2873, 2862, 686])).
% 1.96/1.57 tff(2875,plain,
% 1.96/1.57 (hskp1 | c1_1(a2408) | (~c2_1(a2417))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1091, 204, 1085, 669, 1083, 668, 1082])).
% 1.96/1.57 tff(2876,plain,
% 1.96/1.57 (~c2_1(a2417)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2875, 2874, 22])).
% 1.96/1.57 tff(2877,assumption,(~c2_1(a2410)), introduced(assumption)).
% 1.96/1.57 tff(2878,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2879,plain,
% 1.96/1.57 ((hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417))) <=> (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2880,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2879])).
% 1.96/1.57 tff(2881,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2880, 2878])).
% 1.96/1.57 tff(2882,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2883,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 1.96/1.57 tff(2884,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2883, 204, 686, 1085, 2863, 1083, 2877, 685, 2876, 2872])).
% 1.96/1.57 tff(2885,plain,(hskp14 | hskp23 | (~c3_1(a2417)) | (~c1_1(a2410)) | c1_1(a2417) | c2_1(a2410) | hskp1 | (~c3_1(a2408)) | c2_1(a2408) | (~c0_1(a2410)) | (~c0_1(a2408))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2886,plain,
% 1.96/1.57 (hskp14),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2885, 976, 2830, 686, 2831, 965, 22, 2860, 2861, 987, 2859])).
% 1.96/1.57 tff(2887,plain,
% 1.96/1.57 (c1_1(a2420)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[758, 2886])).
% 1.96/1.57 tff(2888,plain,
% 1.96/1.57 (c2_1(a2420)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[747, 2886])).
% 1.96/1.57 tff(2889,plain,
% 1.96/1.57 (c0_1(a2420)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2782, 2888, 2772, 951, 2887, 957, 43])).
% 1.96/1.57 tff(2890,plain,
% 1.96/1.57 (~c3_1(a2420)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[736, 2886])).
% 1.96/1.57 tff(2891,plain,
% 1.96/1.57 (hskp20),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[802, 204, 2887, 2888, 2890, 722, 2889])).
% 1.96/1.57 tff(2892,plain,
% 1.96/1.57 (~c0_1(a2435)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[820, 2891])).
% 1.96/1.57 tff(2893,plain,
% 1.96/1.57 (c0_1(a2435) | (~c1_1(a2435))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1427, 204, 64, 2814, 785, 75])).
% 1.96/1.57 tff(2894,plain,
% 1.96/1.57 (~c1_1(a2435)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2893, 2892])).
% 1.96/1.57 tff(2895,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2896,plain,
% 1.96/1.57 ((hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2897,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2896])).
% 1.96/1.57 tff(2898,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2897, 2895])).
% 1.96/1.57 tff(2899,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2900,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 1.96/1.57 tff(2901,plain,
% 1.96/1.57 (hskp2),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2900, 204, 2819, 987, 976, 2827, 965, 1384, 2826])).
% 1.96/1.57 tff(2902,plain,
% 1.96/1.57 (~c3_1(a2404)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1397, 2901])).
% 1.96/1.57 tff(2903,plain,
% 1.96/1.57 (~c2_1(a2404)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1403, 2901])).
% 1.96/1.57 tff(2904,plain,
% 1.96/1.57 (c0_1(a2404)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1410, 204, 2814, 22, 2903, 2902, 1039])).
% 1.96/1.57 tff(2905,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2906,plain,
% 1.96/1.57 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2907,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2906])).
% 1.96/1.57 tff(2908,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2907, 2905])).
% 1.96/1.57 tff(2909,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2910,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.96/1.57 tff(2911,plain,
% 1.96/1.57 (c0_1(a2435) | (~c0_1(a2404)) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2910, 204, 2860, 785, 2861, 2903, 2902, 1438])).
% 1.96/1.57 tff(2912,plain,
% 1.96/1.57 (~c1_1(a2408)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2911, 2894, 2892, 2904])).
% 1.96/1.57 tff(2913,assumption,(~c1_1(a2478)), introduced(assumption)).
% 1.96/1.57 tff(2914,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2915,plain,
% 1.96/1.57 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2916,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2915])).
% 1.96/1.57 tff(2917,plain,
% 1.96/1.57 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2916, 2914])).
% 1.96/1.57 tff(2918,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2919,plain,
% 1.96/1.57 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 1.96/1.57 tff(2920,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2919, 204, 1118, 275, 833, 669, 294, 1117, 2913, 1])).
% 1.96/1.57 tff(2921,plain,(c1_1(a2408) | hskp29 | (~c2_1(a2478)) | (~c0_1(a2408)) | (~c3_1(a2408)) | c0_1(a2478) | c1_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2922,plain,
% 1.96/1.57 (hskp29),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2921, 2912, 2819, 2826, 2860, 2818, 2859])).
% 1.96/1.57 tff(2923,plain,
% 1.96/1.57 (c3_1(a2409)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1148, 2922])).
% 1.96/1.57 tff(2924,plain,
% 1.96/1.57 (c2_1(a2409)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1137, 2922])).
% 1.96/1.57 tff(2925,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2926,plain,
% 1.96/1.57 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2927,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2926])).
% 1.96/1.57 tff(2928,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2927, 2925])).
% 1.96/1.57 tff(2929,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2930,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.96/1.57 tff(2931,plain,
% 1.96/1.57 (~c1_1(a2409)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2930, 204, 2924, 2923, 2887, 2772, 2890, 957, 951, 1160, 2889])).
% 1.96/1.57 tff(2932,plain,
% 1.96/1.57 (c0_1(a2409)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1792, 2922])).
% 1.96/1.57 tff(2933,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2934,plain,
% 1.96/1.57 (((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2935,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2934])).
% 1.96/1.57 tff(2936,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.96/1.57 tff(2937,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2938,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.96/1.58 tff(2939,plain,
% 1.96/1.58 ($false),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2938, 204, 2932, 2924, 2819, 2818, 2892, 785, 21, 2931, 2894, 2826])).
% 1.96/1.58 tff(2940,plain,((~hskp6) | c2_1(a2435) | hskp16 | hskp19 | hskp23 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.96/1.58 tff(2941,plain,
% 1.96/1.58 (~hskp6),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2940, 22, 64, 43, 686, 785])).
% 1.96/1.58 tff(2942,plain,
% 1.96/1.58 (hskp11 | hskp6),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2373, 204, 2830, 2832, 2831, 2328])).
% 1.96/1.58 tff(2943,plain,
% 1.96/1.58 (hskp11),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2942, 2941])).
% 1.96/1.58 tff(2944,plain,
% 1.96/1.58 (~c2_1(a2416)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[146, 2943])).
% 1.96/1.58 tff(2945,plain,
% 1.96/1.58 (~c1_1(a2416)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[152, 2943])).
% 1.96/1.58 tff(2946,plain,
% 1.96/1.58 (c3_1(a2416)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[163, 2943])).
% 1.96/1.58 tff(2947,plain,
% 1.96/1.58 (~c2_1(a2417)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2339, 204, 22, 2830, 2946, 2831, 2945, 2944, 1082])).
% 1.96/1.58 tff(2948,plain,
% 1.96/1.58 (~c2_1(a2414)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2855, 204, 2819, 2772, 2818, 2832, 2831, 957, 21, 2947, 2826])).
% 1.96/1.58 tff(2949,plain,
% 1.96/1.58 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(2950,plain,
% 1.96/1.58 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[2949])).
% 1.96/1.58 tff(2951,plain,
% 1.96/1.58 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2952,plain,
% 1.96/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(2953,plain,
% 1.96/1.58 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[2952])).
% 1.96/1.58 tff(2954,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.96/1.58 tff(2955,plain,
% 1.96/1.58 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 1.96/1.58 tff(2956,plain,
% 1.96/1.58 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2955, 2951])).
% 1.96/1.58 tff(2957,plain,(
% 1.96/1.58 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(skolemize,[status(sab)],[2956])).
% 1.96/1.58 tff(2958,plain,
% 1.96/1.58 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2957, 2950])).
% 1.96/1.58 tff(2959,plain,
% 1.96/1.58 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2960,plain,
% 1.96/1.58 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2961,plain,
% 1.96/1.58 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[2960])).
% 1.96/1.58 tff(2962,plain,
% 1.96/1.58 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[2961, 2959])).
% 1.96/1.58 tff(2963,plain,
% 1.96/1.58 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(2964,plain,
% 1.96/1.58 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.96/1.58 tff(2965,plain,
% 1.96/1.58 (hskp7 | hskp6 | c1_1(a2478)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2964, 204, 2819, 2818, 2958])).
% 1.96/1.58 tff(2966,plain,
% 1.96/1.58 (hskp7),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2965, 2941, 2826])).
% 1.96/1.58 tff(2967,plain,
% 1.96/1.58 (((~hskp7) | (~c1_1(a2411))) <=> ((~hskp7) | (~c1_1(a2411)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2968,plain,
% 1.96/1.58 (((~c1_1(a2411)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a2411)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2969,axiom,((~c1_1(a2411)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.96/1.58 tff(2970,plain,
% 1.96/1.58 ((~hskp7) | (~c1_1(a2411))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.96/1.58 tff(2971,plain,
% 1.96/1.58 ((~hskp7) | (~c1_1(a2411))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2970, 2967])).
% 1.96/1.58 tff(2972,plain,
% 1.96/1.58 (~c1_1(a2411)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2971, 2966])).
% 1.96/1.58 tff(2973,plain,
% 1.96/1.58 (((~hskp7) | c2_1(a2411)) <=> ((~hskp7) | c2_1(a2411))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2974,axiom,((~hskp7) | c2_1(a2411)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.96/1.58 tff(2975,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 1.96/1.58 tff(2976,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2975, 2973])).
% 1.96/1.58 tff(2977,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2976, 2973])).
% 1.96/1.58 tff(2978,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2977, 2973])).
% 1.96/1.58 tff(2979,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2978, 2973])).
% 1.96/1.58 tff(2980,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2979, 2973])).
% 1.96/1.58 tff(2981,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2980, 2973])).
% 1.96/1.58 tff(2982,plain,
% 1.96/1.58 ((~hskp7) | c2_1(a2411)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2981, 2973])).
% 1.96/1.58 tff(2983,plain,
% 1.96/1.58 (c2_1(a2411)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2982, 2966])).
% 1.96/1.58 tff(2984,plain,
% 1.96/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2985,plain,
% 1.96/1.58 (((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2986,plain,
% 1.96/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[2985])).
% 1.96/1.58 tff(2987,plain,
% 1.96/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[2986, 2984])).
% 1.96/1.58 tff(2988,plain,
% 1.96/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(2989,plain,
% 1.96/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 1.96/1.58 tff(2990,plain,
% 1.96/1.58 (~c0_1(a2411)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2989, 204, 2819, 2983, 2818, 2832, 2831, 2972, 21, 2947, 2826])).
% 1.96/1.58 tff(2991,plain,
% 1.96/1.58 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(2992,plain,
% 1.96/1.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[2991])).
% 1.96/1.58 tff(2993,plain,
% 1.96/1.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2994,plain,
% 1.96/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(2995,plain,
% 1.96/1.58 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[2994])).
% 1.96/1.58 tff(2996,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.96/1.58 tff(2997,plain,
% 1.96/1.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 1.96/1.58 tff(2998,plain,
% 1.96/1.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2997, 2993])).
% 1.96/1.58 tff(2999,plain,(
% 1.96/1.58 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(skolemize,[status(sab)],[2998])).
% 1.96/1.58 tff(3000,plain,
% 1.96/1.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2999, 2992])).
% 1.96/1.58 tff(3001,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3002,plain,
% 1.96/1.58 ((hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3003,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[3002])).
% 1.96/1.58 tff(3004,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[3003, 3001])).
% 1.96/1.58 tff(3005,plain,
% 1.96/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(3006,plain,
% 1.96/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3005, 3004])).
% 1.96/1.58 tff(3007,plain,
% 1.96/1.58 (hskp0),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[3006, 204, 2830, 2832, 2831, 3000, 2947])).
% 1.96/1.58 tff(3008,plain,
% 1.96/1.58 (~c1_1(a2402)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1614, 3007])).
% 1.96/1.58 tff(3009,plain,
% 1.96/1.58 (c3_1(a2402)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1625, 3007])).
% 1.96/1.58 tff(3010,plain,
% 1.96/1.58 (c0_1(a2402)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1636, 3007])).
% 1.96/1.58 tff(3011,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3012,plain,
% 1.96/1.58 ((hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411))) <=> (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3013,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[3012])).
% 1.96/1.58 tff(3014,plain,
% 1.96/1.58 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[3013, 3011])).
% 1.96/1.58 tff(3015,plain,
% 1.96/1.58 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(3016,plain,
% 1.96/1.58 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 1.96/1.58 tff(3017,plain,
% 1.96/1.58 (hskp29),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[3016, 204, 2983, 3010, 3009, 2972, 3008, 1117, 2990])).
% 1.96/1.58 tff(3018,plain,
% 1.96/1.58 (c2_1(a2409)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1137, 3017])).
% 1.96/1.58 tff(3019,plain,
% 1.96/1.58 (c0_1(a2409)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1792, 3017])).
% 1.96/1.58 tff(3020,plain,
% 1.96/1.58 (c3_1(a2409)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1148, 3017])).
% 1.96/1.58 tff(3021,plain,
% 1.96/1.58 (~hskp24),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[1275, 1254, 43, 22, 1161, 1162, 1185])).
% 1.96/1.58 tff(3022,plain,
% 1.96/1.58 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(3023,plain,
% 1.96/1.58 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[3022])).
% 1.96/1.58 tff(3024,plain,
% 1.96/1.58 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3025,plain,
% 1.96/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(3026,plain,
% 1.96/1.58 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[3025])).
% 1.96/1.58 tff(3027,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.96/1.58 tff(3028,plain,
% 1.96/1.58 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 1.96/1.58 tff(3029,plain,
% 1.96/1.58 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3028, 3024])).
% 1.96/1.58 tff(3030,plain,(
% 1.96/1.58 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(skolemize,[status(sab)],[3029])).
% 1.96/1.58 tff(3031,plain,
% 1.96/1.58 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3030, 3023])).
% 1.96/1.58 tff(3032,plain,
% 1.96/1.58 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3033,plain,
% 1.96/1.58 ((hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409))) <=> (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3034,plain,
% 1.96/1.58 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[3033])).
% 1.96/1.58 tff(3035,plain,
% 1.96/1.58 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.96/1.58 inference(transitivity,[status(thm)],[3034, 3032])).
% 1.96/1.58 tff(3036,plain,
% 1.96/1.58 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(3037,plain,
% 1.96/1.58 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.96/1.58 tff(3038,plain,
% 1.96/1.58 (hskp24 | c1_1(a2409)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[3037, 204, 540, 1209, 1208, 3031])).
% 1.96/1.58 tff(3039,plain,
% 1.96/1.58 (c1_1(a2409)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[3038, 3021])).
% 1.96/1.58 tff(3040,plain,
% 1.96/1.58 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3041,plain,
% 1.96/1.58 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(3042,plain,
% 1.96/1.58 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[3041])).
% 1.96/1.58 tff(3043,plain,
% 1.96/1.58 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[3042, 3040])).
% 1.96/1.58 tff(3044,plain,
% 1.96/1.58 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3045,plain,
% 1.96/1.59 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 1.96/1.59 tff(3046,plain,
% 1.96/1.59 (hskp14 | (~c1_1(a2409))),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3045, 204, 2258, 1805, 1208, 42])).
% 1.96/1.59 tff(3047,plain,
% 1.96/1.59 (hskp14),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3046, 3039])).
% 1.96/1.59 tff(3048,plain,
% 1.96/1.59 (~c3_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[736, 3047])).
% 1.96/1.59 tff(3049,plain,
% 1.96/1.59 (c2_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[747, 3047])).
% 1.96/1.59 tff(3050,plain,
% 1.96/1.59 (c1_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[758, 3047])).
% 1.96/1.59 tff(3051,plain,
% 1.96/1.59 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3052,plain,
% 1.96/1.59 ((hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420))) <=> (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3053,plain,
% 1.96/1.59 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420))))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3052])).
% 1.96/1.59 tff(3054,plain,
% 1.96/1.59 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3053, 3051])).
% 1.96/1.59 tff(3055,plain,
% 1.96/1.59 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))),
% 1.96/1.59 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3056,plain,
% 1.96/1.59 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 1.96/1.59 tff(3057,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3056, 204, 2258, 1254, 3050, 3049, 3048, 2219])).
% 1.96/1.59 tff(3058,plain,(hskp6 | (~c0_1(a2409)) | (~c3_1(a2409)) | hskp15 | (~c2_1(a2409)) | hskp19 | hskp1 | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3059,plain,
% 1.96/1.59 (hskp15),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3058, 3020, 2941, 3019, 3018, 43, 22, 951, 957, 2772])).
% 1.96/1.59 tff(3060,plain,
% 1.96/1.59 (~c2_1(a2422)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[576, 3059])).
% 1.96/1.59 tff(3061,plain,
% 1.96/1.59 (c3_1(a2422)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[559, 3059])).
% 1.96/1.59 tff(3062,plain,
% 1.96/1.59 (c1_1(a2422)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[570, 3059])).
% 1.96/1.59 tff(3063,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3064,plain,
% 1.96/1.59 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3065,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3064])).
% 1.96/1.59 tff(3066,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3065, 3063])).
% 1.96/1.59 tff(3067,plain,
% 1.96/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.59 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3068,plain,
% 1.96/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 1.96/1.59 tff(3069,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3068, 204, 3062, 3061, 2772, 3060, 2832, 2831, 951, 1438, 2947, 2948])).
% 1.96/1.59 tff(3070,plain,(hskp1 | hskp19 | hskp16 | hskp23 | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3071,plain,
% 1.96/1.59 (hskp1),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3070, 785, 64, 686, 43])).
% 1.96/1.59 tff(3072,plain,
% 1.96/1.59 (c1_1(a2403)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2440, 3071])).
% 1.96/1.59 tff(3073,plain,
% 1.96/1.59 (~c2_1(a2403)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2429, 3071])).
% 1.96/1.59 tff(3074,plain,
% 1.96/1.59 (~c3_1(a2403)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2423, 3071])).
% 1.96/1.59 tff(3075,plain,
% 1.96/1.59 (hskp16 | hskp13 | (~c1_1(a2403)) | c0_1(a2403)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2632, 204, 2453, 75])).
% 1.96/1.59 tff(3076,plain,
% 1.96/1.59 (c0_1(a2403)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3075, 64, 2464, 65])).
% 1.96/1.59 tff(3077,plain,
% 1.96/1.59 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3078,plain,
% 1.96/1.59 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403))) <=> (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3079,plain,
% 1.96/1.59 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3078])).
% 1.96/1.59 tff(3080,plain,
% 1.96/1.59 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3079, 3077])).
% 1.96/1.59 tff(3081,plain,
% 1.96/1.59 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))),
% 1.96/1.59 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3082,plain,
% 1.96/1.59 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.96/1.59 tff(3083,plain,
% 1.96/1.59 (hskp5 | c3_1(a2403) | (~c0_1(a2403))),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3082, 204, 43, 2453, 53])).
% 1.96/1.59 tff(3084,plain,
% 1.96/1.59 (hskp5),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3083, 3076, 2452])).
% 1.96/1.59 tff(3085,plain,
% 1.96/1.59 (~c2_1(a2408)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[400, 3084])).
% 1.96/1.59 tff(3086,plain,
% 1.96/1.59 (c3_1(a2408)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[429, 3084])).
% 1.96/1.59 tff(3087,plain,
% 1.96/1.59 (c1_1(a2408)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2470, 204, 686, 3086, 2464, 3085, 2453, 2452, 685])).
% 1.96/1.59 tff(3088,plain,
% 1.96/1.59 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.96/1.59 inference(bind,[status(th)],[])).
% 1.96/1.59 tff(3089,plain,
% 1.96/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(quant_intro,[status(thm)],[3088])).
% 1.96/1.59 tff(3090,plain,
% 1.96/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3091,plain,
% 1.96/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.96/1.59 inference(bind,[status(th)],[])).
% 1.96/1.59 tff(3092,plain,
% 1.96/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(quant_intro,[status(thm)],[3091])).
% 1.96/1.59 tff(3093,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.96/1.59 tff(3094,plain,
% 1.96/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 1.96/1.59 tff(3095,plain,
% 1.96/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3094, 3090])).
% 1.96/1.59 tff(3096,plain,(
% 1.96/1.59 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(skolemize,[status(sab)],[3095])).
% 1.96/1.59 tff(3097,plain,
% 1.96/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3096, 3089])).
% 1.96/1.59 tff(3098,plain,
% 1.96/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3099,plain,
% 1.96/1.59 ((hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3100,plain,
% 1.96/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3099])).
% 1.96/1.59 tff(3101,plain,
% 1.96/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3100, 3098])).
% 1.96/1.59 tff(3102,plain,
% 1.96/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.59 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3103,plain,
% 1.96/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3102, 3101])).
% 1.96/1.59 tff(3104,plain,
% 1.96/1.59 (hskp14 | (~c0_1(a2403))),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3103, 204, 275, 2464, 274, 2452, 3097, 2913])).
% 1.96/1.59 tff(3105,plain,
% 1.96/1.59 (hskp14),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3104, 3076])).
% 1.96/1.59 tff(3106,plain,
% 1.96/1.59 (c2_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[747, 3105])).
% 1.96/1.59 tff(3107,plain,
% 1.96/1.59 (c1_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[758, 3105])).
% 1.96/1.59 tff(3108,plain,
% 1.96/1.59 (c0_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2782, 3107, 1161, 3106, 1185, 1162, 43])).
% 1.96/1.59 tff(3109,plain,
% 1.96/1.59 (~c3_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[736, 3105])).
% 1.96/1.59 tff(3110,plain,
% 1.96/1.59 (hskp20),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[802, 204, 3107, 3106, 3109, 722, 3108])).
% 1.96/1.59 tff(3111,plain,
% 1.96/1.59 (~c0_1(a2435)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[820, 3110])).
% 1.96/1.59 tff(3112,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3113,plain,
% 1.96/1.59 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3114,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3113])).
% 1.96/1.59 tff(3115,plain,
% 1.96/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3114, 3112])).
% 1.96/1.59 tff(3116,plain,
% 1.96/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.96/1.59 inference(quant_inst,[status(thm)],[])).
% 1.96/1.59 tff(3117,plain,
% 1.96/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.96/1.59 tff(3118,plain,
% 1.96/1.59 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3117, 204, 669, 2464, 785, 668, 2453, 2452, 11])).
% 1.96/1.59 tff(3119,plain,
% 1.96/1.59 (c1_1(a2435)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3118, 2279, 822])).
% 1.96/1.59 tff(3120,plain,
% 1.96/1.59 (hskp16 | hskp13 | c0_1(a2435) | (~c1_1(a2435))),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[1427, 204, 785, 75])).
% 1.96/1.59 tff(3121,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3120, 3119, 2279, 64, 65])).
% 1.96/1.59 tff(3122,plain,(c0_1(a2435) | hskp16 | hskp13 | c2_1(a2435) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2403)) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3123,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3122, 3111, 3087, 65, 785, 64, 3086, 2464, 3085, 2453, 2452])).
% 1.96/1.59 tff(3124,plain,(hskp16 | hskp13 | c2_1(a2435) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp23 | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2414) | hskp19 | (~c2_1(a2478)) | c3_1(a2478) | c1_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3125,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3124, 3074, 3073, 64, 2826, 686, 785, 3072, 951, 2772, 957, 43, 2819, 2827, 2814])).
% 1.96/1.59 tff(3126,plain,(c2_1(a2435) | hskp16 | hskp23 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3127,plain,
% 1.96/1.59 (c2_1(a2435)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3126, 686, 64, 43])).
% 1.96/1.59 tff(3128,plain,
% 1.96/1.59 (~hskp20),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[868, 3127])).
% 1.96/1.59 tff(3129,assumption,(hskp14), introduced(assumption)).
% 1.96/1.59 tff(3130,plain,
% 1.96/1.59 (c1_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[758, 3129])).
% 1.96/1.59 tff(3131,plain,
% 1.96/1.59 (c2_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[747, 3129])).
% 1.96/1.59 tff(3132,plain,
% 1.96/1.59 (c0_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2782, 3131, 2772, 951, 3130, 957, 43])).
% 1.96/1.59 tff(3133,plain,
% 1.96/1.59 (~c3_1(a2420)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[736, 3129])).
% 1.96/1.59 tff(3134,assumption,(~hskp20), introduced(assumption)).
% 1.96/1.59 tff(3135,plain,
% 1.96/1.59 ($false),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[802, 204, 3134, 3130, 3131, 3133, 722, 3132])).
% 1.96/1.59 tff(3136,plain,((~hskp14) | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.96/1.59 tff(3137,plain,
% 1.96/1.59 (~hskp14),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3136, 3128, 43])).
% 1.96/1.59 tff(3138,plain,
% 1.96/1.59 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[729, 204, 2859, 2860, 42])).
% 1.96/1.59 tff(3139,plain,
% 1.96/1.59 (~c1_1(a2408)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3138, 3137, 686])).
% 1.96/1.59 tff(3140,plain,
% 1.96/1.59 (hskp29),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[2921, 3139, 2819, 2826, 2860, 2818, 2859])).
% 1.96/1.59 tff(3141,plain,
% 1.96/1.59 (c3_1(a2409)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[1148, 3140])).
% 1.96/1.59 tff(3142,plain,
% 1.96/1.59 (c0_1(a2409)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[1792, 3140])).
% 1.96/1.59 tff(3143,plain,
% 1.96/1.59 (~c1_1(a2409)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[3045, 204, 686, 3137, 3142, 3141, 42])).
% 1.96/1.59 tff(3144,plain,
% 1.96/1.59 (^[U: $i] : refl((hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.96/1.59 inference(bind,[status(th)],[])).
% 1.96/1.59 tff(3145,plain,
% 1.96/1.59 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(quant_intro,[status(thm)],[3144])).
% 1.96/1.59 tff(3146,plain,
% 1.96/1.59 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3147,plain,
% 1.96/1.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> ((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.96/1.59 inference(bind,[status(th)],[])).
% 1.96/1.59 tff(3148,plain,
% 1.96/1.59 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(quant_intro,[status(thm)],[3147])).
% 1.96/1.59 tff(3149,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.96/1.59 tff(3150,plain,
% 1.96/1.59 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.96/1.59 tff(3151,plain,
% 1.96/1.59 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3150, 3146])).
% 1.96/1.59 tff(3152,plain,(
% 1.96/1.59 ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(skolemize,[status(sab)],[3151])).
% 1.96/1.59 tff(3153,plain,
% 1.96/1.59 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.96/1.59 inference(modus_ponens,[status(thm)],[3152, 3145])).
% 1.96/1.59 tff(3154,plain,
% 1.96/1.59 (c2_1(a2409)),
% 1.96/1.59 inference(unit_resolution,[status(thm)],[1137, 3140])).
% 1.96/1.59 tff(3155,plain,
% 1.96/1.59 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3156,plain,
% 1.96/1.59 ((hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409))) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.96/1.59 inference(rewrite,[status(thm)],[])).
% 1.96/1.59 tff(3157,plain,
% 1.96/1.59 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409))))),
% 1.96/1.59 inference(monotonicity,[status(thm)],[3156])).
% 1.96/1.59 tff(3158,plain,
% 1.96/1.59 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.96/1.59 inference(transitivity,[status(thm)],[3157, 3155])).
% 1.96/1.59 tff(3159,plain,
% 1.96/1.59 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3160,plain,
% 1.96/1.60 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 1.96/1.60 tff(3161,plain,
% 1.96/1.60 (hskp18),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3160, 204, 3128, 3142, 3154, 3141, 3153])).
% 1.96/1.60 tff(3162,assumption,(hskp18), introduced(assumption)).
% 1.96/1.60 tff(3163,plain,
% 1.96/1.60 (((~hskp18) | (~c3_1(a2428))) <=> ((~hskp18) | (~c3_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3164,plain,
% 1.96/1.60 (((~c3_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3165,axiom,((~c3_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.96/1.60 tff(3166,plain,
% 1.96/1.60 ((~hskp18) | (~c3_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.96/1.60 tff(3167,plain,
% 1.96/1.60 ((~hskp18) | (~c3_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3166, 3163])).
% 1.96/1.60 tff(3168,plain,
% 1.96/1.60 (~c3_1(a2428)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3167, 3162])).
% 1.96/1.60 tff(3169,plain,
% 1.96/1.60 (((~hskp18) | (~c2_1(a2428))) <=> ((~hskp18) | (~c2_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3170,plain,
% 1.96/1.60 (((~c2_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3171,axiom,((~c2_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.96/1.60 tff(3172,plain,
% 1.96/1.60 ((~hskp18) | (~c2_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 1.96/1.60 tff(3173,plain,
% 1.96/1.60 ((~hskp18) | (~c2_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3172, 3169])).
% 1.96/1.60 tff(3174,plain,
% 1.96/1.60 (~c2_1(a2428)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3173, 3162])).
% 1.96/1.60 tff(3175,plain,
% 1.96/1.60 (((~hskp18) | (~c0_1(a2428))) <=> ((~hskp18) | (~c0_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3176,plain,
% 1.96/1.60 (((~c0_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a2428)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3177,axiom,((~c0_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.96/1.60 tff(3178,plain,
% 1.96/1.60 ((~hskp18) | (~c0_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 1.96/1.60 tff(3179,plain,
% 1.96/1.60 ((~hskp18) | (~c0_1(a2428))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3178, 3175])).
% 1.96/1.60 tff(3180,plain,
% 1.96/1.60 (~c0_1(a2428)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3179, 3162])).
% 1.96/1.60 tff(3181,plain,
% 1.96/1.60 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3182,plain,
% 1.96/1.60 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428)) <=> (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3183,plain,
% 1.96/1.60 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0)))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3182])).
% 1.96/1.60 tff(3184,plain,
% 1.96/1.60 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3183, 3181])).
% 1.96/1.60 tff(3185,plain,
% 1.96/1.60 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3186,plain,
% 1.96/1.60 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0)),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 1.96/1.60 tff(3187,plain,
% 1.96/1.60 ($false),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3186, 204, 65, 22, 3180, 3174, 3168, 1039])).
% 1.96/1.60 tff(3188,plain,((~hskp18) | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.96/1.60 tff(3189,plain,
% 1.96/1.60 (hskp1),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3188, 3161, 2814])).
% 1.96/1.60 tff(3190,plain,
% 1.96/1.60 (~c3_1(a2403)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2423, 3189])).
% 1.96/1.60 tff(3191,plain,
% 1.96/1.60 (~c2_1(a2403)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2429, 3189])).
% 1.96/1.60 tff(3192,plain,
% 1.96/1.60 (c1_1(a2403)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2440, 3189])).
% 1.96/1.60 tff(3193,plain,
% 1.96/1.60 ($false),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2576, 204, 3142, 3154, 3141, 3192, 3191, 3190, 2451, 3143])).
% 1.96/1.60 tff(3194,plain,(hskp23 | hskp19 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.60 tff(3195,plain,
% 1.96/1.60 (hskp23),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3194, 43, 64])).
% 1.96/1.60 tff(3196,plain,
% 1.96/1.60 (hskp15),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[548, 3195])).
% 1.96/1.60 tff(3197,plain,
% 1.96/1.60 (~c2_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[576, 3196])).
% 1.96/1.60 tff(3198,plain,
% 1.96/1.60 (c1_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[570, 3196])).
% 1.96/1.60 tff(3199,plain,
% 1.96/1.60 (c0_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1373, 204, 64, 2814, 3198, 3197, 75])).
% 1.96/1.60 tff(3200,plain,
% 1.96/1.60 (~c0_1(a2455)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[516, 3195])).
% 1.96/1.60 tff(3201,plain,
% 1.96/1.60 (c2_1(a2455)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[538, 3195])).
% 1.96/1.60 tff(3202,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3203,plain,
% 1.96/1.60 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455))) <=> (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3204,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3203])).
% 1.96/1.60 tff(3205,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3204, 3202])).
% 1.96/1.60 tff(3206,plain,
% 1.96/1.60 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3207,plain,
% 1.96/1.60 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 1.96/1.60 tff(3208,plain,
% 1.96/1.60 (~c1_1(a2455)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3207, 204, 43, 3201, 2772, 3200, 957, 951, 85])).
% 1.96/1.60 tff(3209,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3210,plain,
% 1.96/1.60 ((hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3211,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3210])).
% 1.96/1.60 tff(3212,plain,
% 1.96/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3211, 3209])).
% 1.96/1.60 tff(3213,plain,
% 1.96/1.60 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3214,plain,
% 1.96/1.60 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 1.96/1.60 tff(3215,plain,
% 1.96/1.60 (hskp2 | (~c0_1(a2422))),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3214, 204, 2819, 3198, 2827, 3197, 1384, 2826])).
% 1.96/1.60 tff(3216,plain,
% 1.96/1.60 (hskp2),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3215, 3199])).
% 1.96/1.60 tff(3217,plain,
% 1.96/1.60 (~c3_1(a2404)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1397, 3216])).
% 1.96/1.60 tff(3218,plain,
% 1.96/1.60 (~c2_1(a2404)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1403, 3216])).
% 1.96/1.60 tff(3219,plain,
% 1.96/1.60 (c3_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[559, 3196])).
% 1.96/1.60 tff(3220,plain,
% 1.96/1.60 (c3_1(a2455)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[527, 3195])).
% 1.96/1.60 tff(3221,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3222,plain,
% 1.96/1.60 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3223,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3222])).
% 1.96/1.60 tff(3224,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3223, 3221])).
% 1.96/1.60 tff(3225,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3226,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 1.96/1.60 tff(3227,plain,
% 1.96/1.60 (~c0_1(a2404)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3226, 204, 3201, 3220, 3198, 3219, 3218, 3217, 602, 3208, 3199])).
% 1.96/1.60 tff(3228,plain,
% 1.96/1.60 (~c1_1(a2404)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1908, 3216])).
% 1.96/1.60 tff(3229,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3230,plain,
% 1.96/1.60 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3231,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3230])).
% 1.96/1.60 tff(3232,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3231, 3229])).
% 1.96/1.60 tff(3233,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3234,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 1.96/1.60 tff(3235,plain,
% 1.96/1.60 (~c2_1(a2414)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3234, 204, 3201, 2772, 3200, 957, 3228, 3218, 21, 3208, 3227])).
% 1.96/1.60 tff(3236,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3237,plain,
% 1.96/1.60 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(rewrite,[status(thm)],[])).
% 1.96/1.60 tff(3238,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.60 inference(monotonicity,[status(thm)],[3237])).
% 1.96/1.60 tff(3239,plain,
% 1.96/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.60 inference(transitivity,[status(thm)],[3238, 3236])).
% 1.96/1.60 tff(3240,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.96/1.60 inference(quant_inst,[status(thm)],[])).
% 1.96/1.60 tff(3241,plain,
% 1.96/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.60 inference(modus_ponens,[status(thm)],[3240, 3239])).
% 1.96/1.60 tff(3242,plain,
% 1.96/1.60 ($false),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3241, 204, 3201, 3220, 3198, 3219, 2772, 951, 602, 3235, 3208, 3199])).
% 1.96/1.60 tff(3243,plain,(hskp19 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.60 tff(3244,plain,
% 1.96/1.60 (hskp19),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3243, 64])).
% 1.96/1.60 tff(3245,plain,
% 1.96/1.60 (~c0_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[312, 3244])).
% 1.96/1.60 tff(3246,plain,
% 1.96/1.60 (c3_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[891, 3244])).
% 1.96/1.60 tff(3247,plain,
% 1.96/1.60 (c1_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[323, 3244])).
% 1.96/1.60 tff(3248,plain,
% 1.96/1.60 (c2_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2129, 3134])).
% 1.96/1.60 tff(3249,plain,
% 1.96/1.60 (hskp15),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1364, 3248])).
% 1.96/1.60 tff(3250,plain,
% 1.96/1.60 (~c2_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[576, 3249])).
% 1.96/1.60 tff(3251,plain,
% 1.96/1.60 (c3_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[559, 3249])).
% 1.96/1.60 tff(3252,plain,
% 1.96/1.60 (c1_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[570, 3249])).
% 1.96/1.60 tff(3253,plain,
% 1.96/1.60 ($false),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1418, 204, 3134, 1354, 1357, 3252, 3251, 1353, 3250, 920])).
% 1.96/1.60 tff(3254,plain,(hskp20 | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.60 tff(3255,plain,
% 1.96/1.60 (hskp20),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3254, 3247, 3246, 3245])).
% 1.96/1.60 tff(3256,plain,
% 1.96/1.60 (~c2_1(a2435)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[868, 3255])).
% 1.96/1.60 tff(3257,plain,
% 1.96/1.60 (~c0_1(a2435)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[820, 3255])).
% 1.96/1.60 tff(3258,plain,
% 1.96/1.60 (hskp13 | (~c1_1(a2435))),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1427, 204, 64, 3257, 3256, 75])).
% 1.96/1.60 tff(3259,plain,
% 1.96/1.60 (~c1_1(a2435)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3258, 65])).
% 1.96/1.60 tff(3260,plain,
% 1.96/1.60 (hskp13 | c2_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[377, 204, 64, 3247, 3245, 75])).
% 1.96/1.60 tff(3261,plain,
% 1.96/1.60 (c2_1(a2432)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3260, 65])).
% 1.96/1.60 tff(3262,plain,
% 1.96/1.60 (hskp15 | (~c2_1(a2432))),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[1363, 204, 3246, 3245, 511])).
% 1.96/1.60 tff(3263,plain,
% 1.96/1.60 (hskp15),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3262, 3261])).
% 1.96/1.60 tff(3264,plain,
% 1.96/1.60 (~c2_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[576, 3263])).
% 1.96/1.60 tff(3265,plain,
% 1.96/1.60 (c3_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[559, 3263])).
% 1.96/1.60 tff(3266,plain,
% 1.96/1.60 (c1_1(a2422)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[570, 3263])).
% 1.96/1.60 tff(3267,assumption,(~c2_1(a2414)), introduced(assumption)).
% 1.96/1.60 tff(3268,assumption,(~c1_1(a2435)), introduced(assumption)).
% 1.96/1.60 tff(3269,plain,
% 1.96/1.60 ($false),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[2364, 204, 615, 614, 2772, 2279, 785, 613, 951, 1438, 3268, 3267])).
% 1.96/1.60 tff(3270,plain,(c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c1_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.60 tff(3271,plain,
% 1.96/1.60 (c2_1(a2414)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[3270, 3266, 3265, 3257, 3256, 3264, 3259])).
% 1.96/1.60 tff(3272,plain,
% 1.96/1.60 (c3_1(a2435)),
% 1.96/1.60 inference(unit_resolution,[status(thm)],[814, 3255])).
% 1.96/1.61 tff(3273,plain,
% 1.96/1.61 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3274,plain,
% 1.96/1.61 ((hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3275,plain,
% 1.96/1.61 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3274])).
% 1.96/1.61 tff(3276,plain,
% 1.96/1.61 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3275, 3273])).
% 1.96/1.61 tff(3277,plain,
% 1.96/1.61 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3278,plain,
% 1.96/1.61 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 1.96/1.61 tff(3279,plain,
% 1.96/1.61 (hskp12 | c1_1(a2435)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3278, 204, 3272, 3257, 1532])).
% 1.96/1.61 tff(3280,plain,
% 1.96/1.61 (hskp12),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3279, 3259])).
% 1.96/1.61 tff(3281,plain,
% 1.96/1.61 (~c1_1(a2417)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[229, 3280])).
% 1.96/1.61 tff(3282,plain,
% 1.96/1.61 (~c0_1(a2417)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[235, 3280])).
% 1.96/1.61 tff(3283,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3284,plain,
% 1.96/1.61 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3285,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435)))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3284])).
% 1.96/1.61 tff(3286,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3285, 3283])).
% 1.96/1.61 tff(3287,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3288,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.96/1.61 tff(3289,plain,
% 1.96/1.61 ((~c2_1(a2414)) | (~c2_1(a2417))),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3288, 204, 2772, 3257, 3256, 3282, 3281, 957, 21, 3259])).
% 1.96/1.61 tff(3290,plain,
% 1.96/1.61 (~c2_1(a2417)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3289, 3271])).
% 1.96/1.61 tff(3291,plain,
% 1.96/1.61 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.96/1.61 inference(bind,[status(th)],[])).
% 1.96/1.61 tff(3292,plain,
% 1.96/1.61 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(quant_intro,[status(thm)],[3291])).
% 1.96/1.61 tff(3293,plain,
% 1.96/1.61 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3294,plain,
% 1.96/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.96/1.61 inference(bind,[status(th)],[])).
% 1.96/1.61 tff(3295,plain,
% 1.96/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(quant_intro,[status(thm)],[3294])).
% 1.96/1.61 tff(3296,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.96/1.61 tff(3297,plain,
% 1.96/1.61 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 1.96/1.61 tff(3298,plain,
% 1.96/1.61 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3297, 3293])).
% 1.96/1.61 tff(3299,plain,(
% 1.96/1.61 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(skolemize,[status(sab)],[3298])).
% 1.96/1.61 tff(3300,plain,
% 1.96/1.61 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3299, 3292])).
% 1.96/1.61 tff(3301,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3302,plain,
% 1.96/1.61 ((hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3303,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3302])).
% 1.96/1.61 tff(3304,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3303, 3301])).
% 1.96/1.61 tff(3305,plain,
% 1.96/1.61 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3306,plain,
% 1.96/1.61 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 1.96/1.61 tff(3307,plain,
% 1.96/1.61 (hskp2 | (~c2_1(a2414))),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3306, 204, 3272, 2772, 3257, 3256, 951, 3300])).
% 1.96/1.61 tff(3308,plain,
% 1.96/1.61 (hskp2),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3307, 3271])).
% 1.96/1.61 tff(3309,plain,
% 1.96/1.61 (~c3_1(a2404)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[1397, 3308])).
% 1.96/1.61 tff(3310,plain,
% 1.96/1.61 (~c2_1(a2404)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[1403, 3308])).
% 1.96/1.61 tff(3311,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3312,plain,
% 1.96/1.61 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3313,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3312])).
% 1.96/1.61 tff(3314,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3313, 3311])).
% 1.96/1.61 tff(3315,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3316,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 1.96/1.61 tff(3317,plain,
% 1.96/1.61 (~c0_1(a2404)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3316, 204, 3266, 3265, 3264, 3282, 3281, 3310, 3309, 1438, 3290])).
% 1.96/1.61 tff(3318,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3319,plain,
% 1.96/1.61 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404)) <=> (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3320,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3319])).
% 1.96/1.61 tff(3321,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3320, 3318])).
% 1.96/1.61 tff(3322,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3323,plain,
% 1.96/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 1.96/1.61 tff(3324,plain,
% 1.96/1.61 ($false),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3323, 204, 3247, 3266, 3265, 3245, 3264, 3310, 3309, 63, 3261, 3317])).
% 1.96/1.61 tff(3325,plain,(hskp13 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.61 tff(3326,plain,
% 1.96/1.61 (hskp13),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3325, 64])).
% 1.96/1.61 tff(3327,plain,
% 1.96/1.61 (c2_1(a2418)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[350, 3326])).
% 1.96/1.61 tff(3328,plain,
% 1.96/1.61 (~c0_1(a2418)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[339, 3326])).
% 1.96/1.61 tff(3329,plain,
% 1.96/1.61 (c1_1(a2418)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[361, 3326])).
% 1.96/1.61 tff(3330,assumption,(hskp4), introduced(assumption)).
% 1.96/1.61 tff(3331,plain,
% 1.96/1.61 (~c1_1(a2407)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[1512, 3330])).
% 1.96/1.61 tff(3332,plain,
% 1.96/1.61 (c0_1(a2407)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[2081, 3330])).
% 1.96/1.61 tff(3333,plain,
% 1.96/1.61 (~c2_1(a2407)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[1518, 3330])).
% 1.96/1.61 tff(3334,plain,
% 1.96/1.61 ($false),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[2270, 3333, 3332, 1354, 1353, 2186, 540, 3331, 2184, 1357, 2185])).
% 1.96/1.61 tff(3335,plain,((~hskp4) | (~c1_1(a2432)) | c0_1(a2432) | (~c2_1(a2418)) | hskp15 | (~c1_1(a2418)) | (~c3_1(a2432)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.61 tff(3336,plain,
% 1.96/1.61 (~hskp4),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3335, 540, 1353, 2186, 1354, 2184, 1357, 2185])).
% 1.96/1.61 tff(3337,assumption,(hskp9), introduced(assumption)).
% 1.96/1.61 tff(3338,plain,
% 1.96/1.61 (((~hskp9) | (~c1_1(a2413))) <=> ((~hskp9) | (~c1_1(a2413)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3339,plain,
% 1.96/1.61 (((~c1_1(a2413)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2413)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3340,axiom,((~c1_1(a2413)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.96/1.61 tff(3341,plain,
% 1.96/1.61 ((~hskp9) | (~c1_1(a2413))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.96/1.61 tff(3342,plain,
% 1.96/1.61 ((~hskp9) | (~c1_1(a2413))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3341, 3338])).
% 1.96/1.61 tff(3343,plain,
% 1.96/1.61 (~c1_1(a2413)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3342, 3337])).
% 1.96/1.61 tff(3344,plain,
% 1.96/1.61 (((~hskp9) | (~c0_1(a2413))) <=> ((~hskp9) | (~c0_1(a2413)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3345,plain,
% 1.96/1.61 (((~c0_1(a2413)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2413)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3346,axiom,((~c0_1(a2413)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.96/1.61 tff(3347,plain,
% 1.96/1.61 ((~hskp9) | (~c0_1(a2413))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.96/1.61 tff(3348,plain,
% 1.96/1.61 ((~hskp9) | (~c0_1(a2413))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3347, 3344])).
% 1.96/1.61 tff(3349,plain,
% 1.96/1.61 (~c0_1(a2413)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3348, 3337])).
% 1.96/1.61 tff(3350,plain,
% 1.96/1.61 (((~hskp9) | c2_1(a2413)) <=> ((~hskp9) | c2_1(a2413))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3351,axiom,((~hskp9) | c2_1(a2413)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.96/1.61 tff(3352,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.96/1.61 tff(3353,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3352, 3350])).
% 1.96/1.61 tff(3354,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3353, 3350])).
% 1.96/1.61 tff(3355,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3354, 3350])).
% 1.96/1.61 tff(3356,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3355, 3350])).
% 1.96/1.61 tff(3357,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3356, 3350])).
% 1.96/1.61 tff(3358,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3357, 3350])).
% 1.96/1.61 tff(3359,plain,
% 1.96/1.61 ((~hskp9) | c2_1(a2413)),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3358, 3350])).
% 1.96/1.61 tff(3360,plain,
% 1.96/1.61 (c2_1(a2413)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3359, 3337])).
% 1.96/1.61 tff(3361,assumption,(~hskp4), introduced(assumption)).
% 1.96/1.61 tff(3362,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3363,plain,
% 1.96/1.61 ((hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3364,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3363])).
% 1.96/1.61 tff(3365,plain,
% 1.96/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3364, 3362])).
% 1.96/1.61 tff(3366,plain,
% 1.96/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3367,plain,
% 1.96/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 1.96/1.61 tff(3368,plain,
% 1.96/1.61 ($false),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3367, 204, 3361, 1354, 1357, 3360, 1353, 3349, 3343, 1057])).
% 1.96/1.61 tff(3369,plain,((~hskp9) | hskp4 | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.61 tff(3370,plain,
% 1.96/1.61 (~hskp9),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3369, 3336, 1354, 1357, 1353])).
% 1.96/1.61 tff(3371,plain,
% 1.96/1.61 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3372,plain,
% 1.96/1.61 ((hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432))) <=> (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(rewrite,[status(thm)],[])).
% 1.96/1.61 tff(3373,plain,
% 1.96/1.61 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.96/1.61 inference(monotonicity,[status(thm)],[3372])).
% 1.96/1.61 tff(3374,plain,
% 1.96/1.61 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(transitivity,[status(thm)],[3373, 3371])).
% 1.96/1.61 tff(3375,plain,
% 1.96/1.61 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.61 inference(quant_inst,[status(thm)],[])).
% 1.96/1.61 tff(3376,plain,
% 1.96/1.61 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.96/1.61 inference(modus_ponens,[status(thm)],[3375, 3374])).
% 1.96/1.61 tff(3377,plain,
% 1.96/1.61 (hskp9 | hskp1),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3376, 204, 1354, 1357, 1353, 32])).
% 1.96/1.61 tff(3378,plain,
% 1.96/1.61 (hskp1),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[3377, 3370])).
% 1.96/1.61 tff(3379,plain,
% 1.96/1.61 (~c3_1(a2403)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[2423, 3378])).
% 1.96/1.61 tff(3380,plain,
% 1.96/1.61 (~c2_1(a2403)),
% 1.96/1.61 inference(unit_resolution,[status(thm)],[2429, 3378])).
% 1.96/1.61 tff(3381,plain,
% 1.96/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3382,plain,
% 1.96/1.62 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3383,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3382])).
% 1.96/1.62 tff(3384,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3383, 3381])).
% 1.96/1.62 tff(3385,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3386,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 1.96/1.62 tff(3387,plain,
% 1.96/1.62 (c0_1(a2403)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3386, 204, 1354, 1357, 2184, 2186, 2185, 3380, 3379, 63, 2256])).
% 1.96/1.62 tff(3388,plain,
% 1.96/1.62 (c1_1(a2403)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[2440, 3378])).
% 1.96/1.62 tff(3389,plain,
% 1.96/1.62 (hskp20),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3254, 1354, 1357, 1353])).
% 1.96/1.62 tff(3390,plain,
% 1.96/1.62 (~c2_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[868, 3389])).
% 1.96/1.62 tff(3391,plain,
% 1.96/1.62 (~c0_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[820, 3389])).
% 1.96/1.62 tff(3392,plain,
% 1.96/1.62 (c1_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[2547, 204, 1354, 1357, 3388, 3391, 3390, 3380, 3379, 11, 2256])).
% 1.96/1.62 tff(3393,plain,
% 1.96/1.62 (~hskp29),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[2578, 3392, 540, 3379, 3380, 3391, 3390, 3388])).
% 1.96/1.62 tff(3394,plain,
% 1.96/1.62 (hskp0),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[2678, 3393, 2256])).
% 1.96/1.62 tff(3395,plain,
% 1.96/1.62 (~c1_1(a2402)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1614, 3394])).
% 1.96/1.62 tff(3396,plain,
% 1.96/1.62 (c3_1(a2402)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1625, 3394])).
% 1.96/1.62 tff(3397,plain,
% 1.96/1.62 (c3_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[814, 3389])).
% 1.96/1.62 tff(3398,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3399,plain,
% 1.96/1.62 ((hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3400,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3399])).
% 1.96/1.62 tff(3401,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3400, 3398])).
% 1.96/1.62 tff(3402,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3403,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 1.96/1.62 tff(3404,plain,
% 1.96/1.62 (hskp30),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3403, 204, 3397, 3388, 3390, 3379, 612, 3392, 3387])).
% 1.96/1.62 tff(3405,plain,
% 1.96/1.62 (c3_1(a2450)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[633, 3404])).
% 1.96/1.62 tff(3406,plain,
% 1.96/1.62 (c1_1(a2450)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[644, 3404])).
% 1.96/1.62 tff(3407,plain,
% 1.96/1.62 (c0_1(a2450)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[655, 3404])).
% 1.96/1.62 tff(3408,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3409,plain,
% 1.96/1.62 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402))) <=> (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3410,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3409])).
% 1.96/1.62 tff(3411,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3410, 3408])).
% 1.96/1.62 tff(3412,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3413,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.96/1.62 tff(3414,plain,
% 1.96/1.62 (~c2_1(a2402)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3413, 204, 3407, 3406, 3405, 3396, 3380, 3379, 3395, 602, 3387])).
% 1.96/1.62 tff(3415,plain,
% 1.96/1.62 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.96/1.62 inference(bind,[status(th)],[])).
% 1.96/1.62 tff(3416,plain,
% 1.96/1.62 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(quant_intro,[status(thm)],[3415])).
% 1.96/1.62 tff(3417,plain,
% 1.96/1.62 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3418,plain,
% 1.96/1.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.96/1.62 inference(bind,[status(th)],[])).
% 1.96/1.62 tff(3419,plain,
% 1.96/1.62 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(quant_intro,[status(thm)],[3418])).
% 1.96/1.62 tff(3420,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.96/1.62 tff(3421,plain,
% 1.96/1.62 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3420, 3419])).
% 1.96/1.62 tff(3422,plain,
% 1.96/1.62 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3421, 3417])).
% 1.96/1.62 tff(3423,plain,(
% 1.96/1.62 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(skolemize,[status(sab)],[3422])).
% 1.96/1.62 tff(3424,plain,
% 1.96/1.62 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3423, 3416])).
% 1.96/1.62 tff(3425,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3426,plain,
% 1.96/1.62 ((hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418))) <=> (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3427,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3426])).
% 1.96/1.62 tff(3428,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3427, 3425])).
% 1.96/1.62 tff(3429,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3430,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 1.96/1.62 tff(3431,plain,
% 1.96/1.62 ($false),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3430, 204, 3336, 2184, 3396, 2185, 3395, 3424, 2257, 3414])).
% 1.96/1.62 tff(3432,plain,(hskp15 | (~c1_1(a2418)) | c0_1(a2418) | (~c1_1(a2432)) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2418))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.62 tff(3433,plain,
% 1.96/1.62 (hskp15),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3432, 3329, 3328, 3247, 3245, 3246, 3327])).
% 1.96/1.62 tff(3434,plain,
% 1.96/1.62 (c1_1(a2422)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[570, 3433])).
% 1.96/1.62 tff(3435,plain,
% 1.96/1.62 (~c2_1(a2422)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[576, 3433])).
% 1.96/1.62 tff(3436,plain,
% 1.96/1.62 (c3_1(a2422)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[559, 3433])).
% 1.96/1.62 tff(3437,plain,
% 1.96/1.62 (hskp9 | hskp1),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3376, 204, 3247, 3246, 3245, 32])).
% 1.96/1.62 tff(3438,plain,
% 1.96/1.62 (hskp9),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3437, 22])).
% 1.96/1.62 tff(3439,plain,
% 1.96/1.62 (~c1_1(a2413)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3342, 3438])).
% 1.96/1.62 tff(3440,plain,
% 1.96/1.62 (~c0_1(a2413)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3348, 3438])).
% 1.96/1.62 tff(3441,plain,
% 1.96/1.62 (c2_1(a2413)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3359, 3438])).
% 1.96/1.62 tff(3442,plain,
% 1.96/1.62 (c2_1(a2414)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3270, 3268, 614, 2279, 785, 613, 615])).
% 1.96/1.62 tff(3443,assumption,(~c1_1(a2413)), introduced(assumption)).
% 1.96/1.62 tff(3444,assumption,(~c0_1(a2413)), introduced(assumption)).
% 1.96/1.62 tff(3445,assumption,(c2_1(a2413)), introduced(assumption)).
% 1.96/1.62 tff(3446,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3447,plain,
% 1.96/1.62 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3448,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435)))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3447])).
% 1.96/1.62 tff(3449,plain,
% 1.96/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3448, 3446])).
% 1.96/1.62 tff(3450,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3451,plain,
% 1.96/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435)),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3450, 3449])).
% 1.96/1.62 tff(3452,plain,
% 1.96/1.62 ((~c2_1(a2414)) | c1_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3451, 204, 2772, 3445, 2279, 785, 957, 3444, 3443, 21])).
% 1.96/1.62 tff(3453,plain,
% 1.96/1.62 ($false),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3452, 3442, 3268])).
% 1.96/1.62 tff(3454,plain,(c1_1(a2435) | (~c2_1(a2413)) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.62 tff(3455,plain,
% 1.96/1.62 (c1_1(a2435)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3454, 3441, 3257, 3256, 3440, 3439, 3436, 3435, 3434])).
% 1.96/1.62 tff(3456,plain,
% 1.96/1.62 (hskp4),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3369, 3438, 3247, 3246, 3245])).
% 1.96/1.62 tff(3457,plain,
% 1.96/1.62 (~c2_1(a2407)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1518, 3456])).
% 1.96/1.62 tff(3458,plain,
% 1.96/1.62 (~c1_1(a2407)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1512, 3456])).
% 1.96/1.62 tff(3459,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3460,plain,
% 1.96/1.62 ((hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3461,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3460])).
% 1.96/1.62 tff(3462,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3461, 3459])).
% 1.96/1.62 tff(3463,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3464,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 1.96/1.62 tff(3465,plain,
% 1.96/1.62 (~c2_1(a2432)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3464, 204, 2087, 1357, 3360, 1353, 3349, 3343, 2097])).
% 1.96/1.62 tff(3466,plain,
% 1.96/1.62 (hskp4),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3367, 204, 1354, 1357, 3360, 1353, 3349, 3343, 1057])).
% 1.96/1.62 tff(3467,plain,
% 1.96/1.62 (~c2_1(a2407)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1518, 3466])).
% 1.96/1.62 tff(3468,plain,
% 1.96/1.62 (~c1_1(a2407)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[1512, 3466])).
% 1.96/1.62 tff(3469,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3470,plain,
% 1.96/1.62 ((hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.96/1.62 inference(rewrite,[status(thm)],[])).
% 1.96/1.62 tff(3471,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418))))),
% 1.96/1.62 inference(monotonicity,[status(thm)],[3470])).
% 1.96/1.62 tff(3472,plain,
% 1.96/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.96/1.62 inference(transitivity,[status(thm)],[3471, 3469])).
% 1.96/1.62 tff(3473,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.96/1.62 inference(quant_inst,[status(thm)],[])).
% 1.96/1.62 tff(3474,plain,
% 1.96/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418))),
% 1.96/1.62 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 1.96/1.62 tff(3475,plain,
% 1.96/1.62 (~c3_1(a2418)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[3474, 204, 2087, 2186, 3360, 2185, 3349, 3343, 2097])).
% 1.96/1.62 tff(3476,plain,
% 1.96/1.62 (hskp6 | c3_1(a2418)),
% 1.96/1.62 inference(unit_resolution,[status(thm)],[2222, 204, 686, 2184, 2186, 2219])).
% 1.96/1.63 tff(3477,plain,
% 1.96/1.63 (hskp6),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3476, 3475])).
% 1.96/1.63 tff(3478,plain,
% 1.96/1.63 (~c2_1(a2410)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[964, 3477])).
% 1.96/1.63 tff(3479,plain,
% 1.96/1.63 (c0_1(a2407)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2081, 3466])).
% 1.96/1.63 tff(3480,plain,
% 1.96/1.63 (c1_1(a2410)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[975, 3477])).
% 1.96/1.63 tff(3481,plain,
% 1.96/1.63 (c0_1(a2410)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[986, 3477])).
% 1.96/1.63 tff(3482,plain,
% 1.96/1.63 ($false),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2268, 204, 1354, 3481, 3480, 3479, 1353, 3478, 3468, 3467, 2008, 3465])).
% 1.96/1.63 tff(3483,plain,((~hskp9) | (~c1_1(a2432)) | c0_1(a2432) | hskp23 | (~c1_1(a2418)) | (~c2_1(a2418)) | (~c3_1(a2432)) | hskp5 | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.63 tff(3484,plain,
% 1.96/1.63 (hskp5),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3483, 3438, 3245, 686, 3329, 3327, 3246, 3247, 3328])).
% 1.96/1.63 tff(3485,plain,
% 1.96/1.63 (~c2_1(a2408)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[400, 3484])).
% 1.96/1.63 tff(3486,plain,
% 1.96/1.63 (c0_1(a2407)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2081, 3456])).
% 1.96/1.63 tff(3487,plain,
% 1.96/1.63 (c0_1(a2408)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[411, 3484])).
% 1.96/1.63 tff(3488,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3489,plain,
% 1.96/1.63 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3490,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3489])).
% 1.96/1.63 tff(3491,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3490, 3488])).
% 1.96/1.63 tff(3492,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3493,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 1.96/1.63 tff(3494,plain,
% 1.96/1.63 (~c1_1(a2408)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3493, 204, 3247, 3487, 3486, 3245, 3485, 3458, 3457, 2008, 1998])).
% 1.96/1.63 tff(3495,plain,
% 1.96/1.63 (c3_1(a2408)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[429, 3484])).
% 1.96/1.63 tff(3496,plain,
% 1.96/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3497,plain,
% 1.96/1.63 ((hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3498,plain,
% 1.96/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413))))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3497])).
% 1.96/1.63 tff(3499,plain,
% 1.96/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3498, 3496])).
% 1.96/1.63 tff(3500,plain,
% 1.96/1.63 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3501,plain,
% 1.96/1.63 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413))),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3500, 3499])).
% 1.96/1.63 tff(3502,plain,
% 1.96/1.63 (~c3_1(a2413)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3501, 204, 22, 3441, 3495, 3439, 3485, 1082, 3494])).
% 1.96/1.63 tff(3503,plain,
% 1.96/1.63 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3504,plain,
% 1.96/1.63 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413))) <=> (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3505,plain,
% 1.96/1.63 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413)))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3504])).
% 1.96/1.63 tff(3506,plain,
% 1.96/1.63 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3505, 3503])).
% 1.96/1.63 tff(3507,plain,
% 1.96/1.63 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3508,plain,
% 1.96/1.63 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413)),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 1.96/1.63 tff(3509,plain,
% 1.96/1.63 (hskp12 | c3_1(a2413)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3508, 204, 64, 3441, 3439, 273])).
% 1.96/1.63 tff(3510,plain,
% 1.96/1.63 (hskp12),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3509, 3502])).
% 1.96/1.63 tff(3511,plain,
% 1.96/1.63 (~c1_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[229, 3510])).
% 1.96/1.63 tff(3512,plain,
% 1.96/1.63 (c3_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[246, 3510])).
% 1.96/1.63 tff(3513,plain,
% 1.96/1.63 (~c2_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[1091, 204, 22, 3512, 3495, 3511, 3485, 1082, 3494])).
% 1.96/1.63 tff(3514,plain,
% 1.96/1.63 (~c0_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[235, 3510])).
% 1.96/1.63 tff(3515,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3516,plain,
% 1.96/1.63 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3517,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417)))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3516])).
% 1.96/1.63 tff(3518,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3517, 3515])).
% 1.96/1.63 tff(3519,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3520,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417)),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 1.96/1.63 tff(3521,plain,
% 1.96/1.63 (~c2_1(a2414)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3520, 204, 2772, 3441, 3514, 3511, 957, 3440, 3439, 21, 3513])).
% 1.96/1.63 tff(3522,plain,
% 1.96/1.63 (c1_1(a2435)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3270, 3521, 3436, 3257, 3256, 3435, 3434])).
% 1.96/1.63 tff(3523,plain,
% 1.96/1.63 ($false),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2357, 204, 3272, 2772, 3256, 3514, 3511, 951, 1438, 3522, 3513, 3521])).
% 1.96/1.63 tff(3524,plain,(hskp1 | hskp16 | c2_1(a2432) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.96/1.63 tff(3525,plain,
% 1.96/1.63 (hskp1),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3524, 1998, 64, 686])).
% 1.96/1.63 tff(3526,plain,
% 1.96/1.63 (~c3_1(a2403)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2423, 3525])).
% 1.96/1.63 tff(3527,plain,
% 1.96/1.63 (~c2_1(a2403)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2429, 3525])).
% 1.96/1.63 tff(3528,plain,
% 1.96/1.63 (c0_1(a2403)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3386, 204, 3247, 3246, 3329, 3327, 3328, 3527, 3526, 63, 1998])).
% 1.96/1.63 tff(3529,plain,
% 1.96/1.63 (c1_1(a2403)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2440, 3525])).
% 1.96/1.63 tff(3530,plain,
% 1.96/1.63 (c1_1(a2435)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[2547, 204, 3247, 3246, 3529, 3257, 3256, 3527, 3526, 11, 1998])).
% 1.96/1.63 tff(3531,plain,
% 1.96/1.63 (hskp30),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3403, 204, 3272, 3529, 3256, 3526, 612, 3530, 3528])).
% 1.96/1.63 tff(3532,plain,
% 1.96/1.63 (c3_1(a2450)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[633, 3531])).
% 1.96/1.63 tff(3533,plain,
% 1.96/1.63 (c1_1(a2450)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[644, 3531])).
% 1.96/1.63 tff(3534,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3535,plain,
% 1.96/1.63 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3536,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3535])).
% 1.96/1.63 tff(3537,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3536, 3534])).
% 1.96/1.63 tff(3538,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3539,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3538, 3537])).
% 1.96/1.63 tff(3540,plain,
% 1.96/1.63 (~c2_1(a2450)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3539, 204, 3533, 3532, 2772, 3529, 957, 951, 3526, 1160, 3528])).
% 1.96/1.63 tff(3541,plain,
% 1.96/1.63 (c0_1(a2450)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[655, 3531])).
% 1.96/1.63 tff(3542,plain,
% 1.96/1.63 (hskp12),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[938, 204, 3541, 3533, 3532, 3272, 3257, 3256, 832])).
% 1.96/1.63 tff(3543,plain,
% 1.96/1.63 (~c1_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[229, 3542])).
% 1.96/1.63 tff(3544,plain,
% 1.96/1.63 (c3_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[246, 3542])).
% 1.96/1.63 tff(3545,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3546,plain,
% 1.96/1.63 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3547,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3546])).
% 1.96/1.63 tff(3548,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3547, 3545])).
% 1.96/1.63 tff(3549,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3550,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3549, 3548])).
% 1.96/1.63 tff(3551,plain,
% 1.96/1.63 (~c2_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3550, 204, 3541, 3533, 3532, 3544, 3543, 3527, 3526, 602, 3528])).
% 1.96/1.63 tff(3552,plain,
% 1.96/1.63 (~c0_1(a2417)),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[235, 3542])).
% 1.96/1.63 tff(3553,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3554,plain,
% 1.96/1.63 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.96/1.63 inference(rewrite,[status(thm)],[])).
% 1.96/1.63 tff(3555,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417)))),
% 1.96/1.63 inference(monotonicity,[status(thm)],[3554])).
% 1.96/1.63 tff(3556,plain,
% 1.96/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.96/1.63 inference(transitivity,[status(thm)],[3555, 3553])).
% 1.96/1.63 tff(3557,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.96/1.63 inference(quant_inst,[status(thm)],[])).
% 1.96/1.63 tff(3558,plain,
% 1.96/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417)),
% 1.96/1.63 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 1.96/1.63 tff(3559,plain,
% 1.96/1.63 ($false),
% 1.96/1.63 inference(unit_resolution,[status(thm)],[3558, 204, 3533, 3532, 3529, 3552, 3543, 3527, 3526, 11, 3551, 3540])).
% 1.96/1.64 tff(3560,plain,(c2_1(a2432) | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.96/1.64 tff(3561,plain,
% 1.96/1.64 (c2_1(a2432)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3560, 686, 64])).
% 1.96/1.64 tff(3562,plain,
% 1.96/1.64 ((~c1_1(a2408)) | (~c1_1(a2435))),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2170, 204, 3487, 3486, 3257, 3256, 3485, 3458, 3457, 2008])).
% 1.96/1.64 tff(3563,plain,
% 1.96/1.64 (~c1_1(a2408)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3562, 3455])).
% 1.96/1.64 tff(3564,plain,
% 1.96/1.64 (c1_1(a2408) | (~c3_1(a2413))),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3501, 204, 22, 3441, 3495, 3439, 3485, 1082])).
% 1.96/1.64 tff(3565,plain,
% 1.96/1.64 (~c3_1(a2413)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3564, 3563])).
% 1.96/1.64 tff(3566,plain,
% 1.96/1.64 (hskp12),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3509, 3565])).
% 1.96/1.64 tff(3567,plain,
% 1.96/1.64 (~c1_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[229, 3566])).
% 1.96/1.64 tff(3568,plain,
% 1.96/1.64 (c3_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[246, 3566])).
% 1.96/1.64 tff(3569,plain,
% 1.96/1.64 (~c2_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[1091, 204, 22, 3568, 3495, 3567, 3485, 1082, 3563])).
% 1.96/1.64 tff(3570,plain,
% 1.96/1.64 (~c0_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[235, 3566])).
% 1.96/1.64 tff(3571,plain,
% 1.96/1.64 (~c2_1(a2414)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3520, 204, 2772, 3441, 3570, 3567, 957, 3440, 3439, 21, 3569])).
% 1.96/1.64 tff(3572,plain,
% 1.96/1.64 ($false),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2357, 204, 3272, 2772, 3256, 3570, 3567, 951, 1438, 3455, 3569, 3571])).
% 1.96/1.64 tff(3573,plain,(hskp1 | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.96/1.64 tff(3574,plain,
% 1.96/1.64 (hskp1),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3573, 686, 64])).
% 1.96/1.64 tff(3575,plain,
% 1.96/1.64 (~c3_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2423, 3574])).
% 1.96/1.64 tff(3576,plain,
% 1.96/1.64 (~c2_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2429, 3574])).
% 1.96/1.64 tff(3577,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3578,plain,
% 1.96/1.64 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3579,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3578])).
% 1.96/1.64 tff(3580,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3579, 3577])).
% 1.96/1.64 tff(3581,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3582,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3581, 3580])).
% 1.96/1.64 tff(3583,plain,
% 1.96/1.64 (c0_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3582, 204, 3247, 3434, 3436, 3245, 3435, 3576, 3575, 63, 3561])).
% 1.96/1.64 tff(3584,plain,
% 1.96/1.64 (c1_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2440, 3574])).
% 1.96/1.64 tff(3585,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3586,plain,
% 1.96/1.64 (((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3587,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3586])).
% 1.96/1.64 tff(3588,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.96/1.64 tff(3589,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3590,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.96/1.64 tff(3591,plain,
% 1.96/1.64 ($false),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3590, 204, 3247, 3246, 2772, 3584, 957, 951, 3575, 1160, 3561, 3583])).
% 1.96/1.64 tff(3592,plain,(hskp23 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.64 tff(3593,plain,
% 1.96/1.64 (hskp23),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3592, 64])).
% 1.96/1.64 tff(3594,plain,
% 1.96/1.64 (~c0_1(a2455)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[516, 3593])).
% 1.96/1.64 tff(3595,plain,
% 1.96/1.64 (c3_1(a2455)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[527, 3593])).
% 1.96/1.64 tff(3596,plain,
% 1.96/1.64 (c2_1(a2455)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[538, 3593])).
% 1.96/1.64 tff(3597,plain,
% 1.96/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3598,plain,
% 1.96/1.64 ((hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3599,plain,
% 1.96/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3598])).
% 1.96/1.64 tff(3600,plain,
% 1.96/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3599, 3597])).
% 1.96/1.64 tff(3601,plain,
% 1.96/1.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3602,plain,
% 1.96/1.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 1.96/1.64 tff(3603,plain,
% 1.96/1.64 (hskp5),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3602, 204, 3596, 3595, 3441, 3594, 3440, 3439, 2097])).
% 1.96/1.64 tff(3604,plain,
% 1.96/1.64 (~c2_1(a2408)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[400, 3603])).
% 1.96/1.64 tff(3605,plain,
% 1.96/1.64 (c0_1(a2408)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[411, 3603])).
% 1.96/1.64 tff(3606,plain,
% 1.96/1.64 (~c1_1(a2408)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2170, 204, 3605, 3486, 3257, 3256, 3604, 3458, 3457, 2008, 3455])).
% 1.96/1.64 tff(3607,plain,
% 1.96/1.64 (c3_1(a2408)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[429, 3603])).
% 1.96/1.64 tff(3608,plain,
% 1.96/1.64 (~c3_1(a2413)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3501, 204, 22, 3441, 3607, 3439, 3604, 1082, 3606])).
% 1.96/1.64 tff(3609,plain,
% 1.96/1.64 (hskp12),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3509, 3608])).
% 1.96/1.64 tff(3610,plain,
% 1.96/1.64 (~c1_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[229, 3609])).
% 1.96/1.64 tff(3611,plain,
% 1.96/1.64 (c3_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[246, 3609])).
% 1.96/1.64 tff(3612,plain,
% 1.96/1.64 (~c2_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[1091, 204, 22, 3611, 3607, 3610, 3604, 1082, 3606])).
% 1.96/1.64 tff(3613,plain,
% 1.96/1.64 (~c0_1(a2417)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[235, 3609])).
% 1.96/1.64 tff(3614,plain,
% 1.96/1.64 (~c2_1(a2414)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3520, 204, 2772, 3441, 3613, 3610, 957, 3440, 3439, 21, 3612])).
% 1.96/1.64 tff(3615,plain,
% 1.96/1.64 ($false),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2357, 204, 3272, 2772, 3256, 3613, 3610, 951, 1438, 3455, 3612, 3614])).
% 1.96/1.64 tff(3616,plain,(hskp1 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.64 tff(3617,plain,
% 1.96/1.64 (hskp1),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3616, 64])).
% 1.96/1.64 tff(3618,plain,
% 1.96/1.64 (~c3_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2423, 3617])).
% 1.96/1.64 tff(3619,plain,
% 1.96/1.64 (~c2_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2429, 3617])).
% 1.96/1.64 tff(3620,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3621,plain,
% 1.96/1.64 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3622,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3621])).
% 1.96/1.64 tff(3623,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3622, 3620])).
% 1.96/1.64 tff(3624,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3625,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3624, 3623])).
% 1.96/1.64 tff(3626,plain,
% 1.96/1.64 (c0_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3625, 204, 3434, 3436, 3329, 3327, 3435, 3328, 3619, 3618, 63])).
% 1.96/1.64 tff(3627,plain,
% 1.96/1.64 (c1_1(a2403)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2440, 3617])).
% 1.96/1.64 tff(3628,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3629,plain,
% 1.96/1.64 (((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3630,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3629])).
% 1.96/1.64 tff(3631,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3630, 3628])).
% 1.96/1.64 tff(3632,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3633,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 1.96/1.64 tff(3634,plain,
% 1.96/1.64 (~c1_1(a2455)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3633, 204, 3596, 3595, 2772, 3627, 957, 951, 3618, 1160, 3626])).
% 1.96/1.64 tff(3635,plain,
% 1.96/1.64 (c1_1(a2435)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[2602, 204, 3434, 3436, 3627, 3257, 3256, 3435, 3619, 3618, 11])).
% 1.96/1.64 tff(3636,plain,
% 1.96/1.64 (hskp30),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3403, 204, 3272, 3627, 3256, 3618, 612, 3635, 3626])).
% 1.96/1.64 tff(3637,plain,
% 1.96/1.64 (c3_1(a2450)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[633, 3636])).
% 1.96/1.64 tff(3638,plain,
% 1.96/1.64 (c1_1(a2450)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[644, 3636])).
% 1.96/1.64 tff(3639,plain,
% 1.96/1.64 (c0_1(a2450)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[655, 3636])).
% 1.96/1.64 tff(3640,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3641,plain,
% 1.96/1.64 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.64 inference(rewrite,[status(thm)],[])).
% 1.96/1.64 tff(3642,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.64 inference(monotonicity,[status(thm)],[3641])).
% 1.96/1.64 tff(3643,plain,
% 1.96/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.64 inference(transitivity,[status(thm)],[3642, 3640])).
% 1.96/1.64 tff(3644,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.96/1.64 inference(quant_inst,[status(thm)],[])).
% 1.96/1.64 tff(3645,plain,
% 1.96/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.64 inference(modus_ponens,[status(thm)],[3644, 3643])).
% 1.96/1.64 tff(3646,plain,
% 1.96/1.64 ($false),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3645, 204, 3639, 3638, 3637, 3596, 3595, 3619, 3618, 602, 3626, 3634])).
% 1.96/1.64 tff(3647,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.64 tff(3648,plain,
% 1.96/1.64 (~c3_1(a2425)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[444, 3647])).
% 1.96/1.64 tff(3649,plain,
% 1.96/1.64 (~c2_1(a2425)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[450, 3647])).
% 1.96/1.64 tff(3650,plain,
% 1.96/1.64 (c0_1(a2425)),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[461, 3647])).
% 1.96/1.64 tff(3651,plain,
% 1.96/1.64 (hskp19 | hskp5),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[485, 204, 3650, 3649, 3648, 53])).
% 1.96/1.64 tff(3652,plain,
% 1.96/1.64 (hskp5),
% 1.96/1.64 inference(unit_resolution,[status(thm)],[3651, 43])).
% 1.96/1.65 tff(3653,plain,
% 1.96/1.65 (c0_1(a2408)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[411, 3652])).
% 1.96/1.65 tff(3654,plain,
% 1.96/1.65 (~c1_1(a2455)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3207, 204, 43, 539, 2772, 517, 957, 951, 85])).
% 1.96/1.65 tff(3655,plain,
% 1.96/1.65 (c3_1(a2408)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[429, 3652])).
% 1.96/1.65 tff(3656,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3657,plain,
% 1.96/1.65 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3658,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.65 inference(monotonicity,[status(thm)],[3657])).
% 1.96/1.65 tff(3659,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(transitivity,[status(thm)],[3658, 3656])).
% 1.96/1.65 tff(3660,plain,
% 1.96/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.96/1.65 inference(quant_inst,[status(thm)],[])).
% 1.96/1.65 tff(3661,plain,
% 1.96/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.65 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 1.96/1.65 tff(3662,plain,
% 1.96/1.65 (~c1_1(a2408)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3661, 204, 539, 528, 3650, 3653, 3655, 3649, 3648, 602, 3654])).
% 1.96/1.65 tff(3663,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3664,plain,
% 1.96/1.65 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455))) <=> (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3665,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.65 inference(monotonicity,[status(thm)],[3664])).
% 1.96/1.65 tff(3666,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(transitivity,[status(thm)],[3665, 3663])).
% 1.96/1.65 tff(3667,plain,
% 1.96/1.65 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))),
% 1.96/1.65 inference(quant_inst,[status(thm)],[])).
% 1.96/1.65 tff(3668,plain,
% 1.96/1.65 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.65 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 1.96/1.65 tff(3669,plain,
% 1.96/1.65 (hskp29),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3668, 204, 539, 3653, 3655, 517, 1117, 3662, 3654])).
% 1.96/1.65 tff(3670,plain,
% 1.96/1.65 (c3_1(a2409)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[1148, 3669])).
% 1.96/1.65 tff(3671,plain,
% 1.96/1.65 (c0_1(a2409)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[1792, 3669])).
% 1.96/1.65 tff(3672,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3673,plain,
% 1.96/1.65 (((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3674,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.65 inference(monotonicity,[status(thm)],[3673])).
% 1.96/1.65 tff(3675,plain,
% 1.96/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(transitivity,[status(thm)],[3674, 3672])).
% 1.96/1.65 tff(3676,plain,
% 1.96/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.96/1.65 inference(quant_inst,[status(thm)],[])).
% 1.96/1.65 tff(3677,plain,
% 1.96/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.65 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 1.96/1.65 tff(3678,plain,
% 1.96/1.65 (~c1_1(a2409)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3677, 204, 3671, 3670, 539, 528, 3650, 3649, 3648, 602, 3654])).
% 1.96/1.65 tff(3679,plain,
% 1.96/1.65 (~c2_1(a2408)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[400, 3652])).
% 1.96/1.65 tff(3680,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3681,plain,
% 1.96/1.65 ((hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3682,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.96/1.65 inference(monotonicity,[status(thm)],[3681])).
% 1.96/1.65 tff(3683,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.96/1.65 inference(transitivity,[status(thm)],[3682, 3680])).
% 1.96/1.65 tff(3684,plain,
% 1.96/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.96/1.65 inference(quant_inst,[status(thm)],[])).
% 1.96/1.65 tff(3685,plain,
% 1.96/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.96/1.65 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 1.96/1.65 tff(3686,plain,
% 1.96/1.65 (hskp1),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3685, 204, 539, 528, 3655, 3679, 1082, 3662, 3654])).
% 1.96/1.65 tff(3687,plain,
% 1.96/1.65 (~c3_1(a2403)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2423, 3686])).
% 1.96/1.65 tff(3688,plain,
% 1.96/1.65 (~c2_1(a2403)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2429, 3686])).
% 1.96/1.65 tff(3689,plain,
% 1.96/1.65 (c1_1(a2403)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2440, 3686])).
% 1.96/1.65 tff(3690,plain,
% 1.96/1.65 (c2_1(a2409)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[1137, 3669])).
% 1.96/1.65 tff(3691,plain,
% 1.96/1.65 ($false),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2576, 204, 3671, 3690, 3670, 3689, 3688, 3687, 2451, 3678])).
% 1.96/1.65 tff(3692,plain,((~hskp23) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.96/1.65 tff(3693,plain,
% 1.96/1.65 (~hskp23),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3692, 43])).
% 1.96/1.65 tff(3694,plain,
% 1.96/1.65 ($false),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2792, 2743, 2754, 43, 686, 2732, 996])).
% 1.96/1.65 tff(3695,plain,(hskp25 | hskp19 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.96/1.65 tff(3696,plain,
% 1.96/1.65 (hskp25),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3695, 3693, 43])).
% 1.96/1.65 tff(3697,plain,
% 1.96/1.65 (~c0_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[123, 3696])).
% 1.96/1.65 tff(3698,plain,
% 1.96/1.65 (c2_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[117, 3696])).
% 1.96/1.65 tff(3699,plain,
% 1.96/1.65 (hskp25),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[3695, 686, 43])).
% 1.96/1.65 tff(3700,plain,
% 1.96/1.65 (~c0_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[123, 3699])).
% 1.96/1.65 tff(3701,plain,
% 1.96/1.65 (c2_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[117, 3699])).
% 1.96/1.65 tff(3702,plain,
% 1.96/1.65 (~c1_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2825, 204, 43, 3701, 2772, 3700, 957, 951, 85])).
% 1.96/1.65 tff(3703,plain,
% 1.96/1.65 (~c3_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[129, 3699])).
% 1.96/1.65 tff(3704,assumption,(hskp1), introduced(assumption)).
% 1.96/1.65 tff(3705,plain,
% 1.96/1.65 (~c2_1(a2403)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2429, 3704])).
% 1.96/1.65 tff(3706,plain,
% 1.96/1.65 (~c3_1(a2403)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2423, 3704])).
% 1.96/1.65 tff(3707,plain,
% 1.96/1.65 (hskp10),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[862, 686, 785, 43, 294, 274, 275])).
% 1.96/1.65 tff(3708,plain,
% 1.96/1.65 (~c3_1(a2414)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[950, 3707])).
% 1.96/1.65 tff(3709,plain,
% 1.96/1.65 (~c1_1(a2414)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[956, 3707])).
% 1.96/1.65 tff(3710,plain,
% 1.96/1.65 (c0_1(a2414)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[1105, 3707])).
% 1.96/1.65 tff(3711,plain,
% 1.96/1.65 (~c1_1(a2478)),
% 1.96/1.65 inference(unit_resolution,[status(thm)],[2825, 204, 43, 275, 3710, 294, 3709, 3708, 85])).
% 1.96/1.65 tff(3712,assumption,(~c1_1(a2403)), introduced(assumption)).
% 1.96/1.65 tff(3713,assumption,(c0_1(a2403)), introduced(assumption)).
% 1.96/1.65 tff(3714,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3715,plain,
% 1.96/1.65 ((hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403))) <=> (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.96/1.65 inference(rewrite,[status(thm)],[])).
% 1.96/1.65 tff(3716,plain,
% 1.96/1.65 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))))),
% 1.96/1.65 inference(monotonicity,[status(thm)],[3715])).
% 1.96/1.65 tff(3717,plain,
% 2.04/1.65 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 2.04/1.65 inference(transitivity,[status(thm)],[3716, 3714])).
% 2.04/1.65 tff(3718,plain,
% 2.04/1.65 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))),
% 2.04/1.65 inference(quant_inst,[status(thm)],[])).
% 2.04/1.65 tff(3719,plain,
% 2.04/1.65 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))),
% 2.04/1.65 inference(modus_ponens,[status(thm)],[3718, 3717])).
% 2.04/1.65 tff(3720,plain,
% 2.04/1.65 (hskp10 | c1_1(a2403) | (~c0_1(a2403))),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3719, 204, 2453, 2452, 95])).
% 2.04/1.65 tff(3721,plain,
% 2.04/1.65 (hskp10),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3720, 3713, 3712])).
% 2.04/1.65 tff(3722,plain,
% 2.04/1.65 (~c3_1(a2414)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[950, 3721])).
% 2.04/1.65 tff(3723,plain,
% 2.04/1.65 (~c1_1(a2414)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[956, 3721])).
% 2.04/1.65 tff(3724,plain,
% 2.04/1.65 (hskp5),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3083, 3713, 2452])).
% 2.04/1.65 tff(3725,plain,
% 2.04/1.65 (c0_1(a2408)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[411, 3724])).
% 2.04/1.65 tff(3726,plain,
% 2.04/1.65 (~c2_1(a2408)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[400, 3724])).
% 2.04/1.65 tff(3727,plain,
% 2.04/1.65 (c3_1(a2408)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[429, 3724])).
% 2.04/1.65 tff(3728,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3729,plain,
% 2.04/1.65 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3730,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 2.04/1.65 inference(monotonicity,[status(thm)],[3729])).
% 2.04/1.65 tff(3731,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.04/1.65 inference(transitivity,[status(thm)],[3730, 3728])).
% 2.04/1.65 tff(3732,plain,
% 2.04/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 2.04/1.65 inference(quant_inst,[status(thm)],[])).
% 2.04/1.65 tff(3733,plain,
% 2.04/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 2.04/1.65 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 2.04/1.65 tff(3734,plain,
% 2.04/1.65 (c0_1(a2435) | (~c1_1(a2408)) | (~c1_1(a2435))),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3733, 204, 833, 3712, 785, 668, 2453, 2008, 3713])).
% 2.04/1.65 tff(3735,plain,
% 2.04/1.65 (~c1_1(a2435)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3734, 2279, 822])).
% 2.04/1.65 tff(3736,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3737,plain,
% 2.04/1.65 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3738,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 2.04/1.65 inference(monotonicity,[status(thm)],[3737])).
% 2.04/1.65 tff(3739,plain,
% 2.04/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 2.04/1.65 inference(transitivity,[status(thm)],[3738, 3736])).
% 2.04/1.65 tff(3740,plain,
% 2.04/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 2.04/1.65 inference(quant_inst,[status(thm)],[])).
% 2.04/1.65 tff(3741,plain,
% 2.04/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 2.04/1.65 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 2.04/1.65 tff(3742,plain,
% 2.04/1.65 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3741, 204, 669, 785, 668, 2453, 2452, 1438, 3713])).
% 2.04/1.65 tff(3743,plain,
% 2.04/1.65 ($false),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3742, 3735, 2279, 822])).
% 2.04/1.65 tff(3744,plain,(c0_1(a2435) | (~c1_1(a2408)) | (~c3_1(a2408)) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | (~c0_1(a2408)) | c1_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.65 tff(3745,plain,
% 2.04/1.65 (c0_1(a2435)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3744, 822, 3727, 785, 3726, 2453, 2452, 3713, 3725, 3712])).
% 2.04/1.65 tff(3746,plain,
% 2.04/1.65 (~hskp20),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[820, 3745])).
% 2.04/1.65 tff(3747,plain,
% 2.04/1.65 (hskp23 | hskp14 | (~c1_1(a2408))),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[729, 204, 3725, 3727, 42])).
% 2.04/1.65 tff(3748,plain,
% 2.04/1.65 (hskp14),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3747, 822, 686])).
% 2.04/1.65 tff(3749,plain,
% 2.04/1.65 (~c3_1(a2420)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[736, 3748])).
% 2.04/1.65 tff(3750,plain,
% 2.04/1.65 (c2_1(a2420)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[747, 3748])).
% 2.04/1.65 tff(3751,plain,
% 2.04/1.65 (c1_1(a2420)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[758, 3748])).
% 2.04/1.65 tff(3752,plain,
% 2.04/1.65 (hskp20 | (~c0_1(a2420))),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[802, 204, 3751, 3750, 3749, 722])).
% 2.04/1.65 tff(3753,plain,
% 2.04/1.65 (~c0_1(a2420)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3752, 3746])).
% 2.04/1.65 tff(3754,plain,
% 2.04/1.65 (c0_1(a2414)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[1105, 3721])).
% 2.04/1.65 tff(3755,plain,
% 2.04/1.65 ($false),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[2780, 204, 43, 3751, 3750, 3754, 3723, 3722, 85, 3753])).
% 2.04/1.65 tff(3756,plain,((~c1_1(a2408)) | hskp19 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2403) | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.04/1.65 tff(3757,plain,
% 2.04/1.65 (~c1_1(a2408)),
% 2.04/1.65 inference(unit_resolution,[status(thm)],[3756, 686, 785, 2453, 2452, 3713, 3712, 43])).
% 2.04/1.65 tff(3758,plain,
% 2.04/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3759,plain,
% 2.04/1.65 ((hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.04/1.65 inference(rewrite,[status(thm)],[])).
% 2.04/1.65 tff(3760,plain,
% 2.04/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 2.04/1.65 inference(monotonicity,[status(thm)],[3759])).
% 2.04/1.65 tff(3761,plain,
% 2.04/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.04/1.65 inference(transitivity,[status(thm)],[3760, 3758])).
% 2.04/1.65 tff(3762,plain,
% 2.04/1.65 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3763,plain,
% 2.04/1.66 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 2.04/1.66 tff(3764,plain,
% 2.04/1.66 (c1_1(a2403) | (~c0_1(a2403)) | (~c1_1(a2478))),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3763, 204, 43, 275, 294, 2452, 85])).
% 2.04/1.66 tff(3765,plain,
% 2.04/1.66 (~c1_1(a2478)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3764, 3713, 3712])).
% 2.04/1.66 tff(3766,plain,
% 2.04/1.66 (hskp29),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[2921, 3757, 275, 3725, 3727, 294, 3765])).
% 2.04/1.66 tff(3767,plain,
% 2.04/1.66 (c0_1(a2409)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[1792, 3766])).
% 2.04/1.66 tff(3768,plain,
% 2.04/1.66 (c3_1(a2409)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[1148, 3766])).
% 2.04/1.66 tff(3769,plain,
% 2.04/1.66 (c2_1(a2409)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[1137, 3766])).
% 2.04/1.66 tff(3770,plain,
% 2.04/1.66 (hskp14 | (~c1_1(a2409))),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3045, 204, 686, 1805, 1208, 42])).
% 2.04/1.66 tff(3771,plain,
% 2.04/1.66 (hskp14),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3770, 1816])).
% 2.04/1.66 tff(3772,plain,
% 2.04/1.66 (~c3_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[736, 3771])).
% 2.04/1.66 tff(3773,plain,
% 2.04/1.66 (c1_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[758, 3771])).
% 2.04/1.66 tff(3774,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3775,plain,
% 2.04/1.66 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403))) <=> (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3776,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 2.04/1.66 inference(monotonicity,[status(thm)],[3775])).
% 2.04/1.66 tff(3777,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.66 inference(transitivity,[status(thm)],[3776, 3774])).
% 2.04/1.66 tff(3778,plain,
% 2.04/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3779,plain,
% 2.04/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 2.04/1.66 tff(3780,plain,
% 2.04/1.66 (~c0_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3779, 204, 1209, 1208, 3773, 3712, 3772, 2452, 1160, 1816, 3713])).
% 2.04/1.66 tff(3781,plain,
% 2.04/1.66 (c2_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[747, 3771])).
% 2.04/1.66 tff(3782,plain,
% 2.04/1.66 ($false),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[2780, 204, 43, 3773, 3781, 1185, 1162, 1161, 85, 3780])).
% 2.04/1.66 tff(3783,plain,((~c1_1(a2409)) | hskp19 | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | (~c2_1(a2409)) | (~c3_1(a2409)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | hskp23 | (~c0_1(a2409))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.66 tff(3784,plain,
% 2.04/1.66 (~c1_1(a2409)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3783, 3769, 43, 3723, 3722, 3754, 3768, 3712, 2452, 3713, 686, 3767])).
% 2.04/1.66 tff(3785,plain,
% 2.04/1.66 (~hskp1),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[2440, 3712])).
% 2.04/1.66 tff(3786,plain,
% 2.04/1.66 ($false),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[1222, 204, 3785, 3769, 3768, 3727, 3726, 1082, 3784, 3757])).
% 2.04/1.66 tff(3787,plain,(hskp23 | hskp19 | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435) | c2_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.66 tff(3788,plain,
% 2.04/1.66 (hskp23),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3787, 3713, 3712, 2452, 43, 275, 294, 785, 2453])).
% 2.04/1.66 tff(3789,plain,
% 2.04/1.66 (~c0_1(a2455)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[516, 3788])).
% 2.04/1.66 tff(3790,plain,
% 2.04/1.66 (c2_1(a2455)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[538, 3788])).
% 2.04/1.66 tff(3791,plain,
% 2.04/1.66 (~c1_1(a2455)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3207, 204, 43, 3790, 3754, 3789, 3723, 3722, 85])).
% 2.04/1.66 tff(3792,plain,
% 2.04/1.66 (c3_1(a2455)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[527, 3788])).
% 2.04/1.66 tff(3793,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3794,plain,
% 2.04/1.66 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3795,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 2.04/1.66 inference(monotonicity,[status(thm)],[3794])).
% 2.04/1.66 tff(3796,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.04/1.66 inference(transitivity,[status(thm)],[3795, 3793])).
% 2.04/1.66 tff(3797,plain,
% 2.04/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3798,plain,
% 2.04/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3797, 3796])).
% 2.04/1.66 tff(3799,plain,
% 2.04/1.66 (~c1_1(a2408)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3798, 204, 3790, 3792, 3725, 3727, 2453, 2452, 602, 3713, 3791])).
% 2.04/1.66 tff(3800,plain,
% 2.04/1.66 ($false),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3685, 204, 3785, 3790, 3792, 3727, 3726, 1082, 3799, 3791])).
% 2.04/1.66 tff(3801,plain,((~c0_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp19 | c1_1(a2403) | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.66 tff(3802,plain,
% 2.04/1.66 (~c0_1(a2403)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3801, 3712, 2452, 43, 2453, 275, 294, 785])).
% 2.04/1.66 tff(3803,plain,
% 2.04/1.66 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3804,plain,
% 2.04/1.66 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403)) <=> (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3805,plain,
% 2.04/1.66 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)))),
% 2.04/1.66 inference(monotonicity,[status(thm)],[3804])).
% 2.04/1.66 tff(3806,plain,
% 2.04/1.66 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(transitivity,[status(thm)],[3805, 3803])).
% 2.04/1.66 tff(3807,plain,
% 2.04/1.66 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3808,plain,
% 2.04/1.66 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 2.04/1.66 tff(3809,plain,
% 2.04/1.66 (hskp13 | hskp1 | c3_1(a2403) | c0_1(a2403)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3808, 204, 2453, 1039])).
% 2.04/1.66 tff(3810,plain,
% 2.04/1.66 (hskp13),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3809, 3802, 2452, 3785])).
% 2.04/1.66 tff(3811,plain,
% 2.04/1.66 (~c0_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[339, 3810])).
% 2.04/1.66 tff(3812,plain,
% 2.04/1.66 (c2_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[350, 3810])).
% 2.04/1.66 tff(3813,plain,
% 2.04/1.66 (c1_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[361, 3810])).
% 2.04/1.66 tff(3814,plain,
% 2.04/1.66 (~hskp10),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[2811, 3813, 43, 3812, 3811])).
% 2.04/1.66 tff(3815,plain,
% 2.04/1.66 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.04/1.66 inference(bind,[status(th)],[])).
% 2.04/1.66 tff(3816,plain,
% 2.04/1.66 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(quant_intro,[status(thm)],[3815])).
% 2.04/1.66 tff(3817,plain,
% 2.04/1.66 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3818,plain,
% 2.04/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.04/1.66 inference(bind,[status(th)],[])).
% 2.04/1.66 tff(3819,plain,
% 2.04/1.66 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(quant_intro,[status(thm)],[3818])).
% 2.04/1.66 tff(3820,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 2.04/1.66 tff(3821,plain,
% 2.04/1.66 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 2.04/1.66 tff(3822,plain,
% 2.04/1.66 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3821, 3817])).
% 2.04/1.66 tff(3823,plain,(
% 2.04/1.66 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(skolemize,[status(sab)],[3822])).
% 2.04/1.66 tff(3824,plain,
% 2.04/1.66 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3823, 3816])).
% 2.04/1.66 tff(3825,plain,
% 2.04/1.66 (^[U: $i] : refl((hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 2.04/1.66 inference(bind,[status(th)],[])).
% 2.04/1.66 tff(3826,plain,
% 2.04/1.66 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(quant_intro,[status(thm)],[3825])).
% 2.04/1.66 tff(3827,plain,
% 2.04/1.66 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3828,plain,
% 2.04/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 2.04/1.66 inference(bind,[status(th)],[])).
% 2.04/1.66 tff(3829,plain,
% 2.04/1.66 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(quant_intro,[status(thm)],[3828])).
% 2.04/1.66 tff(3830,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 2.04/1.66 tff(3831,plain,
% 2.04/1.66 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 2.04/1.66 tff(3832,plain,
% 2.04/1.66 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3831, 3827])).
% 2.04/1.66 tff(3833,plain,(
% 2.04/1.66 ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(skolemize,[status(sab)],[3832])).
% 2.04/1.66 tff(3834,plain,
% 2.04/1.66 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3833, 3826])).
% 2.04/1.66 tff(3835,plain,
% 2.04/1.66 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3836,plain,
% 2.04/1.66 ((hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403)) <=> (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3837,plain,
% 2.04/1.66 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)))),
% 2.04/1.66 inference(monotonicity,[status(thm)],[3836])).
% 2.04/1.66 tff(3838,plain,
% 2.04/1.66 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 2.04/1.66 inference(transitivity,[status(thm)],[3837, 3835])).
% 2.04/1.66 tff(3839,plain,
% 2.04/1.66 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3840,plain,
% 2.04/1.66 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 2.04/1.66 tff(3841,plain,
% 2.04/1.66 (hskp14 | hskp1 | c3_1(a2403) | c0_1(a2403)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3840, 204, 2453, 3834])).
% 2.04/1.66 tff(3842,plain,
% 2.04/1.66 (hskp14),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3841, 2617, 2452, 22])).
% 2.04/1.66 tff(3843,plain,
% 2.04/1.66 (~c3_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[736, 3842])).
% 2.04/1.66 tff(3844,plain,
% 2.04/1.66 (c2_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[747, 3842])).
% 2.04/1.66 tff(3845,plain,
% 2.04/1.66 (c1_1(a2420)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[758, 3842])).
% 2.04/1.66 tff(3846,plain,
% 2.04/1.66 (hskp23 | hskp6),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3056, 204, 3845, 3844, 3843, 2219])).
% 2.04/1.66 tff(3847,plain,
% 2.04/1.66 (hskp6),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3846, 686])).
% 2.04/1.66 tff(3848,plain,
% 2.04/1.66 (~c2_1(a2410)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[964, 3847])).
% 2.04/1.66 tff(3849,plain,
% 2.04/1.66 (c1_1(a2410)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[975, 3847])).
% 2.04/1.66 tff(3850,plain,
% 2.04/1.66 (c0_1(a2410)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[986, 3847])).
% 2.04/1.66 tff(3851,plain,
% 2.04/1.66 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3852,plain,
% 2.04/1.66 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.04/1.66 inference(rewrite,[status(thm)],[])).
% 2.04/1.66 tff(3853,plain,
% 2.04/1.66 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 2.04/1.66 inference(monotonicity,[status(thm)],[3852])).
% 2.04/1.66 tff(3854,plain,
% 2.04/1.66 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.04/1.66 inference(transitivity,[status(thm)],[3853, 3851])).
% 2.04/1.66 tff(3855,plain,
% 2.04/1.66 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.04/1.66 inference(quant_inst,[status(thm)],[])).
% 2.04/1.66 tff(3856,plain,
% 2.04/1.66 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 2.04/1.66 inference(modus_ponens,[status(thm)],[3855, 3854])).
% 2.04/1.66 tff(3857,plain,
% 2.04/1.66 (hskp5),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3856, 204, 22, 3850, 3849, 3848, 3824])).
% 2.04/1.66 tff(3858,plain,
% 2.04/1.66 (c3_1(a2408)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[429, 3857])).
% 2.04/1.66 tff(3859,plain,
% 2.04/1.66 (~c2_1(a2408)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[400, 3857])).
% 2.04/1.66 tff(3860,plain,
% 2.04/1.66 (c1_1(a2408)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[694, 3859, 96, 686, 3858])).
% 2.04/1.66 tff(3861,plain,
% 2.04/1.66 (hskp13),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[3809, 2617, 2452, 22])).
% 2.04/1.66 tff(3862,plain,
% 2.04/1.66 (~c0_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[339, 3861])).
% 2.04/1.66 tff(3863,plain,
% 2.04/1.66 (c2_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[350, 3861])).
% 2.04/1.66 tff(3864,plain,
% 2.04/1.66 (c1_1(a2418)),
% 2.04/1.66 inference(unit_resolution,[status(thm)],[361, 3861])).
% 2.04/1.66 tff(3865,plain,
% 2.04/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3866,plain,
% 2.04/1.67 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3867,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3866])).
% 2.04/1.67 tff(3868,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3867, 3865])).
% 2.04/1.67 tff(3869,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3870,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 2.04/1.67 tff(3871,plain,
% 2.04/1.67 ($false),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3870, 204, 3864, 3863, 3858, 3862, 3859, 2453, 2452, 63, 2617, 3860])).
% 2.04/1.67 tff(3872,plain,(hskp23 | c2_1(a2403) | c3_1(a2403) | c0_1(a2403) | hskp10 | hskp1), inference(lemma,lemma(discharge,[]))).
% 2.04/1.67 tff(3873,plain,
% 2.04/1.67 (hskp23),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3872, 3802, 2452, 2453, 3814, 3785])).
% 2.04/1.67 tff(3874,plain,
% 2.04/1.67 (hskp15),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[548, 3873])).
% 2.04/1.67 tff(3875,plain,
% 2.04/1.67 (~c2_1(a2422)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[576, 3874])).
% 2.04/1.67 tff(3876,plain,
% 2.04/1.67 (c3_1(a2422)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[559, 3874])).
% 2.04/1.67 tff(3877,plain,
% 2.04/1.67 (c1_1(a2422)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[570, 3874])).
% 2.04/1.67 tff(3878,plain,
% 2.04/1.67 ($false),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3625, 204, 3877, 3876, 3813, 3812, 3875, 3811, 2453, 2452, 63, 3802])).
% 2.04/1.67 tff(3879,plain,(c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | hskp19 | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.67 tff(3880,plain,
% 2.04/1.67 (c1_1(a2403)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3879, 785, 2452, 43, 275, 294, 2453])).
% 2.04/1.67 tff(3881,plain,
% 2.04/1.67 (~hskp13),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[2813, 3707, 43])).
% 2.04/1.67 tff(3882,plain,
% 2.04/1.67 (hskp16),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3124, 3881, 785, 3880, 2453, 2452, 686, 3708, 3710, 3709, 43, 275, 274, 3711])).
% 2.04/1.67 tff(3883,plain,
% 2.04/1.67 (~c3_1(a2425)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[444, 3882])).
% 2.04/1.67 tff(3884,plain,
% 2.04/1.67 (~c2_1(a2425)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[450, 3882])).
% 2.04/1.67 tff(3885,plain,
% 2.04/1.67 (c0_1(a2425)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[461, 3882])).
% 2.04/1.67 tff(3886,plain,
% 2.04/1.67 (hskp5),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[485, 204, 43, 3885, 3884, 3883, 53])).
% 2.04/1.67 tff(3887,plain,
% 2.04/1.67 (~c2_1(a2408)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[400, 3886])).
% 2.04/1.67 tff(3888,plain,
% 2.04/1.67 (c3_1(a2408)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[429, 3886])).
% 2.04/1.67 tff(3889,plain,
% 2.04/1.67 (c1_1(a2408)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[2470, 204, 686, 3888, 3880, 3887, 2453, 2452, 685])).
% 2.04/1.67 tff(3890,plain,
% 2.04/1.67 (c0_1(a2408)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[411, 3886])).
% 2.04/1.67 tff(3891,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3892,plain,
% 2.04/1.67 ((hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3893,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3892])).
% 2.04/1.67 tff(3894,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3893, 3891])).
% 2.04/1.67 tff(3895,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3896,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 2.04/1.67 tff(3897,plain,
% 2.04/1.67 (hskp2 | (~c1_1(a2408))),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3896, 204, 275, 3890, 274, 3887, 1384, 3711])).
% 2.04/1.67 tff(3898,plain,
% 2.04/1.67 (hskp2),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3897, 3889])).
% 2.04/1.67 tff(3899,plain,
% 2.04/1.67 (~c2_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[1403, 3898])).
% 2.04/1.67 tff(3900,plain,
% 2.04/1.67 (~c1_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[1908, 3898])).
% 2.04/1.67 tff(3901,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3902,plain,
% 2.04/1.67 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3903,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3902])).
% 2.04/1.67 tff(3904,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3903, 3901])).
% 2.04/1.67 tff(3905,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3906,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 2.04/1.67 tff(3907,plain,
% 2.04/1.67 (c0_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3906, 204, 3888, 3880, 3887, 3900, 3899, 2453, 2452, 11, 3889])).
% 2.04/1.67 tff(3908,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3909,plain,
% 2.04/1.67 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403))) <=> (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3910,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3909])).
% 2.04/1.67 tff(3911,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3910, 3908])).
% 2.04/1.67 tff(3912,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3913,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3912, 3911])).
% 2.04/1.67 tff(3914,plain,
% 2.04/1.67 (c0_1(a2403) | (~c0_1(a2404))),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3913, 204, 3890, 3880, 3887, 3900, 3899, 2453, 2008, 3889])).
% 2.04/1.67 tff(3915,plain,
% 2.04/1.67 (c0_1(a2403)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3914, 3907])).
% 2.04/1.67 tff(3916,plain,
% 2.04/1.67 (hskp14 | (~c1_1(a2408))),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[729, 204, 686, 3890, 3888, 42])).
% 2.04/1.67 tff(3917,plain,
% 2.04/1.67 (hskp14),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3916, 3889])).
% 2.04/1.67 tff(3918,plain,
% 2.04/1.67 (c2_1(a2420)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[747, 3917])).
% 2.04/1.67 tff(3919,plain,
% 2.04/1.67 (c1_1(a2420)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[758, 3917])).
% 2.04/1.67 tff(3920,plain,
% 2.04/1.67 (c0_1(a2420)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[2782, 3919, 3708, 3918, 3710, 3709, 43])).
% 2.04/1.67 tff(3921,plain,
% 2.04/1.67 (~c3_1(a2420)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[736, 3917])).
% 2.04/1.67 tff(3922,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3923,plain,
% 2.04/1.67 ((hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408))) <=> (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3924,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3923])).
% 2.04/1.67 tff(3925,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3924, 3922])).
% 2.04/1.67 tff(3926,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3927,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 2.04/1.67 tff(3928,plain,
% 2.04/1.67 (hskp30),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3927, 204, 3919, 3888, 3921, 3887, 612, 3889, 3920])).
% 2.04/1.67 tff(3929,plain,
% 2.04/1.67 (c0_1(a2450)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[655, 3928])).
% 2.04/1.67 tff(3930,plain,
% 2.04/1.67 (c3_1(a2450)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[633, 3928])).
% 2.04/1.67 tff(3931,plain,
% 2.04/1.67 (c1_1(a2450)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[644, 3928])).
% 2.04/1.67 tff(3932,plain,
% 2.04/1.67 (hskp6),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3056, 204, 686, 3919, 3918, 3921, 2219])).
% 2.04/1.67 tff(3933,plain,
% 2.04/1.67 (~c2_1(a2410)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[964, 3932])).
% 2.04/1.67 tff(3934,plain,
% 2.04/1.67 (c0_1(a2410)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[986, 3932])).
% 2.04/1.67 tff(3935,plain,
% 2.04/1.67 (c1_1(a2410)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[975, 3932])).
% 2.04/1.67 tff(3936,assumption,(c3_1(a2450)), introduced(assumption)).
% 2.04/1.67 tff(3937,assumption,(c1_1(a2450)), introduced(assumption)).
% 2.04/1.67 tff(3938,plain,
% 2.04/1.67 (~c2_1(a2450)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3539, 204, 3937, 3936, 1106, 3880, 1150, 1107, 2452, 1160, 3713])).
% 2.04/1.67 tff(3939,plain,
% 2.04/1.67 (~c1_1(a2478)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[2825, 204, 43, 275, 1106, 294, 1150, 1107, 85])).
% 2.04/1.67 tff(3940,assumption,(c0_1(a2450)), introduced(assumption)).
% 2.04/1.67 tff(3941,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3942,plain,
% 2.04/1.67 ((hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3943,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3942])).
% 2.04/1.67 tff(3944,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3943, 3941])).
% 2.04/1.67 tff(3945,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3946,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3945, 3944])).
% 2.04/1.67 tff(3947,plain,
% 2.04/1.67 (hskp2),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3946, 204, 3940, 3937, 275, 274, 1384, 3939, 3938])).
% 2.04/1.67 tff(3948,plain,
% 2.04/1.67 (~c2_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[1403, 3947])).
% 2.04/1.67 tff(3949,plain,
% 2.04/1.67 (~c1_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[1908, 3947])).
% 2.04/1.67 tff(3950,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3951,plain,
% 2.04/1.67 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3952,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3951])).
% 2.04/1.67 tff(3953,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3952, 3950])).
% 2.04/1.67 tff(3954,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3955,plain,
% 2.04/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 2.04/1.67 tff(3956,plain,
% 2.04/1.67 (c0_1(a2404)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3955, 204, 3937, 3936, 3880, 3949, 3948, 2453, 2452, 11, 3938])).
% 2.04/1.67 tff(3957,plain,
% 2.04/1.67 (c0_1(a2420)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[2782, 1106, 787, 786, 43, 1150, 1107])).
% 2.04/1.67 tff(3958,plain,
% 2.04/1.67 (hskp20),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[803, 3957])).
% 2.04/1.67 tff(3959,plain,
% 2.04/1.67 (~c0_1(a2435)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[820, 3958])).
% 2.04/1.67 tff(3960,plain,
% 2.04/1.67 (c3_1(a2435)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[814, 3958])).
% 2.04/1.67 tff(3961,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3962,plain,
% 2.04/1.67 ((hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435))) <=> (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3963,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))))),
% 2.04/1.67 inference(monotonicity,[status(thm)],[3962])).
% 2.04/1.67 tff(3964,plain,
% 2.04/1.67 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 2.04/1.67 inference(transitivity,[status(thm)],[3963, 3961])).
% 2.04/1.67 tff(3965,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))),
% 2.04/1.67 inference(quant_inst,[status(thm)],[])).
% 2.04/1.67 tff(3966,plain,
% 2.04/1.67 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))),
% 2.04/1.67 inference(modus_ponens,[status(thm)],[3965, 3964])).
% 2.04/1.67 tff(3967,plain,
% 2.04/1.67 (hskp23 | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3966, 204, 785, 2453, 2452, 685])).
% 2.04/1.67 tff(3968,plain,
% 2.04/1.67 (c1_1(a2435)),
% 2.04/1.67 inference(unit_resolution,[status(thm)],[3967, 3960, 3880, 686])).
% 2.04/1.67 tff(3969,plain,
% 2.04/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 2.04/1.67 inference(rewrite,[status(thm)],[])).
% 2.04/1.67 tff(3970,plain,
% 2.04/1.67 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(3971,plain,
% 2.04/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435))))),
% 2.04/1.68 inference(monotonicity,[status(thm)],[3970])).
% 2.04/1.68 tff(3972,plain,
% 2.04/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 2.04/1.68 inference(transitivity,[status(thm)],[3971, 3969])).
% 2.04/1.68 tff(3973,plain,
% 2.04/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 2.04/1.68 inference(quant_inst,[status(thm)],[])).
% 2.04/1.68 tff(3974,plain,
% 2.04/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[3973, 3972])).
% 2.04/1.68 tff(3975,plain,
% 2.04/1.68 (c0_1(a2435) | (~c0_1(a2404)) | (~c1_1(a2435))),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3974, 204, 2864, 2863, 785, 2877, 3949, 3948, 2008])).
% 2.04/1.68 tff(3976,plain,
% 2.04/1.68 ($false),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3975, 3968, 3959, 3956])).
% 2.04/1.68 tff(3977,plain,((~hskp10) | (~c0_1(a2410)) | (~c1_1(a2410)) | c2_1(a2435) | c2_1(a2410) | hskp23 | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2420)) | (~c2_1(a2420)) | c3_1(a2420) | hskp19 | (~c1_1(a2450)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c2_1(a2478)) | c3_1(a2478) | c0_1(a2478) | (~c0_1(a2403))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.68 tff(3978,plain,
% 2.04/1.68 ($false),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3977, 3935, 3934, 3707, 785, 3933, 686, 2453, 2452, 3919, 3918, 3921, 43, 3931, 3930, 3929, 275, 274, 294, 3915])).
% 2.04/1.68 tff(3979,plain,(hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | hskp19 | (~c2_1(a2478)) | c3_1(a2478) | c0_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.68 tff(3980,plain,
% 2.04/1.68 ($false),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3979, 3706, 3705, 43, 785, 686, 3701, 3703, 3700])).
% 2.04/1.68 tff(3981,plain,((~hskp1) | hskp19 | c2_1(a2435) | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.04/1.68 tff(3982,plain,
% 2.04/1.68 (~hskp1),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3981, 686, 785, 43])).
% 2.04/1.68 tff(3983,plain,
% 2.04/1.68 (~hskp18),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3188, 3982, 2814])).
% 2.04/1.68 tff(3984,assumption,(hskp17), introduced(assumption)).
% 2.04/1.68 tff(3985,plain,
% 2.04/1.68 (~c1_1(a2427)),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[1934, 3984])).
% 2.04/1.68 tff(3986,plain,
% 2.04/1.68 (c3_1(a2427)),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[1945, 3984])).
% 2.04/1.68 tff(3987,plain,
% 2.04/1.68 (c2_1(a2427)),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[1956, 3984])).
% 2.04/1.68 tff(3988,plain,
% 2.04/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(3989,plain,
% 2.04/1.68 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427))) <=> (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(3990,plain,
% 2.04/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 2.04/1.68 inference(monotonicity,[status(thm)],[3989])).
% 2.04/1.68 tff(3991,plain,
% 2.04/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(transitivity,[status(thm)],[3990, 3988])).
% 2.04/1.68 tff(3992,plain,
% 2.04/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(quant_inst,[status(thm)],[])).
% 2.04/1.68 tff(3993,plain,
% 2.04/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 2.04/1.68 tff(3994,plain,
% 2.04/1.68 (~c1_1(a2408)),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[3993, 204, 3987, 3986, 3650, 833, 669, 3985, 3649, 3648, 602])).
% 2.04/1.68 tff(3995,plain,
% 2.04/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(3996,plain,
% 2.04/1.68 ((hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(3997,plain,
% 2.04/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 2.04/1.68 inference(monotonicity,[status(thm)],[3996])).
% 2.04/1.68 tff(3998,plain,
% 2.04/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 2.04/1.68 inference(transitivity,[status(thm)],[3997, 3995])).
% 2.04/1.68 tff(3999,plain,
% 2.04/1.68 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 2.04/1.68 inference(quant_inst,[status(thm)],[])).
% 2.04/1.68 tff(4000,plain,
% 2.04/1.68 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 2.04/1.68 tff(4001,plain,
% 2.04/1.68 ($false),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[4000, 204, 22, 3987, 3986, 669, 3985, 668, 1082, 3994])).
% 2.04/1.68 tff(4002,plain,((~hskp17) | hskp1 | (~c3_1(a2408)) | c2_1(a2408) | (~c0_1(a2408))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.68 tff(4003,plain,
% 2.04/1.68 (~hskp17),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[4002, 3982, 3655, 3679, 3653])).
% 2.04/1.68 tff(4004,plain,
% 2.04/1.68 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 2.04/1.68 inference(bind,[status(th)],[])).
% 2.04/1.68 tff(4005,plain,
% 2.04/1.68 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(quant_intro,[status(thm)],[4004])).
% 2.04/1.68 tff(4006,plain,
% 2.04/1.68 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(4007,plain,
% 2.04/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp18))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 2.04/1.68 inference(bind,[status(th)],[])).
% 2.04/1.68 tff(4008,plain,
% 2.04/1.68 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(quant_intro,[status(thm)],[4007])).
% 2.04/1.68 tff(4009,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 2.04/1.68 tff(4010,plain,
% 2.04/1.68 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 2.04/1.68 tff(4011,plain,
% 2.04/1.68 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[4010, 4006])).
% 2.04/1.68 tff(4012,plain,(
% 2.04/1.68 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(skolemize,[status(sab)],[4011])).
% 2.04/1.68 tff(4013,plain,
% 2.04/1.68 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[4012, 4005])).
% 2.04/1.68 tff(4014,plain,
% 2.04/1.68 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(4015,plain,
% 2.04/1.68 ((hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))) <=> (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(4016,plain,
% 2.04/1.68 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))))),
% 2.04/1.68 inference(monotonicity,[status(thm)],[4015])).
% 2.04/1.68 tff(4017,plain,
% 2.04/1.68 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 2.04/1.68 inference(transitivity,[status(thm)],[4016, 4014])).
% 2.04/1.68 tff(4018,plain,
% 2.04/1.68 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))),
% 2.04/1.68 inference(quant_inst,[status(thm)],[])).
% 2.04/1.68 tff(4019,plain,
% 2.04/1.68 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))),
% 2.04/1.68 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 2.04/1.68 tff(4020,plain,
% 2.04/1.68 (hskp18 | hskp17 | c0_1(a2435) | (~c1_1(a2435))),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[4019, 204, 785, 4013])).
% 2.04/1.68 tff(4021,plain,
% 2.04/1.68 (~c1_1(a2435)),
% 2.04/1.68 inference(unit_resolution,[status(thm)],[4020, 2279, 4003, 3983])).
% 2.04/1.68 tff(4022,plain,
% 2.04/1.68 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(4023,plain,
% 2.04/1.68 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435)) <=> (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 2.04/1.68 inference(rewrite,[status(thm)],[])).
% 2.04/1.68 tff(4024,plain,
% 2.04/1.68 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0)))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[4023])).
% 2.07/1.68 tff(4025,plain,
% 2.07/1.68 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 2.07/1.68 inference(transitivity,[status(thm)],[4024, 4022])).
% 2.07/1.68 tff(4026,plain,
% 2.07/1.68 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(4027,plain,
% 2.07/1.68 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[4026, 4025])).
% 2.07/1.68 tff(4028,plain,
% 2.07/1.68 (hskp1 | c3_1(a2435) | c0_1(a2435)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4027, 204, 2814, 785, 1039])).
% 2.07/1.68 tff(4029,plain,
% 2.07/1.68 (c3_1(a2435)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4028, 2279, 3982])).
% 2.07/1.68 tff(4030,plain,
% 2.07/1.68 (hskp12 | c1_1(a2435)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[3278, 204, 4029, 2279, 1532])).
% 2.07/1.68 tff(4031,plain,
% 2.07/1.68 (hskp12),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4030, 3268])).
% 2.07/1.68 tff(4032,plain,
% 2.07/1.68 (~c0_1(a2417)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[235, 4031])).
% 2.07/1.68 tff(4033,plain,
% 2.07/1.68 (c3_1(a2417)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[246, 4031])).
% 2.07/1.68 tff(4034,plain,
% 2.07/1.68 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(4035,plain,
% 2.07/1.68 ((hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417))) <=> (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(4036,plain,
% 2.07/1.68 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[4035])).
% 2.07/1.68 tff(4037,plain,
% 2.07/1.68 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[4036, 4034])).
% 2.07/1.68 tff(4038,plain,
% 2.07/1.68 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(4039,plain,
% 2.07/1.68 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[4038, 4037])).
% 2.07/1.68 tff(4040,plain,
% 2.07/1.68 (~c2_1(a2417)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4039, 204, 540, 4033, 4032, 511])).
% 2.07/1.68 tff(4041,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(4042,plain,
% 2.07/1.68 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(4043,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435)))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[4042])).
% 2.07/1.68 tff(4044,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 2.07/1.68 inference(transitivity,[status(thm)],[4043, 4041])).
% 2.07/1.68 tff(4045,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(4046,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 2.07/1.68 tff(4047,plain,
% 2.07/1.68 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4046, 204, 3650, 3655, 785, 3649, 3648, 3679, 1438])).
% 2.07/1.68 tff(4048,plain,
% 2.07/1.68 (~c1_1(a2408)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[4047, 3268, 2279])).
% 2.07/1.68 tff(4049,plain,
% 2.07/1.68 (hskp29),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2921, 4048, 3702, 3701, 3655, 3700, 3653])).
% 2.07/1.68 tff(4050,plain,
% 2.07/1.68 (c2_1(a2409)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1137, 4049])).
% 2.07/1.68 tff(4051,plain,
% 2.07/1.68 (c0_1(a2409)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1792, 4049])).
% 2.07/1.68 tff(4052,plain,
% 2.07/1.68 (c3_1(a2409)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1148, 4049])).
% 2.07/1.68 tff(4053,plain,
% 2.07/1.68 (hskp6),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[3058, 4052, 540, 4051, 4050, 43, 3982, 951, 957, 2772])).
% 2.07/1.68 tff(4054,plain,
% 2.07/1.68 (c0_1(a2410)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[986, 4053])).
% 2.07/1.68 tff(4055,plain,
% 2.07/1.68 (c1_1(a2410)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[975, 4053])).
% 2.07/1.68 tff(4056,plain,
% 2.07/1.68 (~c1_1(a2417)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[229, 4031])).
% 2.07/1.68 tff(4057,plain,
% 2.07/1.68 (~c2_1(a2410)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[964, 4053])).
% 2.07/1.68 tff(4058,plain,
% 2.07/1.68 (hskp14),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2885, 4057, 3655, 686, 4056, 4033, 3982, 4055, 3679, 4054, 3653])).
% 2.07/1.68 tff(4059,plain,
% 2.07/1.68 (c2_1(a2420)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[747, 4058])).
% 2.07/1.68 tff(4060,plain,
% 2.07/1.68 (c1_1(a2420)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[758, 4058])).
% 2.07/1.68 tff(4061,plain,
% 2.07/1.68 (c0_1(a2420)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2782, 4060, 2772, 951, 43, 957, 4059])).
% 2.07/1.68 tff(4062,plain,
% 2.07/1.68 (~c3_1(a2420)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[736, 4058])).
% 2.07/1.69 tff(4063,plain,
% 2.07/1.69 (~c1_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2930, 204, 4050, 4052, 4060, 2772, 4062, 957, 951, 1160, 4061])).
% 2.07/1.69 tff(4064,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4065,plain,
% 2.07/1.69 (((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4066,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4065])).
% 2.07/1.69 tff(4067,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4066, 4064])).
% 2.07/1.69 tff(4068,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4069,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4068, 4067])).
% 2.07/1.69 tff(4070,plain,
% 2.07/1.69 ($false),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4069, 204, 4051, 4050, 3701, 3700, 4032, 4056, 21, 4063, 4040, 3702])).
% 2.07/1.69 tff(4071,plain,(c1_1(a2435) | hskp15 | hskp19 | hskp23 | c0_1(a2435) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.69 tff(4072,plain,
% 2.07/1.69 (hskp15),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4071, 4021, 43, 686, 2279, 785])).
% 2.07/1.69 tff(4073,plain,
% 2.07/1.69 (c1_1(a2422)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[570, 4072])).
% 2.07/1.69 tff(4074,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4075,plain,
% 2.07/1.69 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4076,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4075])).
% 2.07/1.69 tff(4077,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4076, 4074])).
% 2.07/1.69 tff(4078,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4079,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4078, 4077])).
% 2.07/1.69 tff(4080,plain,
% 2.07/1.69 (c0_1(a2435) | (~c2_1(a2414)) | c1_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4079, 204, 3701, 2772, 3700, 785, 957, 21, 3702])).
% 2.07/1.69 tff(4081,plain,
% 2.07/1.69 (~c2_1(a2414)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4080, 4021, 2279])).
% 2.07/1.69 tff(4082,plain,
% 2.07/1.69 (c3_1(a2422)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[559, 4072])).
% 2.07/1.69 tff(4083,plain,
% 2.07/1.69 (~c2_1(a2422)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[576, 4072])).
% 2.07/1.69 tff(4084,plain,
% 2.07/1.69 ($false),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3270, 4083, 4082, 4021, 2279, 785, 4081, 4073])).
% 2.07/1.69 tff(4085,plain,(c0_1(a2435) | c2_1(a2435) | hskp19 | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.07/1.69 tff(4086,plain,
% 2.07/1.69 (c0_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4085, 686, 43, 785])).
% 2.07/1.69 tff(4087,plain,
% 2.07/1.69 (~hskp20),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[820, 4086])).
% 2.07/1.69 tff(4088,plain,
% 2.07/1.69 (~hskp14),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3136, 4087, 43])).
% 2.07/1.69 tff(4089,plain,
% 2.07/1.69 (hskp23 | hskp14 | (~c1_1(a2408))),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[729, 204, 3653, 3655, 42])).
% 2.07/1.69 tff(4090,plain,
% 2.07/1.69 (~c1_1(a2408)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4089, 4088, 686])).
% 2.07/1.69 tff(4091,plain,
% 2.07/1.69 (hskp29),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2921, 4090, 3702, 3701, 3655, 3700, 3653])).
% 2.07/1.69 tff(4092,plain,
% 2.07/1.69 (c3_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1148, 4091])).
% 2.07/1.69 tff(4093,plain,
% 2.07/1.69 (c2_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1137, 4091])).
% 2.07/1.69 tff(4094,plain,
% 2.07/1.69 (c0_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1792, 4091])).
% 2.07/1.69 tff(4095,plain,
% 2.07/1.69 ($false),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3160, 204, 4087, 3983, 4094, 4093, 4092, 3153])).
% 2.07/1.69 tff(4096,plain,(hskp23 | hskp19 | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.69 tff(4097,plain,
% 2.07/1.69 (c2_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4096, 3693, 43])).
% 2.07/1.69 tff(4098,plain,
% 2.07/1.69 (~hskp20),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[868, 4097])).
% 2.07/1.69 tff(4099,plain,
% 2.07/1.69 (~hskp14),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3136, 4098, 43])).
% 2.07/1.69 tff(4100,plain,
% 2.07/1.69 (~c1_1(a2408)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4089, 4099, 3693])).
% 2.07/1.69 tff(4101,plain,
% 2.07/1.69 (hskp23 | c1_1(a2408) | (~c1_1(a2425))),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[692, 204, 3655, 3649, 3648, 3679, 685])).
% 2.07/1.69 tff(4102,plain,
% 2.07/1.69 (~c1_1(a2425)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4101, 4100, 3693])).
% 2.07/1.69 tff(4103,plain,
% 2.07/1.69 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4104,plain,
% 2.07/1.69 ((hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4105,plain,
% 2.07/1.69 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4104])).
% 2.07/1.69 tff(4106,plain,
% 2.07/1.69 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4105, 4103])).
% 2.07/1.69 tff(4107,plain,
% 2.07/1.69 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4108,plain,
% 2.07/1.69 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 2.07/1.69 tff(4109,plain,
% 2.07/1.69 (~c1_1(a2478)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4108, 204, 43, 3698, 3650, 3697, 3648, 85, 4102])).
% 2.07/1.69 tff(4110,plain,
% 2.07/1.69 (hskp29),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2921, 4109, 4100, 3698, 3655, 3697, 3653])).
% 2.07/1.69 tff(4111,plain,
% 2.07/1.69 (c3_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1148, 4110])).
% 2.07/1.69 tff(4112,plain,
% 2.07/1.69 (c0_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1792, 4110])).
% 2.07/1.69 tff(4113,plain,
% 2.07/1.69 (~c1_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3045, 204, 3693, 4099, 4112, 4111, 42])).
% 2.07/1.69 tff(4114,plain,
% 2.07/1.69 (c2_1(a2409)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1137, 4110])).
% 2.07/1.69 tff(4115,plain,
% 2.07/1.69 (hskp18),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3160, 204, 4098, 4112, 4114, 4111, 3153])).
% 2.07/1.69 tff(4116,plain,
% 2.07/1.69 (hskp1),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3188, 4115, 2814])).
% 2.07/1.69 tff(4117,plain,
% 2.07/1.69 (~c3_1(a2403)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2423, 4116])).
% 2.07/1.69 tff(4118,plain,
% 2.07/1.69 (~c2_1(a2403)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2429, 4116])).
% 2.07/1.69 tff(4119,plain,
% 2.07/1.69 (c1_1(a2403)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2440, 4116])).
% 2.07/1.69 tff(4120,plain,
% 2.07/1.69 ($false),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2576, 204, 4112, 4114, 4111, 4119, 4118, 4117, 2451, 4113])).
% 2.07/1.69 tff(4121,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 2.07/1.69 tff(4122,plain,
% 2.07/1.69 (~c0_1(a2432)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[312, 4121])).
% 2.07/1.69 tff(4123,plain,
% 2.07/1.69 (c3_1(a2432)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[891, 4121])).
% 2.07/1.69 tff(4124,plain,
% 2.07/1.69 (c1_1(a2432)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[323, 4121])).
% 2.07/1.69 tff(4125,plain,
% 2.07/1.69 (hskp9 | hskp1),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3376, 204, 4124, 4123, 4122, 32])).
% 2.07/1.69 tff(4126,plain,
% 2.07/1.69 (hskp9),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4125, 22])).
% 2.07/1.69 tff(4127,plain,
% 2.07/1.69 (~c1_1(a2413)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3342, 4126])).
% 2.07/1.69 tff(4128,plain,
% 2.07/1.69 (~c0_1(a2413)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3348, 4126])).
% 2.07/1.69 tff(4129,plain,
% 2.07/1.69 (hskp20),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3254, 4124, 4123, 4122])).
% 2.07/1.69 tff(4130,plain,
% 2.07/1.69 (~c2_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[868, 4129])).
% 2.07/1.69 tff(4131,plain,
% 2.07/1.69 (~c0_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[820, 4129])).
% 2.07/1.69 tff(4132,plain,
% 2.07/1.69 (c2_1(a2413)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3359, 4126])).
% 2.07/1.69 tff(4133,plain,
% 2.07/1.69 (hskp5 | (~c2_1(a2432))),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3464, 204, 4123, 4132, 4122, 4128, 4127, 2097])).
% 2.07/1.69 tff(4134,plain,
% 2.07/1.69 (~c2_1(a2432)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4133, 2087])).
% 2.07/1.69 tff(4135,plain,
% 2.07/1.69 (c2_1(a2432) | c1_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2138, 204, 4124, 4123, 3650, 4131, 4130, 3649, 3648, 1438])).
% 2.07/1.69 tff(4136,plain,
% 2.07/1.69 (c1_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4135, 4134])).
% 2.07/1.69 tff(4137,plain,
% 2.07/1.69 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4138,plain,
% 2.07/1.69 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4139,plain,
% 2.07/1.69 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4138])).
% 2.07/1.69 tff(4140,plain,
% 2.07/1.69 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4139, 4137])).
% 2.07/1.69 tff(4141,plain,
% 2.07/1.69 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4142,plain,
% 2.07/1.69 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 2.07/1.69 tff(4143,plain,
% 2.07/1.69 (hskp5 | hskp1 | (~c1_1(a2425))),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4142, 204, 3650, 3649, 3824])).
% 2.07/1.69 tff(4144,plain,
% 2.07/1.69 (~c1_1(a2425)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4143, 2087, 22])).
% 2.07/1.69 tff(4145,plain,
% 2.07/1.69 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4146,plain,
% 2.07/1.69 ((hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425))) <=> (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4147,plain,
% 2.07/1.69 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4146])).
% 2.07/1.69 tff(4148,plain,
% 2.07/1.69 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4147, 4145])).
% 2.07/1.69 tff(4149,plain,
% 2.07/1.69 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4150,plain,
% 2.07/1.69 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4149, 4148])).
% 2.07/1.69 tff(4151,plain,
% 2.07/1.69 (hskp22 | hskp5 | c1_1(a2425)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4150, 204, 3650, 3649, 1597])).
% 2.07/1.69 tff(4152,plain,
% 2.07/1.69 (hskp22),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4151, 2087, 4144])).
% 2.07/1.69 tff(4153,plain,
% 2.07/1.69 (~c2_1(a2453)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1558, 4152])).
% 2.07/1.69 tff(4154,plain,
% 2.07/1.69 (~c1_1(a2453)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1577, 4152])).
% 2.07/1.69 tff(4155,plain,
% 2.07/1.69 (~c0_1(a2453)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1564, 4152])).
% 2.07/1.69 tff(4156,plain,
% 2.07/1.69 (c3_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[814, 4129])).
% 2.07/1.69 tff(4157,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4158,plain,
% 2.07/1.69 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4159,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4158])).
% 2.07/1.69 tff(4160,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4159, 4157])).
% 2.07/1.69 tff(4161,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4162,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 2.07/1.69 tff(4163,plain,
% 2.07/1.69 ($false),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4162, 204, 4156, 3650, 4155, 4154, 4153, 4130, 3649, 3648, 1438, 4136])).
% 2.07/1.69 tff(4164,plain,(hskp5 | hskp1), inference(lemma,lemma(discharge,[]))).
% 2.07/1.69 tff(4165,plain,
% 2.07/1.69 (hskp5),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4164, 22])).
% 2.07/1.69 tff(4166,plain,
% 2.07/1.69 (c0_1(a2408)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[411, 4165])).
% 2.07/1.69 tff(4167,plain,
% 2.07/1.69 (~c2_1(a2408)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[400, 4165])).
% 2.07/1.69 tff(4168,plain,
% 2.07/1.69 (c3_1(a2408)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[429, 4165])).
% 2.07/1.69 tff(4169,plain,
% 2.07/1.69 (~hskp17),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4002, 4168, 22, 4167, 4166])).
% 2.07/1.69 tff(4170,plain,
% 2.07/1.69 (hskp21 | hskp17),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1927, 204, 4124, 4123, 4122, 1871])).
% 2.07/1.69 tff(4171,plain,
% 2.07/1.69 (hskp21),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4170, 4169])).
% 2.07/1.69 tff(4172,plain,
% 2.07/1.69 (~c1_1(a2437)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1822, 4171])).
% 2.07/1.69 tff(4173,plain,
% 2.07/1.69 (c2_1(a2437)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1833, 4171])).
% 2.07/1.69 tff(4174,plain,
% 2.07/1.69 (c0_1(a2437)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[1851, 4171])).
% 2.07/1.69 tff(4175,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4176,plain,
% 2.07/1.69 (((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4177,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[4176])).
% 2.07/1.69 tff(4178,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.69 inference(transitivity,[status(thm)],[4177, 4175])).
% 2.07/1.69 tff(4179,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(4180,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[4179, 4178])).
% 2.07/1.69 tff(4181,plain,
% 2.07/1.69 (c1_1(a2435)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4180, 204, 4174, 4173, 4132, 4172, 4131, 4130, 4128, 4127, 21])).
% 2.07/1.69 tff(4182,plain,
% 2.07/1.69 (hskp18 | hskp17 | (~c1_1(a2435))),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4019, 204, 4131, 4130, 4013])).
% 2.07/1.69 tff(4183,plain,
% 2.07/1.69 (hskp18),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[4182, 4181, 4169])).
% 2.07/1.69 tff(4184,plain,
% 2.07/1.69 (hskp13),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3188, 4183, 22])).
% 2.07/1.69 tff(4185,plain,
% 2.07/1.69 (~c0_1(a2418)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[339, 4184])).
% 2.07/1.69 tff(4186,plain,
% 2.07/1.69 (~c3_1(a2428)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3167, 4183])).
% 2.07/1.69 tff(4187,plain,
% 2.07/1.69 (~c2_1(a2428)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3173, 4183])).
% 2.07/1.69 tff(4188,plain,
% 2.07/1.69 (~c0_1(a2428)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[3179, 4183])).
% 2.07/1.69 tff(4189,plain,
% 2.07/1.69 (c2_1(a2418)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[350, 4184])).
% 2.07/1.69 tff(4190,plain,
% 2.07/1.69 (c1_1(a2418)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[361, 4184])).
% 2.07/1.69 tff(4191,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4192,plain,
% 2.07/1.69 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(4193,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4192])).
% 2.07/1.70 tff(4194,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4193, 4191])).
% 2.07/1.70 tff(4195,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4196,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 2.07/1.70 tff(4197,plain,
% 2.07/1.70 ($false),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4196, 204, 4156, 4190, 4189, 4130, 4188, 4187, 4186, 4185, 63, 4181])).
% 2.07/1.70 tff(4198,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 2.07/1.70 tff(4199,plain,
% 2.07/1.70 (~c3_1(a2403)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2423, 4198])).
% 2.07/1.70 tff(4200,plain,
% 2.07/1.70 (~c2_1(a2403)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2429, 4198])).
% 2.07/1.70 tff(4201,plain,
% 2.07/1.70 (c1_1(a2403)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2440, 4198])).
% 2.07/1.70 tff(4202,plain,
% 2.07/1.70 (hskp23 | c1_1(a2435)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[3966, 204, 4156, 4201, 4130, 4200, 4199, 685])).
% 2.07/1.70 tff(4203,plain,
% 2.07/1.70 (c1_1(a2435)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4202, 686])).
% 2.07/1.70 tff(4204,plain,
% 2.07/1.70 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 2.07/1.70 inference(bind,[status(th)],[])).
% 2.07/1.70 tff(4205,plain,
% 2.07/1.70 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(quant_intro,[status(thm)],[4204])).
% 2.07/1.70 tff(4206,plain,
% 2.07/1.70 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4207,plain,
% 2.07/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 2.07/1.70 inference(bind,[status(th)],[])).
% 2.07/1.70 tff(4208,plain,
% 2.07/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(quant_intro,[status(thm)],[4207])).
% 2.07/1.70 tff(4209,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 2.07/1.70 tff(4210,plain,
% 2.07/1.70 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4209, 4208])).
% 2.07/1.70 tff(4211,plain,
% 2.07/1.70 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4210, 4206])).
% 2.07/1.70 tff(4212,plain,(
% 2.07/1.70 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(skolemize,[status(sab)],[4211])).
% 2.07/1.70 tff(4213,plain,
% 2.07/1.70 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4212, 4205])).
% 2.07/1.70 tff(4214,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4215,plain,
% 2.07/1.70 (((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427))) <=> (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4216,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4215])).
% 2.07/1.70 tff(4217,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4216, 4214])).
% 2.07/1.70 tff(4218,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4219,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4218, 4217])).
% 2.07/1.70 tff(4220,plain,
% 2.07/1.70 (~c0_1(a2427)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4219, 204, 3987, 3986, 4201, 3985, 4200, 4199, 2451])).
% 2.07/1.70 tff(4221,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4222,plain,
% 2.07/1.70 ((hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427))) <=> (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4223,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4222])).
% 2.07/1.70 tff(4224,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4223, 4221])).
% 2.07/1.70 tff(4225,plain,
% 2.07/1.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4226,plain,
% 2.07/1.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 2.07/1.70 tff(4227,plain,
% 2.07/1.70 ($false),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4226, 204, 2087, 3987, 3986, 3985, 2097, 4220])).
% 2.07/1.70 tff(4228,plain,((~hskp17) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.07/1.70 tff(4229,plain,
% 2.07/1.70 (~hskp17),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4228, 2087])).
% 2.07/1.70 tff(4230,plain,
% 2.07/1.70 (hskp18),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4182, 4229, 4203])).
% 2.07/1.70 tff(4231,plain,
% 2.07/1.70 (~c3_1(a2428)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[3167, 4230])).
% 2.07/1.70 tff(4232,plain,
% 2.07/1.70 (~c2_1(a2428)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[3173, 4230])).
% 2.07/1.70 tff(4233,plain,
% 2.07/1.70 (~c0_1(a2428)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[3179, 4230])).
% 2.07/1.70 tff(4234,assumption,(~c2_1(a2428)), introduced(assumption)).
% 2.07/1.70 tff(4235,assumption,(~c0_1(a2428)), introduced(assumption)).
% 2.07/1.70 tff(4236,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4237,plain,
% 2.07/1.70 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428)) <=> (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4238,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4237])).
% 2.07/1.70 tff(4239,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4238, 4236])).
% 2.07/1.70 tff(4240,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4241,plain,
% 2.07/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4240, 4239])).
% 2.07/1.70 tff(4242,plain,
% 2.07/1.70 (c1_1(a2428)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4241, 204, 4156, 4201, 4130, 4235, 4234, 4200, 4199, 11, 4203])).
% 2.07/1.70 tff(4243,plain,
% 2.07/1.70 (hskp14 | (~c3_1(a2498))),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2768, 204, 686, 2732, 2754, 42])).
% 2.07/1.70 tff(4244,plain,
% 2.07/1.70 (~c3_1(a2498)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4243, 2862])).
% 2.07/1.70 tff(4245,plain,
% 2.07/1.70 (hskp6 | c3_1(a2498)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2759, 204, 686, 2754, 2743, 2219])).
% 2.07/1.70 tff(4246,plain,
% 2.07/1.70 (hskp6),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4245, 4244])).
% 2.07/1.70 tff(4247,plain,
% 2.07/1.70 (c1_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[975, 4246])).
% 2.07/1.70 tff(4248,plain,
% 2.07/1.70 (c0_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[986, 4246])).
% 2.07/1.70 tff(4249,plain,
% 2.07/1.70 (~c3_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2870, 204, 686, 2862, 4248, 4247, 42])).
% 2.07/1.70 tff(4250,plain,
% 2.07/1.70 (^[U: $i] : refl((hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.07/1.70 inference(bind,[status(th)],[])).
% 2.07/1.70 tff(4251,plain,
% 2.07/1.70 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(quant_intro,[status(thm)],[4250])).
% 2.07/1.70 tff(4252,plain,
% 2.07/1.70 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4253,plain,
% 2.07/1.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.07/1.70 inference(bind,[status(th)],[])).
% 2.07/1.70 tff(4254,plain,
% 2.07/1.70 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(quant_intro,[status(thm)],[4253])).
% 2.07/1.70 tff(4255,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.07/1.70 tff(4256,plain,
% 2.07/1.70 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 2.07/1.70 tff(4257,plain,
% 2.07/1.70 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4256, 4252])).
% 2.07/1.70 tff(4258,plain,(
% 2.07/1.70 ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(skolemize,[status(sab)],[4257])).
% 2.07/1.70 tff(4259,plain,
% 2.07/1.70 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4258, 4251])).
% 2.07/1.70 tff(4260,plain,
% 2.07/1.70 (~c2_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[964, 4246])).
% 2.07/1.70 tff(4261,plain,
% 2.07/1.70 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4262,plain,
% 2.07/1.70 ((hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4263,plain,
% 2.07/1.70 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4262])).
% 2.07/1.70 tff(4264,plain,
% 2.07/1.70 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4263, 4261])).
% 2.07/1.70 tff(4265,plain,
% 2.07/1.70 ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4266,plain,
% 2.07/1.70 ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 2.07/1.70 tff(4267,plain,
% 2.07/1.70 (hskp7),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4266, 204, 958, 4248, 4247, 4260, 4259])).
% 2.07/1.70 tff(4268,plain,
% 2.07/1.70 (((~hskp7) | (~c3_1(a2411))) <=> ((~hskp7) | (~c3_1(a2411)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4269,plain,
% 2.07/1.70 (((~c3_1(a2411)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2411)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4270,axiom,((~c3_1(a2411)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 2.07/1.70 tff(4271,plain,
% 2.07/1.70 ((~hskp7) | (~c3_1(a2411))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4270, 4269])).
% 2.07/1.70 tff(4272,plain,
% 2.07/1.70 ((~hskp7) | (~c3_1(a2411))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4271, 4268])).
% 2.07/1.70 tff(4273,plain,
% 2.07/1.70 (~c3_1(a2411)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4272, 4267])).
% 2.07/1.70 tff(4274,plain,
% 2.07/1.70 (~c1_1(a2411)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2971, 4267])).
% 2.07/1.70 tff(4275,plain,
% 2.07/1.70 (c2_1(a2411)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[2982, 4267])).
% 2.07/1.70 tff(4276,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4277,plain,
% 2.07/1.70 ((hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411))) <=> (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 2.07/1.70 inference(rewrite,[status(thm)],[])).
% 2.07/1.70 tff(4278,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411))))),
% 2.07/1.70 inference(monotonicity,[status(thm)],[4277])).
% 2.07/1.70 tff(4279,plain,
% 2.07/1.70 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 2.07/1.70 inference(transitivity,[status(thm)],[4278, 4276])).
% 2.07/1.70 tff(4280,plain,
% 2.07/1.70 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))),
% 2.07/1.70 inference(quant_inst,[status(thm)],[])).
% 2.07/1.70 tff(4281,plain,
% 2.07/1.70 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411))),
% 2.07/1.70 inference(modus_ponens,[status(thm)],[4280, 4279])).
% 2.07/1.70 tff(4282,plain,
% 2.07/1.70 ($false),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4281, 204, 2862, 4275, 4248, 4247, 4274, 4273, 3097, 4249])).
% 2.07/1.70 tff(4283,plain,(hskp14 | hskp25 | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.07/1.70 tff(4284,plain,
% 2.07/1.70 (hskp14),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[4283, 958, 686])).
% 2.07/1.70 tff(4285,plain,
% 2.07/1.70 (~c3_1(a2420)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[736, 4284])).
% 2.07/1.70 tff(4286,plain,
% 2.07/1.70 (c2_1(a2420)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[747, 4284])).
% 2.07/1.70 tff(4287,plain,
% 2.07/1.70 (c1_1(a2420)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[758, 4284])).
% 2.07/1.70 tff(4288,plain,
% 2.07/1.70 (hskp6),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[3056, 204, 686, 4287, 4286, 4285, 2219])).
% 2.07/1.70 tff(4289,plain,
% 2.07/1.70 (~c2_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[964, 4288])).
% 2.07/1.70 tff(4290,plain,
% 2.07/1.70 (c1_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[975, 4288])).
% 2.07/1.70 tff(4291,plain,
% 2.07/1.70 (c0_1(a2410)),
% 2.07/1.70 inference(unit_resolution,[status(thm)],[986, 4288])).
% 2.07/1.70 tff(4292,plain,
% 2.07/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4293,plain,
% 2.07/1.71 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4294,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4293])).
% 2.07/1.71 tff(4295,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4294, 4292])).
% 2.07/1.71 tff(4296,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4297,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 2.07/1.71 tff(4298,plain,
% 2.07/1.71 (c1_1(a2425)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4297, 204, 3650, 4291, 4290, 4131, 4130, 3649, 4289, 2008, 4203])).
% 2.07/1.71 tff(4299,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4300,plain,
% 2.07/1.71 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4301,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4300])).
% 2.07/1.71 tff(4302,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4301, 4299])).
% 2.07/1.71 tff(4303,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4304,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4303, 4302])).
% 2.07/1.71 tff(4305,plain,
% 2.07/1.71 (hskp30 | (~c1_1(a2425)) | (~c1_1(a2435))),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4304, 204, 4156, 3650, 4130, 3648, 612])).
% 2.07/1.71 tff(4306,plain,
% 2.07/1.71 (hskp30),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4305, 4298, 4203])).
% 2.07/1.71 tff(4307,plain,
% 2.07/1.71 ((~hskp11) | hskp23 | (~c1_1(a2425))),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[778, 3649, 3648])).
% 2.07/1.71 tff(4308,plain,
% 2.07/1.71 (~hskp11),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4307, 4298, 686])).
% 2.07/1.71 tff(4309,assumption,(hskp30), introduced(assumption)).
% 2.07/1.71 tff(4310,plain,
% 2.07/1.71 (c3_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[633, 4309])).
% 2.07/1.71 tff(4311,plain,
% 2.07/1.71 (c1_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[644, 4309])).
% 2.07/1.71 tff(4312,plain,
% 2.07/1.71 (c0_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[655, 4309])).
% 2.07/1.71 tff(4313,plain,
% 2.07/1.71 (hskp19 | c2_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[1233, 204, 958, 3940, 3937, 106])).
% 2.07/1.71 tff(4314,plain,
% 2.07/1.71 (c2_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4313, 43])).
% 2.07/1.71 tff(4315,plain,
% 2.07/1.71 (^[U: $i] : refl((hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))),
% 2.07/1.71 inference(bind,[status(th)],[])).
% 2.07/1.71 tff(4316,plain,
% 2.07/1.71 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(quant_intro,[status(thm)],[4315])).
% 2.07/1.71 tff(4317,plain,
% 2.07/1.71 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4318,plain,
% 2.07/1.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> ((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))))),
% 2.07/1.71 inference(bind,[status(th)],[])).
% 2.07/1.71 tff(4319,plain,
% 2.07/1.71 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(quant_intro,[status(thm)],[4318])).
% 2.07/1.71 tff(4320,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 2.07/1.71 tff(4321,plain,
% 2.07/1.71 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 2.07/1.71 tff(4322,plain,
% 2.07/1.71 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4321, 4317])).
% 2.07/1.71 tff(4323,plain,(
% 2.07/1.71 ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(skolemize,[status(sab)],[4322])).
% 2.07/1.71 tff(4324,plain,
% 2.07/1.71 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4323, 4316])).
% 2.07/1.71 tff(4325,plain,
% 2.07/1.71 (((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4326,plain,
% 2.07/1.71 ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4327,plain,
% 2.07/1.71 ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 2.07/1.71 tff(4328,plain,
% 2.07/1.71 (hskp15 | (~c2_1(a2450))),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4327, 204, 325, 3937, 3936, 4324])).
% 2.07/1.71 tff(4329,plain,
% 2.07/1.71 (hskp15),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4328, 4314])).
% 2.07/1.71 tff(4330,plain,
% 2.07/1.71 (~c2_1(a2422)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[576, 4329])).
% 2.07/1.71 tff(4331,plain,
% 2.07/1.71 (c3_1(a2422)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[559, 4329])).
% 2.07/1.71 tff(4332,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4333,plain,
% 2.07/1.71 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422))) <=> (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4334,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422))))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4333])).
% 2.07/1.71 tff(4335,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4334, 4332])).
% 2.07/1.71 tff(4336,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4337,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4336, 4335])).
% 2.07/1.71 tff(4338,plain,
% 2.07/1.71 (c0_1(a2422)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4337, 204, 326, 3940, 3937, 3936, 4331, 4330, 832])).
% 2.07/1.71 tff(4339,plain,
% 2.07/1.71 (c1_1(a2422)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[570, 4329])).
% 2.07/1.71 tff(4340,plain,
% 2.07/1.71 ($false),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[2802, 204, 958, 43, 4339, 4330, 106, 4338])).
% 2.07/1.71 tff(4341,plain,(hskp19 | hskp25 | hskp12 | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2450)) | hskp11), inference(lemma,lemma(discharge,[]))).
% 2.07/1.71 tff(4342,plain,
% 2.07/1.71 (hskp19),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4341, 4312, 326, 958, 4311, 4310, 325])).
% 2.07/1.71 tff(4343,plain,
% 2.07/1.71 (~c0_1(a2432)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[312, 4342])).
% 2.07/1.71 tff(4344,plain,
% 2.07/1.71 (c1_1(a2432)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[323, 4342])).
% 2.07/1.71 tff(4345,plain,
% 2.07/1.71 (~c2_1(a2432)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[332, 204, 326, 325, 4344, 4343, 293])).
% 2.07/1.71 tff(4346,plain,
% 2.07/1.71 (c3_1(a2432)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[891, 4342])).
% 2.07/1.71 tff(4347,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4348,plain,
% 2.07/1.71 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432))) <=> (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4349,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432)))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4348])).
% 2.07/1.71 tff(4350,plain,
% 2.07/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4349, 4347])).
% 2.07/1.71 tff(4351,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4352,plain,
% 2.07/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432)),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 2.07/1.71 tff(4353,plain,
% 2.07/1.71 ($false),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4352, 204, 326, 4312, 4311, 4310, 4346, 4343, 832, 4345])).
% 2.07/1.71 tff(4354,plain,((~hskp30) | hskp12 | hskp11 | hskp25), inference(lemma,lemma(discharge,[]))).
% 2.07/1.71 tff(4355,plain,
% 2.07/1.71 (hskp12),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4354, 4308, 4306, 958])).
% 2.07/1.71 tff(4356,plain,
% 2.07/1.71 (~c1_1(a2417)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[229, 4355])).
% 2.07/1.71 tff(4357,plain,
% 2.07/1.71 (~c0_1(a2417)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[235, 4355])).
% 2.07/1.71 tff(4358,assumption,(~c3_1(a2428)), introduced(assumption)).
% 2.07/1.71 tff(4359,plain,
% 2.07/1.71 (c3_1(a2417)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[246, 4355])).
% 2.07/1.71 tff(4360,plain,
% 2.07/1.71 (c3_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[633, 4306])).
% 2.07/1.71 tff(4361,plain,
% 2.07/1.71 (c1_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[644, 4306])).
% 2.07/1.71 tff(4362,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4363,plain,
% 2.07/1.71 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4364,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417))))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4363])).
% 2.07/1.71 tff(4365,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4364, 4362])).
% 2.07/1.71 tff(4366,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4367,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 2.07/1.71 tff(4368,plain,
% 2.07/1.71 (~c2_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4367, 204, 4361, 4360, 4359, 4235, 4234, 4358, 4357, 4356, 2665])).
% 2.07/1.71 tff(4369,plain,
% 2.07/1.71 (c0_1(a2450)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[655, 4306])).
% 2.07/1.71 tff(4370,plain,
% 2.07/1.71 (~c2_1(a2417)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[852, 204, 4369, 4361, 4360, 3650, 4359, 3649, 3648, 4356, 602])).
% 2.07/1.71 tff(4371,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4372,plain,
% 2.07/1.71 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4373,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428))))),
% 2.07/1.71 inference(monotonicity,[status(thm)],[4372])).
% 2.07/1.71 tff(4374,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 2.07/1.71 inference(transitivity,[status(thm)],[4373, 4371])).
% 2.07/1.71 tff(4375,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 2.07/1.71 inference(quant_inst,[status(thm)],[])).
% 2.07/1.71 tff(4376,plain,
% 2.07/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428))),
% 2.07/1.71 inference(modus_ponens,[status(thm)],[4375, 4374])).
% 2.07/1.71 tff(4377,plain,
% 2.07/1.71 ($false),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4376, 204, 4361, 4360, 4234, 4358, 4357, 4356, 11, 4370, 4368, 4242])).
% 2.07/1.71 tff(4378,plain,(hskp25 | c2_1(a2428) | c3_1(a2428) | c0_1(a2428) | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.07/1.71 tff(4379,plain,
% 2.07/1.71 (hskp25),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[4378, 4232, 4231, 4233, 686])).
% 2.07/1.71 tff(4380,plain,
% 2.07/1.71 (~c0_1(a2478)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[123, 4379])).
% 2.07/1.71 tff(4381,plain,
% 2.07/1.71 (c2_1(a2478)),
% 2.07/1.71 inference(unit_resolution,[status(thm)],[117, 4379])).
% 2.07/1.71 tff(4382,plain,
% 2.07/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.71 inference(rewrite,[status(thm)],[])).
% 2.07/1.71 tff(4383,plain,
% 2.07/1.72 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4384,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4383])).
% 2.07/1.72 tff(4385,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4384, 4382])).
% 2.07/1.72 tff(4386,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4387,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4386, 4385])).
% 2.07/1.72 tff(4388,plain,
% 2.07/1.72 (~c1_1(a2478)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4387, 204, 4381, 4156, 4380, 4130, 4233, 4232, 4231, 63, 4203])).
% 2.07/1.72 tff(4389,plain,
% 2.07/1.72 (hskp21),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4170, 4229])).
% 2.07/1.72 tff(4390,plain,
% 2.07/1.72 (~c1_1(a2437)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1822, 4389])).
% 2.07/1.72 tff(4391,plain,
% 2.07/1.72 (~c3_1(a2478)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[129, 4379])).
% 2.07/1.72 tff(4392,plain,
% 2.07/1.72 (c2_1(a2437)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1833, 4389])).
% 2.07/1.72 tff(4393,plain,
% 2.07/1.72 (c0_1(a2437)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1851, 4389])).
% 2.07/1.72 tff(4394,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4395,plain,
% 2.07/1.72 ((hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4396,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4395])).
% 2.07/1.72 tff(4397,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4396, 4394])).
% 2.07/1.72 tff(4398,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4399,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4398, 4397])).
% 2.07/1.72 tff(4400,plain,
% 2.07/1.72 (hskp3),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4399, 204, 4381, 4393, 4392, 4391, 4390, 1804, 4388])).
% 2.07/1.72 tff(4401,plain,
% 2.07/1.72 (~c3_1(a2405)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1299, 4400])).
% 2.07/1.72 tff(4402,plain,
% 2.07/1.72 (c2_1(a2405)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1330, 4400])).
% 2.07/1.72 tff(4403,plain,
% 2.07/1.72 (c0_1(a2405)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1310, 4400])).
% 2.07/1.72 tff(4404,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4405,plain,
% 2.07/1.72 ((hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4406,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4405])).
% 2.07/1.72 tff(4407,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4406, 4404])).
% 2.07/1.72 tff(4408,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4409,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 2.07/1.72 tff(4410,plain,
% 2.07/1.72 (hskp7),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4409, 204, 4156, 4403, 4402, 4131, 4401, 4213, 4203])).
% 2.07/1.72 tff(4411,plain,
% 2.07/1.72 (~c1_1(a2411)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2971, 4410])).
% 2.07/1.72 tff(4412,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4413,plain,
% 2.07/1.72 ((hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4414,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4413])).
% 2.07/1.72 tff(4415,plain,
% 2.07/1.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4414, 4412])).
% 2.07/1.72 tff(4416,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4417,plain,
% 2.07/1.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 2.07/1.72 tff(4418,plain,
% 2.07/1.72 (hskp4),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4417, 204, 4381, 4156, 4380, 4131, 1057, 4203, 4388])).
% 2.07/1.72 tff(4419,plain,
% 2.07/1.72 (~c2_1(a2407)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1518, 4418])).
% 2.07/1.72 tff(4420,plain,
% 2.07/1.72 (~c1_1(a2407)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1512, 4418])).
% 2.07/1.72 tff(4421,plain,
% 2.07/1.72 (c0_1(a2407)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2081, 4418])).
% 2.07/1.72 tff(4422,plain,
% 2.07/1.72 (hskp22),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1603, 204, 2087, 4421, 4420, 4419, 1597])).
% 2.07/1.72 tff(4423,plain,
% 2.07/1.72 (~c2_1(a2453)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1558, 4422])).
% 2.07/1.72 tff(4424,plain,
% 2.07/1.72 (~c1_1(a2453)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1577, 4422])).
% 2.07/1.72 tff(4425,plain,
% 2.07/1.72 (~c0_1(a2453)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[1564, 4422])).
% 2.07/1.72 tff(4426,plain,
% 2.07/1.72 (c2_1(a2411)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2982, 4410])).
% 2.07/1.72 tff(4427,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4428,plain,
% 2.07/1.72 (((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4429,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4428])).
% 2.07/1.72 tff(4430,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4429, 4427])).
% 2.07/1.72 tff(4431,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4432,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4431, 4430])).
% 2.07/1.72 tff(4433,plain,
% 2.07/1.72 (c0_1(a2411)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4432, 204, 4393, 4392, 4426, 4425, 4424, 4423, 4390, 4411, 21])).
% 2.07/1.72 tff(4434,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4435,plain,
% 2.07/1.72 (((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4436,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4435])).
% 2.07/1.72 tff(4437,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4436, 4434])).
% 2.07/1.72 tff(4438,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4439,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4438, 4437])).
% 2.07/1.72 tff(4440,plain,
% 2.07/1.72 ($false),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4439, 204, 4381, 4426, 4380, 4425, 4424, 4423, 4411, 21, 4388, 4433])).
% 2.07/1.72 tff(4441,plain,(hskp5 | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.07/1.72 tff(4442,plain,
% 2.07/1.72 (hskp5),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4441, 686])).
% 2.07/1.72 tff(4443,plain,
% 2.07/1.72 (~c2_1(a2408)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[400, 4442])).
% 2.07/1.72 tff(4444,plain,
% 2.07/1.72 (c3_1(a2408)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[429, 4442])).
% 2.07/1.72 tff(4445,plain,
% 2.07/1.72 (c1_1(a2408)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2470, 204, 686, 4444, 4201, 4443, 4200, 4199, 685])).
% 2.07/1.72 tff(4446,plain,
% 2.07/1.72 (c0_1(a2408)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[411, 4442])).
% 2.07/1.72 tff(4447,plain,
% 2.07/1.72 ((~c1_1(a2408)) | c1_1(a2425)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2412, 204, 3650, 4446, 4131, 4130, 3649, 4443, 2008, 4203])).
% 2.07/1.72 tff(4448,plain,
% 2.07/1.72 (c1_1(a2425)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4447, 4445])).
% 2.07/1.72 tff(4449,plain,
% 2.07/1.72 (hskp30 | (~c1_1(a2408)) | (~c1_1(a2425))),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[701, 204, 3650, 4444, 3648, 4443, 612])).
% 2.07/1.72 tff(4450,plain,
% 2.07/1.72 (hskp30),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4449, 4445, 4448])).
% 2.07/1.72 tff(4451,plain,
% 2.07/1.72 (c3_1(a2450)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[633, 4450])).
% 2.07/1.72 tff(4452,plain,
% 2.07/1.72 (c1_1(a2450)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[644, 4450])).
% 2.07/1.72 tff(4453,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4454,plain,
% 2.07/1.72 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4455,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 2.07/1.72 inference(monotonicity,[status(thm)],[4454])).
% 2.07/1.72 tff(4456,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 2.07/1.72 inference(transitivity,[status(thm)],[4455, 4453])).
% 2.07/1.72 tff(4457,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 2.07/1.72 inference(quant_inst,[status(thm)],[])).
% 2.07/1.72 tff(4458,plain,
% 2.07/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 2.07/1.72 inference(modus_ponens,[status(thm)],[4457, 4456])).
% 2.07/1.72 tff(4459,plain,
% 2.07/1.72 (~c2_1(a2450)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4458, 204, 4452, 4451, 3650, 2772, 3648, 957, 951, 1160, 4448])).
% 2.07/1.72 tff(4460,plain,
% 2.07/1.72 (hskp12 | (~c1_1(a2408))),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[839, 204, 4156, 4446, 4444, 4131, 4130, 832])).
% 2.07/1.72 tff(4461,plain,
% 2.07/1.72 (hskp12),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4460, 4445])).
% 2.07/1.72 tff(4462,plain,
% 2.07/1.72 (~c1_1(a2417)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[229, 4461])).
% 2.07/1.72 tff(4463,plain,
% 2.07/1.72 (c3_1(a2417)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[246, 4461])).
% 2.07/1.72 tff(4464,plain,
% 2.07/1.72 (c0_1(a2450)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[655, 4450])).
% 2.07/1.72 tff(4465,plain,
% 2.07/1.72 (~c2_1(a2417)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[852, 204, 4464, 4452, 4451, 3650, 4463, 3649, 3648, 4462, 602])).
% 2.07/1.72 tff(4466,plain,
% 2.07/1.72 (~c0_1(a2417)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[235, 4461])).
% 2.07/1.72 tff(4467,plain,
% 2.07/1.72 ($false),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[860, 204, 4452, 4451, 3649, 3648, 4466, 4462, 11, 4465, 4459, 4448])).
% 2.07/1.72 tff(4468,plain,(hskp23), inference(lemma,lemma(discharge,[]))).
% 2.07/1.72 tff(4469,plain,
% 2.07/1.72 (hskp15),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[548, 4468])).
% 2.07/1.72 tff(4470,plain,
% 2.07/1.72 (~c2_1(a2422)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[576, 4469])).
% 2.07/1.72 tff(4471,plain,
% 2.07/1.72 (c3_1(a2422)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[559, 4469])).
% 2.07/1.72 tff(4472,plain,
% 2.07/1.72 (c1_1(a2422)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[570, 4469])).
% 2.07/1.72 tff(4473,plain,
% 2.07/1.72 (c1_1(a2435)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[2602, 204, 4472, 4471, 4201, 4131, 4130, 4470, 4200, 4199, 11])).
% 2.07/1.72 tff(4474,plain,
% 2.07/1.72 (hskp18),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[4182, 4229, 4473])).
% 2.07/1.72 tff(4475,plain,
% 2.07/1.72 (~c3_1(a2428)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[3167, 4474])).
% 2.07/1.72 tff(4476,plain,
% 2.07/1.72 (~c2_1(a2428)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[3173, 4474])).
% 2.07/1.72 tff(4477,plain,
% 2.07/1.72 (~c0_1(a2428)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[3179, 4474])).
% 2.07/1.72 tff(4478,plain,
% 2.07/1.72 (~c0_1(a2455)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[516, 4468])).
% 2.07/1.72 tff(4479,plain,
% 2.07/1.72 (c2_1(a2455)),
% 2.07/1.72 inference(unit_resolution,[status(thm)],[538, 4468])).
% 2.07/1.72 tff(4480,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4481,plain,
% 2.07/1.72 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.72 inference(rewrite,[status(thm)],[])).
% 2.07/1.72 tff(4482,plain,
% 2.07/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 2.07/1.73 inference(monotonicity,[status(thm)],[4481])).
% 2.07/1.73 tff(4483,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(transitivity,[status(thm)],[4482, 4480])).
% 2.07/1.73 tff(4484,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 2.07/1.73 inference(quant_inst,[status(thm)],[])).
% 2.07/1.73 tff(4485,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 2.07/1.73 inference(modus_ponens,[status(thm)],[4484, 4483])).
% 2.07/1.73 tff(4486,plain,
% 2.07/1.73 (~c1_1(a2455)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4485, 204, 4479, 4156, 4478, 4130, 4477, 4476, 4475, 63, 4473])).
% 2.07/1.73 tff(4487,plain,
% 2.07/1.73 (c3_1(a2455)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[527, 4468])).
% 2.07/1.73 tff(4488,plain,
% 2.07/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4489,plain,
% 2.07/1.73 ((hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455))) <=> (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4490,plain,
% 2.07/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 2.07/1.73 inference(monotonicity,[status(thm)],[4489])).
% 2.07/1.73 tff(4491,plain,
% 2.07/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 2.07/1.73 inference(transitivity,[status(thm)],[4490, 4488])).
% 2.07/1.73 tff(4492,plain,
% 2.07/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))),
% 2.07/1.73 inference(quant_inst,[status(thm)],[])).
% 2.07/1.73 tff(4493,plain,
% 2.07/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 2.07/1.73 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 2.07/1.73 tff(4494,plain,
% 2.07/1.73 ($false),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4493, 204, 2087, 4479, 4487, 4478, 2097, 4486])).
% 2.07/1.73 tff(4495,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 2.07/1.73 tff(4496,plain,
% 2.07/1.73 (~c2_1(a2408)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[400, 4495])).
% 2.07/1.73 tff(4497,plain,
% 2.07/1.73 (c0_1(a2408)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[411, 4495])).
% 2.07/1.73 tff(4498,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4499,plain,
% 2.07/1.73 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4500,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 2.07/1.73 inference(monotonicity,[status(thm)],[4499])).
% 2.07/1.73 tff(4501,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 2.07/1.73 inference(transitivity,[status(thm)],[4500, 4498])).
% 2.07/1.73 tff(4502,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 2.07/1.73 inference(quant_inst,[status(thm)],[])).
% 2.07/1.73 tff(4503,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 2.07/1.73 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 2.07/1.73 tff(4504,plain,
% 2.07/1.73 ((~c0_1(a2403)) | c1_1(a2408)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4503, 204, 4497, 4201, 4131, 4130, 4496, 4200, 2008, 4473])).
% 2.07/1.73 tff(4505,plain,
% 2.07/1.73 (~c0_1(a2403)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4504, 1])).
% 2.07/1.73 tff(4506,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4507,plain,
% 2.07/1.73 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4508,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 2.07/1.73 inference(monotonicity,[status(thm)],[4507])).
% 2.07/1.73 tff(4509,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(transitivity,[status(thm)],[4508, 4506])).
% 2.07/1.73 tff(4510,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 2.07/1.73 inference(quant_inst,[status(thm)],[])).
% 2.07/1.73 tff(4511,plain,
% 2.07/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 2.07/1.73 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 2.07/1.73 tff(4512,plain,
% 2.07/1.73 (c0_1(a2403) | (~c1_1(a2455))),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4511, 204, 4479, 4472, 4471, 4478, 4470, 4200, 4199, 63])).
% 2.07/1.73 tff(4513,plain,
% 2.07/1.73 (~c1_1(a2455)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4512, 4505])).
% 2.07/1.73 tff(4514,plain,
% 2.07/1.73 (c3_1(a2408)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[429, 4495])).
% 2.07/1.73 tff(4515,plain,
% 2.07/1.73 (hskp29),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[3668, 204, 4479, 4497, 4514, 4478, 1117, 1, 4513])).
% 2.07/1.73 tff(4516,plain,
% 2.07/1.73 (c3_1(a2409)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[1148, 4515])).
% 2.07/1.73 tff(4517,plain,
% 2.07/1.73 (c0_1(a2409)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[1792, 4515])).
% 2.07/1.73 tff(4518,plain,
% 2.07/1.73 (~c1_1(a2409)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[3677, 204, 4517, 4516, 4479, 4487, 3650, 3649, 3648, 602, 4513])).
% 2.07/1.73 tff(4519,plain,
% 2.07/1.73 (c2_1(a2409)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[1137, 4515])).
% 2.07/1.73 tff(4520,plain,
% 2.07/1.73 ($false),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[2576, 204, 4517, 4519, 4516, 4201, 4200, 4199, 2451, 4518])).
% 2.07/1.73 tff(4521,plain,(c1_1(a2408)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.73 tff(4522,plain,
% 2.07/1.73 ((~c1_1(a2408)) | c1_1(a2425)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[2412, 204, 3650, 4497, 4131, 4130, 3649, 4496, 2008, 4473])).
% 2.07/1.73 tff(4523,plain,
% 2.07/1.73 (c1_1(a2425)),
% 2.07/1.73 inference(unit_resolution,[status(thm)],[4522, 4521])).
% 2.07/1.73 tff(4524,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4525,plain,
% 2.07/1.73 (((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.73 inference(rewrite,[status(thm)],[])).
% 2.07/1.73 tff(4526,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 2.07/1.73 inference(monotonicity,[status(thm)],[4525])).
% 2.07/1.73 tff(4527,plain,
% 2.07/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 2.07/1.74 inference(transitivity,[status(thm)],[4526, 4524])).
% 2.07/1.74 tff(4528,plain,
% 2.07/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 2.07/1.74 inference(quant_inst,[status(thm)],[])).
% 2.07/1.74 tff(4529,plain,
% 2.07/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 2.07/1.74 inference(modus_ponens,[status(thm)],[4528, 4527])).
% 2.07/1.74 tff(4530,plain,
% 2.07/1.74 ((~c1_1(a2425)) | (~c1_1(a2455))),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[4529, 204, 4479, 4487, 3650, 2772, 3648, 957, 951, 1160])).
% 2.07/1.74 tff(4531,plain,
% 2.07/1.74 (~c1_1(a2455)),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[4530, 4523])).
% 2.07/1.74 tff(4532,plain,
% 2.07/1.74 (hskp30 | (~c1_1(a2408)) | (~c1_1(a2425))),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[701, 204, 3650, 4514, 3648, 4496, 612])).
% 2.07/1.74 tff(4533,plain,
% 2.07/1.74 (hskp30),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[4532, 4521, 4523])).
% 2.07/1.74 tff(4534,plain,
% 2.07/1.74 (c3_1(a2450)),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[633, 4533])).
% 2.07/1.74 tff(4535,plain,
% 2.07/1.74 (c1_1(a2450)),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[644, 4533])).
% 2.07/1.74 tff(4536,plain,
% 2.07/1.74 (c0_1(a2450)),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[655, 4533])).
% 2.07/1.74 tff(4537,plain,
% 2.07/1.74 ($false),
% 2.07/1.74 inference(unit_resolution,[status(thm)],[662, 204, 4536, 4535, 4534, 4479, 4487, 3650, 3649, 3648, 602, 4531])).
% 2.07/1.74 % SZS output end Proof
%------------------------------------------------------------------------------