TSTP Solution File: SYN478-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN478-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:55:47 EDT 2022
% Result : Unsatisfiable 1.15s 0.97s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN478-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 04:18:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.15/0.97 % SZS status Unsatisfiable
% 1.15/0.97 % SZS output start Proof
% 1.15/0.97 tff(c3_1_type, type, (
% 1.15/0.97 c3_1: $i > $o)).
% 1.15/0.97 tff(a1307_type, type, (
% 1.15/0.97 a1307: $i)).
% 1.15/0.97 tff(c0_1_type, type, (
% 1.15/0.97 c0_1: $i > $o)).
% 1.15/0.97 tff(a1338_type, type, (
% 1.15/0.97 a1338: $i)).
% 1.15/0.97 tff(c2_1_type, type, (
% 1.15/0.97 c2_1: $i > $o)).
% 1.15/0.97 tff(hskp29_type, type, (
% 1.15/0.97 hskp29: $o)).
% 1.15/0.97 tff(a1315_type, type, (
% 1.15/0.97 a1315: $i)).
% 1.15/0.97 tff(c1_1_type, type, (
% 1.15/0.97 c1_1: $i > $o)).
% 1.15/0.97 tff(ndr1_0_type, type, (
% 1.15/0.97 ndr1_0: $o)).
% 1.15/0.97 tff(hskp6_type, type, (
% 1.15/0.97 hskp6: $o)).
% 1.15/0.97 tff(a1326_type, type, (
% 1.15/0.97 a1326: $i)).
% 1.15/0.97 tff(hskp18_type, type, (
% 1.15/0.97 hskp18: $o)).
% 1.15/0.97 tff(hskp13_type, type, (
% 1.15/0.97 hskp13: $o)).
% 1.15/0.97 tff(hskp27_type, type, (
% 1.15/0.97 hskp27: $o)).
% 1.15/0.97 tff(a1339_type, type, (
% 1.15/0.97 a1339: $i)).
% 1.15/0.97 tff(a1319_type, type, (
% 1.15/0.97 a1319: $i)).
% 1.15/0.97 tff(hskp8_type, type, (
% 1.15/0.97 hskp8: $o)).
% 1.15/0.97 tff(a1320_type, type, (
% 1.15/0.97 a1320: $i)).
% 1.15/0.97 tff(hskp9_type, type, (
% 1.15/0.97 hskp9: $o)).
% 1.15/0.97 tff(a1324_type, type, (
% 1.15/0.97 a1324: $i)).
% 1.15/0.97 tff(hskp11_type, type, (
% 1.15/0.97 hskp11: $o)).
% 1.15/0.97 tff(a1356_type, type, (
% 1.15/0.97 a1356: $i)).
% 1.15/0.97 tff(hskp22_type, type, (
% 1.15/0.97 hskp22: $o)).
% 1.15/0.97 tff(a1348_type, type, (
% 1.15/0.97 a1348: $i)).
% 1.15/0.97 tff(hskp28_type, type, (
% 1.15/0.97 hskp28: $o)).
% 1.15/0.97 tff(hskp20_type, type, (
% 1.15/0.97 hskp20: $o)).
% 1.15/0.97 tff(a1308_type, type, (
% 1.15/0.97 a1308: $i)).
% 1.15/0.97 tff(a1330_type, type, (
% 1.15/0.97 a1330: $i)).
% 1.15/0.97 tff(hskp14_type, type, (
% 1.15/0.97 hskp14: $o)).
% 1.15/0.97 tff(hskp1_type, type, (
% 1.15/0.97 hskp1: $o)).
% 1.15/0.97 tff(a1328_type, type, (
% 1.15/0.97 a1328: $i)).
% 1.15/0.97 tff(hskp7_type, type, (
% 1.15/0.97 hskp7: $o)).
% 1.15/0.97 tff(a1316_type, type, (
% 1.15/0.97 a1316: $i)).
% 1.15/0.97 tff(hskp3_type, type, (
% 1.15/0.97 hskp3: $o)).
% 1.15/0.97 tff(a1311_type, type, (
% 1.15/0.97 a1311: $i)).
% 1.15/0.97 tff(a1325_type, type, (
% 1.15/0.97 a1325: $i)).
% 1.15/0.97 tff(a1333_type, type, (
% 1.15/0.97 a1333: $i)).
% 1.15/0.97 tff(a1309_type, type, (
% 1.15/0.97 a1309: $i)).
% 1.15/0.97 tff(hskp2_type, type, (
% 1.15/0.97 hskp2: $o)).
% 1.15/0.97 tff(hskp16_type, type, (
% 1.15/0.97 hskp16: $o)).
% 1.15/0.97 tff(a1312_type, type, (
% 1.15/0.97 a1312: $i)).
% 1.15/0.97 tff(hskp4_type, type, (
% 1.15/0.97 hskp4: $o)).
% 1.15/0.97 tff(a1314_type, type, (
% 1.15/0.97 a1314: $i)).
% 1.15/0.97 tff(hskp5_type, type, (
% 1.15/0.97 hskp5: $o)).
% 1.15/0.97 tff(a1334_type, type, (
% 1.15/0.97 a1334: $i)).
% 1.15/0.97 tff(hskp17_type, type, (
% 1.15/0.97 hskp17: $o)).
% 1.15/0.97 tff(a1331_type, type, (
% 1.15/0.97 a1331: $i)).
% 1.15/0.97 tff(hskp15_type, type, (
% 1.15/0.97 hskp15: $o)).
% 1.15/0.97 tff(hskp12_type, type, (
% 1.15/0.97 hskp12: $o)).
% 1.15/0.97 tff(a1352_type, type, (
% 1.15/0.97 a1352: $i)).
% 1.15/0.97 tff(hskp21_type, type, (
% 1.15/0.97 hskp21: $o)).
% 1.15/0.97 tff(a1372_type, type, (
% 1.15/0.97 a1372: $i)).
% 1.15/0.97 tff(hskp30_type, type, (
% 1.15/0.97 hskp30: $o)).
% 1.15/0.97 tff(a1394_type, type, (
% 1.15/0.97 a1394: $i)).
% 1.15/0.97 tff(hskp25_type, type, (
% 1.15/0.97 hskp25: $o)).
% 1.15/0.97 tff(1,plain,
% 1.15/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.15/0.97 inference(bind,[status(th)],[])).
% 1.15/0.97 tff(2,plain,
% 1.15/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.97 inference(quant_intro,[status(thm)],[1])).
% 1.15/0.97 tff(3,plain,
% 1.15/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.97 inference(rewrite,[status(thm)],[])).
% 1.15/0.97 tff(4,plain,
% 1.15/0.97 (^[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))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(5,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[4])).
% 1.15/0.98 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.15/0.98 tff(7,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.15/0.98 tff(8,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.15/0.98 tff(9,plain,(
% 1.15/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.98 inference(skolemize,[status(sab)],[8])).
% 1.15/0.98 tff(10,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.15/0.98 tff(11,assumption,(~hskp29), introduced(assumption)).
% 1.15/0.98 tff(12,plain,
% 1.15/0.98 (^[U: $i] : refl((hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(13,plain,
% 1.15/0.98 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[12])).
% 1.15/0.98 tff(14,plain,
% 1.15/0.98 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(15,plain,
% 1.15/0.98 (^[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) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(16,plain,
% 1.15/0.98 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[15])).
% 1.15/0.98 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.15/0.98 tff(18,plain,
% 1.15/0.98 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.15/0.98 tff(19,plain,
% 1.15/0.98 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.15/0.98 tff(20,plain,(
% 1.15/0.98 ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(skolemize,[status(sab)],[19])).
% 1.15/0.98 tff(21,plain,
% 1.15/0.98 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.15/0.98 tff(22,assumption,(~hskp27), introduced(assumption)).
% 1.15/0.98 tff(23,assumption,(~c2_1(a1339)), introduced(assumption)).
% 1.15/0.98 tff(24,assumption,(~c0_1(a1339)), introduced(assumption)).
% 1.15/0.98 tff(25,assumption,(c3_1(a1339)), introduced(assumption)).
% 1.15/0.98 tff(26,plain,
% 1.15/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(27,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[26])).
% 1.15/0.98 tff(28,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(29,plain,
% 1.15/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(30,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[29])).
% 1.15/0.98 tff(31,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.15/0.98 tff(32,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.15/0.98 tff(33,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.15/0.98 tff(34,plain,(
% 1.15/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(skolemize,[status(sab)],[33])).
% 1.15/0.98 tff(35,plain,
% 1.15/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[34, 27])).
% 1.15/0.98 tff(36,plain,
% 1.15/0.98 (^[U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(37,plain,
% 1.15/0.98 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[36])).
% 1.15/0.98 tff(38,plain,
% 1.15/0.98 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(39,plain,
% 1.15/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(40,plain,
% 1.15/0.98 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[39])).
% 1.15/0.98 tff(41,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.15/0.98 tff(42,plain,
% 1.15/0.98 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.15/0.98 tff(43,plain,
% 1.15/0.98 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.15/0.98 tff(44,plain,(
% 1.15/0.98 ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(skolemize,[status(sab)],[43])).
% 1.15/0.98 tff(45,plain,
% 1.15/0.98 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.15/0.98 tff(46,assumption,(~hskp11), introduced(assumption)).
% 1.15/0.98 tff(47,assumption,(~hskp20), introduced(assumption)).
% 1.15/0.98 tff(48,plain,
% 1.15/0.98 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(49,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[48])).
% 1.15/0.98 tff(50,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(51,plain,
% 1.15/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(52,plain,
% 1.15/0.98 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[51])).
% 1.15/0.98 tff(53,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.15/0.98 tff(54,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.15/0.98 tff(55,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.15/0.98 tff(56,plain,(
% 1.15/0.98 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(skolemize,[status(sab)],[55])).
% 1.15/0.98 tff(57,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.15/0.98 tff(58,plain,
% 1.15/0.98 ((hskp20 | hskp18) <=> (hskp20 | hskp18)),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(59,axiom,(hskp20 | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.15/0.98 tff(60,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.15/0.98 tff(61,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[60, 58])).
% 1.15/0.98 tff(62,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[61, 58])).
% 1.15/0.98 tff(63,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.15/0.98 tff(64,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[63, 58])).
% 1.15/0.98 tff(65,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[64, 58])).
% 1.15/0.98 tff(66,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[65, 58])).
% 1.15/0.98 tff(67,plain,
% 1.15/0.98 (hskp20 | hskp18),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[66, 58])).
% 1.15/0.98 tff(68,plain,
% 1.15/0.98 (hskp18),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[67, 47])).
% 1.15/0.98 tff(69,plain,
% 1.15/0.98 (((~hskp18) | (~c2_1(a1339))) <=> ((~hskp18) | (~c2_1(a1339)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(70,plain,
% 1.15/0.98 (((~c2_1(a1339)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1339)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(71,axiom,((~c2_1(a1339)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.15/0.98 tff(72,plain,
% 1.15/0.98 ((~hskp18) | (~c2_1(a1339))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.15/0.98 tff(73,plain,
% 1.15/0.98 ((~hskp18) | (~c2_1(a1339))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[72, 69])).
% 1.15/0.98 tff(74,plain,
% 1.15/0.98 (~c2_1(a1339)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[73, 68])).
% 1.15/0.98 tff(75,plain,
% 1.15/0.98 (((~hskp18) | (~c0_1(a1339))) <=> ((~hskp18) | (~c0_1(a1339)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(76,plain,
% 1.15/0.98 (((~c0_1(a1339)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a1339)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(77,axiom,((~c0_1(a1339)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.15/0.98 tff(78,plain,
% 1.15/0.98 ((~hskp18) | (~c0_1(a1339))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.15/0.98 tff(79,plain,
% 1.15/0.98 ((~hskp18) | (~c0_1(a1339))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[78, 75])).
% 1.15/0.98 tff(80,plain,
% 1.15/0.98 (~c0_1(a1339)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[79, 68])).
% 1.15/0.98 tff(81,plain,
% 1.15/0.98 (((~hskp18) | c1_1(a1339)) <=> ((~hskp18) | c1_1(a1339))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(82,axiom,((~hskp18) | c1_1(a1339)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.15/0.98 tff(83,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.15/0.98 tff(84,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[83, 81])).
% 1.15/0.98 tff(85,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[84, 81])).
% 1.15/0.98 tff(86,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.15/0.98 tff(87,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[86, 81])).
% 1.15/0.98 tff(88,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[87, 81])).
% 1.15/0.98 tff(89,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.15/0.98 tff(90,plain,
% 1.15/0.98 ((~hskp18) | c1_1(a1339)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[89, 81])).
% 1.15/0.98 tff(91,plain,
% 1.15/0.98 (c1_1(a1339)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[90, 68])).
% 1.15/0.98 tff(92,assumption,(hskp11), introduced(assumption)).
% 1.15/0.98 tff(93,plain,
% 1.15/0.98 (((~hskp11) | (~c1_1(a1324))) <=> ((~hskp11) | (~c1_1(a1324)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(94,plain,
% 1.15/0.98 (((~c1_1(a1324)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a1324)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(95,axiom,((~c1_1(a1324)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.15/0.98 tff(96,plain,
% 1.15/0.98 ((~hskp11) | (~c1_1(a1324))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.15/0.98 tff(97,plain,
% 1.15/0.98 ((~hskp11) | (~c1_1(a1324))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[96, 93])).
% 1.15/0.98 tff(98,plain,
% 1.15/0.98 (~c1_1(a1324)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[97, 92])).
% 1.15/0.98 tff(99,plain,
% 1.15/0.98 (((~hskp11) | c0_1(a1324)) <=> ((~hskp11) | c0_1(a1324))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(100,axiom,((~hskp11) | c0_1(a1324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.15/0.98 tff(101,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.15/0.98 tff(102,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[101, 99])).
% 1.15/0.98 tff(103,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[102, 99])).
% 1.15/0.98 tff(104,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.15/0.98 tff(105,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[104, 99])).
% 1.15/0.98 tff(106,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[105, 99])).
% 1.15/0.98 tff(107,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[106, 99])).
% 1.15/0.98 tff(108,plain,
% 1.15/0.98 ((~hskp11) | c0_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[107, 99])).
% 1.15/0.98 tff(109,plain,
% 1.15/0.98 (c0_1(a1324)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[108, 92])).
% 1.15/0.98 tff(110,plain,
% 1.15/0.98 (((~hskp11) | c3_1(a1324)) <=> ((~hskp11) | c3_1(a1324))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(111,axiom,((~hskp11) | c3_1(a1324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.15/0.98 tff(112,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.15/0.98 tff(113,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[112, 110])).
% 1.15/0.98 tff(114,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[113, 110])).
% 1.15/0.98 tff(115,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[114, 110])).
% 1.15/0.98 tff(116,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[115, 110])).
% 1.15/0.98 tff(117,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[116, 110])).
% 1.15/0.98 tff(118,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[117, 110])).
% 1.15/0.98 tff(119,plain,
% 1.15/0.98 ((~hskp11) | c3_1(a1324)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[118, 110])).
% 1.15/0.98 tff(120,plain,
% 1.15/0.98 (c3_1(a1324)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[119, 92])).
% 1.15/0.98 tff(121,assumption,(~c1_1(a1324)), introduced(assumption)).
% 1.15/0.98 tff(122,plain,
% 1.15/0.98 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(123,plain,
% 1.15/0.98 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(124,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause15')).
% 1.15/0.98 tff(125,plain,
% 1.15/0.98 (ndr1_0 | (~hskp18)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.15/0.98 tff(126,plain,
% 1.15/0.98 (ndr1_0 | (~hskp18)),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[125, 122])).
% 1.15/0.98 tff(127,plain,
% 1.15/0.98 (ndr1_0),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[126, 68])).
% 1.15/0.98 tff(128,plain,
% 1.15/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(129,plain,
% 1.15/0.98 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(130,plain,
% 1.15/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.15/0.98 inference(monotonicity,[status(thm)],[129])).
% 1.15/0.98 tff(131,plain,
% 1.15/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.98 inference(transitivity,[status(thm)],[130, 128])).
% 1.15/0.98 tff(132,plain,
% 1.15/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 1.15/0.98 inference(quant_inst,[status(thm)],[])).
% 1.15/0.98 tff(133,plain,
% 1.15/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.15/0.98 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.15/0.98 tff(134,plain,
% 1.15/0.98 ((~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[133, 127, 91, 80, 74, 121, 35])).
% 1.15/0.98 tff(135,plain,
% 1.15/0.98 (~c3_1(a1339)),
% 1.15/0.98 inference(unit_resolution,[status(thm)],[134, 120, 109])).
% 1.15/0.98 tff(136,plain,
% 1.15/0.98 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(137,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[136])).
% 1.15/0.98 tff(138,plain,
% 1.15/0.98 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.98 inference(rewrite,[status(thm)],[])).
% 1.15/0.98 tff(139,plain,
% 1.15/0.98 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.15/0.98 inference(bind,[status(th)],[])).
% 1.15/0.98 tff(140,plain,
% 1.15/0.98 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.98 inference(quant_intro,[status(thm)],[139])).
% 1.15/0.98 tff(141,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.15/0.99 tff(142,plain,
% 1.15/0.99 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.15/0.99 tff(143,plain,
% 1.15/0.99 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[142, 138])).
% 1.15/0.99 tff(144,plain,(
% 1.15/0.99 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.99 inference(skolemize,[status(sab)],[143])).
% 1.15/0.99 tff(145,plain,
% 1.15/0.99 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[144, 137])).
% 1.15/0.99 tff(146,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(147,plain,
% 1.15/0.99 ((hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324))) <=> (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(148,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[147])).
% 1.15/0.99 tff(149,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.15/0.99 inference(transitivity,[status(thm)],[148, 146])).
% 1.15/0.99 tff(150,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(151,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.15/0.99 tff(152,plain,
% 1.15/0.99 (c3_1(a1339) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[151, 47, 127, 91, 74, 121, 145])).
% 1.15/0.99 tff(153,plain,
% 1.15/0.99 ($false),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[152, 135, 120, 109])).
% 1.15/0.99 tff(154,plain,((~hskp11) | hskp20 | c1_1(a1324)), inference(lemma,lemma(discharge,[]))).
% 1.15/0.99 tff(155,plain,
% 1.15/0.99 ($false),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[154, 98, 92, 47])).
% 1.15/0.99 tff(156,plain,((~hskp11) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.15/0.99 tff(157,plain,
% 1.15/0.99 (~hskp11),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[156, 47])).
% 1.15/0.99 tff(158,assumption,(hskp13), introduced(assumption)).
% 1.15/0.99 tff(159,plain,
% 1.15/0.99 (((~hskp13) | (~c3_1(a1326))) <=> ((~hskp13) | (~c3_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(160,plain,
% 1.15/0.99 (((~c3_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(161,axiom,((~c3_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.15/0.99 tff(162,plain,
% 1.15/0.99 ((~hskp13) | (~c3_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.15/0.99 tff(163,plain,
% 1.15/0.99 ((~hskp13) | (~c3_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[162, 159])).
% 1.15/0.99 tff(164,plain,
% 1.15/0.99 (~c3_1(a1326)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[163, 158])).
% 1.15/0.99 tff(165,plain,
% 1.15/0.99 (((~hskp13) | (~c2_1(a1326))) <=> ((~hskp13) | (~c2_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(166,plain,
% 1.15/0.99 (((~c2_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(167,axiom,((~c2_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.15/0.99 tff(168,plain,
% 1.15/0.99 ((~hskp13) | (~c2_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.15/0.99 tff(169,plain,
% 1.15/0.99 ((~hskp13) | (~c2_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[168, 165])).
% 1.15/0.99 tff(170,plain,
% 1.15/0.99 (~c2_1(a1326)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[169, 158])).
% 1.15/0.99 tff(171,plain,
% 1.15/0.99 (((~hskp13) | (~c1_1(a1326))) <=> ((~hskp13) | (~c1_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(172,plain,
% 1.15/0.99 (((~c1_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1326)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(173,axiom,((~c1_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.15/0.99 tff(174,plain,
% 1.15/0.99 ((~hskp13) | (~c1_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.15/0.99 tff(175,plain,
% 1.15/0.99 ((~hskp13) | (~c1_1(a1326))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[174, 171])).
% 1.15/0.99 tff(176,plain,
% 1.15/0.99 (~c1_1(a1326)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[175, 158])).
% 1.15/0.99 tff(177,assumption,(c1_1(a1339)), introduced(assumption)).
% 1.15/0.99 tff(178,assumption,(ndr1_0), introduced(assumption)).
% 1.15/0.99 tff(179,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(180,plain,
% 1.15/0.99 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(181,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339))))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[180])).
% 1.15/0.99 tff(182,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 1.15/0.99 inference(transitivity,[status(thm)],[181, 179])).
% 1.15/0.99 tff(183,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(184,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.15/0.99 tff(185,plain,
% 1.15/0.99 ($false),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[184, 178, 46, 177, 24, 23, 176, 170, 164, 57])).
% 1.15/0.99 tff(186,plain,((~hskp13) | (~ndr1_0) | hskp11 | (~c1_1(a1339)) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.15/0.99 tff(187,plain,
% 1.15/0.99 (~hskp13),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[186, 127, 157, 91, 80, 74])).
% 1.15/0.99 tff(188,assumption,(~c3_1(a1339)), introduced(assumption)).
% 1.15/0.99 tff(189,plain,
% 1.15/0.99 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.15/0.99 inference(bind,[status(th)],[])).
% 1.15/0.99 tff(190,plain,
% 1.15/0.99 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(quant_intro,[status(thm)],[189])).
% 1.15/0.99 tff(191,plain,
% 1.15/0.99 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(192,plain,
% 1.15/0.99 (^[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) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.15/0.99 inference(bind,[status(th)],[])).
% 1.15/0.99 tff(193,plain,
% 1.15/0.99 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(quant_intro,[status(thm)],[192])).
% 1.15/0.99 tff(194,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.15/0.99 tff(195,plain,
% 1.15/0.99 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.15/0.99 tff(196,plain,
% 1.15/0.99 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.15/0.99 tff(197,plain,(
% 1.15/0.99 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(skolemize,[status(sab)],[196])).
% 1.15/0.99 tff(198,plain,
% 1.15/0.99 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[197, 190])).
% 1.15/0.99 tff(199,plain,
% 1.15/0.99 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(200,plain,
% 1.15/0.99 ((hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339))) <=> (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(201,plain,
% 1.15/0.99 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[200])).
% 1.15/0.99 tff(202,plain,
% 1.15/0.99 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.15/0.99 inference(transitivity,[status(thm)],[201, 199])).
% 1.15/0.99 tff(203,plain,
% 1.15/0.99 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(204,plain,
% 1.15/0.99 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.15/0.99 tff(205,plain,
% 1.15/0.99 (hskp14 | hskp13 | c3_1(a1339)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[204, 127, 91, 74, 198])).
% 1.15/0.99 tff(206,plain,
% 1.15/0.99 (hskp14),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[205, 188, 187])).
% 1.15/0.99 tff(207,plain,
% 1.15/0.99 (((~hskp14) | (~c2_1(a1330))) <=> ((~hskp14) | (~c2_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(208,plain,
% 1.15/0.99 (((~c2_1(a1330)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(209,axiom,((~c2_1(a1330)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.15/0.99 tff(210,plain,
% 1.15/0.99 ((~hskp14) | (~c2_1(a1330))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.15/0.99 tff(211,plain,
% 1.15/0.99 ((~hskp14) | (~c2_1(a1330))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[210, 207])).
% 1.15/0.99 tff(212,plain,
% 1.15/0.99 (~c2_1(a1330)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[211, 206])).
% 1.15/0.99 tff(213,plain,
% 1.15/0.99 (((~hskp14) | (~c1_1(a1330))) <=> ((~hskp14) | (~c1_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(214,plain,
% 1.15/0.99 (((~c1_1(a1330)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(215,axiom,((~c1_1(a1330)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.15/0.99 tff(216,plain,
% 1.15/0.99 ((~hskp14) | (~c1_1(a1330))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.15/0.99 tff(217,plain,
% 1.15/0.99 ((~hskp14) | (~c1_1(a1330))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[216, 213])).
% 1.15/0.99 tff(218,plain,
% 1.15/0.99 (~c1_1(a1330)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[217, 206])).
% 1.15/0.99 tff(219,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(220,plain,
% 1.15/0.99 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(221,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330)))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[220])).
% 1.15/0.99 tff(222,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 1.15/0.99 inference(transitivity,[status(thm)],[221, 219])).
% 1.15/0.99 tff(223,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(224,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.15/0.99 tff(225,plain,
% 1.15/0.99 (c3_1(a1330)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[224, 127, 157, 91, 80, 74, 218, 212, 57])).
% 1.15/0.99 tff(226,plain,
% 1.15/0.99 (((~hskp14) | c0_1(a1330)) <=> ((~hskp14) | c0_1(a1330))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(227,axiom,((~hskp14) | c0_1(a1330)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.15/0.99 tff(228,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.15/0.99 tff(229,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[228, 226])).
% 1.15/0.99 tff(230,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[229, 226])).
% 1.15/0.99 tff(231,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[230, 226])).
% 1.15/0.99 tff(232,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[231, 226])).
% 1.15/0.99 tff(233,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[232, 226])).
% 1.15/0.99 tff(234,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[233, 226])).
% 1.15/0.99 tff(235,plain,
% 1.15/0.99 ((~hskp14) | c0_1(a1330)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[234, 226])).
% 1.15/0.99 tff(236,plain,
% 1.15/0.99 (c0_1(a1330)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[235, 206])).
% 1.15/0.99 tff(237,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(238,plain,
% 1.15/0.99 ((hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330))) <=> (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(239,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[238])).
% 1.15/0.99 tff(240,plain,
% 1.15/0.99 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/0.99 inference(transitivity,[status(thm)],[239, 237])).
% 1.15/0.99 tff(241,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(242,plain,
% 1.15/0.99 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.15/0.99 tff(243,plain,
% 1.15/0.99 ($false),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[242, 47, 127, 91, 236, 74, 218, 145, 188, 225])).
% 1.15/0.99 tff(244,plain,(c3_1(a1339) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.15/0.99 tff(245,plain,
% 1.15/0.99 (c3_1(a1339)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[244, 47])).
% 1.15/0.99 tff(246,assumption,(hskp28), introduced(assumption)).
% 1.15/0.99 tff(247,plain,
% 1.15/0.99 (((~hskp28) | c2_1(a1328)) <=> ((~hskp28) | c2_1(a1328))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(248,axiom,((~hskp28) | c2_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.15/0.99 tff(249,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.15/0.99 tff(250,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[249, 247])).
% 1.15/0.99 tff(251,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[250, 247])).
% 1.15/0.99 tff(252,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[251, 247])).
% 1.15/0.99 tff(253,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[252, 247])).
% 1.15/0.99 tff(254,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[253, 247])).
% 1.15/0.99 tff(255,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[254, 247])).
% 1.15/0.99 tff(256,plain,
% 1.15/0.99 ((~hskp28) | c2_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[255, 247])).
% 1.15/0.99 tff(257,plain,
% 1.15/0.99 (c2_1(a1328)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[256, 246])).
% 1.15/0.99 tff(258,plain,
% 1.15/0.99 (((~hskp28) | c0_1(a1328)) <=> ((~hskp28) | c0_1(a1328))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(259,axiom,((~hskp28) | c0_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.15/0.99 tff(260,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.15/0.99 tff(261,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[260, 258])).
% 1.15/0.99 tff(262,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[261, 258])).
% 1.15/0.99 tff(263,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[262, 258])).
% 1.15/0.99 tff(264,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[263, 258])).
% 1.15/0.99 tff(265,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[264, 258])).
% 1.15/0.99 tff(266,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[265, 258])).
% 1.15/0.99 tff(267,plain,
% 1.15/0.99 ((~hskp28) | c0_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[266, 258])).
% 1.15/0.99 tff(268,plain,
% 1.15/0.99 (c0_1(a1328)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[267, 246])).
% 1.15/0.99 tff(269,assumption,(~hskp13), introduced(assumption)).
% 1.15/0.99 tff(270,plain,
% 1.15/0.99 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(271,plain,
% 1.15/0.99 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))),
% 1.15/0.99 inference(quant_inst,[status(thm)],[])).
% 1.15/0.99 tff(272,plain,
% 1.15/0.99 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328))),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.15/0.99 tff(273,plain,
% 1.15/0.99 (~c1_1(a1328)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[272, 178, 269, 268, 257, 45])).
% 1.15/0.99 tff(274,plain,
% 1.15/0.99 (((~hskp28) | c3_1(a1328)) <=> ((~hskp28) | c3_1(a1328))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(275,axiom,((~hskp28) | c3_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.15/0.99 tff(276,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[275, 274])).
% 1.15/0.99 tff(277,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[276, 274])).
% 1.15/0.99 tff(278,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[277, 274])).
% 1.15/0.99 tff(279,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[278, 274])).
% 1.15/0.99 tff(280,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[279, 274])).
% 1.15/0.99 tff(281,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[280, 274])).
% 1.15/0.99 tff(282,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[281, 274])).
% 1.15/0.99 tff(283,plain,
% 1.15/0.99 ((~hskp28) | c3_1(a1328)),
% 1.15/0.99 inference(modus_ponens,[status(thm)],[282, 274])).
% 1.15/0.99 tff(284,plain,
% 1.15/0.99 (c3_1(a1328)),
% 1.15/0.99 inference(unit_resolution,[status(thm)],[283, 246])).
% 1.15/0.99 tff(285,plain,
% 1.15/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(286,plain,
% 1.15/0.99 (((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 1.15/0.99 inference(rewrite,[status(thm)],[])).
% 1.15/0.99 tff(287,plain,
% 1.15/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328))))),
% 1.15/0.99 inference(monotonicity,[status(thm)],[286])).
% 1.15/0.99 tff(288,plain,
% 1.15/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 1.15/0.99 inference(transitivity,[status(thm)],[287, 285])).
% 1.15/0.99 tff(289,plain,
% 1.15/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(290,plain,
% 1.15/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.15/1.00 tff(291,plain,
% 1.15/1.00 ($false),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[290, 178, 268, 284, 177, 24, 23, 35, 25, 273])).
% 1.15/1.00 tff(292,plain,((~hskp28) | (~ndr1_0) | (~c1_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.15/1.00 tff(293,plain,
% 1.15/1.00 (~hskp28),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[292, 127, 91, 80, 74, 245, 187])).
% 1.15/1.00 tff(294,assumption,(hskp7), introduced(assumption)).
% 1.15/1.00 tff(295,plain,
% 1.15/1.00 (((~hskp7) | (~c2_1(a1316))) <=> ((~hskp7) | (~c2_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(296,plain,
% 1.15/1.00 (((~c2_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(297,axiom,((~c2_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.15/1.00 tff(298,plain,
% 1.15/1.00 ((~hskp7) | (~c2_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.15/1.00 tff(299,plain,
% 1.15/1.00 ((~hskp7) | (~c2_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[298, 295])).
% 1.15/1.00 tff(300,plain,
% 1.15/1.00 (~c2_1(a1316)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[299, 294])).
% 1.15/1.00 tff(301,plain,
% 1.15/1.00 (((~hskp7) | (~c3_1(a1316))) <=> ((~hskp7) | (~c3_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(302,plain,
% 1.15/1.00 (((~c3_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(303,axiom,((~c3_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.15/1.00 tff(304,plain,
% 1.15/1.00 ((~hskp7) | (~c3_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.15/1.00 tff(305,plain,
% 1.15/1.00 ((~hskp7) | (~c3_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[304, 301])).
% 1.15/1.00 tff(306,plain,
% 1.15/1.00 (~c3_1(a1316)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[305, 294])).
% 1.15/1.00 tff(307,assumption,(~c3_1(a1316)), introduced(assumption)).
% 1.15/1.00 tff(308,assumption,(~c2_1(a1316)), introduced(assumption)).
% 1.15/1.00 tff(309,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(310,plain,
% 1.15/1.00 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(311,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316)))),
% 1.15/1.00 inference(monotonicity,[status(thm)],[310])).
% 1.15/1.00 tff(312,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 1.15/1.00 inference(transitivity,[status(thm)],[311, 309])).
% 1.15/1.00 tff(313,plain,
% 1.15/1.00 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(314,plain,
% 1.15/1.00 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[313, 312])).
% 1.15/1.00 tff(315,plain,
% 1.15/1.00 (c3_1(a1316) | c1_1(a1316)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[314, 127, 157, 91, 80, 74, 308, 57])).
% 1.15/1.00 tff(316,plain,
% 1.15/1.00 (c1_1(a1316)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[315, 307])).
% 1.15/1.00 tff(317,plain,
% 1.15/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.15/1.00 inference(bind,[status(th)],[])).
% 1.15/1.00 tff(318,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(quant_intro,[status(thm)],[317])).
% 1.15/1.00 tff(319,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(320,plain,
% 1.15/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.15/1.00 inference(bind,[status(th)],[])).
% 1.15/1.00 tff(321,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(quant_intro,[status(thm)],[320])).
% 1.15/1.00 tff(322,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.15/1.00 tff(323,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.15/1.00 tff(324,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[323, 319])).
% 1.15/1.00 tff(325,plain,(
% 1.15/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(skolemize,[status(sab)],[324])).
% 1.15/1.00 tff(326,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[325, 318])).
% 1.15/1.00 tff(327,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(328,plain,
% 1.15/1.00 (((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(329,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316))))),
% 1.15/1.00 inference(monotonicity,[status(thm)],[328])).
% 1.15/1.00 tff(330,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 1.15/1.00 inference(transitivity,[status(thm)],[329, 327])).
% 1.15/1.00 tff(331,plain,
% 1.15/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(332,plain,
% 1.15/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.15/1.00 tff(333,plain,
% 1.15/1.00 (c3_1(a1316) | (~c3_1(a1339)) | (~c1_1(a1316))),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[332, 127, 91, 80, 74, 308, 326])).
% 1.15/1.00 tff(334,plain,
% 1.15/1.00 (~c3_1(a1339)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[333, 316, 307])).
% 1.15/1.00 tff(335,plain,
% 1.15/1.00 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(336,plain,
% 1.15/1.00 ((hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316))) <=> (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(337,plain,
% 1.15/1.00 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))))),
% 1.15/1.00 inference(monotonicity,[status(thm)],[336])).
% 1.15/1.00 tff(338,plain,
% 1.15/1.00 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.15/1.00 inference(transitivity,[status(thm)],[337, 335])).
% 1.15/1.00 tff(339,plain,
% 1.15/1.00 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(340,plain,
% 1.15/1.00 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.15/1.00 tff(341,plain,
% 1.15/1.00 (hskp14 | c3_1(a1316) | (~c1_1(a1316))),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[340, 127, 187, 308, 198])).
% 1.15/1.00 tff(342,plain,
% 1.15/1.00 (hskp14),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[341, 307, 316])).
% 1.15/1.00 tff(343,plain,
% 1.15/1.00 (~c1_1(a1330)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[217, 342])).
% 1.15/1.00 tff(344,plain,
% 1.15/1.00 (c0_1(a1330)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[235, 342])).
% 1.15/1.00 tff(345,plain,
% 1.15/1.00 (~c3_1(a1330)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[242, 47, 127, 91, 344, 74, 343, 145, 334])).
% 1.15/1.00 tff(346,plain,
% 1.15/1.00 (~c2_1(a1330)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[211, 342])).
% 1.15/1.00 tff(347,plain,
% 1.15/1.00 ($false),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[224, 127, 157, 91, 80, 74, 343, 346, 57, 345])).
% 1.15/1.00 tff(348,plain,(c3_1(a1316) | hskp20 | c2_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.00 tff(349,plain,
% 1.15/1.00 ($false),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[348, 306, 300, 47])).
% 1.15/1.00 tff(350,plain,((~hskp7) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.15/1.00 tff(351,plain,
% 1.15/1.00 (~hskp7),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[350, 47])).
% 1.15/1.00 tff(352,plain,
% 1.15/1.00 ((hskp28 | hskp7 | hskp1) <=> (hskp28 | hskp7 | hskp1)),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(353,plain,
% 1.15/1.00 (((hskp28 | hskp1) | hskp7) <=> (hskp28 | hskp7 | hskp1)),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(354,plain,
% 1.15/1.00 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(355,plain,
% 1.15/1.00 (((hskp28 | hskp1) | hskp7) <=> ((hskp28 | hskp1) | hskp7)),
% 1.15/1.00 inference(monotonicity,[status(thm)],[354])).
% 1.15/1.00 tff(356,plain,
% 1.15/1.00 (((hskp28 | hskp1) | hskp7) <=> (hskp28 | hskp7 | hskp1)),
% 1.15/1.00 inference(transitivity,[status(thm)],[355, 353])).
% 1.15/1.00 tff(357,axiom,((hskp28 | hskp1) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.15/1.00 tff(358,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[357, 356])).
% 1.15/1.00 tff(359,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[358, 352])).
% 1.15/1.00 tff(360,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[359, 352])).
% 1.15/1.00 tff(361,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[360, 352])).
% 1.15/1.00 tff(362,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[361, 352])).
% 1.15/1.00 tff(363,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[362, 352])).
% 1.15/1.00 tff(364,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[363, 352])).
% 1.15/1.00 tff(365,plain,
% 1.15/1.00 (hskp28 | hskp7 | hskp1),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[364, 352])).
% 1.15/1.00 tff(366,plain,
% 1.15/1.00 (hskp1),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[365, 351, 293])).
% 1.15/1.00 tff(367,plain,
% 1.15/1.00 (((~hskp1) | (~c1_1(a1308))) <=> ((~hskp1) | (~c1_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(368,plain,
% 1.15/1.00 (((~c1_1(a1308)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(369,axiom,((~c1_1(a1308)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.15/1.00 tff(370,plain,
% 1.15/1.00 ((~hskp1) | (~c1_1(a1308))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.15/1.00 tff(371,plain,
% 1.15/1.00 ((~hskp1) | (~c1_1(a1308))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[370, 367])).
% 1.15/1.00 tff(372,plain,
% 1.15/1.00 (~c1_1(a1308)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[371, 366])).
% 1.15/1.00 tff(373,plain,
% 1.15/1.00 (((~hskp1) | c3_1(a1308)) <=> ((~hskp1) | c3_1(a1308))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(374,axiom,((~hskp1) | c3_1(a1308)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.15/1.00 tff(375,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.15/1.00 tff(376,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[375, 373])).
% 1.15/1.00 tff(377,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[376, 373])).
% 1.15/1.00 tff(378,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[377, 373])).
% 1.15/1.00 tff(379,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[378, 373])).
% 1.15/1.00 tff(380,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[379, 373])).
% 1.15/1.00 tff(381,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[380, 373])).
% 1.15/1.00 tff(382,plain,
% 1.15/1.00 ((~hskp1) | c3_1(a1308)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[381, 373])).
% 1.15/1.00 tff(383,plain,
% 1.15/1.00 (c3_1(a1308)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[382, 366])).
% 1.15/1.00 tff(384,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(385,plain,
% 1.15/1.00 (((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(386,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308))))),
% 1.15/1.00 inference(monotonicity,[status(thm)],[385])).
% 1.15/1.00 tff(387,plain,
% 1.15/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 1.15/1.00 inference(transitivity,[status(thm)],[386, 384])).
% 1.15/1.00 tff(388,plain,
% 1.15/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(389,plain,
% 1.15/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.15/1.00 tff(390,plain,
% 1.15/1.00 (~c0_1(a1308)),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[389, 127, 91, 383, 80, 74, 372, 35, 245])).
% 1.15/1.00 tff(391,plain,
% 1.15/1.00 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.15/1.00 inference(bind,[status(th)],[])).
% 1.15/1.00 tff(392,plain,
% 1.15/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(quant_intro,[status(thm)],[391])).
% 1.15/1.00 tff(393,plain,
% 1.15/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(394,plain,
% 1.15/1.00 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.15/1.00 inference(bind,[status(th)],[])).
% 1.15/1.00 tff(395,plain,
% 1.15/1.00 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(quant_intro,[status(thm)],[394])).
% 1.15/1.00 tff(396,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.15/1.00 tff(397,plain,
% 1.15/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.15/1.00 tff(398,plain,
% 1.15/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[397, 393])).
% 1.15/1.00 tff(399,plain,(
% 1.15/1.00 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(skolemize,[status(sab)],[398])).
% 1.15/1.00 tff(400,plain,
% 1.15/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[399, 392])).
% 1.15/1.00 tff(401,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(402,plain,
% 1.15/1.00 ((hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308))) <=> (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(403,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308))))),
% 1.15/1.00 inference(monotonicity,[status(thm)],[402])).
% 1.15/1.00 tff(404,plain,
% 1.15/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 1.15/1.00 inference(transitivity,[status(thm)],[403, 401])).
% 1.15/1.00 tff(405,plain,
% 1.15/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))),
% 1.15/1.00 inference(quant_inst,[status(thm)],[])).
% 1.15/1.00 tff(406,plain,
% 1.15/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308))),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.15/1.00 tff(407,plain,
% 1.15/1.00 ($false),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[406, 127, 351, 91, 383, 74, 372, 400, 245, 390])).
% 1.15/1.00 tff(408,plain,(hskp20), inference(lemma,lemma(discharge,[]))).
% 1.15/1.00 tff(409,plain,
% 1.15/1.00 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(410,plain,
% 1.15/1.00 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(411,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause13')).
% 1.15/1.00 tff(412,plain,
% 1.15/1.00 (ndr1_0 | (~hskp20)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.15/1.00 tff(413,plain,
% 1.15/1.00 (ndr1_0 | (~hskp20)),
% 1.15/1.00 inference(modus_ponens,[status(thm)],[412, 409])).
% 1.15/1.00 tff(414,plain,
% 1.15/1.00 (ndr1_0),
% 1.15/1.00 inference(unit_resolution,[status(thm)],[413, 408])).
% 1.15/1.00 tff(415,assumption,(~c1_1(a1339)), introduced(assumption)).
% 1.15/1.00 tff(416,plain,
% 1.15/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.15/1.00 inference(bind,[status(th)],[])).
% 1.15/1.00 tff(417,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.00 inference(quant_intro,[status(thm)],[416])).
% 1.15/1.00 tff(418,plain,
% 1.15/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.00 inference(rewrite,[status(thm)],[])).
% 1.15/1.00 tff(419,plain,
% 1.15/1.00 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(420,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[419])).
% 1.15/1.01 tff(421,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.15/1.01 tff(422,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.15/1.01 tff(423,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[422, 418])).
% 1.15/1.01 tff(424,plain,(
% 1.15/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.01 inference(skolemize,[status(sab)],[423])).
% 1.15/1.01 tff(425,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[424, 417])).
% 1.15/1.01 tff(426,plain,
% 1.15/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(427,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[426])).
% 1.15/1.01 tff(428,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(429,plain,
% 1.15/1.01 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(430,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[429])).
% 1.15/1.01 tff(431,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.15/1.01 tff(432,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.15/1.01 tff(433,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[432, 428])).
% 1.15/1.01 tff(434,plain,(
% 1.15/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(skolemize,[status(sab)],[433])).
% 1.15/1.01 tff(435,plain,
% 1.15/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[434, 427])).
% 1.15/1.01 tff(436,plain,
% 1.15/1.01 (^[U: $i] : refl((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(437,plain,
% 1.15/1.01 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[436])).
% 1.15/1.01 tff(438,plain,
% 1.15/1.01 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(439,plain,
% 1.15/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite(((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(440,plain,
% 1.15/1.01 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[439])).
% 1.15/1.01 tff(441,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.15/1.01 tff(442,plain,
% 1.15/1.01 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.15/1.01 tff(443,plain,
% 1.15/1.01 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[442, 438])).
% 1.15/1.01 tff(444,plain,(
% 1.15/1.01 ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(skolemize,[status(sab)],[443])).
% 1.15/1.01 tff(445,plain,
% 1.15/1.01 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[444, 437])).
% 1.15/1.01 tff(446,plain,
% 1.15/1.01 (~hskp18),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[90, 415])).
% 1.15/1.01 tff(447,assumption,(hskp27), introduced(assumption)).
% 1.15/1.01 tff(448,plain,
% 1.15/1.01 (((~hskp27) | c2_1(a1307)) <=> ((~hskp27) | c2_1(a1307))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(449,axiom,((~hskp27) | c2_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.15/1.01 tff(450,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.15/1.01 tff(451,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[450, 448])).
% 1.15/1.01 tff(452,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[451, 448])).
% 1.15/1.01 tff(453,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[452, 448])).
% 1.15/1.01 tff(454,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[453, 448])).
% 1.15/1.01 tff(455,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[454, 448])).
% 1.15/1.01 tff(456,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[455, 448])).
% 1.15/1.01 tff(457,plain,
% 1.15/1.01 ((~hskp27) | c2_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[456, 448])).
% 1.15/1.01 tff(458,plain,
% 1.15/1.01 (c2_1(a1307)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[457, 447])).
% 1.15/1.01 tff(459,plain,
% 1.15/1.01 (((~hskp27) | c1_1(a1307)) <=> ((~hskp27) | c1_1(a1307))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(460,axiom,((~hskp27) | c1_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.15/1.01 tff(461,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.15/1.01 tff(462,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[461, 459])).
% 1.15/1.01 tff(463,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[462, 459])).
% 1.15/1.01 tff(464,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[463, 459])).
% 1.15/1.01 tff(465,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[464, 459])).
% 1.15/1.01 tff(466,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[465, 459])).
% 1.15/1.01 tff(467,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[466, 459])).
% 1.15/1.01 tff(468,plain,
% 1.15/1.01 ((~hskp27) | c1_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[467, 459])).
% 1.15/1.01 tff(469,plain,
% 1.15/1.01 (c1_1(a1307)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[468, 447])).
% 1.15/1.01 tff(470,plain,
% 1.15/1.01 (((~hskp27) | c0_1(a1307)) <=> ((~hskp27) | c0_1(a1307))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(471,axiom,((~hskp27) | c0_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.15/1.01 tff(472,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.15/1.01 tff(473,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[472, 470])).
% 1.15/1.01 tff(474,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[473, 470])).
% 1.15/1.01 tff(475,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[474, 470])).
% 1.15/1.01 tff(476,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[475, 470])).
% 1.15/1.01 tff(477,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[476, 470])).
% 1.15/1.01 tff(478,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[477, 470])).
% 1.15/1.01 tff(479,plain,
% 1.15/1.01 ((~hskp27) | c0_1(a1307)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[478, 470])).
% 1.15/1.01 tff(480,plain,
% 1.15/1.01 (c0_1(a1307)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[479, 447])).
% 1.15/1.01 tff(481,plain,
% 1.15/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(482,plain,
% 1.15/1.01 ((hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307))) <=> (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(483,plain,
% 1.15/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))))),
% 1.15/1.01 inference(monotonicity,[status(thm)],[482])).
% 1.15/1.01 tff(484,plain,
% 1.15/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.15/1.01 inference(transitivity,[status(thm)],[483, 481])).
% 1.15/1.01 tff(485,plain,
% 1.15/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))),
% 1.15/1.01 inference(quant_inst,[status(thm)],[])).
% 1.15/1.01 tff(486,plain,
% 1.15/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.15/1.01 tff(487,plain,
% 1.15/1.01 ($false),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[486, 414, 269, 480, 469, 458, 45])).
% 1.15/1.01 tff(488,plain,((~hskp27) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.15/1.01 tff(489,plain,
% 1.15/1.01 (~hskp27),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[488, 269])).
% 1.15/1.01 tff(490,plain,
% 1.15/1.01 ((hskp18 | hskp27 | hskp14) <=> (hskp18 | hskp27 | hskp14)),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(491,plain,
% 1.15/1.01 (((hskp27 | hskp14) | hskp18) <=> (hskp18 | hskp27 | hskp14)),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(492,plain,
% 1.15/1.01 ((hskp27 | hskp14) <=> (hskp27 | hskp14)),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(493,plain,
% 1.15/1.01 (((hskp27 | hskp14) | hskp18) <=> ((hskp27 | hskp14) | hskp18)),
% 1.15/1.01 inference(monotonicity,[status(thm)],[492])).
% 1.15/1.01 tff(494,plain,
% 1.15/1.01 (((hskp27 | hskp14) | hskp18) <=> (hskp18 | hskp27 | hskp14)),
% 1.15/1.01 inference(transitivity,[status(thm)],[493, 491])).
% 1.15/1.01 tff(495,axiom,((hskp27 | hskp14) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.15/1.01 tff(496,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.15/1.01 tff(497,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[496, 490])).
% 1.15/1.01 tff(498,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[497, 490])).
% 1.15/1.01 tff(499,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[498, 490])).
% 1.15/1.01 tff(500,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[499, 490])).
% 1.15/1.01 tff(501,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[500, 490])).
% 1.15/1.01 tff(502,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[501, 490])).
% 1.15/1.01 tff(503,plain,
% 1.15/1.01 (hskp18 | hskp27 | hskp14),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[502, 490])).
% 1.15/1.01 tff(504,plain,
% 1.15/1.01 (hskp14),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[503, 489, 446])).
% 1.15/1.01 tff(505,plain,
% 1.15/1.01 (~c2_1(a1330)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[211, 504])).
% 1.15/1.01 tff(506,plain,
% 1.15/1.01 (~c1_1(a1330)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[217, 504])).
% 1.15/1.01 tff(507,plain,
% 1.15/1.01 (c0_1(a1330)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[235, 504])).
% 1.15/1.01 tff(508,plain,
% 1.15/1.01 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(509,plain,
% 1.15/1.01 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(510,plain,
% 1.15/1.01 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))))),
% 1.15/1.01 inference(monotonicity,[status(thm)],[509])).
% 1.15/1.01 tff(511,plain,
% 1.15/1.01 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.15/1.01 inference(transitivity,[status(thm)],[510, 508])).
% 1.15/1.01 tff(512,plain,
% 1.15/1.01 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 1.15/1.01 inference(quant_inst,[status(thm)],[])).
% 1.15/1.01 tff(513,plain,
% 1.15/1.01 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.15/1.01 tff(514,plain,
% 1.15/1.01 (hskp29),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[513, 446, 414, 507, 506, 505, 21])).
% 1.15/1.01 tff(515,plain,
% 1.15/1.01 (((~hskp29) | c3_1(a1338)) <=> ((~hskp29) | c3_1(a1338))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(516,axiom,((~hskp29) | c3_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.15/1.01 tff(517,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.15/1.01 tff(518,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[517, 515])).
% 1.15/1.01 tff(519,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[518, 515])).
% 1.15/1.01 tff(520,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[519, 515])).
% 1.15/1.01 tff(521,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[520, 515])).
% 1.15/1.01 tff(522,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[521, 515])).
% 1.15/1.01 tff(523,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[522, 515])).
% 1.15/1.01 tff(524,plain,
% 1.15/1.01 ((~hskp29) | c3_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[523, 515])).
% 1.15/1.01 tff(525,plain,
% 1.15/1.01 (c3_1(a1338)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[524, 514])).
% 1.15/1.01 tff(526,plain,
% 1.15/1.01 (((~hskp29) | c2_1(a1338)) <=> ((~hskp29) | c2_1(a1338))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(527,axiom,((~hskp29) | c2_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.15/1.01 tff(528,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.15/1.01 tff(529,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[528, 526])).
% 1.15/1.01 tff(530,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[529, 526])).
% 1.15/1.01 tff(531,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[530, 526])).
% 1.15/1.01 tff(532,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[531, 526])).
% 1.15/1.01 tff(533,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[532, 526])).
% 1.15/1.01 tff(534,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[533, 526])).
% 1.15/1.01 tff(535,plain,
% 1.15/1.01 ((~hskp29) | c2_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[534, 526])).
% 1.15/1.01 tff(536,plain,
% 1.15/1.01 (c2_1(a1338)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[535, 514])).
% 1.15/1.01 tff(537,plain,
% 1.15/1.01 (((~hskp29) | c1_1(a1338)) <=> ((~hskp29) | c1_1(a1338))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(538,axiom,((~hskp29) | c1_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.15/1.01 tff(539,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[538, 537])).
% 1.15/1.01 tff(540,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[539, 537])).
% 1.15/1.01 tff(541,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[540, 537])).
% 1.15/1.01 tff(542,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[541, 537])).
% 1.15/1.01 tff(543,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[542, 537])).
% 1.15/1.01 tff(544,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[543, 537])).
% 1.15/1.01 tff(545,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[544, 537])).
% 1.15/1.01 tff(546,plain,
% 1.15/1.01 ((~hskp29) | c1_1(a1338)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[545, 537])).
% 1.15/1.01 tff(547,plain,
% 1.15/1.01 (c1_1(a1338)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[546, 514])).
% 1.15/1.01 tff(548,plain,
% 1.15/1.01 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(549,plain,
% 1.15/1.01 ((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(550,plain,
% 1.15/1.01 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 1.15/1.01 inference(monotonicity,[status(thm)],[549])).
% 1.15/1.01 tff(551,plain,
% 1.15/1.01 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.15/1.01 inference(transitivity,[status(thm)],[550, 548])).
% 1.15/1.01 tff(552,plain,
% 1.15/1.01 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))),
% 1.15/1.01 inference(quant_inst,[status(thm)],[])).
% 1.15/1.01 tff(553,plain,
% 1.15/1.01 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.15/1.01 tff(554,plain,
% 1.15/1.01 (hskp22),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[553, 414, 46, 547, 536, 525, 445])).
% 1.15/1.01 tff(555,plain,
% 1.15/1.01 (((~hskp22) | c1_1(a1356)) <=> ((~hskp22) | c1_1(a1356))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(556,axiom,((~hskp22) | c1_1(a1356)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.15/1.01 tff(557,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.15/1.01 tff(558,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[557, 555])).
% 1.15/1.01 tff(559,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[558, 555])).
% 1.15/1.01 tff(560,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[559, 555])).
% 1.15/1.01 tff(561,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[560, 555])).
% 1.15/1.01 tff(562,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[561, 555])).
% 1.15/1.01 tff(563,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[562, 555])).
% 1.15/1.01 tff(564,plain,
% 1.15/1.01 ((~hskp22) | c1_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[563, 555])).
% 1.15/1.01 tff(565,plain,
% 1.15/1.01 (c1_1(a1356)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[564, 554])).
% 1.15/1.01 tff(566,plain,
% 1.15/1.01 (((~hskp22) | c0_1(a1356)) <=> ((~hskp22) | c0_1(a1356))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(567,axiom,((~hskp22) | c0_1(a1356)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.15/1.01 tff(568,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.15/1.01 tff(569,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[568, 566])).
% 1.15/1.01 tff(570,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[569, 566])).
% 1.15/1.01 tff(571,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[570, 566])).
% 1.15/1.01 tff(572,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[571, 566])).
% 1.15/1.01 tff(573,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[572, 566])).
% 1.15/1.01 tff(574,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[573, 566])).
% 1.15/1.01 tff(575,plain,
% 1.15/1.01 ((~hskp22) | c0_1(a1356)),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[574, 566])).
% 1.15/1.01 tff(576,plain,
% 1.15/1.01 (c0_1(a1356)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[575, 554])).
% 1.15/1.01 tff(577,plain,
% 1.15/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(578,plain,
% 1.15/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 1.15/1.01 inference(quant_inst,[status(thm)],[])).
% 1.15/1.01 tff(579,plain,
% 1.15/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.15/1.01 tff(580,plain,
% 1.15/1.01 (~c2_1(a1356)),
% 1.15/1.01 inference(unit_resolution,[status(thm)],[579, 414, 269, 576, 565, 45])).
% 1.15/1.01 tff(581,plain,
% 1.15/1.01 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(582,plain,
% 1.15/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[581])).
% 1.15/1.01 tff(583,plain,
% 1.15/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(rewrite,[status(thm)],[])).
% 1.15/1.01 tff(584,plain,
% 1.15/1.01 (^[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)) | (~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))) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_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)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.15/1.01 inference(bind,[status(th)],[])).
% 1.15/1.01 tff(585,plain,
% 1.15/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(quant_intro,[status(thm)],[584])).
% 1.15/1.01 tff(586,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.15/1.01 tff(587,plain,
% 1.15/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[586, 585])).
% 1.15/1.01 tff(588,plain,
% 1.15/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(modus_ponens,[status(thm)],[587, 583])).
% 1.15/1.01 tff(589,plain,(
% 1.15/1.01 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.01 inference(skolemize,[status(sab)],[588])).
% 1.15/1.01 tff(590,plain,
% 1.15/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[589, 582])).
% 1.15/1.02 tff(591,plain,
% 1.15/1.02 (((~hskp22) | (~c3_1(a1356))) <=> ((~hskp22) | (~c3_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(592,plain,
% 1.15/1.02 (((~c3_1(a1356)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(593,axiom,((~c3_1(a1356)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.15/1.02 tff(594,plain,
% 1.15/1.02 ((~hskp22) | (~c3_1(a1356))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.15/1.02 tff(595,plain,
% 1.15/1.02 ((~hskp22) | (~c3_1(a1356))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[594, 591])).
% 1.15/1.02 tff(596,plain,
% 1.15/1.02 (~c3_1(a1356)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[595, 554])).
% 1.15/1.02 tff(597,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(598,plain,
% 1.15/1.02 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330))) <=> (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(599,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 1.15/1.02 inference(monotonicity,[status(thm)],[598])).
% 1.15/1.02 tff(600,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.15/1.02 inference(transitivity,[status(thm)],[599, 597])).
% 1.15/1.02 tff(601,plain,
% 1.15/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))),
% 1.15/1.02 inference(quant_inst,[status(thm)],[])).
% 1.15/1.02 tff(602,plain,
% 1.15/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.15/1.02 tff(603,plain,
% 1.15/1.02 (c3_1(a1330)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[602, 414, 489, 576, 565, 507, 596, 505, 590])).
% 1.15/1.02 tff(604,plain,
% 1.15/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(605,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(quant_intro,[status(thm)],[604])).
% 1.15/1.02 tff(606,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(607,plain,
% 1.15/1.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(608,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(quant_intro,[status(thm)],[607])).
% 1.15/1.02 tff(609,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.15/1.02 tff(610,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.15/1.02 tff(611,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[610, 606])).
% 1.15/1.02 tff(612,plain,(
% 1.15/1.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(skolemize,[status(sab)],[611])).
% 1.15/1.02 tff(613,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[612, 605])).
% 1.15/1.02 tff(614,plain,
% 1.15/1.02 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(615,plain,
% 1.15/1.02 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 1.15/1.02 inference(quant_inst,[status(thm)],[])).
% 1.15/1.02 tff(616,plain,
% 1.15/1.02 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[615, 614])).
% 1.15/1.02 tff(617,plain,
% 1.15/1.02 (~c0_1(a1338)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[616, 414, 269, 547, 536, 45])).
% 1.15/1.02 tff(618,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(619,plain,
% 1.15/1.02 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(620,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338))))),
% 1.15/1.02 inference(monotonicity,[status(thm)],[619])).
% 1.15/1.02 tff(621,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 1.15/1.02 inference(transitivity,[status(thm)],[620, 618])).
% 1.15/1.02 tff(622,plain,
% 1.15/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 1.15/1.02 inference(quant_inst,[status(thm)],[])).
% 1.15/1.02 tff(623,plain,
% 1.15/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[622, 621])).
% 1.15/1.02 tff(624,plain,
% 1.15/1.02 ((~c3_1(a1339)) | (~c3_1(a1330))),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[623, 414, 547, 525, 507, 24, 23, 506, 35, 617])).
% 1.15/1.02 tff(625,plain,
% 1.15/1.02 (~c3_1(a1339)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[624, 603])).
% 1.15/1.02 tff(626,plain,
% 1.15/1.02 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(627,plain,
% 1.15/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(quant_intro,[status(thm)],[626])).
% 1.15/1.02 tff(628,plain,
% 1.15/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(629,plain,
% 1.15/1.02 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(630,plain,
% 1.15/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(quant_intro,[status(thm)],[629])).
% 1.15/1.02 tff(631,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.15/1.02 tff(632,plain,
% 1.15/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.15/1.02 tff(633,plain,
% 1.15/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[632, 628])).
% 1.15/1.02 tff(634,plain,(
% 1.15/1.02 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(skolemize,[status(sab)],[633])).
% 1.15/1.02 tff(635,plain,
% 1.15/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[634, 627])).
% 1.15/1.02 tff(636,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(637,plain,
% 1.15/1.02 ((hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(638,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 1.15/1.02 inference(monotonicity,[status(thm)],[637])).
% 1.15/1.02 tff(639,plain,
% 1.15/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.15/1.02 inference(transitivity,[status(thm)],[638, 636])).
% 1.15/1.02 tff(640,plain,
% 1.15/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 1.15/1.02 inference(quant_inst,[status(thm)],[])).
% 1.15/1.02 tff(641,plain,
% 1.15/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.15/1.02 tff(642,plain,
% 1.15/1.02 (hskp3 | c3_1(a1339) | (~c3_1(a1330))),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[641, 414, 415, 507, 24, 505, 635])).
% 1.15/1.02 tff(643,plain,
% 1.15/1.02 (hskp3),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[642, 625, 603])).
% 1.15/1.02 tff(644,plain,
% 1.15/1.02 (((~hskp3) | (~c1_1(a1311))) <=> ((~hskp3) | (~c1_1(a1311)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(645,plain,
% 1.15/1.02 (((~c1_1(a1311)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a1311)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(646,axiom,((~c1_1(a1311)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.15/1.02 tff(647,plain,
% 1.15/1.02 ((~hskp3) | (~c1_1(a1311))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[646, 645])).
% 1.15/1.02 tff(648,plain,
% 1.15/1.02 ((~hskp3) | (~c1_1(a1311))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[647, 644])).
% 1.15/1.02 tff(649,plain,
% 1.15/1.02 (~c1_1(a1311)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[648, 643])).
% 1.15/1.02 tff(650,plain,
% 1.15/1.02 (((~hskp3) | c2_1(a1311)) <=> ((~hskp3) | c2_1(a1311))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(651,axiom,((~hskp3) | c2_1(a1311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.15/1.02 tff(652,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.15/1.02 tff(653,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[652, 650])).
% 1.15/1.02 tff(654,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[653, 650])).
% 1.15/1.02 tff(655,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[654, 650])).
% 1.15/1.02 tff(656,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[655, 650])).
% 1.15/1.02 tff(657,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[656, 650])).
% 1.15/1.02 tff(658,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[657, 650])).
% 1.15/1.02 tff(659,plain,
% 1.15/1.02 ((~hskp3) | c2_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[658, 650])).
% 1.15/1.02 tff(660,plain,
% 1.15/1.02 (c2_1(a1311)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[659, 643])).
% 1.15/1.02 tff(661,plain,
% 1.15/1.02 (((~hskp3) | c0_1(a1311)) <=> ((~hskp3) | c0_1(a1311))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(662,axiom,((~hskp3) | c0_1(a1311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.15/1.02 tff(663,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.15/1.02 tff(664,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[663, 661])).
% 1.15/1.02 tff(665,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[664, 661])).
% 1.15/1.02 tff(666,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[665, 661])).
% 1.15/1.02 tff(667,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[666, 661])).
% 1.15/1.02 tff(668,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[667, 661])).
% 1.15/1.02 tff(669,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[668, 661])).
% 1.15/1.02 tff(670,plain,
% 1.15/1.02 ((~hskp3) | c0_1(a1311)),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[669, 661])).
% 1.15/1.02 tff(671,plain,
% 1.15/1.02 (c0_1(a1311)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[670, 643])).
% 1.15/1.02 tff(672,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(673,plain,
% 1.15/1.02 (((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(674,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356))))),
% 1.15/1.02 inference(monotonicity,[status(thm)],[673])).
% 1.15/1.02 tff(675,plain,
% 1.15/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.15/1.02 inference(transitivity,[status(thm)],[674, 672])).
% 1.15/1.02 tff(676,plain,
% 1.15/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 1.15/1.02 inference(quant_inst,[status(thm)],[])).
% 1.15/1.02 tff(677,plain,
% 1.15/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.15/1.02 tff(678,plain,
% 1.15/1.02 ($false),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[677, 414, 576, 671, 660, 596, 506, 505, 649, 613, 603, 580])).
% 1.15/1.02 tff(679,plain,(hskp13 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.15/1.02 tff(680,plain,
% 1.15/1.02 (hskp13),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[679, 46, 24, 23, 415])).
% 1.15/1.02 tff(681,plain,
% 1.15/1.02 (~c3_1(a1326)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[163, 680])).
% 1.15/1.02 tff(682,plain,
% 1.15/1.02 (~c2_1(a1326)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[169, 680])).
% 1.15/1.02 tff(683,plain,
% 1.15/1.02 (~c1_1(a1326)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[175, 680])).
% 1.15/1.02 tff(684,plain,
% 1.15/1.02 (((~hskp20) | (~c0_1(a1348))) <=> ((~hskp20) | (~c0_1(a1348)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(685,plain,
% 1.15/1.02 (((~c0_1(a1348)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1348)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(686,axiom,((~c0_1(a1348)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.15/1.02 tff(687,plain,
% 1.15/1.02 ((~hskp20) | (~c0_1(a1348))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.15/1.02 tff(688,plain,
% 1.15/1.02 ((~hskp20) | (~c0_1(a1348))),
% 1.15/1.02 inference(modus_ponens,[status(thm)],[687, 684])).
% 1.15/1.02 tff(689,plain,
% 1.15/1.02 (~c0_1(a1348)),
% 1.15/1.02 inference(unit_resolution,[status(thm)],[688, 408])).
% 1.15/1.02 tff(690,plain,
% 1.15/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(691,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_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)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(quant_intro,[status(thm)],[690])).
% 1.15/1.02 tff(692,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_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)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.02 inference(rewrite,[status(thm)],[])).
% 1.15/1.02 tff(693,plain,
% 1.15/1.02 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.15/1.02 inference(bind,[status(th)],[])).
% 1.15/1.02 tff(694,plain,
% 1.15/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[693])).
% 1.15/1.03 tff(695,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.15/1.03 tff(696,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.15/1.03 tff(697,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[696, 692])).
% 1.15/1.03 tff(698,plain,(
% 1.15/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.03 inference(skolemize,[status(sab)],[697])).
% 1.15/1.03 tff(699,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[698, 691])).
% 1.15/1.03 tff(700,assumption,(~hskp14), introduced(assumption)).
% 1.15/1.03 tff(701,plain,
% 1.15/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.15/1.03 inference(bind,[status(th)],[])).
% 1.15/1.03 tff(702,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[701])).
% 1.15/1.03 tff(703,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(704,plain,
% 1.15/1.03 (^[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)) | (~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)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.15/1.03 inference(bind,[status(th)],[])).
% 1.15/1.03 tff(705,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[704])).
% 1.15/1.03 tff(706,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.15/1.03 tff(707,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[706, 705])).
% 1.15/1.03 tff(708,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[707, 703])).
% 1.15/1.03 tff(709,plain,(
% 1.15/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(skolemize,[status(sab)],[708])).
% 1.15/1.03 tff(710,plain,
% 1.15/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[709, 702])).
% 1.15/1.03 tff(711,assumption,(~hskp1), introduced(assumption)).
% 1.15/1.03 tff(712,plain,
% 1.15/1.03 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.15/1.03 inference(bind,[status(th)],[])).
% 1.15/1.03 tff(713,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[712])).
% 1.15/1.03 tff(714,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(715,plain,
% 1.15/1.03 (^[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)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.15/1.03 inference(bind,[status(th)],[])).
% 1.15/1.03 tff(716,plain,
% 1.15/1.03 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[715])).
% 1.15/1.03 tff(717,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.15/1.03 tff(718,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.15/1.03 tff(719,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[718, 714])).
% 1.15/1.03 tff(720,plain,(
% 1.15/1.03 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(skolemize,[status(sab)],[719])).
% 1.15/1.03 tff(721,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[720, 713])).
% 1.15/1.03 tff(722,plain,
% 1.15/1.03 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(723,plain,
% 1.15/1.03 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(724,plain,
% 1.15/1.03 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)))),
% 1.15/1.03 inference(monotonicity,[status(thm)],[723])).
% 1.15/1.03 tff(725,plain,
% 1.15/1.03 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.15/1.03 inference(transitivity,[status(thm)],[724, 722])).
% 1.23/1.03 tff(726,plain,
% 1.23/1.03 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(727,plain,
% 1.23/1.03 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[726, 725])).
% 1.23/1.03 tff(728,plain,
% 1.23/1.03 (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[727, 414, 23, 721])).
% 1.23/1.03 tff(729,plain,
% 1.23/1.03 (hskp2),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[728, 711, 415, 24])).
% 1.23/1.03 tff(730,plain,
% 1.23/1.03 (((~hskp2) | (~c2_1(a1309))) <=> ((~hskp2) | (~c2_1(a1309)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(731,plain,
% 1.23/1.03 (((~c2_1(a1309)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1309)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(732,axiom,((~c2_1(a1309)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.23/1.03 tff(733,plain,
% 1.23/1.03 ((~hskp2) | (~c2_1(a1309))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.23/1.03 tff(734,plain,
% 1.23/1.03 ((~hskp2) | (~c2_1(a1309))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[733, 730])).
% 1.23/1.03 tff(735,plain,
% 1.23/1.03 (~c2_1(a1309)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[734, 729])).
% 1.23/1.03 tff(736,plain,
% 1.23/1.03 ((hskp14 | hskp4 | hskp1) <=> (hskp14 | hskp4 | hskp1)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(737,plain,
% 1.23/1.03 (((hskp14 | hskp4) | hskp1) <=> (hskp14 | hskp4 | hskp1)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(738,axiom,((hskp14 | hskp4) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.23/1.03 tff(739,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.23/1.03 tff(740,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[739, 736])).
% 1.23/1.03 tff(741,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[740, 736])).
% 1.23/1.03 tff(742,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[741, 736])).
% 1.23/1.03 tff(743,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[742, 736])).
% 1.23/1.03 tff(744,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[743, 736])).
% 1.23/1.03 tff(745,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[744, 736])).
% 1.23/1.03 tff(746,plain,
% 1.23/1.03 (hskp14 | hskp4 | hskp1),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[745, 736])).
% 1.23/1.03 tff(747,plain,
% 1.23/1.03 (hskp4),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[746, 711, 700])).
% 1.23/1.03 tff(748,plain,
% 1.23/1.03 (((~hskp4) | (~c1_1(a1312))) <=> ((~hskp4) | (~c1_1(a1312)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(749,plain,
% 1.23/1.03 (((~c1_1(a1312)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1312)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(750,axiom,((~c1_1(a1312)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.23/1.03 tff(751,plain,
% 1.23/1.03 ((~hskp4) | (~c1_1(a1312))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.23/1.03 tff(752,plain,
% 1.23/1.03 ((~hskp4) | (~c1_1(a1312))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[751, 748])).
% 1.23/1.03 tff(753,plain,
% 1.23/1.03 (~c1_1(a1312)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[752, 747])).
% 1.23/1.03 tff(754,plain,
% 1.23/1.03 (((~hskp4) | c0_1(a1312)) <=> ((~hskp4) | c0_1(a1312))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(755,axiom,((~hskp4) | c0_1(a1312)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.23/1.03 tff(756,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.23/1.03 tff(757,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[756, 754])).
% 1.23/1.03 tff(758,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[757, 754])).
% 1.23/1.03 tff(759,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[758, 754])).
% 1.23/1.03 tff(760,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[759, 754])).
% 1.23/1.03 tff(761,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[760, 754])).
% 1.23/1.03 tff(762,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[761, 754])).
% 1.23/1.03 tff(763,plain,
% 1.23/1.03 ((~hskp4) | c0_1(a1312)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[762, 754])).
% 1.23/1.03 tff(764,plain,
% 1.23/1.03 (c0_1(a1312)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[763, 747])).
% 1.23/1.03 tff(765,plain,
% 1.23/1.03 (^[U: $i] : refl((hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(766,plain,
% 1.23/1.03 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[765])).
% 1.23/1.03 tff(767,plain,
% 1.23/1.03 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(768,plain,
% 1.23/1.03 (^[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) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(769,plain,
% 1.23/1.03 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[768])).
% 1.23/1.03 tff(770,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.23/1.03 tff(771,plain,
% 1.23/1.03 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[770, 769])).
% 1.23/1.03 tff(772,plain,
% 1.23/1.03 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[771, 767])).
% 1.23/1.03 tff(773,plain,(
% 1.23/1.03 ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(skolemize,[status(sab)],[772])).
% 1.23/1.03 tff(774,plain,
% 1.23/1.03 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[773, 766])).
% 1.23/1.03 tff(775,assumption,(~hskp18), introduced(assumption)).
% 1.23/1.03 tff(776,assumption,(~hskp16), introduced(assumption)).
% 1.23/1.03 tff(777,plain,
% 1.23/1.03 ((hskp18 | hskp16 | hskp5) <=> (hskp18 | hskp16 | hskp5)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(778,plain,
% 1.23/1.03 (((hskp18 | hskp5) | hskp16) <=> (hskp18 | hskp16 | hskp5)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(779,axiom,((hskp18 | hskp5) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.23/1.03 tff(780,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[779, 778])).
% 1.23/1.03 tff(781,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[780, 777])).
% 1.23/1.03 tff(782,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[781, 777])).
% 1.23/1.03 tff(783,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[782, 777])).
% 1.23/1.03 tff(784,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[783, 777])).
% 1.23/1.03 tff(785,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[784, 777])).
% 1.23/1.03 tff(786,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[785, 777])).
% 1.23/1.03 tff(787,plain,
% 1.23/1.03 (hskp18 | hskp16 | hskp5),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[786, 777])).
% 1.23/1.03 tff(788,plain,
% 1.23/1.03 (hskp5),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[787, 776, 775])).
% 1.23/1.03 tff(789,plain,
% 1.23/1.03 (((~hskp5) | (~c3_1(a1314))) <=> ((~hskp5) | (~c3_1(a1314)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(790,plain,
% 1.23/1.03 (((~c3_1(a1314)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1314)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(791,axiom,((~c3_1(a1314)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.23/1.03 tff(792,plain,
% 1.23/1.03 ((~hskp5) | (~c3_1(a1314))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.23/1.03 tff(793,plain,
% 1.23/1.03 ((~hskp5) | (~c3_1(a1314))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[792, 789])).
% 1.23/1.03 tff(794,plain,
% 1.23/1.03 (~c3_1(a1314)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[793, 788])).
% 1.23/1.03 tff(795,plain,
% 1.23/1.03 (((~hskp5) | c1_1(a1314)) <=> ((~hskp5) | c1_1(a1314))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(796,axiom,((~hskp5) | c1_1(a1314)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.23/1.03 tff(797,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.23/1.03 tff(798,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[797, 795])).
% 1.23/1.03 tff(799,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[798, 795])).
% 1.23/1.03 tff(800,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[799, 795])).
% 1.23/1.03 tff(801,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[800, 795])).
% 1.23/1.03 tff(802,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[801, 795])).
% 1.23/1.03 tff(803,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[802, 795])).
% 1.23/1.03 tff(804,plain,
% 1.23/1.03 ((~hskp5) | c1_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[803, 795])).
% 1.23/1.03 tff(805,plain,
% 1.23/1.03 (c1_1(a1314)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[804, 788])).
% 1.23/1.03 tff(806,plain,
% 1.23/1.03 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(807,plain,
% 1.23/1.03 ((hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314))) <=> (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(808,plain,
% 1.23/1.03 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314)))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[807])).
% 1.23/1.03 tff(809,plain,
% 1.23/1.03 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 1.23/1.03 inference(transitivity,[status(thm)],[808, 806])).
% 1.23/1.03 tff(810,plain,
% 1.23/1.03 ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(811,plain,
% 1.23/1.03 ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.23/1.03 tff(812,plain,
% 1.23/1.03 (c2_1(a1314)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[811, 414, 776, 700, 805, 794, 774])).
% 1.23/1.03 tff(813,assumption,(~c1_1(a1312)), introduced(assumption)).
% 1.23/1.03 tff(814,plain,
% 1.23/1.03 (((~hskp5) | (~c0_1(a1314))) <=> ((~hskp5) | (~c0_1(a1314)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(815,plain,
% 1.23/1.03 (((~c0_1(a1314)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1314)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(816,axiom,((~c0_1(a1314)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.23/1.03 tff(817,plain,
% 1.23/1.03 ((~hskp5) | (~c0_1(a1314))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.23/1.03 tff(818,plain,
% 1.23/1.03 ((~hskp5) | (~c0_1(a1314))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[817, 814])).
% 1.23/1.03 tff(819,plain,
% 1.23/1.03 (~c0_1(a1314)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[818, 788])).
% 1.23/1.03 tff(820,plain,
% 1.23/1.03 (^[U: $i] : refl((hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(821,plain,
% 1.23/1.03 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[820])).
% 1.23/1.03 tff(822,plain,
% 1.23/1.03 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(823,plain,
% 1.23/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(824,plain,
% 1.23/1.03 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[823])).
% 1.23/1.03 tff(825,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.23/1.03 tff(826,plain,
% 1.23/1.03 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.23/1.03 tff(827,plain,
% 1.23/1.03 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[826, 822])).
% 1.23/1.03 tff(828,plain,(
% 1.23/1.03 ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(skolemize,[status(sab)],[827])).
% 1.23/1.03 tff(829,plain,
% 1.23/1.03 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[828, 821])).
% 1.23/1.03 tff(830,plain,
% 1.23/1.03 (((~hskp20) | c2_1(a1348)) <=> ((~hskp20) | c2_1(a1348))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(831,axiom,((~hskp20) | c2_1(a1348)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.23/1.03 tff(832,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.23/1.03 tff(833,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[832, 830])).
% 1.23/1.03 tff(834,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[833, 830])).
% 1.23/1.03 tff(835,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[834, 830])).
% 1.23/1.03 tff(836,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[835, 830])).
% 1.23/1.03 tff(837,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[836, 830])).
% 1.23/1.03 tff(838,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[837, 830])).
% 1.23/1.03 tff(839,plain,
% 1.23/1.03 ((~hskp20) | c2_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[838, 830])).
% 1.23/1.03 tff(840,plain,
% 1.23/1.03 (c2_1(a1348)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[839, 408])).
% 1.23/1.03 tff(841,plain,
% 1.23/1.03 (((~hskp20) | c1_1(a1348)) <=> ((~hskp20) | c1_1(a1348))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(842,axiom,((~hskp20) | c1_1(a1348)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.23/1.03 tff(843,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[842, 841])).
% 1.23/1.03 tff(844,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[843, 841])).
% 1.23/1.03 tff(845,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[844, 841])).
% 1.23/1.03 tff(846,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[845, 841])).
% 1.23/1.03 tff(847,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[846, 841])).
% 1.23/1.03 tff(848,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[847, 841])).
% 1.23/1.03 tff(849,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[848, 841])).
% 1.23/1.03 tff(850,plain,
% 1.23/1.03 ((~hskp20) | c1_1(a1348)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[849, 841])).
% 1.23/1.03 tff(851,plain,
% 1.23/1.03 (c1_1(a1348)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[850, 408])).
% 1.23/1.03 tff(852,plain,
% 1.23/1.03 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(853,plain,
% 1.23/1.03 ((hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348))) <=> (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(854,plain,
% 1.23/1.03 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[853])).
% 1.23/1.03 tff(855,plain,
% 1.23/1.03 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.03 inference(transitivity,[status(thm)],[854, 852])).
% 1.23/1.03 tff(856,plain,
% 1.23/1.03 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(857,plain,
% 1.23/1.03 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.23/1.04 tff(858,plain,
% 1.23/1.04 (hskp17 | hskp16),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[857, 414, 851, 840, 689, 829])).
% 1.23/1.04 tff(859,plain,
% 1.23/1.04 (hskp17),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[858, 776])).
% 1.23/1.04 tff(860,plain,
% 1.23/1.04 (((~hskp17) | (~c0_1(a1334))) <=> ((~hskp17) | (~c0_1(a1334)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(861,plain,
% 1.23/1.04 (((~c0_1(a1334)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1334)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(862,axiom,((~c0_1(a1334)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.23/1.04 tff(863,plain,
% 1.23/1.04 ((~hskp17) | (~c0_1(a1334))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.23/1.04 tff(864,plain,
% 1.23/1.04 ((~hskp17) | (~c0_1(a1334))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[863, 860])).
% 1.23/1.04 tff(865,plain,
% 1.23/1.04 (~c0_1(a1334)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[864, 859])).
% 1.23/1.04 tff(866,assumption,(c0_1(a1312)), introduced(assumption)).
% 1.23/1.04 tff(867,plain,
% 1.23/1.04 (((~hskp17) | c3_1(a1334)) <=> ((~hskp17) | c3_1(a1334))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(868,axiom,((~hskp17) | c3_1(a1334)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.23/1.04 tff(869,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.23/1.04 tff(870,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[869, 867])).
% 1.23/1.04 tff(871,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[870, 867])).
% 1.23/1.04 tff(872,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[871, 867])).
% 1.23/1.04 tff(873,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[872, 867])).
% 1.23/1.04 tff(874,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[873, 867])).
% 1.23/1.04 tff(875,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[874, 867])).
% 1.23/1.04 tff(876,plain,
% 1.23/1.04 ((~hskp17) | c3_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[875, 867])).
% 1.23/1.04 tff(877,plain,
% 1.23/1.04 (c3_1(a1334)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[876, 859])).
% 1.23/1.04 tff(878,plain,
% 1.23/1.04 (((~hskp17) | c2_1(a1334)) <=> ((~hskp17) | c2_1(a1334))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(879,axiom,((~hskp17) | c2_1(a1334)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.23/1.04 tff(880,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.23/1.04 tff(881,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[880, 878])).
% 1.23/1.04 tff(882,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[881, 878])).
% 1.23/1.04 tff(883,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[882, 878])).
% 1.23/1.04 tff(884,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[883, 878])).
% 1.23/1.04 tff(885,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[884, 878])).
% 1.23/1.04 tff(886,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[885, 878])).
% 1.23/1.04 tff(887,plain,
% 1.23/1.04 ((~hskp17) | c2_1(a1334)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[886, 878])).
% 1.23/1.04 tff(888,plain,
% 1.23/1.04 (c2_1(a1334)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[887, 859])).
% 1.23/1.04 tff(889,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(890,plain,
% 1.23/1.04 (((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314))) <=> (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(891,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[890])).
% 1.23/1.04 tff(892,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[891, 889])).
% 1.23/1.04 tff(893,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(894,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.23/1.04 tff(895,plain,
% 1.23/1.04 (~c2_1(a1312)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[894, 414, 888, 877, 866, 865, 819, 794, 813, 425, 812])).
% 1.23/1.04 tff(896,plain,
% 1.23/1.04 (hskp27),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[503, 700, 775])).
% 1.23/1.04 tff(897,plain,
% 1.23/1.04 (c1_1(a1307)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[468, 896])).
% 1.23/1.04 tff(898,plain,
% 1.23/1.04 (c0_1(a1307)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[479, 896])).
% 1.23/1.04 tff(899,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(900,plain,
% 1.23/1.04 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314))) <=> (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(901,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[900])).
% 1.23/1.04 tff(902,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[901, 899])).
% 1.23/1.04 tff(903,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(904,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.23/1.04 tff(905,plain,
% 1.23/1.04 (~c3_1(a1307)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[904, 414, 898, 897, 888, 877, 865, 819, 794, 10, 812])).
% 1.23/1.04 tff(906,plain,
% 1.23/1.04 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(907,plain,
% 1.23/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[906])).
% 1.23/1.04 tff(908,plain,
% 1.23/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(909,plain,
% 1.23/1.04 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(910,plain,
% 1.23/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[909])).
% 1.23/1.04 tff(911,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.23/1.04 tff(912,plain,
% 1.23/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.23/1.04 tff(913,plain,
% 1.23/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[912, 908])).
% 1.23/1.04 tff(914,plain,(
% 1.23/1.04 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(skolemize,[status(sab)],[913])).
% 1.23/1.04 tff(915,plain,
% 1.23/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[914, 907])).
% 1.23/1.04 tff(916,plain,
% 1.23/1.04 (c2_1(a1307)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[457, 896])).
% 1.23/1.04 tff(917,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(918,plain,
% 1.23/1.04 ((hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312))) <=> (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(919,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[918])).
% 1.23/1.04 tff(920,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[919, 917])).
% 1.23/1.04 tff(921,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(922,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.23/1.04 tff(923,plain,
% 1.23/1.04 ($false),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[922, 414, 700, 898, 916, 866, 813, 915, 905, 895])).
% 1.23/1.04 tff(924,plain,(hskp16 | hskp14 | (~c0_1(a1312)) | c1_1(a1312) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.23/1.04 tff(925,plain,
% 1.23/1.04 (hskp16),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[924, 764, 700, 753, 446])).
% 1.23/1.04 tff(926,plain,
% 1.23/1.04 (((~hskp16) | (~c3_1(a1333))) <=> ((~hskp16) | (~c3_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(927,plain,
% 1.23/1.04 (((~c3_1(a1333)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(928,axiom,((~c3_1(a1333)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.23/1.04 tff(929,plain,
% 1.23/1.04 ((~hskp16) | (~c3_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.23/1.04 tff(930,plain,
% 1.23/1.04 ((~hskp16) | (~c3_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[929, 926])).
% 1.23/1.04 tff(931,plain,
% 1.23/1.04 (~c3_1(a1333)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[930, 925])).
% 1.23/1.04 tff(932,plain,
% 1.23/1.04 (((~hskp2) | c3_1(a1309)) <=> ((~hskp2) | c3_1(a1309))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(933,axiom,((~hskp2) | c3_1(a1309)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.23/1.04 tff(934,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.23/1.04 tff(935,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[934, 932])).
% 1.23/1.04 tff(936,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[935, 932])).
% 1.23/1.04 tff(937,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[936, 932])).
% 1.23/1.04 tff(938,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[937, 932])).
% 1.23/1.04 tff(939,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[938, 932])).
% 1.23/1.04 tff(940,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[939, 932])).
% 1.23/1.04 tff(941,plain,
% 1.23/1.04 ((~hskp2) | c3_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[940, 932])).
% 1.23/1.04 tff(942,plain,
% 1.23/1.04 (c3_1(a1309)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[941, 729])).
% 1.23/1.04 tff(943,plain,
% 1.23/1.04 (((~hskp2) | c1_1(a1309)) <=> ((~hskp2) | c1_1(a1309))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(944,axiom,((~hskp2) | c1_1(a1309)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.23/1.04 tff(945,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.23/1.04 tff(946,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[945, 943])).
% 1.23/1.04 tff(947,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[946, 943])).
% 1.23/1.04 tff(948,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[947, 943])).
% 1.23/1.04 tff(949,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[948, 943])).
% 1.23/1.04 tff(950,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[949, 943])).
% 1.23/1.04 tff(951,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[950, 943])).
% 1.23/1.04 tff(952,plain,
% 1.23/1.04 ((~hskp2) | c1_1(a1309)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[951, 943])).
% 1.23/1.04 tff(953,plain,
% 1.23/1.04 (c1_1(a1309)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[952, 729])).
% 1.23/1.04 tff(954,plain,
% 1.23/1.04 (((~hskp16) | c1_1(a1333)) <=> ((~hskp16) | c1_1(a1333))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(955,axiom,((~hskp16) | c1_1(a1333)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.23/1.04 tff(956,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.23/1.04 tff(957,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[956, 954])).
% 1.23/1.04 tff(958,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[957, 954])).
% 1.23/1.04 tff(959,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[958, 954])).
% 1.23/1.04 tff(960,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[959, 954])).
% 1.23/1.04 tff(961,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[960, 954])).
% 1.23/1.04 tff(962,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[961, 954])).
% 1.23/1.04 tff(963,plain,
% 1.23/1.04 ((~hskp16) | c1_1(a1333)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[962, 954])).
% 1.23/1.04 tff(964,plain,
% 1.23/1.04 (c1_1(a1333)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[963, 925])).
% 1.23/1.04 tff(965,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(966,plain,
% 1.23/1.04 (((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)) <=> (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(967,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[966])).
% 1.23/1.04 tff(968,plain,
% 1.23/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[967, 965])).
% 1.23/1.04 tff(969,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(970,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.23/1.04 tff(971,plain,
% 1.23/1.04 (~c0_1(a1333)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[970, 414, 415, 964, 953, 942, 24, 23, 931, 735, 710])).
% 1.23/1.04 tff(972,plain,
% 1.23/1.04 (((~hskp16) | (~c2_1(a1333))) <=> ((~hskp16) | (~c2_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(973,plain,
% 1.23/1.04 (((~c2_1(a1333)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(974,axiom,((~c2_1(a1333)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.23/1.04 tff(975,plain,
% 1.23/1.04 ((~hskp16) | (~c2_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.23/1.04 tff(976,plain,
% 1.23/1.04 ((~hskp16) | (~c2_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[975, 972])).
% 1.23/1.04 tff(977,plain,
% 1.23/1.04 (~c2_1(a1333)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[976, 925])).
% 1.23/1.04 tff(978,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(979,plain,
% 1.23/1.04 ((hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326)) <=> (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(980,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[979])).
% 1.23/1.04 tff(981,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[980, 978])).
% 1.23/1.04 tff(982,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(983,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[982, 981])).
% 1.23/1.04 tff(984,plain,
% 1.23/1.04 ($false),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[983, 414, 46, 964, 977, 683, 682, 681, 57, 971])).
% 1.23/1.04 tff(985,plain,(hskp1 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.04 tff(986,plain,
% 1.23/1.04 (hskp1),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[985, 700, 415, 24, 23, 46])).
% 1.23/1.04 tff(987,plain,
% 1.23/1.04 (((~hskp1) | (~c2_1(a1308))) <=> ((~hskp1) | (~c2_1(a1308)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(988,plain,
% 1.23/1.05 (((~c2_1(a1308)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a1308)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(989,axiom,((~c2_1(a1308)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.23/1.05 tff(990,plain,
% 1.23/1.05 ((~hskp1) | (~c2_1(a1308))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.23/1.05 tff(991,plain,
% 1.23/1.05 ((~hskp1) | (~c2_1(a1308))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[990, 987])).
% 1.23/1.05 tff(992,plain,
% 1.23/1.05 (~c2_1(a1308)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[991, 986])).
% 1.23/1.05 tff(993,plain,
% 1.23/1.05 (~c1_1(a1308)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[371, 986])).
% 1.23/1.05 tff(994,plain,
% 1.23/1.05 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(995,plain,
% 1.23/1.05 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[994])).
% 1.23/1.05 tff(996,plain,
% 1.23/1.05 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(997,plain,
% 1.23/1.05 (^[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)) | 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) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(998,plain,
% 1.23/1.05 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[997])).
% 1.23/1.05 tff(999,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.23/1.05 tff(1000,plain,
% 1.23/1.05 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[999, 998])).
% 1.23/1.05 tff(1001,plain,
% 1.23/1.05 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1000, 996])).
% 1.23/1.05 tff(1002,plain,(
% 1.23/1.05 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1001])).
% 1.23/1.05 tff(1003,plain,
% 1.23/1.05 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1002, 995])).
% 1.23/1.05 tff(1004,plain,
% 1.23/1.05 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1005,plain,
% 1.23/1.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1004])).
% 1.23/1.05 tff(1006,plain,
% 1.23/1.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1007,plain,
% 1.23/1.05 (^[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) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1008,plain,
% 1.23/1.05 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1007])).
% 1.23/1.05 tff(1009,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.23/1.05 tff(1010,plain,
% 1.23/1.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 1.23/1.05 tff(1011,plain,
% 1.23/1.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1010, 1006])).
% 1.23/1.05 tff(1012,plain,(
% 1.23/1.05 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1011])).
% 1.23/1.05 tff(1013,plain,
% 1.23/1.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1012, 1005])).
% 1.23/1.05 tff(1014,assumption,(~hskp7), introduced(assumption)).
% 1.23/1.05 tff(1015,plain,
% 1.23/1.05 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1016,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1015])).
% 1.23/1.05 tff(1017,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1018,plain,
% 1.23/1.05 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1019,plain,
% 1.23/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1018])).
% 1.23/1.05 tff(1020,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.23/1.05 tff(1021,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.23/1.05 tff(1022,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1021, 1017])).
% 1.23/1.05 tff(1023,plain,(
% 1.23/1.05 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1022])).
% 1.23/1.05 tff(1024,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1023, 1016])).
% 1.23/1.05 tff(1025,plain,
% 1.23/1.05 (hskp27),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[503, 700, 446])).
% 1.23/1.05 tff(1026,plain,
% 1.23/1.05 (c2_1(a1307)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[457, 1025])).
% 1.23/1.05 tff(1027,plain,
% 1.23/1.05 (c1_1(a1307)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[468, 1025])).
% 1.23/1.05 tff(1028,plain,
% 1.23/1.05 (c0_1(a1307)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[479, 1025])).
% 1.23/1.05 tff(1029,assumption,(~hskp8), introduced(assumption)).
% 1.23/1.05 tff(1030,plain,
% 1.23/1.05 (^[U: $i] : refl((hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1031,plain,
% 1.23/1.05 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1030])).
% 1.23/1.05 tff(1032,plain,
% 1.23/1.05 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1033,plain,
% 1.23/1.05 (^[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)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | 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))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1034,plain,
% 1.23/1.05 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1033])).
% 1.23/1.05 tff(1035,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.23/1.05 tff(1036,plain,
% 1.23/1.05 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.23/1.05 tff(1037,plain,
% 1.23/1.05 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 1.23/1.05 tff(1038,plain,(
% 1.23/1.05 ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1037])).
% 1.23/1.05 tff(1039,plain,
% 1.23/1.05 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1038, 1031])).
% 1.23/1.05 tff(1040,assumption,(c1_1(a1307)), introduced(assumption)).
% 1.23/1.05 tff(1041,assumption,(c0_1(a1307)), introduced(assumption)).
% 1.23/1.05 tff(1042,plain,
% 1.23/1.05 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1043,plain,
% 1.23/1.05 ((hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307))) <=> (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1044,plain,
% 1.23/1.05 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[1043])).
% 1.23/1.05 tff(1045,plain,
% 1.23/1.05 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.23/1.05 inference(transitivity,[status(thm)],[1044, 1042])).
% 1.23/1.05 tff(1046,plain,
% 1.23/1.05 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(1047,plain,
% 1.23/1.05 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.23/1.05 tff(1048,plain,
% 1.23/1.05 (hskp8 | c3_1(a1307)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1047, 414, 700, 1041, 1040, 1039])).
% 1.23/1.05 tff(1049,plain,
% 1.23/1.05 (c3_1(a1307)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1048, 1029])).
% 1.23/1.05 tff(1050,assumption,(~c2_1(a1326)), introduced(assumption)).
% 1.23/1.05 tff(1051,assumption,(~c1_1(a1326)), introduced(assumption)).
% 1.23/1.05 tff(1052,plain,
% 1.23/1.05 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1053,plain,
% 1.23/1.05 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326))) <=> (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1054,plain,
% 1.23/1.05 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[1053])).
% 1.23/1.05 tff(1055,plain,
% 1.23/1.05 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[1054, 1052])).
% 1.23/1.05 tff(1056,plain,
% 1.23/1.05 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(1057,plain,
% 1.23/1.05 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.23/1.05 tff(1058,plain,
% 1.23/1.05 (hskp8 | hskp7 | (~c0_1(a1326))),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1057, 414, 1051, 1050, 1013])).
% 1.23/1.05 tff(1059,plain,
% 1.23/1.05 (~c0_1(a1326)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1058, 1029, 1014])).
% 1.23/1.05 tff(1060,plain,
% 1.23/1.05 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1061,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1060])).
% 1.23/1.05 tff(1062,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1063,plain,
% 1.23/1.05 (^[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) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1064,plain,
% 1.23/1.05 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1063])).
% 1.23/1.05 tff(1065,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.23/1.05 tff(1066,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 1.23/1.05 tff(1067,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1066, 1062])).
% 1.23/1.05 tff(1068,plain,(
% 1.23/1.05 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1067])).
% 1.23/1.05 tff(1069,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1068, 1061])).
% 1.23/1.05 tff(1070,assumption,(~c3_1(a1326)), introduced(assumption)).
% 1.23/1.05 tff(1071,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1072,plain,
% 1.23/1.05 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1073,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[1072])).
% 1.23/1.05 tff(1074,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.23/1.05 inference(transitivity,[status(thm)],[1073, 1071])).
% 1.23/1.05 tff(1075,plain,
% 1.23/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(1076,plain,
% 1.23/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.23/1.05 tff(1077,plain,
% 1.23/1.05 (hskp8 | (~c3_1(a1348)) | c0_1(a1326)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1076, 414, 840, 689, 1050, 1070, 1069])).
% 1.23/1.05 tff(1078,plain,
% 1.23/1.05 (~c3_1(a1348)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[1077, 1059, 1029])).
% 1.23/1.05 tff(1079,plain,
% 1.23/1.05 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1080,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1079])).
% 1.23/1.05 tff(1081,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1082,plain,
% 1.23/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_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) | (~c1_1(U)) | (~c2_1(U)) | (~c3_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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(1083,plain,
% 1.23/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[1082])).
% 1.23/1.05 tff(1084,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.23/1.05 tff(1085,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.23/1.05 tff(1086,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1085, 1081])).
% 1.23/1.05 tff(1087,plain,(
% 1.23/1.05 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[1086])).
% 1.23/1.05 tff(1088,plain,
% 1.23/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[1087, 1080])).
% 1.23/1.05 tff(1089,assumption,(c2_1(a1307)), introduced(assumption)).
% 1.23/1.05 tff(1090,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(1091,plain,
% 1.23/1.05 ((hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1092,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1091])).
% 1.23/1.06 tff(1093,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.23/1.06 tff(1094,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1095,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.23/1.06 tff(1096,plain,
% 1.23/1.06 (hskp17 | (~c3_1(a1307))),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1095, 414, 1041, 1040, 1089, 1088])).
% 1.23/1.06 tff(1097,plain,
% 1.23/1.06 (hskp17),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1096, 1049])).
% 1.23/1.06 tff(1098,plain,
% 1.23/1.06 (~c0_1(a1334)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[864, 1097])).
% 1.23/1.06 tff(1099,plain,
% 1.23/1.06 (c3_1(a1334)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[876, 1097])).
% 1.23/1.06 tff(1100,plain,
% 1.23/1.06 (c2_1(a1334)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[887, 1097])).
% 1.23/1.06 tff(1101,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1102,plain,
% 1.23/1.06 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1103,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1102])).
% 1.23/1.06 tff(1104,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1103, 1101])).
% 1.23/1.06 tff(1105,plain,
% 1.23/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1106,plain,
% 1.23/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.23/1.06 tff(1107,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1106, 414, 1041, 1040, 840, 1100, 1099, 689, 1098, 10, 1078, 1049])).
% 1.23/1.06 tff(1108,plain,(hskp8 | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | c2_1(a1326) | c3_1(a1326) | hskp14 | hskp7 | c1_1(a1326)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(1109,plain,
% 1.23/1.06 (hskp8),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1108, 1028, 1027, 1026, 682, 681, 700, 1014, 683])).
% 1.23/1.06 tff(1110,plain,
% 1.23/1.06 (((~hskp8) | (~c3_1(a1319))) <=> ((~hskp8) | (~c3_1(a1319)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1111,plain,
% 1.23/1.06 (((~c3_1(a1319)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1319)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1112,axiom,((~c3_1(a1319)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.23/1.06 tff(1113,plain,
% 1.23/1.06 ((~hskp8) | (~c3_1(a1319))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 1.23/1.06 tff(1114,plain,
% 1.23/1.06 ((~hskp8) | (~c3_1(a1319))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1113, 1110])).
% 1.23/1.06 tff(1115,plain,
% 1.23/1.06 (~c3_1(a1319)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1114, 1109])).
% 1.23/1.06 tff(1116,plain,
% 1.23/1.06 (((~hskp8) | (~c0_1(a1319))) <=> ((~hskp8) | (~c0_1(a1319)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1117,plain,
% 1.23/1.06 (((~c0_1(a1319)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1319)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1118,axiom,((~c0_1(a1319)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.23/1.06 tff(1119,plain,
% 1.23/1.06 ((~hskp8) | (~c0_1(a1319))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.23/1.06 tff(1120,plain,
% 1.23/1.06 ((~hskp8) | (~c0_1(a1319))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1119, 1116])).
% 1.23/1.06 tff(1121,plain,
% 1.23/1.06 (~c0_1(a1319)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1120, 1109])).
% 1.23/1.06 tff(1122,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1123,plain,
% 1.23/1.06 ((hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339))) <=> (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1124,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1123])).
% 1.23/1.06 tff(1125,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.23/1.06 tff(1126,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1127,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.23/1.06 tff(1128,plain,
% 1.23/1.06 (~c3_1(a1339)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1127, 414, 1014, 415, 953, 942, 24, 735, 400])).
% 1.23/1.06 tff(1129,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1130,plain,
% 1.23/1.06 ((hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339)) <=> (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1131,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1130])).
% 1.23/1.06 tff(1132,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1131, 1129])).
% 1.23/1.06 tff(1133,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1134,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.23/1.06 tff(1135,plain,
% 1.23/1.06 (c0_1(a1309)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1134, 414, 46, 415, 953, 23, 735, 57, 1128])).
% 1.23/1.06 tff(1136,plain,
% 1.23/1.06 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(1137,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[1136])).
% 1.23/1.06 tff(1138,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1139,plain,
% 1.23/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(1140,plain,
% 1.23/1.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[1139])).
% 1.23/1.06 tff(1141,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.23/1.06 tff(1142,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.23/1.06 tff(1143,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1142, 1138])).
% 1.23/1.06 tff(1144,plain,(
% 1.23/1.06 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(skolemize,[status(sab)],[1143])).
% 1.23/1.06 tff(1145,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1144, 1137])).
% 1.23/1.06 tff(1146,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1147,plain,
% 1.23/1.06 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1148,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1147])).
% 1.23/1.06 tff(1149,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.23/1.06 tff(1150,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1151,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.23/1.06 tff(1152,plain,
% 1.23/1.06 (hskp6 | c0_1(a1339) | c3_1(a1339)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1151, 414, 851, 840, 689, 23, 1145])).
% 1.23/1.06 tff(1153,plain,
% 1.23/1.06 (hskp6),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1152, 1128, 24])).
% 1.23/1.06 tff(1154,plain,
% 1.23/1.06 (((~hskp6) | (~c0_1(a1315))) <=> ((~hskp6) | (~c0_1(a1315)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1155,plain,
% 1.23/1.06 (((~c0_1(a1315)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a1315)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1156,axiom,((~c0_1(a1315)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.23/1.06 tff(1157,plain,
% 1.23/1.06 ((~hskp6) | (~c0_1(a1315))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.23/1.06 tff(1158,plain,
% 1.23/1.06 ((~hskp6) | (~c0_1(a1315))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 1.23/1.06 tff(1159,plain,
% 1.23/1.06 (~c0_1(a1315)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1158, 1153])).
% 1.23/1.06 tff(1160,plain,
% 1.23/1.06 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(1161,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[1160])).
% 1.23/1.06 tff(1162,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1163,plain,
% 1.23/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(1164,plain,
% 1.23/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[1163])).
% 1.23/1.06 tff(1165,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.23/1.06 tff(1166,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 1.23/1.06 tff(1167,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 1.23/1.06 tff(1168,plain,(
% 1.23/1.06 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(skolemize,[status(sab)],[1167])).
% 1.23/1.06 tff(1169,plain,
% 1.23/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1168, 1161])).
% 1.23/1.06 tff(1170,plain,
% 1.23/1.06 (((~hskp4) | (~c3_1(a1312))) <=> ((~hskp4) | (~c3_1(a1312)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1171,plain,
% 1.23/1.06 (((~c3_1(a1312)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1312)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1172,axiom,((~c3_1(a1312)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.23/1.06 tff(1173,plain,
% 1.23/1.06 ((~hskp4) | (~c3_1(a1312))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 1.23/1.06 tff(1174,plain,
% 1.23/1.06 ((~hskp4) | (~c3_1(a1312))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1173, 1170])).
% 1.23/1.06 tff(1175,plain,
% 1.23/1.06 (~c3_1(a1312)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1174, 747])).
% 1.23/1.06 tff(1176,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1177,plain,
% 1.23/1.06 ((hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312))) <=> (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(1178,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[1177])).
% 1.23/1.06 tff(1179,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.23/1.06 tff(1180,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(1181,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.23/1.06 tff(1182,plain,
% 1.23/1.06 ((~c0_1(a1309)) | (~c2_1(a1312))),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[1181, 414, 46, 764, 953, 942, 1175, 1169])).
% 1.23/1.07 tff(1183,plain,
% 1.23/1.07 (~c2_1(a1312)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1182, 1135])).
% 1.23/1.07 tff(1184,plain,
% 1.23/1.07 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1185,plain,
% 1.23/1.07 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312))) <=> (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1186,plain,
% 1.23/1.07 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1185])).
% 1.23/1.07 tff(1187,plain,
% 1.23/1.07 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1186, 1184])).
% 1.23/1.07 tff(1188,plain,
% 1.23/1.07 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1189,plain,
% 1.23/1.07 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 1.23/1.07 tff(1190,plain,
% 1.23/1.07 (hskp8 | c2_1(a1312)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1189, 414, 1014, 764, 753, 1013])).
% 1.23/1.07 tff(1191,plain,
% 1.23/1.07 (hskp8),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1190, 1183])).
% 1.23/1.07 tff(1192,plain,
% 1.23/1.07 (~c3_1(a1319)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1114, 1191])).
% 1.23/1.07 tff(1193,plain,
% 1.23/1.07 (~c0_1(a1319)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1120, 1191])).
% 1.23/1.07 tff(1194,plain,
% 1.23/1.07 (((~hskp6) | c3_1(a1315)) <=> ((~hskp6) | c3_1(a1315))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1195,axiom,((~hskp6) | c3_1(a1315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.23/1.07 tff(1196,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.23/1.07 tff(1197,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1196, 1194])).
% 1.23/1.07 tff(1198,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1197, 1194])).
% 1.23/1.07 tff(1199,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1198, 1194])).
% 1.23/1.07 tff(1200,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1199, 1194])).
% 1.23/1.07 tff(1201,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1200, 1194])).
% 1.23/1.07 tff(1202,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 1.23/1.07 tff(1203,plain,
% 1.23/1.07 ((~hskp6) | c3_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1202, 1194])).
% 1.23/1.07 tff(1204,plain,
% 1.23/1.07 (c3_1(a1315)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1203, 1153])).
% 1.23/1.07 tff(1205,plain,
% 1.23/1.07 (((~hskp8) | c2_1(a1319)) <=> ((~hskp8) | c2_1(a1319))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1206,axiom,((~hskp8) | c2_1(a1319)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.23/1.07 tff(1207,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.23/1.07 tff(1208,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1207, 1205])).
% 1.23/1.07 tff(1209,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1208, 1205])).
% 1.23/1.07 tff(1210,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 1.23/1.07 tff(1211,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1210, 1205])).
% 1.23/1.07 tff(1212,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1211, 1205])).
% 1.23/1.07 tff(1213,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1212, 1205])).
% 1.23/1.07 tff(1214,plain,
% 1.23/1.07 ((~hskp8) | c2_1(a1319)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1213, 1205])).
% 1.23/1.07 tff(1215,plain,
% 1.23/1.07 (c2_1(a1319)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1214, 1191])).
% 1.23/1.07 tff(1216,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1217,plain,
% 1.23/1.07 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1218,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1217])).
% 1.23/1.07 tff(1219,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.23/1.07 tff(1220,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1221,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.23/1.07 tff(1222,plain,
% 1.23/1.07 (~c2_1(a1315)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1221, 414, 1215, 1204, 953, 942, 1193, 1192, 1159, 10, 1135])).
% 1.23/1.07 tff(1223,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1224,plain,
% 1.23/1.07 ((hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1225,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1224])).
% 1.23/1.07 tff(1226,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1225, 1223])).
% 1.23/1.07 tff(1227,plain,
% 1.23/1.07 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1228,plain,
% 1.23/1.07 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 1.23/1.07 tff(1229,plain,
% 1.23/1.07 (hskp3 | (~c0_1(a1309))),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1228, 414, 415, 942, 24, 735, 635, 1128])).
% 1.23/1.07 tff(1230,plain,
% 1.23/1.07 (hskp3),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1229, 1135])).
% 1.23/1.07 tff(1231,plain,
% 1.23/1.07 (~c1_1(a1311)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[648, 1230])).
% 1.23/1.07 tff(1232,plain,
% 1.23/1.07 (((~hskp6) | (~c1_1(a1315))) <=> ((~hskp6) | (~c1_1(a1315)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1233,plain,
% 1.23/1.07 (((~c1_1(a1315)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a1315)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1234,axiom,((~c1_1(a1315)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.23/1.07 tff(1235,plain,
% 1.23/1.07 ((~hskp6) | (~c1_1(a1315))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.23/1.07 tff(1236,plain,
% 1.23/1.07 ((~hskp6) | (~c1_1(a1315))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1235, 1232])).
% 1.23/1.07 tff(1237,plain,
% 1.23/1.07 (~c1_1(a1315)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1236, 1153])).
% 1.23/1.07 tff(1238,plain,
% 1.23/1.07 (c2_1(a1311)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[659, 1230])).
% 1.23/1.07 tff(1239,plain,
% 1.23/1.07 (c0_1(a1311)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[670, 1230])).
% 1.23/1.07 tff(1240,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1241,plain,
% 1.23/1.07 (((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1242,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315)))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1241])).
% 1.23/1.07 tff(1243,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.23/1.07 tff(1244,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1245,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.23/1.07 tff(1246,plain,
% 1.23/1.07 ($false),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1245, 414, 1204, 764, 1239, 1238, 1237, 1175, 1231, 613, 1183, 1222])).
% 1.23/1.07 tff(1247,plain,(hskp1 | hskp7 | c1_1(a1339) | c0_1(a1339) | hskp11 | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.07 tff(1248,plain,
% 1.23/1.07 (hskp1),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1247, 700, 415, 24, 46, 23, 1014])).
% 1.23/1.07 tff(1249,plain,
% 1.23/1.07 (~c2_1(a1308)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[991, 1248])).
% 1.23/1.07 tff(1250,plain,
% 1.23/1.07 (~c1_1(a1308)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[371, 1248])).
% 1.23/1.07 tff(1251,plain,
% 1.23/1.07 (c2_1(a1319)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1214, 1109])).
% 1.23/1.07 tff(1252,plain,
% 1.23/1.07 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1253,plain,
% 1.23/1.07 ((hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1254,plain,
% 1.23/1.07 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1253])).
% 1.23/1.07 tff(1255,plain,
% 1.23/1.07 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1254, 1252])).
% 1.23/1.07 tff(1256,plain,
% 1.23/1.07 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1257,plain,
% 1.23/1.07 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 1.23/1.07 tff(1258,plain,
% 1.23/1.07 (hskp15),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1257, 414, 700, 1251, 1121, 1115, 1003])).
% 1.23/1.07 tff(1259,plain,
% 1.23/1.07 (((~hskp15) | (~c3_1(a1331))) <=> ((~hskp15) | (~c3_1(a1331)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1260,plain,
% 1.23/1.07 (((~c3_1(a1331)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1331)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1261,axiom,((~c3_1(a1331)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.23/1.07 tff(1262,plain,
% 1.23/1.07 ((~hskp15) | (~c3_1(a1331))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 1.23/1.07 tff(1263,plain,
% 1.23/1.07 ((~hskp15) | (~c3_1(a1331))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1262, 1259])).
% 1.23/1.07 tff(1264,plain,
% 1.23/1.07 (~c3_1(a1331)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1263, 1258])).
% 1.23/1.07 tff(1265,plain,
% 1.23/1.07 (c3_1(a1308)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[382, 1248])).
% 1.23/1.07 tff(1266,plain,
% 1.23/1.07 (((~hskp15) | c2_1(a1331)) <=> ((~hskp15) | c2_1(a1331))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1267,axiom,((~hskp15) | c2_1(a1331)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.23/1.07 tff(1268,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 1.23/1.07 tff(1269,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1268, 1266])).
% 1.23/1.07 tff(1270,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1269, 1266])).
% 1.23/1.07 tff(1271,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1270, 1266])).
% 1.23/1.07 tff(1272,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1271, 1266])).
% 1.23/1.07 tff(1273,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1272, 1266])).
% 1.23/1.07 tff(1274,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1273, 1266])).
% 1.23/1.07 tff(1275,plain,
% 1.23/1.07 ((~hskp15) | c2_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1274, 1266])).
% 1.23/1.07 tff(1276,plain,
% 1.23/1.07 (c2_1(a1331)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1275, 1258])).
% 1.23/1.07 tff(1277,plain,
% 1.23/1.07 (((~hskp15) | c1_1(a1331)) <=> ((~hskp15) | c1_1(a1331))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1278,axiom,((~hskp15) | c1_1(a1331)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.23/1.07 tff(1279,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.23/1.07 tff(1280,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1279, 1277])).
% 1.23/1.07 tff(1281,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1280, 1277])).
% 1.23/1.07 tff(1282,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 1.23/1.07 tff(1283,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1282, 1277])).
% 1.23/1.07 tff(1284,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1283, 1277])).
% 1.23/1.07 tff(1285,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 1.23/1.07 tff(1286,plain,
% 1.23/1.07 ((~hskp15) | c1_1(a1331)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1285, 1277])).
% 1.23/1.07 tff(1287,plain,
% 1.23/1.07 (c1_1(a1331)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1286, 1258])).
% 1.23/1.07 tff(1288,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1289,plain,
% 1.23/1.07 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1290,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1289])).
% 1.23/1.07 tff(1291,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.23/1.07 tff(1292,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1293,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.23/1.07 tff(1294,plain,
% 1.23/1.07 (~c0_1(a1331)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1293, 414, 1287, 1276, 1265, 1264, 1250, 1249, 699])).
% 1.23/1.07 tff(1295,plain,
% 1.23/1.07 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1296,plain,
% 1.23/1.07 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1295])).
% 1.23/1.07 tff(1297,plain,
% 1.23/1.07 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1298,plain,
% 1.23/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_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) | (~c1_1(U)) | (~c2_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1299,plain,
% 1.23/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1298])).
% 1.23/1.07 tff(1300,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.23/1.07 tff(1301,plain,
% 1.23/1.07 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.23/1.07 tff(1302,plain,
% 1.23/1.07 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1301, 1297])).
% 1.23/1.07 tff(1303,plain,(
% 1.23/1.07 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(skolemize,[status(sab)],[1302])).
% 1.23/1.07 tff(1304,plain,
% 1.23/1.07 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1303, 1296])).
% 1.23/1.07 tff(1305,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1306,plain,
% 1.23/1.08 ((hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331))) <=> (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1307,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1306])).
% 1.23/1.08 tff(1308,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1307, 1305])).
% 1.23/1.08 tff(1309,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1310,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.23/1.08 tff(1311,plain,
% 1.23/1.08 (hskp12),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1310, 414, 1028, 1027, 1026, 1287, 1264, 1304, 1294])).
% 1.23/1.08 tff(1312,plain,
% 1.23/1.08 (((~hskp12) | (~c0_1(a1325))) <=> ((~hskp12) | (~c0_1(a1325)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1313,plain,
% 1.23/1.08 (((~c0_1(a1325)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1325)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1314,axiom,((~c0_1(a1325)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.23/1.08 tff(1315,plain,
% 1.23/1.08 ((~hskp12) | (~c0_1(a1325))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.23/1.08 tff(1316,plain,
% 1.23/1.08 ((~hskp12) | (~c0_1(a1325))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1315, 1312])).
% 1.23/1.08 tff(1317,plain,
% 1.23/1.08 (~c0_1(a1325)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1316, 1311])).
% 1.23/1.08 tff(1318,plain,
% 1.23/1.08 (((~hskp12) | c3_1(a1325)) <=> ((~hskp12) | c3_1(a1325))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1319,axiom,((~hskp12) | c3_1(a1325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.23/1.08 tff(1320,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.23/1.08 tff(1321,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1320, 1318])).
% 1.23/1.08 tff(1322,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1321, 1318])).
% 1.23/1.08 tff(1323,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 1.23/1.08 tff(1324,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1323, 1318])).
% 1.23/1.08 tff(1325,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1324, 1318])).
% 1.23/1.08 tff(1326,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1325, 1318])).
% 1.23/1.08 tff(1327,plain,
% 1.23/1.08 ((~hskp12) | c3_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1326, 1318])).
% 1.23/1.08 tff(1328,plain,
% 1.23/1.08 (c3_1(a1325)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1327, 1311])).
% 1.23/1.08 tff(1329,plain,
% 1.23/1.08 (((~hskp12) | c1_1(a1325)) <=> ((~hskp12) | c1_1(a1325))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1330,axiom,((~hskp12) | c1_1(a1325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.23/1.08 tff(1331,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 1.23/1.08 tff(1332,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1331, 1329])).
% 1.23/1.08 tff(1333,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1332, 1329])).
% 1.23/1.08 tff(1334,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 1.23/1.08 tff(1335,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1334, 1329])).
% 1.23/1.08 tff(1336,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1335, 1329])).
% 1.23/1.08 tff(1337,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1336, 1329])).
% 1.23/1.08 tff(1338,plain,
% 1.23/1.08 ((~hskp12) | c1_1(a1325)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1337, 1329])).
% 1.23/1.08 tff(1339,plain,
% 1.23/1.08 (c1_1(a1325)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1338, 1311])).
% 1.23/1.08 tff(1340,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1341,plain,
% 1.23/1.08 ((hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1342,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1341])).
% 1.23/1.08 tff(1343,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1342, 1340])).
% 1.23/1.08 tff(1344,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1345,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 1.23/1.08 tff(1346,plain,
% 1.23/1.08 (hskp4),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1345, 414, 1339, 1328, 1251, 1317, 1121, 1115, 1024])).
% 1.23/1.08 tff(1347,plain,
% 1.23/1.08 (~c1_1(a1312)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[752, 1346])).
% 1.23/1.08 tff(1348,plain,
% 1.23/1.08 (c0_1(a1312)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[763, 1346])).
% 1.23/1.08 tff(1349,plain,
% 1.23/1.08 (hskp16),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[924, 700, 1348, 1347, 446])).
% 1.23/1.08 tff(1350,plain,
% 1.23/1.08 (~c2_1(a1333)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[976, 1349])).
% 1.23/1.08 tff(1351,plain,
% 1.23/1.08 (c1_1(a1333)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[963, 1349])).
% 1.23/1.08 tff(1352,plain,
% 1.23/1.08 (c0_1(a1333)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[983, 414, 46, 1351, 1350, 683, 682, 681, 57])).
% 1.23/1.08 tff(1353,plain,
% 1.23/1.08 (~c3_1(a1333)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[930, 1349])).
% 1.23/1.08 tff(1354,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1355,plain,
% 1.23/1.08 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1356,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1355])).
% 1.23/1.08 tff(1357,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1356, 1354])).
% 1.23/1.08 tff(1358,plain,
% 1.23/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1359,plain,
% 1.23/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.23/1.08 tff(1360,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1359, 414, 1351, 1287, 1276, 1265, 1353, 1264, 1250, 1249, 699, 1352])).
% 1.23/1.08 tff(1361,plain,(hskp14 | hskp11 | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1362,plain,
% 1.23/1.08 (hskp14),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1361, 1014, 46, 415, 24, 23])).
% 1.23/1.08 tff(1363,plain,
% 1.23/1.08 (~c2_1(a1330)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[211, 1362])).
% 1.23/1.08 tff(1364,plain,
% 1.23/1.08 (~c1_1(a1330)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[217, 1362])).
% 1.23/1.08 tff(1365,plain,
% 1.23/1.08 (c0_1(a1330)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[235, 1362])).
% 1.23/1.08 tff(1366,plain,
% 1.23/1.08 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1367,plain,
% 1.23/1.08 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1368,plain,
% 1.23/1.08 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1367])).
% 1.23/1.08 tff(1369,plain,
% 1.23/1.08 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1368, 1366])).
% 1.23/1.08 tff(1370,plain,
% 1.23/1.08 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1371,plain,
% 1.23/1.08 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 1.23/1.08 tff(1372,plain,
% 1.23/1.08 (hskp8),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1371, 414, 1014, 1365, 1364, 1363, 1013])).
% 1.23/1.08 tff(1373,plain,
% 1.23/1.08 (~c3_1(a1319)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1114, 1372])).
% 1.23/1.08 tff(1374,plain,
% 1.23/1.08 (~c0_1(a1319)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1120, 1372])).
% 1.23/1.08 tff(1375,plain,
% 1.23/1.08 (hskp29),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[513, 446, 414, 1365, 1364, 1363, 21])).
% 1.23/1.08 tff(1376,plain,
% 1.23/1.08 (c3_1(a1338)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[524, 1375])).
% 1.23/1.08 tff(1377,plain,
% 1.23/1.08 (c2_1(a1338)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[535, 1375])).
% 1.23/1.08 tff(1378,plain,
% 1.23/1.08 (c1_1(a1338)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[546, 1375])).
% 1.23/1.08 tff(1379,plain,
% 1.23/1.08 (hskp22),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[553, 414, 46, 1378, 1377, 1376, 445])).
% 1.23/1.08 tff(1380,plain,
% 1.23/1.08 (~c3_1(a1356)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[595, 1379])).
% 1.23/1.08 tff(1381,plain,
% 1.23/1.08 (c1_1(a1356)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[564, 1379])).
% 1.23/1.08 tff(1382,plain,
% 1.23/1.08 (c0_1(a1356)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[575, 1379])).
% 1.23/1.08 tff(1383,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1384,plain,
% 1.23/1.08 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1385,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319))))),
% 1.28/1.08 inference(monotonicity,[status(thm)],[1384])).
% 1.28/1.08 tff(1386,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 1.28/1.08 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.28/1.08 tff(1387,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 1.28/1.08 inference(quant_inst,[status(thm)],[])).
% 1.28/1.08 tff(1388,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.28/1.08 tff(1389,plain,
% 1.28/1.08 (~c1_1(a1319)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[1388, 414, 1382, 1381, 1380, 683, 682, 681, 1374, 1373, 435])).
% 1.28/1.08 tff(1390,plain,
% 1.28/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.28/1.08 inference(bind,[status(th)],[])).
% 1.28/1.08 tff(1391,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(quant_intro,[status(thm)],[1390])).
% 1.28/1.08 tff(1392,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1393,plain,
% 1.28/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_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) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.28/1.08 inference(bind,[status(th)],[])).
% 1.28/1.08 tff(1394,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(quant_intro,[status(thm)],[1393])).
% 1.28/1.08 tff(1395,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.28/1.08 tff(1396,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.28/1.08 tff(1397,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1396, 1392])).
% 1.28/1.08 tff(1398,plain,(
% 1.28/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(skolemize,[status(sab)],[1397])).
% 1.28/1.08 tff(1399,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1398, 1391])).
% 1.28/1.08 tff(1400,plain,
% 1.28/1.08 (c2_1(a1319)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[1214, 1372])).
% 1.28/1.08 tff(1401,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1402,plain,
% 1.28/1.08 (((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319)) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1403,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319))))),
% 1.28/1.08 inference(monotonicity,[status(thm)],[1402])).
% 1.28/1.08 tff(1404,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.08 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.28/1.08 tff(1405,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))),
% 1.28/1.08 inference(quant_inst,[status(thm)],[])).
% 1.28/1.08 tff(1406,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.28/1.08 tff(1407,plain,
% 1.28/1.08 ($false),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[1406, 414, 1400, 1374, 1373, 1399, 1389])).
% 1.28/1.08 tff(1408,plain,(hskp7 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.08 tff(1409,plain,
% 1.28/1.08 (hskp7),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[1408, 46, 415, 24, 23])).
% 1.28/1.08 tff(1410,plain,
% 1.28/1.08 (~c3_1(a1316)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[305, 1409])).
% 1.28/1.08 tff(1411,plain,
% 1.28/1.08 (~c2_1(a1316)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[299, 1409])).
% 1.28/1.08 tff(1412,plain,
% 1.28/1.08 (((~hskp7) | (~c0_1(a1316))) <=> ((~hskp7) | (~c0_1(a1316)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1413,plain,
% 1.28/1.08 (((~c0_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a1316)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1414,axiom,((~c0_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.28/1.08 tff(1415,plain,
% 1.28/1.08 ((~hskp7) | (~c0_1(a1316))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.28/1.08 tff(1416,plain,
% 1.28/1.08 ((~hskp7) | (~c0_1(a1316))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1415, 1412])).
% 1.28/1.08 tff(1417,plain,
% 1.28/1.08 (~c0_1(a1316)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[1416, 1409])).
% 1.28/1.08 tff(1418,assumption,(~c0_1(a1316)), introduced(assumption)).
% 1.28/1.08 tff(1419,plain,
% 1.28/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1420,plain,
% 1.28/1.08 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(1421,plain,
% 1.28/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))))),
% 1.28/1.08 inference(monotonicity,[status(thm)],[1420])).
% 1.28/1.08 tff(1422,plain,
% 1.28/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.08 inference(transitivity,[status(thm)],[1421, 1419])).
% 1.28/1.08 tff(1423,plain,
% 1.28/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.28/1.08 inference(quant_inst,[status(thm)],[])).
% 1.28/1.08 tff(1424,plain,
% 1.28/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.28/1.08 tff(1425,plain,
% 1.28/1.08 (hskp8 | (~c3_1(a1348))),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1424, 414, 840, 689, 1418, 308, 307, 1069])).
% 1.28/1.09 tff(1426,plain,
% 1.28/1.09 (~c3_1(a1348)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1425, 1029])).
% 1.28/1.09 tff(1427,plain,
% 1.28/1.09 ($false),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1106, 414, 1041, 1040, 840, 1100, 1099, 689, 1098, 10, 1426, 1049])).
% 1.28/1.09 tff(1428,plain,(hskp8 | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | hskp14 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.09 tff(1429,plain,
% 1.28/1.09 (hskp8),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1428, 1028, 1027, 1026, 700, 1417, 1411, 1410])).
% 1.28/1.09 tff(1430,plain,
% 1.28/1.09 (~c3_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1114, 1429])).
% 1.28/1.09 tff(1431,plain,
% 1.28/1.09 (~c0_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1120, 1429])).
% 1.28/1.09 tff(1432,plain,
% 1.28/1.09 (c2_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1214, 1429])).
% 1.28/1.09 tff(1433,plain,
% 1.28/1.09 (hskp15),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1257, 414, 700, 1432, 1431, 1430, 1003])).
% 1.28/1.09 tff(1434,plain,
% 1.28/1.09 (~c3_1(a1331)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1263, 1433])).
% 1.28/1.09 tff(1435,plain,
% 1.28/1.09 (c3_1(a1308)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[382, 986])).
% 1.28/1.09 tff(1436,plain,
% 1.28/1.09 (c2_1(a1331)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1275, 1433])).
% 1.28/1.09 tff(1437,plain,
% 1.28/1.09 (c1_1(a1331)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1286, 1433])).
% 1.28/1.09 tff(1438,plain,
% 1.28/1.09 (~c0_1(a1331)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1293, 414, 1437, 1436, 1435, 1434, 993, 992, 699])).
% 1.28/1.09 tff(1439,plain,
% 1.28/1.09 (hskp12),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1310, 414, 1028, 1027, 1026, 1437, 1434, 1304, 1438])).
% 1.28/1.09 tff(1440,plain,
% 1.28/1.09 (~c0_1(a1325)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1316, 1439])).
% 1.28/1.09 tff(1441,plain,
% 1.28/1.09 (c3_1(a1325)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1327, 1439])).
% 1.28/1.09 tff(1442,plain,
% 1.28/1.09 (c1_1(a1325)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1338, 1439])).
% 1.28/1.09 tff(1443,plain,
% 1.28/1.09 (hskp4),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1345, 414, 1442, 1441, 1432, 1440, 1431, 1430, 1024])).
% 1.28/1.09 tff(1444,plain,
% 1.28/1.09 (~c1_1(a1312)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[752, 1443])).
% 1.28/1.09 tff(1445,plain,
% 1.28/1.09 (c0_1(a1312)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[763, 1443])).
% 1.28/1.09 tff(1446,plain,
% 1.28/1.09 (hskp16),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[924, 1445, 700, 1444, 446])).
% 1.28/1.09 tff(1447,plain,
% 1.28/1.09 (~c3_1(a1333)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[930, 1446])).
% 1.28/1.09 tff(1448,plain,
% 1.28/1.09 (c1_1(a1333)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[963, 1446])).
% 1.28/1.09 tff(1449,plain,
% 1.28/1.09 (~c0_1(a1333)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1359, 414, 1448, 1437, 1436, 1435, 1447, 1434, 993, 992, 699])).
% 1.28/1.09 tff(1450,plain,
% 1.28/1.09 (~c2_1(a1333)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[976, 1446])).
% 1.28/1.09 tff(1451,plain,
% 1.28/1.09 ($false),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[983, 414, 46, 1448, 1450, 683, 682, 681, 57, 1449])).
% 1.28/1.09 tff(1452,plain,(hskp14 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.09 tff(1453,plain,
% 1.28/1.09 (hskp14),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1452, 46, 415, 24, 23])).
% 1.28/1.09 tff(1454,plain,
% 1.28/1.09 (~c2_1(a1330)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[211, 1453])).
% 1.28/1.09 tff(1455,plain,
% 1.28/1.09 (~c1_1(a1330)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[217, 1453])).
% 1.28/1.09 tff(1456,plain,
% 1.28/1.09 (c0_1(a1330)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[235, 1453])).
% 1.28/1.09 tff(1457,plain,
% 1.28/1.09 (hskp29),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[513, 446, 414, 1456, 1455, 1454, 21])).
% 1.28/1.09 tff(1458,plain,
% 1.28/1.09 (c3_1(a1338)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[524, 1457])).
% 1.28/1.09 tff(1459,plain,
% 1.28/1.09 (c2_1(a1338)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[535, 1457])).
% 1.28/1.09 tff(1460,plain,
% 1.28/1.09 (c1_1(a1338)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[546, 1457])).
% 1.28/1.09 tff(1461,plain,
% 1.28/1.09 (hskp22),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[553, 414, 46, 1460, 1459, 1458, 445])).
% 1.28/1.09 tff(1462,plain,
% 1.28/1.09 (~c3_1(a1356)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[595, 1461])).
% 1.28/1.09 tff(1463,plain,
% 1.28/1.09 (c1_1(a1356)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[564, 1461])).
% 1.28/1.09 tff(1464,plain,
% 1.28/1.09 (c0_1(a1356)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[575, 1461])).
% 1.28/1.09 tff(1465,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1466,plain,
% 1.28/1.09 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1467,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1466])).
% 1.28/1.09 tff(1468,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1467, 1465])).
% 1.28/1.09 tff(1469,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1470,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.28/1.09 tff(1471,plain,
% 1.28/1.09 (c3_1(a1348)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1470, 414, 1464, 1463, 851, 1462, 689, 683, 682, 681, 435])).
% 1.28/1.09 tff(1472,plain,
% 1.28/1.09 (hskp8 | (~c3_1(a1348))),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1424, 414, 840, 689, 1417, 1411, 1410, 1069])).
% 1.28/1.09 tff(1473,plain,
% 1.28/1.09 (hskp8),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1472, 1471])).
% 1.28/1.09 tff(1474,plain,
% 1.28/1.09 (~c3_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1114, 1473])).
% 1.28/1.09 tff(1475,plain,
% 1.28/1.09 (~c0_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1120, 1473])).
% 1.28/1.09 tff(1476,plain,
% 1.28/1.09 (~c1_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1388, 414, 1464, 1463, 1462, 683, 682, 681, 1475, 1474, 435])).
% 1.28/1.09 tff(1477,plain,
% 1.28/1.09 (c2_1(a1319)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1214, 1473])).
% 1.28/1.09 tff(1478,plain,
% 1.28/1.09 ($false),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1406, 414, 1477, 1475, 1474, 1399, 1476])).
% 1.28/1.09 tff(1479,plain,(hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.09 tff(1480,plain,
% 1.28/1.09 (hskp11),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1479, 24, 415, 23])).
% 1.28/1.09 tff(1481,plain,
% 1.28/1.09 (~c1_1(a1324)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[97, 1480])).
% 1.28/1.09 tff(1482,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1483,plain,
% 1.28/1.09 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1484,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1483])).
% 1.28/1.09 tff(1485,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.28/1.09 tff(1486,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1487,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.28/1.09 tff(1488,plain,
% 1.28/1.09 (~c3_1(a1339)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1487, 414, 964, 24, 23, 977, 931, 326, 971])).
% 1.28/1.09 tff(1489,plain,
% 1.28/1.09 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.28/1.09 inference(bind,[status(th)],[])).
% 1.28/1.09 tff(1490,plain,
% 1.28/1.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(quant_intro,[status(thm)],[1489])).
% 1.28/1.09 tff(1491,plain,
% 1.28/1.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1492,plain,
% 1.28/1.09 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.28/1.09 inference(bind,[status(th)],[])).
% 1.28/1.09 tff(1493,plain,
% 1.28/1.09 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(quant_intro,[status(thm)],[1492])).
% 1.28/1.09 tff(1494,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.28/1.09 tff(1495,plain,
% 1.28/1.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.28/1.09 tff(1496,plain,
% 1.28/1.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1495, 1491])).
% 1.28/1.09 tff(1497,plain,(
% 1.28/1.09 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(skolemize,[status(sab)],[1496])).
% 1.28/1.09 tff(1498,plain,
% 1.28/1.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1497, 1490])).
% 1.28/1.09 tff(1499,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1500,plain,
% 1.28/1.09 ((hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333))) <=> (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1501,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1500])).
% 1.28/1.09 tff(1502,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1501, 1499])).
% 1.28/1.09 tff(1503,plain,
% 1.28/1.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1504,plain,
% 1.28/1.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.28/1.09 tff(1505,plain,
% 1.28/1.09 (hskp9),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1504, 414, 964, 977, 931, 1498, 971])).
% 1.28/1.09 tff(1506,plain,
% 1.28/1.09 (((~hskp9) | (~c1_1(a1320))) <=> ((~hskp9) | (~c1_1(a1320)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1507,plain,
% 1.28/1.09 (((~c1_1(a1320)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1320)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1508,axiom,((~c1_1(a1320)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.28/1.09 tff(1509,plain,
% 1.28/1.09 ((~hskp9) | (~c1_1(a1320))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 1.28/1.09 tff(1510,plain,
% 1.28/1.09 ((~hskp9) | (~c1_1(a1320))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1509, 1506])).
% 1.28/1.09 tff(1511,plain,
% 1.28/1.09 (~c1_1(a1320)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1510, 1505])).
% 1.28/1.09 tff(1512,plain,
% 1.28/1.09 (((~hskp9) | (~c0_1(a1320))) <=> ((~hskp9) | (~c0_1(a1320)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1513,plain,
% 1.28/1.09 (((~c0_1(a1320)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1320)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1514,axiom,((~c0_1(a1320)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.28/1.09 tff(1515,plain,
% 1.28/1.09 ((~hskp9) | (~c0_1(a1320))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 1.28/1.09 tff(1516,plain,
% 1.28/1.09 ((~hskp9) | (~c0_1(a1320))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1515, 1512])).
% 1.28/1.09 tff(1517,plain,
% 1.28/1.09 (~c0_1(a1320)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1516, 1505])).
% 1.28/1.09 tff(1518,plain,
% 1.28/1.09 (((~hskp9) | c2_1(a1320)) <=> ((~hskp9) | c2_1(a1320))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1519,axiom,((~hskp9) | c2_1(a1320)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.28/1.09 tff(1520,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.28/1.09 tff(1521,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1520, 1518])).
% 1.28/1.09 tff(1522,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1521, 1518])).
% 1.28/1.09 tff(1523,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 1.28/1.09 tff(1524,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1523, 1518])).
% 1.28/1.09 tff(1525,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1524, 1518])).
% 1.28/1.09 tff(1526,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1525, 1518])).
% 1.28/1.09 tff(1527,plain,
% 1.28/1.09 ((~hskp9) | c2_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1526, 1518])).
% 1.28/1.09 tff(1528,plain,
% 1.28/1.09 (c2_1(a1320)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1527, 1505])).
% 1.28/1.09 tff(1529,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1530,plain,
% 1.28/1.09 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1531,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320)))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1530])).
% 1.28/1.09 tff(1532,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.28/1.09 tff(1533,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1534,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.28/1.09 tff(1535,plain,
% 1.28/1.09 (c3_1(a1320)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1534, 414, 415, 1528, 24, 1517, 1511, 1399, 1488])).
% 1.28/1.09 tff(1536,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1537,plain,
% 1.28/1.09 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1538,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1537])).
% 1.28/1.09 tff(1539,plain,
% 1.28/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1538, 1536])).
% 1.28/1.09 tff(1540,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1541,plain,
% 1.28/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333))),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.28/1.09 tff(1542,plain,
% 1.28/1.09 (c0_1(a1309)),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1541, 414, 964, 942, 977, 931, 735, 326, 971])).
% 1.28/1.09 tff(1543,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1544,plain,
% 1.28/1.09 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333)) <=> (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 1.28/1.09 inference(rewrite,[status(thm)],[])).
% 1.28/1.09 tff(1545,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333)))),
% 1.28/1.09 inference(monotonicity,[status(thm)],[1544])).
% 1.28/1.09 tff(1546,plain,
% 1.28/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 1.28/1.09 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.28/1.09 tff(1547,plain,
% 1.28/1.09 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))),
% 1.28/1.09 inference(quant_inst,[status(thm)],[])).
% 1.28/1.09 tff(1548,plain,
% 1.28/1.09 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333)),
% 1.28/1.09 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.28/1.09 tff(1549,plain,
% 1.28/1.09 (hskp6),
% 1.28/1.09 inference(unit_resolution,[status(thm)],[1548, 414, 851, 840, 689, 977, 931, 1145, 971])).
% 1.28/1.10 tff(1550,plain,
% 1.28/1.10 (~c1_1(a1315)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1236, 1549])).
% 1.28/1.10 tff(1551,plain,
% 1.28/1.10 (~c0_1(a1315)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1158, 1549])).
% 1.28/1.10 tff(1552,plain,
% 1.28/1.10 (c3_1(a1315)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1203, 1549])).
% 1.28/1.10 tff(1553,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1554,plain,
% 1.28/1.10 ((hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315))) <=> (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1555,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1554])).
% 1.28/1.10 tff(1556,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1555, 1553])).
% 1.28/1.10 tff(1557,plain,
% 1.28/1.10 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1558,plain,
% 1.28/1.10 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 1.28/1.10 tff(1559,plain,
% 1.28/1.10 ($false),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1558, 414, 1014, 1552, 953, 942, 1551, 1550, 735, 400])).
% 1.28/1.10 tff(1560,plain,(hskp1 | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.28/1.10 tff(1561,plain,
% 1.28/1.10 (hskp1),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1560, 1014, 415, 24, 23, 700])).
% 1.28/1.10 tff(1562,plain,
% 1.28/1.10 (~c2_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[991, 1561])).
% 1.28/1.10 tff(1563,plain,
% 1.28/1.10 (~c1_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[371, 1561])).
% 1.28/1.10 tff(1564,plain,
% 1.28/1.10 (hskp13),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[488, 1025])).
% 1.28/1.10 tff(1565,plain,
% 1.28/1.10 (~c1_1(a1326)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[175, 1564])).
% 1.28/1.10 tff(1566,plain,
% 1.28/1.10 (~c3_1(a1326)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[163, 1564])).
% 1.28/1.10 tff(1567,plain,
% 1.28/1.10 (~c2_1(a1326)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[169, 1564])).
% 1.28/1.10 tff(1568,plain,
% 1.28/1.10 (hskp8),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1108, 1014, 1027, 1026, 1567, 1566, 700, 1028, 1565])).
% 1.28/1.10 tff(1569,plain,
% 1.28/1.10 (~c3_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1114, 1568])).
% 1.28/1.10 tff(1570,plain,
% 1.28/1.10 (~c0_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1120, 1568])).
% 1.28/1.10 tff(1571,plain,
% 1.28/1.10 (c2_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1214, 1568])).
% 1.28/1.10 tff(1572,plain,
% 1.28/1.10 (hskp15),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1257, 414, 700, 1571, 1570, 1569, 1003])).
% 1.28/1.10 tff(1573,plain,
% 1.28/1.10 (~c3_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1263, 1572])).
% 1.28/1.10 tff(1574,plain,
% 1.28/1.10 (c3_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[382, 1561])).
% 1.28/1.10 tff(1575,plain,
% 1.28/1.10 (c2_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1275, 1572])).
% 1.28/1.10 tff(1576,plain,
% 1.28/1.10 (c1_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1286, 1572])).
% 1.28/1.10 tff(1577,plain,
% 1.28/1.10 (~c0_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1293, 414, 1576, 1575, 1574, 1573, 1563, 1562, 699])).
% 1.28/1.10 tff(1578,plain,
% 1.28/1.10 (hskp12),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1310, 414, 1028, 1027, 1026, 1576, 1573, 1304, 1577])).
% 1.28/1.10 tff(1579,plain,
% 1.28/1.10 (~c0_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1316, 1578])).
% 1.28/1.10 tff(1580,plain,
% 1.28/1.10 (c3_1(a1324)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[119, 1480])).
% 1.28/1.10 tff(1581,plain,
% 1.28/1.10 (c0_1(a1324)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[108, 1480])).
% 1.28/1.10 tff(1582,plain,
% 1.28/1.10 (c3_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1327, 1578])).
% 1.28/1.10 tff(1583,plain,
% 1.28/1.10 (c1_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1338, 1578])).
% 1.28/1.10 tff(1584,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1585,plain,
% 1.28/1.10 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325))) <=> (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1586,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1585])).
% 1.28/1.10 tff(1587,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1586, 1584])).
% 1.28/1.10 tff(1588,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1589,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.28/1.10 tff(1590,plain,
% 1.28/1.10 (c2_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1589, 414, 1583, 1582, 1581, 1580, 1579, 1481, 35])).
% 1.28/1.10 tff(1591,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1592,plain,
% 1.28/1.10 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1593,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1592])).
% 1.28/1.10 tff(1594,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.28/1.10 tff(1595,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1596,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.28/1.10 tff(1597,plain,
% 1.28/1.10 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1596, 414, 1028, 1027, 1575, 1582, 1573, 1579, 10, 1577])).
% 1.28/1.10 tff(1598,plain,
% 1.28/1.10 (~c3_1(a1307)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1597, 1590])).
% 1.28/1.10 tff(1599,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1600,plain,
% 1.28/1.10 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1601,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1600])).
% 1.28/1.10 tff(1602,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.28/1.10 tff(1603,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1604,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.28/1.10 tff(1605,plain,
% 1.28/1.10 ((~c2_1(a1324)) | (~c2_1(a1325))),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1604, 414, 1575, 1582, 1581, 1573, 1579, 1481, 425, 1577])).
% 1.28/1.10 tff(1606,plain,
% 1.28/1.10 (~c2_1(a1324)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1605, 1590])).
% 1.28/1.10 tff(1607,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1608,plain,
% 1.28/1.10 ((hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324))) <=> (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1609,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1608])).
% 1.28/1.10 tff(1610,plain,
% 1.28/1.10 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1609, 1607])).
% 1.28/1.10 tff(1611,plain,
% 1.28/1.10 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1612,plain,
% 1.28/1.10 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.28/1.10 tff(1613,plain,
% 1.28/1.10 ($false),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1612, 414, 700, 1028, 1026, 1581, 1481, 915, 1606, 1598])).
% 1.28/1.10 tff(1614,plain,(hskp7 | hskp14 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.10 tff(1615,plain,
% 1.28/1.10 (hskp7),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1614, 700, 415, 24, 23])).
% 1.28/1.10 tff(1616,plain,
% 1.28/1.10 (~c3_1(a1316)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[305, 1615])).
% 1.28/1.10 tff(1617,plain,
% 1.28/1.10 (~c2_1(a1316)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[299, 1615])).
% 1.28/1.10 tff(1618,plain,
% 1.28/1.10 (~c0_1(a1316)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1416, 1615])).
% 1.28/1.10 tff(1619,plain,
% 1.28/1.10 (hskp8),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1428, 1618, 1027, 1026, 700, 1028, 1617, 1616])).
% 1.28/1.10 tff(1620,plain,
% 1.28/1.10 (~c3_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1114, 1619])).
% 1.28/1.10 tff(1621,plain,
% 1.28/1.10 (~c0_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1120, 1619])).
% 1.28/1.10 tff(1622,plain,
% 1.28/1.10 (c2_1(a1319)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1214, 1619])).
% 1.28/1.10 tff(1623,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1624,plain,
% 1.28/1.10 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1625,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1624])).
% 1.28/1.10 tff(1626,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1625, 1623])).
% 1.28/1.10 tff(1627,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1628,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.28/1.10 tff(1629,plain,
% 1.28/1.10 ((~c3_1(a1348)) | (~c0_1(a1309))),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1628, 414, 840, 1622, 953, 942, 689, 1621, 1620, 10])).
% 1.28/1.10 tff(1630,plain,
% 1.28/1.10 (~c3_1(a1348)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1629, 1542])).
% 1.28/1.10 tff(1631,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1632,plain,
% 1.28/1.10 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.28/1.10 inference(rewrite,[status(thm)],[])).
% 1.28/1.10 tff(1633,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.28/1.10 inference(monotonicity,[status(thm)],[1632])).
% 1.28/1.10 tff(1634,plain,
% 1.28/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.28/1.10 inference(transitivity,[status(thm)],[1633, 1631])).
% 1.28/1.10 tff(1635,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 1.28/1.10 inference(quant_inst,[status(thm)],[])).
% 1.28/1.10 tff(1636,plain,
% 1.28/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.28/1.10 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 1.28/1.10 tff(1637,plain,
% 1.28/1.10 ($false),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1636, 414, 840, 1528, 953, 942, 689, 1517, 10, 1630, 1542, 1535])).
% 1.28/1.10 tff(1638,plain,(hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.28/1.10 tff(1639,plain,
% 1.28/1.10 (hskp1),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1638, 700, 24, 23, 415])).
% 1.28/1.10 tff(1640,plain,
% 1.28/1.10 (~c2_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[991, 1639])).
% 1.28/1.10 tff(1641,plain,
% 1.28/1.10 (~c1_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[371, 1639])).
% 1.28/1.10 tff(1642,plain,
% 1.28/1.10 (hskp15),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1257, 414, 700, 1622, 1621, 1620, 1003])).
% 1.28/1.10 tff(1643,plain,
% 1.28/1.10 (~c3_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1263, 1642])).
% 1.28/1.10 tff(1644,plain,
% 1.28/1.10 (c3_1(a1308)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[382, 1639])).
% 1.28/1.10 tff(1645,plain,
% 1.28/1.10 (c2_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1275, 1642])).
% 1.28/1.10 tff(1646,plain,
% 1.28/1.10 (c1_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1286, 1642])).
% 1.28/1.10 tff(1647,plain,
% 1.28/1.10 (~c0_1(a1331)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1293, 414, 1646, 1645, 1644, 1643, 1641, 1640, 699])).
% 1.28/1.10 tff(1648,plain,
% 1.28/1.10 (hskp12),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1310, 414, 1028, 1027, 1026, 1646, 1643, 1304, 1647])).
% 1.28/1.10 tff(1649,plain,
% 1.28/1.10 (~c0_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1316, 1648])).
% 1.28/1.10 tff(1650,plain,
% 1.28/1.10 (c3_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1327, 1648])).
% 1.28/1.10 tff(1651,plain,
% 1.28/1.10 (c1_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1338, 1648])).
% 1.28/1.10 tff(1652,plain,
% 1.28/1.10 (c2_1(a1325)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1589, 414, 1651, 1650, 1581, 1580, 1649, 1481, 35])).
% 1.28/1.10 tff(1653,plain,
% 1.28/1.10 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1596, 414, 1028, 1027, 1645, 1650, 1643, 1649, 10, 1647])).
% 1.28/1.10 tff(1654,plain,
% 1.28/1.10 (~c3_1(a1307)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1653, 1652])).
% 1.28/1.10 tff(1655,plain,
% 1.28/1.10 ((~c2_1(a1324)) | (~c2_1(a1325))),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1604, 414, 1645, 1650, 1581, 1643, 1649, 1481, 425, 1647])).
% 1.28/1.10 tff(1656,plain,
% 1.28/1.10 (~c2_1(a1324)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1655, 1652])).
% 1.28/1.10 tff(1657,plain,
% 1.28/1.10 ($false),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1612, 414, 700, 1028, 1026, 1581, 1481, 915, 1656, 1654])).
% 1.28/1.10 tff(1658,plain,(hskp14 | c0_1(a1339) | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.10 tff(1659,plain,
% 1.28/1.10 (hskp14),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[1658, 24, 23, 415])).
% 1.28/1.10 tff(1660,plain,
% 1.28/1.10 (~c2_1(a1330)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[211, 1659])).
% 1.28/1.10 tff(1661,plain,
% 1.28/1.10 (~c1_1(a1330)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[217, 1659])).
% 1.28/1.10 tff(1662,plain,
% 1.28/1.10 (c0_1(a1330)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[235, 1659])).
% 1.28/1.10 tff(1663,plain,
% 1.28/1.10 (hskp29),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[513, 446, 414, 1662, 1661, 1660, 21])).
% 1.28/1.10 tff(1664,plain,
% 1.28/1.10 (c1_1(a1338)),
% 1.28/1.10 inference(unit_resolution,[status(thm)],[546, 1663])).
% 1.28/1.10 tff(1665,plain,
% 1.28/1.11 (c2_1(a1338)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[535, 1663])).
% 1.28/1.11 tff(1666,plain,
% 1.28/1.11 (c3_1(a1338)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[524, 1663])).
% 1.28/1.11 tff(1667,assumption,(~hskp3), introduced(assumption)).
% 1.28/1.11 tff(1668,plain,
% 1.28/1.11 ((hskp21 | hskp7 | hskp3) <=> (hskp21 | hskp7 | hskp3)),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1669,plain,
% 1.28/1.11 (((hskp21 | hskp3) | hskp7) <=> (hskp21 | hskp7 | hskp3)),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1670,plain,
% 1.28/1.11 ((hskp3 | hskp21) <=> (hskp21 | hskp3)),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1671,plain,
% 1.28/1.11 (((hskp3 | hskp21) | hskp7) <=> ((hskp21 | hskp3) | hskp7)),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1670])).
% 1.28/1.11 tff(1672,plain,
% 1.28/1.11 (((hskp3 | hskp21) | hskp7) <=> (hskp21 | hskp7 | hskp3)),
% 1.28/1.11 inference(transitivity,[status(thm)],[1671, 1669])).
% 1.28/1.11 tff(1673,axiom,((hskp3 | hskp21) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.28/1.11 tff(1674,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.28/1.11 tff(1675,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1674, 1668])).
% 1.28/1.11 tff(1676,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1675, 1668])).
% 1.28/1.11 tff(1677,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1676, 1668])).
% 1.28/1.11 tff(1678,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1677, 1668])).
% 1.28/1.11 tff(1679,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1678, 1668])).
% 1.28/1.11 tff(1680,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1679, 1668])).
% 1.28/1.11 tff(1681,plain,
% 1.28/1.11 (hskp21 | hskp7 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1680, 1668])).
% 1.28/1.11 tff(1682,plain,
% 1.28/1.11 (hskp21),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1681, 1667, 1014])).
% 1.28/1.11 tff(1683,plain,
% 1.28/1.11 (((~hskp21) | (~c2_1(a1352))) <=> ((~hskp21) | (~c2_1(a1352)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1684,plain,
% 1.28/1.11 (((~c2_1(a1352)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a1352)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1685,axiom,((~c2_1(a1352)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.28/1.11 tff(1686,plain,
% 1.28/1.11 ((~hskp21) | (~c2_1(a1352))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.28/1.11 tff(1687,plain,
% 1.28/1.11 ((~hskp21) | (~c2_1(a1352))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1686, 1683])).
% 1.28/1.11 tff(1688,plain,
% 1.28/1.11 (~c2_1(a1352)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1687, 1682])).
% 1.28/1.11 tff(1689,plain,
% 1.28/1.11 (((~hskp21) | (~c0_1(a1352))) <=> ((~hskp21) | (~c0_1(a1352)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1690,plain,
% 1.28/1.11 (((~c0_1(a1352)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1352)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1691,axiom,((~c0_1(a1352)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.28/1.11 tff(1692,plain,
% 1.28/1.11 ((~hskp21) | (~c0_1(a1352))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.28/1.11 tff(1693,plain,
% 1.28/1.11 ((~hskp21) | (~c0_1(a1352))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1692, 1689])).
% 1.28/1.11 tff(1694,plain,
% 1.28/1.11 (~c0_1(a1352)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1693, 1682])).
% 1.28/1.11 tff(1695,assumption,(c3_1(a1324)), introduced(assumption)).
% 1.28/1.11 tff(1696,assumption,(c0_1(a1324)), introduced(assumption)).
% 1.28/1.11 tff(1697,plain,
% 1.28/1.11 (((~hskp21) | c3_1(a1352)) <=> ((~hskp21) | c3_1(a1352))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1698,axiom,((~hskp21) | c3_1(a1352)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.28/1.11 tff(1699,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 1.28/1.11 tff(1700,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1699, 1697])).
% 1.28/1.11 tff(1701,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1700, 1697])).
% 1.28/1.11 tff(1702,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1701, 1697])).
% 1.28/1.11 tff(1703,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1702, 1697])).
% 1.28/1.11 tff(1704,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1703, 1697])).
% 1.28/1.11 tff(1705,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1704, 1697])).
% 1.28/1.11 tff(1706,plain,
% 1.28/1.11 ((~hskp21) | c3_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1705, 1697])).
% 1.28/1.11 tff(1707,plain,
% 1.28/1.11 (c3_1(a1352)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1706, 1682])).
% 1.28/1.11 tff(1708,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1709,plain,
% 1.28/1.11 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1710,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1709])).
% 1.28/1.11 tff(1711,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(transitivity,[status(thm)],[1710, 1708])).
% 1.28/1.11 tff(1712,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 1.28/1.11 inference(quant_inst,[status(thm)],[])).
% 1.28/1.11 tff(1713,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 1.28/1.11 tff(1714,plain,
% 1.28/1.11 (~c1_1(a1352)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1713, 414, 1707, 1696, 1695, 1694, 1688, 121, 35])).
% 1.28/1.11 tff(1715,plain,
% 1.28/1.11 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.28/1.11 inference(bind,[status(th)],[])).
% 1.28/1.11 tff(1716,plain,
% 1.28/1.11 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(quant_intro,[status(thm)],[1715])).
% 1.28/1.11 tff(1717,plain,
% 1.28/1.11 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1718,plain,
% 1.28/1.11 (^[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) | c1_1(U) | c3_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) | c3_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) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_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)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_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) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_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) | c1_1(U) | c3_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)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_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)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.28/1.11 inference(bind,[status(th)],[])).
% 1.28/1.11 tff(1719,plain,
% 1.28/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(quant_intro,[status(thm)],[1718])).
% 1.28/1.11 tff(1720,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)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.28/1.11 tff(1721,plain,
% 1.28/1.11 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 1.28/1.11 tff(1722,plain,
% 1.28/1.11 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1721, 1717])).
% 1.28/1.11 tff(1723,plain,(
% 1.28/1.11 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(skolemize,[status(sab)],[1722])).
% 1.28/1.11 tff(1724,plain,
% 1.28/1.11 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1723, 1716])).
% 1.28/1.11 tff(1725,plain,
% 1.28/1.11 ((hskp7 | hskp4 | hskp3) <=> (hskp7 | hskp4 | hskp3)),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1726,plain,
% 1.28/1.11 (((hskp3 | hskp4) | hskp7) <=> (hskp7 | hskp4 | hskp3)),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1727,axiom,((hskp3 | hskp4) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.28/1.11 tff(1728,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 1.28/1.11 tff(1729,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1728, 1725])).
% 1.28/1.11 tff(1730,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1729, 1725])).
% 1.28/1.11 tff(1731,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1730, 1725])).
% 1.28/1.11 tff(1732,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1731, 1725])).
% 1.28/1.11 tff(1733,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1732, 1725])).
% 1.28/1.11 tff(1734,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1733, 1725])).
% 1.28/1.11 tff(1735,plain,
% 1.28/1.11 (hskp7 | hskp4 | hskp3),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1734, 1725])).
% 1.28/1.11 tff(1736,plain,
% 1.28/1.11 (hskp4),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1735, 1667, 1014])).
% 1.28/1.11 tff(1737,plain,
% 1.28/1.11 (~c3_1(a1312)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1174, 1736])).
% 1.28/1.11 tff(1738,plain,
% 1.28/1.11 (~c1_1(a1312)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[752, 1736])).
% 1.28/1.11 tff(1739,assumption,(~c2_1(a1330)), introduced(assumption)).
% 1.28/1.11 tff(1740,assumption,(~c1_1(a1330)), introduced(assumption)).
% 1.28/1.11 tff(1741,plain,
% 1.28/1.11 (c0_1(a1312)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[763, 1736])).
% 1.28/1.11 tff(1742,assumption,(c0_1(a1330)), introduced(assumption)).
% 1.28/1.11 tff(1743,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1744,plain,
% 1.28/1.11 ((hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1745,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312))))),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1744])).
% 1.28/1.11 tff(1746,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 1.28/1.11 inference(transitivity,[status(thm)],[1745, 1743])).
% 1.28/1.11 tff(1747,plain,
% 1.28/1.11 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 1.28/1.11 inference(quant_inst,[status(thm)],[])).
% 1.28/1.11 tff(1748,plain,
% 1.28/1.11 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.28/1.11 tff(1749,plain,
% 1.28/1.11 (hskp15),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1748, 414, 1742, 1741, 1740, 1739, 1738, 1737, 1724])).
% 1.28/1.11 tff(1750,plain,
% 1.28/1.11 (~c3_1(a1331)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1263, 1749])).
% 1.28/1.11 tff(1751,plain,
% 1.28/1.11 (c2_1(a1331)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1275, 1749])).
% 1.28/1.11 tff(1752,plain,
% 1.28/1.11 (c1_1(a1331)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1286, 1749])).
% 1.28/1.11 tff(1753,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1754,plain,
% 1.28/1.11 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1755,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352)))),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1754])).
% 1.28/1.11 tff(1756,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 1.28/1.11 inference(transitivity,[status(thm)],[1755, 1753])).
% 1.28/1.11 tff(1757,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 1.28/1.11 inference(quant_inst,[status(thm)],[])).
% 1.28/1.11 tff(1758,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352)),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 1.28/1.11 tff(1759,plain,
% 1.28/1.11 (~c0_1(a1331)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1758, 414, 1707, 1752, 1751, 1688, 1750, 699, 1714])).
% 1.28/1.11 tff(1760,assumption,(c1_1(a1338)), introduced(assumption)).
% 1.28/1.11 tff(1761,assumption,(c3_1(a1338)), introduced(assumption)).
% 1.28/1.11 tff(1762,assumption,(~c0_1(a1338)), introduced(assumption)).
% 1.28/1.11 tff(1763,assumption,(~c2_1(a1352)), introduced(assumption)).
% 1.28/1.11 tff(1764,assumption,(~c0_1(a1352)), introduced(assumption)).
% 1.28/1.11 tff(1765,assumption,(c3_1(a1352)), introduced(assumption)).
% 1.28/1.11 tff(1766,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1767,plain,
% 1.28/1.11 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1768,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1767])).
% 1.28/1.11 tff(1769,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.28/1.11 inference(transitivity,[status(thm)],[1768, 1766])).
% 1.28/1.11 tff(1770,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 1.28/1.11 inference(quant_inst,[status(thm)],[])).
% 1.28/1.11 tff(1771,plain,
% 1.28/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.28/1.11 tff(1772,plain,
% 1.28/1.11 ($false),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1771, 414, 1760, 1761, 1765, 1696, 1695, 1764, 1763, 121, 35, 1762])).
% 1.28/1.11 tff(1773,plain,(c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.11 tff(1774,plain,
% 1.28/1.11 (c0_1(a1338)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1773, 1707, 1761, 1760, 1696, 1695, 1694, 1688, 121])).
% 1.28/1.11 tff(1775,assumption,(c2_1(a1338)), introduced(assumption)).
% 1.28/1.11 tff(1776,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1777,plain,
% 1.28/1.11 ((hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338))) <=> (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1778,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))))),
% 1.28/1.11 inference(monotonicity,[status(thm)],[1777])).
% 1.28/1.11 tff(1779,plain,
% 1.28/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 1.28/1.11 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.28/1.11 tff(1780,plain,
% 1.28/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))),
% 1.28/1.11 inference(quant_inst,[status(thm)],[])).
% 1.28/1.11 tff(1781,plain,
% 1.28/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))),
% 1.28/1.11 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.28/1.11 tff(1782,plain,
% 1.28/1.11 (hskp17 | (~c0_1(a1338))),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1781, 414, 1760, 1775, 1761, 1088])).
% 1.28/1.11 tff(1783,plain,
% 1.28/1.11 (hskp17),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[1782, 1774])).
% 1.28/1.11 tff(1784,plain,
% 1.28/1.11 (~c0_1(a1334)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[864, 1783])).
% 1.28/1.11 tff(1785,plain,
% 1.28/1.11 (c3_1(a1334)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[876, 1783])).
% 1.28/1.11 tff(1786,plain,
% 1.28/1.11 (c2_1(a1334)),
% 1.28/1.11 inference(unit_resolution,[status(thm)],[887, 1783])).
% 1.28/1.11 tff(1787,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1788,plain,
% 1.28/1.11 (((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.11 inference(rewrite,[status(thm)],[])).
% 1.28/1.11 tff(1789,plain,
% 1.28/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1788])).
% 1.28/1.12 tff(1790,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.28/1.12 tff(1791,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1792,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.28/1.12 tff(1793,plain,
% 1.28/1.12 ($false),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1792, 414, 1760, 1761, 1786, 1785, 1751, 1784, 1750, 10, 1774, 1759])).
% 1.28/1.12 tff(1794,plain,(hskp3 | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1324) | (~c0_1(a1330)) | c1_1(a1330) | c2_1(a1330) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.28/1.12 tff(1795,plain,
% 1.28/1.12 (hskp3),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1794, 1014, 1666, 1665, 1581, 1580, 1481, 1662, 1661, 1660, 1664])).
% 1.28/1.12 tff(1796,plain,
% 1.28/1.12 (~c1_1(a1311)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[648, 1795])).
% 1.28/1.12 tff(1797,assumption,(hskp2), introduced(assumption)).
% 1.28/1.12 tff(1798,plain,
% 1.28/1.12 (~c2_1(a1309)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[734, 1797])).
% 1.28/1.12 tff(1799,plain,
% 1.28/1.12 (c3_1(a1309)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[941, 1797])).
% 1.28/1.12 tff(1800,plain,
% 1.28/1.12 (c1_1(a1309)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[952, 1797])).
% 1.28/1.12 tff(1801,plain,
% 1.28/1.12 (~c3_1(a1339)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1127, 414, 1014, 415, 1800, 1799, 24, 1798, 400])).
% 1.28/1.12 tff(1802,plain,
% 1.28/1.12 (hskp6),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1152, 1801, 24])).
% 1.28/1.12 tff(1803,plain,
% 1.28/1.12 (~c1_1(a1315)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1236, 1802])).
% 1.28/1.12 tff(1804,plain,
% 1.28/1.12 (~c0_1(a1315)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1158, 1802])).
% 1.28/1.12 tff(1805,plain,
% 1.28/1.12 (c3_1(a1315)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1203, 1802])).
% 1.28/1.12 tff(1806,plain,
% 1.28/1.12 ($false),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1558, 414, 1014, 1805, 1800, 1799, 1804, 1803, 1798, 400])).
% 1.28/1.12 tff(1807,plain,((~hskp2) | hskp7 | c0_1(a1339) | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.12 tff(1808,plain,
% 1.28/1.12 (~hskp2),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1807, 1014, 24, 23, 415])).
% 1.28/1.12 tff(1809,plain,
% 1.28/1.12 (hskp1),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[728, 1808, 415, 24])).
% 1.28/1.12 tff(1810,plain,
% 1.28/1.12 (~c2_1(a1308)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[991, 1809])).
% 1.28/1.12 tff(1811,plain,
% 1.28/1.12 (~c1_1(a1308)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[371, 1809])).
% 1.28/1.12 tff(1812,plain,
% 1.28/1.12 (c3_1(a1308)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[382, 1809])).
% 1.28/1.12 tff(1813,assumption,(~c2_1(a1308)), introduced(assumption)).
% 1.28/1.12 tff(1814,assumption,(~c1_1(a1308)), introduced(assumption)).
% 1.28/1.12 tff(1815,assumption,(hskp3), introduced(assumption)).
% 1.28/1.12 tff(1816,plain,
% 1.28/1.12 (~c1_1(a1311)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[648, 1815])).
% 1.28/1.12 tff(1817,assumption,(c3_1(a1308)), introduced(assumption)).
% 1.28/1.12 tff(1818,plain,
% 1.28/1.12 (c2_1(a1311)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[659, 1815])).
% 1.28/1.12 tff(1819,plain,
% 1.28/1.12 (c0_1(a1311)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[670, 1815])).
% 1.28/1.12 tff(1820,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1821,plain,
% 1.28/1.12 (((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1822,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311))))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1821])).
% 1.28/1.12 tff(1823,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1822, 1820])).
% 1.28/1.12 tff(1824,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1825,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.28/1.12 tff(1826,plain,
% 1.28/1.12 (c3_1(a1330)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1825, 414, 1742, 1819, 1818, 1817, 1739, 1816, 1814, 1813, 613])).
% 1.28/1.12 tff(1827,plain,
% 1.28/1.12 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.28/1.12 inference(bind,[status(th)],[])).
% 1.28/1.12 tff(1828,plain,
% 1.28/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(quant_intro,[status(thm)],[1827])).
% 1.28/1.12 tff(1829,plain,
% 1.28/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1830,plain,
% 1.28/1.12 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.28/1.12 inference(bind,[status(th)],[])).
% 1.28/1.12 tff(1831,plain,
% 1.28/1.12 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(quant_intro,[status(thm)],[1830])).
% 1.28/1.12 tff(1832,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.28/1.12 tff(1833,plain,
% 1.28/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 1.28/1.12 tff(1834,plain,
% 1.28/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1833, 1829])).
% 1.28/1.12 tff(1835,plain,(
% 1.28/1.12 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(skolemize,[status(sab)],[1834])).
% 1.28/1.12 tff(1836,plain,
% 1.28/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1835, 1828])).
% 1.28/1.12 tff(1837,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1838,plain,
% 1.28/1.12 ((hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311))) <=> (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1839,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311))))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1838])).
% 1.28/1.12 tff(1840,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1839, 1837])).
% 1.28/1.12 tff(1841,plain,
% 1.28/1.12 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1842,plain,
% 1.28/1.12 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 1.28/1.12 tff(1843,plain,
% 1.28/1.12 (~c3_1(a1311)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1842, 414, 22, 1742, 1818, 1739, 1816, 1836, 1826])).
% 1.28/1.12 tff(1844,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1845,plain,
% 1.28/1.12 ((hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1846,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311)))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1845])).
% 1.28/1.12 tff(1847,plain,
% 1.28/1.12 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.28/1.12 tff(1848,plain,
% 1.28/1.12 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1849,plain,
% 1.28/1.12 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.28/1.12 tff(1850,plain,
% 1.28/1.12 (hskp15),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1849, 414, 1742, 1819, 1740, 1739, 1816, 1724, 1843])).
% 1.28/1.12 tff(1851,plain,
% 1.28/1.12 (~c3_1(a1331)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1263, 1850])).
% 1.28/1.12 tff(1852,plain,
% 1.28/1.12 (c2_1(a1331)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1275, 1850])).
% 1.28/1.12 tff(1853,plain,
% 1.28/1.12 (c1_1(a1331)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1286, 1850])).
% 1.28/1.12 tff(1854,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1855,plain,
% 1.28/1.12 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1856,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1855])).
% 1.28/1.12 tff(1857,plain,
% 1.28/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1856, 1854])).
% 1.28/1.12 tff(1858,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1859,plain,
% 1.28/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 1.28/1.12 tff(1860,plain,
% 1.28/1.12 (~c0_1(a1331)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1859, 414, 1853, 1852, 1851, 1740, 1739, 699, 1826])).
% 1.28/1.12 tff(1861,plain,
% 1.28/1.12 (^[U: $i] : refl((hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.28/1.12 inference(bind,[status(th)],[])).
% 1.28/1.12 tff(1862,plain,
% 1.28/1.12 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(quant_intro,[status(thm)],[1861])).
% 1.28/1.12 tff(1863,plain,
% 1.28/1.12 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1864,plain,
% 1.28/1.12 (^[U: $i] : 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(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)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.28/1.12 inference(bind,[status(th)],[])).
% 1.28/1.12 tff(1865,plain,
% 1.28/1.12 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(quant_intro,[status(thm)],[1864])).
% 1.28/1.12 tff(1866,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.28/1.12 tff(1867,plain,
% 1.28/1.12 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.28/1.12 tff(1868,plain,
% 1.28/1.12 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1867, 1863])).
% 1.28/1.12 tff(1869,plain,(
% 1.28/1.12 ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(skolemize,[status(sab)],[1868])).
% 1.28/1.12 tff(1870,plain,
% 1.28/1.12 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1869, 1862])).
% 1.28/1.12 tff(1871,plain,
% 1.28/1.12 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1872,plain,
% 1.28/1.12 ((hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311))) <=> (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1873,plain,
% 1.28/1.12 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))))),
% 1.28/1.12 inference(monotonicity,[status(thm)],[1872])).
% 1.28/1.12 tff(1874,plain,
% 1.28/1.12 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.28/1.12 inference(transitivity,[status(thm)],[1873, 1871])).
% 1.28/1.12 tff(1875,plain,
% 1.28/1.12 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))),
% 1.28/1.12 inference(quant_inst,[status(thm)],[])).
% 1.28/1.12 tff(1876,plain,
% 1.28/1.12 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.28/1.12 tff(1877,plain,
% 1.28/1.12 (hskp30),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1876, 775, 414, 1819, 1818, 1870, 1843])).
% 1.28/1.12 tff(1878,plain,
% 1.28/1.12 (((~hskp30) | c3_1(a1372)) <=> ((~hskp30) | c3_1(a1372))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1879,axiom,((~hskp30) | c3_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.28/1.12 tff(1880,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.28/1.12 tff(1881,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1880, 1878])).
% 1.28/1.12 tff(1882,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1881, 1878])).
% 1.28/1.12 tff(1883,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1882, 1878])).
% 1.28/1.12 tff(1884,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1883, 1878])).
% 1.28/1.12 tff(1885,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1884, 1878])).
% 1.28/1.12 tff(1886,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1885, 1878])).
% 1.28/1.12 tff(1887,plain,
% 1.28/1.12 ((~hskp30) | c3_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1886, 1878])).
% 1.28/1.12 tff(1888,plain,
% 1.28/1.12 (c3_1(a1372)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1887, 1877])).
% 1.28/1.12 tff(1889,plain,
% 1.28/1.12 (((~hskp30) | c1_1(a1372)) <=> ((~hskp30) | c1_1(a1372))),
% 1.28/1.12 inference(rewrite,[status(thm)],[])).
% 1.28/1.12 tff(1890,axiom,((~hskp30) | c1_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.28/1.12 tff(1891,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 1.28/1.12 tff(1892,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1891, 1889])).
% 1.28/1.12 tff(1893,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1892, 1889])).
% 1.28/1.12 tff(1894,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1893, 1889])).
% 1.28/1.12 tff(1895,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1894, 1889])).
% 1.28/1.12 tff(1896,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1895, 1889])).
% 1.28/1.12 tff(1897,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1896, 1889])).
% 1.28/1.12 tff(1898,plain,
% 1.28/1.12 ((~hskp30) | c1_1(a1372)),
% 1.28/1.12 inference(modus_ponens,[status(thm)],[1897, 1889])).
% 1.28/1.12 tff(1899,plain,
% 1.28/1.12 (c1_1(a1372)),
% 1.28/1.12 inference(unit_resolution,[status(thm)],[1898, 1877])).
% 1.28/1.12 tff(1900,plain,
% 1.28/1.12 (((~hskp30) | c0_1(a1372)) <=> ((~hskp30) | c0_1(a1372))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1901,axiom,((~hskp30) | c0_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.28/1.13 tff(1902,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 1.28/1.13 tff(1903,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1902, 1900])).
% 1.28/1.13 tff(1904,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1903, 1900])).
% 1.28/1.13 tff(1905,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1904, 1900])).
% 1.28/1.13 tff(1906,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1905, 1900])).
% 1.28/1.13 tff(1907,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1906, 1900])).
% 1.28/1.13 tff(1908,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1907, 1900])).
% 1.28/1.13 tff(1909,plain,
% 1.28/1.13 ((~hskp30) | c0_1(a1372)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1908, 1900])).
% 1.28/1.13 tff(1910,plain,
% 1.28/1.13 (c0_1(a1372)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1909, 1877])).
% 1.28/1.13 tff(1911,assumption,(~c0_1(a1331)), introduced(assumption)).
% 1.28/1.13 tff(1912,assumption,(~c3_1(a1331)), introduced(assumption)).
% 1.28/1.13 tff(1913,assumption,(hskp17), introduced(assumption)).
% 1.28/1.13 tff(1914,plain,
% 1.28/1.13 (~c0_1(a1334)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[864, 1913])).
% 1.28/1.13 tff(1915,assumption,(c2_1(a1331)), introduced(assumption)).
% 1.28/1.13 tff(1916,plain,
% 1.28/1.13 (c3_1(a1334)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[876, 1913])).
% 1.28/1.13 tff(1917,plain,
% 1.28/1.13 (c2_1(a1334)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[887, 1913])).
% 1.28/1.13 tff(1918,assumption,(c3_1(a1372)), introduced(assumption)).
% 1.28/1.13 tff(1919,assumption,(c1_1(a1372)), introduced(assumption)).
% 1.28/1.13 tff(1920,assumption,(c0_1(a1372)), introduced(assumption)).
% 1.28/1.13 tff(1921,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1922,plain,
% 1.28/1.13 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1923,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1922])).
% 1.28/1.13 tff(1924,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.28/1.13 tff(1925,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1926,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.28/1.13 tff(1927,plain,
% 1.28/1.13 ($false),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1926, 414, 1920, 1919, 1918, 1917, 1916, 1915, 1914, 1912, 10, 1911])).
% 1.28/1.13 tff(1928,plain,((~hskp17) | (~c0_1(a1372)) | (~c1_1(a1372)) | (~c3_1(a1372)) | (~c2_1(a1331)) | c3_1(a1331) | c0_1(a1331)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.13 tff(1929,plain,
% 1.28/1.13 (~hskp17),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1928, 1910, 1899, 1888, 1852, 1851, 1860])).
% 1.28/1.13 tff(1930,plain,
% 1.28/1.13 (hskp29),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[513, 775, 414, 1742, 1740, 1739, 21])).
% 1.28/1.13 tff(1931,plain,
% 1.28/1.13 (c3_1(a1338)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[524, 1930])).
% 1.28/1.13 tff(1932,plain,
% 1.28/1.13 (c2_1(a1338)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[535, 1930])).
% 1.28/1.13 tff(1933,plain,
% 1.28/1.13 (c1_1(a1338)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[546, 1930])).
% 1.28/1.13 tff(1934,plain,
% 1.28/1.13 (hskp17 | (~c0_1(a1338))),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1781, 414, 1933, 1932, 1931, 1088])).
% 1.28/1.13 tff(1935,plain,
% 1.28/1.13 (~c0_1(a1338)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1934, 1929])).
% 1.28/1.13 tff(1936,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1937,plain,
% 1.28/1.13 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1938,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1937])).
% 1.28/1.13 tff(1939,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.28/1.13 tff(1940,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1941,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.28/1.13 tff(1942,plain,
% 1.28/1.13 ($false),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1941, 414, 1910, 1899, 1888, 1932, 1931, 1852, 1851, 10, 1935, 1860])).
% 1.28/1.13 tff(1943,plain,((~hskp3) | c1_1(a1330) | c2_1(a1330) | hskp18 | (~c0_1(a1330)) | hskp27 | (~c3_1(a1308)) | c1_1(a1308) | c2_1(a1308)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.13 tff(1944,plain,
% 1.28/1.13 (hskp27),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1943, 1795, 1660, 446, 1662, 1661, 1812, 1811, 1810])).
% 1.28/1.13 tff(1945,plain,
% 1.28/1.13 (hskp13),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[488, 1944])).
% 1.28/1.13 tff(1946,plain,
% 1.28/1.13 (~c3_1(a1326)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[163, 1945])).
% 1.28/1.13 tff(1947,plain,
% 1.28/1.13 (~c2_1(a1326)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[169, 1945])).
% 1.28/1.13 tff(1948,plain,
% 1.28/1.13 (c2_1(a1311)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[659, 1795])).
% 1.28/1.13 tff(1949,plain,
% 1.28/1.13 (c0_1(a1311)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[670, 1795])).
% 1.28/1.13 tff(1950,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1951,plain,
% 1.28/1.13 (((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1952,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1951])).
% 1.28/1.13 tff(1953,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1952, 1950])).
% 1.28/1.13 tff(1954,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1955,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 1.28/1.13 tff(1956,plain,
% 1.28/1.13 (~c0_1(a1326)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1955, 414, 1949, 1948, 1812, 1947, 1946, 1796, 1811, 1810, 613])).
% 1.28/1.13 tff(1957,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1958,plain,
% 1.28/1.13 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1959,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1958])).
% 1.28/1.13 tff(1960,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1959, 1957])).
% 1.28/1.13 tff(1961,plain,
% 1.28/1.13 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1962,plain,
% 1.28/1.13 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.28/1.13 tff(1963,plain,
% 1.28/1.13 (hskp6),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1962, 414, 851, 840, 689, 1947, 1946, 1145, 1956])).
% 1.28/1.13 tff(1964,plain,
% 1.28/1.13 (~c0_1(a1315)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1158, 1963])).
% 1.28/1.13 tff(1965,plain,
% 1.28/1.13 (hskp8 | hskp7),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1371, 414, 1662, 1661, 1660, 1013])).
% 1.28/1.13 tff(1966,plain,
% 1.28/1.13 (hskp8),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1965, 1014])).
% 1.28/1.13 tff(1967,plain,
% 1.28/1.13 (~c3_1(a1319)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1114, 1966])).
% 1.28/1.13 tff(1968,plain,
% 1.28/1.13 (~c0_1(a1319)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1120, 1966])).
% 1.28/1.13 tff(1969,plain,
% 1.28/1.13 (c3_1(a1315)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1203, 1963])).
% 1.28/1.13 tff(1970,plain,
% 1.28/1.13 (c2_1(a1319)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1214, 1966])).
% 1.28/1.13 tff(1971,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1972,plain,
% 1.28/1.13 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1973,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1972])).
% 1.28/1.13 tff(1974,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1973, 1971])).
% 1.28/1.13 tff(1975,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1976,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 1.28/1.13 tff(1977,plain,
% 1.28/1.13 (~c2_1(a1315)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1976, 414, 1970, 1969, 1949, 1948, 1968, 1967, 1964, 1796, 425])).
% 1.28/1.13 tff(1978,plain,
% 1.28/1.13 (c3_1(a1330)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1825, 414, 1662, 1949, 1948, 1812, 1660, 1796, 1811, 1810, 613])).
% 1.28/1.13 tff(1979,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1980,plain,
% 1.28/1.13 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1981,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1980])).
% 1.28/1.13 tff(1982,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1981, 1979])).
% 1.28/1.13 tff(1983,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1984,plain,
% 1.28/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.28/1.13 tff(1985,plain,
% 1.28/1.13 (~c3_1(a1348)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1984, 414, 840, 1970, 1949, 1948, 689, 1968, 1967, 1796, 425])).
% 1.28/1.13 tff(1986,plain,
% 1.28/1.13 (c2_1(a1307)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[457, 1944])).
% 1.28/1.13 tff(1987,plain,
% 1.28/1.13 (c1_1(a1307)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[468, 1944])).
% 1.28/1.13 tff(1988,plain,
% 1.28/1.13 (c0_1(a1307)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[479, 1944])).
% 1.28/1.13 tff(1989,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1990,plain,
% 1.28/1.13 ((hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348))) <=> (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(1991,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[1990])).
% 1.28/1.13 tff(1992,plain,
% 1.28/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 1.28/1.13 inference(transitivity,[status(thm)],[1991, 1989])).
% 1.28/1.13 tff(1993,plain,
% 1.28/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))),
% 1.28/1.13 inference(quant_inst,[status(thm)],[])).
% 1.28/1.13 tff(1994,plain,
% 1.28/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))),
% 1.28/1.13 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.28/1.13 tff(1995,plain,
% 1.28/1.13 (hskp12 | c3_1(a1348)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1994, 414, 1988, 1987, 1986, 851, 689, 1304])).
% 1.28/1.13 tff(1996,plain,
% 1.28/1.13 (hskp12),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1995, 1985])).
% 1.28/1.13 tff(1997,plain,
% 1.28/1.13 (~c0_1(a1325)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1316, 1996])).
% 1.28/1.13 tff(1998,plain,
% 1.28/1.13 (c3_1(a1325)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1327, 1996])).
% 1.28/1.13 tff(1999,plain,
% 1.28/1.13 (c1_1(a1325)),
% 1.28/1.13 inference(unit_resolution,[status(thm)],[1338, 1996])).
% 1.28/1.13 tff(2000,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(2001,plain,
% 1.28/1.13 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.28/1.13 inference(rewrite,[status(thm)],[])).
% 1.28/1.13 tff(2002,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 1.28/1.13 inference(monotonicity,[status(thm)],[2001])).
% 1.28/1.13 tff(2003,plain,
% 1.28/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2002, 2000])).
% 1.28/1.14 tff(2004,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2005,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.28/1.14 tff(2006,plain,
% 1.28/1.14 ($false),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2005, 414, 1662, 1999, 1998, 1969, 1661, 1997, 1964, 35, 1978, 1977])).
% 1.28/1.14 tff(2007,plain,(hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.14 tff(2008,plain,
% 1.28/1.14 (hskp7),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2007, 24, 415, 23])).
% 1.28/1.14 tff(2009,plain,
% 1.28/1.14 (~c3_1(a1316)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[305, 2008])).
% 1.28/1.14 tff(2010,plain,
% 1.28/1.14 (~c2_1(a1316)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[299, 2008])).
% 1.28/1.14 tff(2011,plain,
% 1.28/1.14 (~c0_1(a1316)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1416, 2008])).
% 1.28/1.14 tff(2012,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2013,plain,
% 1.28/1.14 ((hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2014,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2013])).
% 1.28/1.14 tff(2015,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2014, 2012])).
% 1.28/1.14 tff(2016,plain,
% 1.28/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2017,plain,
% 1.28/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.28/1.14 tff(2018,plain,
% 1.28/1.14 (hskp17),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2017, 414, 1760, 1775, 1761, 480, 469, 458, 1088])).
% 1.28/1.14 tff(2019,plain,
% 1.28/1.14 (~c0_1(a1334)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[864, 2018])).
% 1.28/1.14 tff(2020,plain,
% 1.28/1.14 (c3_1(a1334)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[876, 2018])).
% 1.28/1.14 tff(2021,plain,
% 1.28/1.14 (c2_1(a1334)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[887, 2018])).
% 1.28/1.14 tff(2022,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2023,plain,
% 1.28/1.14 ((hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2024,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2023])).
% 1.28/1.14 tff(2025,plain,
% 1.28/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2024, 2022])).
% 1.28/1.14 tff(2026,plain,
% 1.28/1.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2027,plain,
% 1.28/1.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.28/1.14 tff(2028,plain,
% 1.28/1.14 (hskp8),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2027, 414, 2021, 2020, 2019, 1418, 308, 307, 1069])).
% 1.28/1.14 tff(2029,plain,
% 1.28/1.14 (~c3_1(a1319)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1114, 2028])).
% 1.28/1.14 tff(2030,plain,
% 1.28/1.14 (~c0_1(a1319)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1120, 2028])).
% 1.28/1.14 tff(2031,plain,
% 1.28/1.14 (c2_1(a1319)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1214, 2028])).
% 1.28/1.14 tff(2032,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2033,plain,
% 1.28/1.14 (((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2034,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2033])).
% 1.28/1.14 tff(2035,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2034, 2032])).
% 1.28/1.14 tff(2036,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2037,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 1.28/1.14 tff(2038,plain,
% 1.28/1.14 (~c0_1(a1338)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2037, 414, 1760, 1761, 2021, 2020, 2031, 2019, 2030, 2029, 10])).
% 1.28/1.14 tff(2039,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2040,plain,
% 1.28/1.14 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2041,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2040])).
% 1.28/1.14 tff(2042,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2041, 2039])).
% 1.28/1.14 tff(2043,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2044,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 1.28/1.14 tff(2045,plain,
% 1.28/1.14 (~c3_1(a1307)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2044, 414, 480, 469, 2021, 2020, 2031, 2019, 2030, 2029, 10])).
% 1.28/1.14 tff(2046,plain,
% 1.28/1.14 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2047,plain,
% 1.28/1.14 ((hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307))) <=> (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2048,plain,
% 1.28/1.14 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307)))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2047])).
% 1.28/1.14 tff(2049,plain,
% 1.28/1.14 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2048, 2046])).
% 1.28/1.14 tff(2050,plain,
% 1.28/1.14 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2051,plain,
% 1.28/1.14 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307)),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 1.28/1.14 tff(2052,plain,
% 1.28/1.14 (hskp30 | c3_1(a1307)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2051, 775, 414, 480, 458, 1870])).
% 1.28/1.14 tff(2053,plain,
% 1.28/1.14 (hskp30),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2052, 2045])).
% 1.28/1.14 tff(2054,plain,
% 1.28/1.14 (c3_1(a1372)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1887, 2053])).
% 1.28/1.14 tff(2055,plain,
% 1.28/1.14 (c1_1(a1372)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1898, 2053])).
% 1.28/1.14 tff(2056,plain,
% 1.28/1.14 (c0_1(a1372)),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[1909, 2053])).
% 1.28/1.14 tff(2057,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2058,plain,
% 1.28/1.14 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2059,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))))),
% 1.28/1.14 inference(monotonicity,[status(thm)],[2058])).
% 1.28/1.14 tff(2060,plain,
% 1.28/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.28/1.14 inference(transitivity,[status(thm)],[2059, 2057])).
% 1.28/1.14 tff(2061,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.28/1.14 inference(quant_inst,[status(thm)],[])).
% 1.28/1.14 tff(2062,plain,
% 1.28/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 1.28/1.14 tff(2063,plain,
% 1.28/1.14 ($false),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2062, 414, 2056, 2055, 2054, 1775, 1761, 2031, 2030, 2029, 10, 2038])).
% 1.28/1.14 tff(2064,plain,((~hskp27) | (~c2_1(a1338)) | (~c3_1(a1338)) | hskp18 | (~c1_1(a1338)) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.14 tff(2065,plain,
% 1.28/1.14 (~hskp27),
% 1.28/1.14 inference(unit_resolution,[status(thm)],[2064, 1665, 1666, 446, 1664, 2011, 2010, 2009])).
% 1.28/1.14 tff(2066,plain,
% 1.28/1.14 (^[U: $i] : refl((hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.28/1.14 inference(bind,[status(th)],[])).
% 1.28/1.14 tff(2067,plain,
% 1.28/1.14 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(quant_intro,[status(thm)],[2066])).
% 1.28/1.14 tff(2068,plain,
% 1.28/1.14 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2069,plain,
% 1.28/1.14 (^[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)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.28/1.14 inference(bind,[status(th)],[])).
% 1.28/1.14 tff(2070,plain,
% 1.28/1.14 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(quant_intro,[status(thm)],[2069])).
% 1.28/1.14 tff(2071,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.28/1.14 tff(2072,plain,
% 1.28/1.14 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 1.28/1.14 tff(2073,plain,
% 1.28/1.14 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2072, 2068])).
% 1.28/1.14 tff(2074,plain,(
% 1.28/1.14 ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(skolemize,[status(sab)],[2073])).
% 1.28/1.14 tff(2075,plain,
% 1.28/1.14 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.14 inference(modus_ponens,[status(thm)],[2074, 2067])).
% 1.28/1.14 tff(2076,plain,
% 1.28/1.14 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2077,plain,
% 1.28/1.14 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.28/1.14 inference(rewrite,[status(thm)],[])).
% 1.28/1.14 tff(2078,plain,
% 1.28/1.14 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)))),
% 1.28/1.15 inference(monotonicity,[status(thm)],[2077])).
% 1.28/1.15 tff(2079,plain,
% 1.28/1.15 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 1.28/1.15 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.28/1.15 tff(2080,plain,
% 1.28/1.15 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 1.28/1.15 inference(quant_inst,[status(thm)],[])).
% 1.28/1.15 tff(2081,plain,
% 1.28/1.15 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)),
% 1.28/1.15 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.28/1.15 tff(2082,plain,
% 1.28/1.15 (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[2081, 414, 23, 2075])).
% 1.28/1.15 tff(2083,plain,
% 1.28/1.15 (hskp1),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[2082, 2065, 415, 24])).
% 1.28/1.15 tff(2084,plain,
% 1.28/1.15 (~c2_1(a1308)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[991, 2083])).
% 1.28/1.15 tff(2085,plain,
% 1.28/1.15 (~c1_1(a1308)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[371, 2083])).
% 1.28/1.15 tff(2086,plain,
% 1.28/1.15 (c3_1(a1308)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[382, 2083])).
% 1.28/1.15 tff(2087,plain,
% 1.28/1.15 (~hskp3),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[1943, 2086, 1660, 446, 1662, 1661, 2065, 2085, 2084])).
% 1.28/1.15 tff(2088,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2089,plain,
% 1.28/1.15 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2090,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 1.28/1.15 inference(monotonicity,[status(thm)],[2089])).
% 1.28/1.15 tff(2091,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.28/1.15 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.28/1.15 tff(2092,plain,
% 1.28/1.15 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.28/1.15 inference(quant_inst,[status(thm)],[])).
% 1.28/1.15 tff(2093,plain,
% 1.28/1.15 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 1.28/1.15 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.28/1.15 tff(2094,plain,
% 1.28/1.15 (hskp6),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[2093, 414, 851, 840, 689, 1418, 308, 307, 1145])).
% 1.28/1.15 tff(2095,plain,
% 1.28/1.15 (~c0_1(a1315)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[1158, 2094])).
% 1.28/1.15 tff(2096,plain,
% 1.28/1.15 (c3_1(a1315)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[1203, 2094])).
% 1.28/1.15 tff(2097,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2098,plain,
% 1.28/1.15 ((hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2099,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 1.28/1.15 inference(monotonicity,[status(thm)],[2098])).
% 1.28/1.15 tff(2100,plain,
% 1.28/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.28/1.15 inference(transitivity,[status(thm)],[2099, 2097])).
% 1.28/1.15 tff(2101,plain,
% 1.28/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.28/1.15 inference(quant_inst,[status(thm)],[])).
% 1.28/1.15 tff(2102,plain,
% 1.28/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 1.28/1.15 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 1.28/1.15 tff(2103,plain,
% 1.28/1.15 (hskp8 | (~c2_1(a1315))),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[2102, 414, 2096, 1418, 308, 307, 2095, 1069])).
% 1.28/1.15 tff(2104,plain,
% 1.28/1.15 (~c2_1(a1315)),
% 1.28/1.15 inference(unit_resolution,[status(thm)],[2103, 1029])).
% 1.28/1.15 tff(2105,plain,
% 1.28/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2106,plain,
% 1.28/1.15 (((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316))) <=> (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 1.28/1.15 inference(rewrite,[status(thm)],[])).
% 1.28/1.15 tff(2107,plain,
% 1.28/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316))))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2106])).
% 1.34/1.15 tff(2108,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 1.34/1.15 inference(transitivity,[status(thm)],[2107, 2105])).
% 1.34/1.15 tff(2109,plain,
% 1.34/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(2110,plain,
% 1.34/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.34/1.15 tff(2111,plain,
% 1.34/1.15 (~c1_1(a1316)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2110, 414, 2096, 1418, 308, 307, 2095, 326, 2104])).
% 1.34/1.15 tff(2112,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2113,plain,
% 1.34/1.15 ((hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2114,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316)))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2113])).
% 1.34/1.15 tff(2115,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 1.34/1.15 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.34/1.15 tff(2116,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(2117,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316)),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.34/1.15 tff(2118,plain,
% 1.34/1.15 (~c3_1(a1330)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2117, 414, 1667, 1742, 1739, 1418, 307, 635, 2111])).
% 1.34/1.15 tff(2119,plain,
% 1.34/1.15 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(2120,plain,
% 1.34/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[2119])).
% 1.34/1.15 tff(2121,plain,
% 1.34/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2122,plain,
% 1.34/1.15 (^[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)) | 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) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(2123,plain,
% 1.34/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[2122])).
% 1.34/1.15 tff(2124,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.34/1.15 tff(2125,plain,
% 1.34/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.34/1.15 tff(2126,plain,
% 1.34/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2125, 2121])).
% 1.34/1.15 tff(2127,plain,(
% 1.34/1.15 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(skolemize,[status(sab)],[2126])).
% 1.34/1.15 tff(2128,plain,
% 1.34/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2127, 2120])).
% 1.34/1.15 tff(2129,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2130,plain,
% 1.34/1.15 ((hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2131,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330))))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2130])).
% 1.34/1.15 tff(2132,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 1.34/1.15 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.34/1.15 tff(2133,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(2134,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.34/1.15 tff(2135,plain,
% 1.34/1.15 (hskp9 | c3_1(a1330)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2134, 414, 1742, 1739, 1418, 308, 307, 2128])).
% 1.34/1.15 tff(2136,plain,
% 1.34/1.15 (hskp9),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2135, 2118])).
% 1.34/1.15 tff(2137,plain,
% 1.34/1.15 (~c0_1(a1320)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1516, 2136])).
% 1.34/1.15 tff(2138,plain,
% 1.34/1.15 (c2_1(a1320)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1527, 2136])).
% 1.34/1.15 tff(2139,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2140,plain,
% 1.34/1.15 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2141,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2140])).
% 1.34/1.15 tff(2142,plain,
% 1.34/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.34/1.15 inference(transitivity,[status(thm)],[2141, 2139])).
% 1.34/1.15 tff(2143,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(2144,plain,
% 1.34/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.34/1.15 tff(2145,plain,
% 1.34/1.15 (~c3_1(a1320)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2144, 414, 1029, 2138, 2137, 1418, 308, 307, 1069])).
% 1.34/1.15 tff(2146,plain,
% 1.34/1.15 (~c1_1(a1320)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1510, 2136])).
% 1.34/1.15 tff(2147,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2148,plain,
% 1.34/1.15 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316)) <=> (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2149,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320)))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2148])).
% 1.34/1.15 tff(2150,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.34/1.15 inference(transitivity,[status(thm)],[2149, 2147])).
% 1.34/1.15 tff(2151,plain,
% 1.34/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(2152,plain,
% 1.34/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320)),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.34/1.15 tff(2153,plain,
% 1.34/1.15 ($false),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2152, 414, 2138, 2137, 2146, 1418, 307, 1399, 2111, 2145])).
% 1.34/1.15 tff(2154,plain,(hskp8 | c0_1(a1316) | c3_1(a1316) | c2_1(a1316) | (~c0_1(a1330)) | c2_1(a1330) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.34/1.15 tff(2155,plain,
% 1.34/1.15 (hskp8),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2154, 2011, 2009, 2010, 1662, 1660, 2087])).
% 1.34/1.15 tff(2156,plain,
% 1.34/1.15 (~c3_1(a1319)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1114, 2155])).
% 1.34/1.15 tff(2157,plain,
% 1.34/1.15 (~c0_1(a1319)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1120, 2155])).
% 1.34/1.15 tff(2158,plain,
% 1.34/1.15 (c2_1(a1319)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1214, 2155])).
% 1.34/1.15 tff(2159,plain,
% 1.34/1.15 (hskp6),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2093, 414, 851, 840, 689, 2011, 2010, 2009, 1145])).
% 1.34/1.15 tff(2160,plain,
% 1.34/1.15 (~c0_1(a1315)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1158, 2159])).
% 1.34/1.15 tff(2161,plain,
% 1.34/1.15 (~c1_1(a1315)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1236, 2159])).
% 1.34/1.15 tff(2162,plain,
% 1.34/1.15 (c3_1(a1315)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[1203, 2159])).
% 1.34/1.15 tff(2163,assumption,(~c0_1(a1315)), introduced(assumption)).
% 1.34/1.15 tff(2164,assumption,(c3_1(a1315)), introduced(assumption)).
% 1.34/1.15 tff(2165,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2166,plain,
% 1.34/1.15 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(2167,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[2166])).
% 1.34/1.15 tff(2168,plain,
% 1.34/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.34/1.16 tff(2169,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2170,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.34/1.16 tff(2171,plain,
% 1.34/1.16 (c2_1(a1315)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2170, 414, 1760, 1761, 1696, 1695, 2164, 121, 2163, 35, 1762])).
% 1.34/1.16 tff(2172,assumption,(~c3_1(a1319)), introduced(assumption)).
% 1.34/1.16 tff(2173,assumption,(~c0_1(a1319)), introduced(assumption)).
% 1.34/1.16 tff(2174,assumption,(c2_1(a1319)), introduced(assumption)).
% 1.34/1.16 tff(2175,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2176,plain,
% 1.34/1.16 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2177,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2176])).
% 1.34/1.16 tff(2178,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2177, 2175])).
% 1.34/1.16 tff(2179,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2180,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.34/1.16 tff(2181,plain,
% 1.34/1.16 (~c2_1(a1324)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2180, 414, 1775, 1761, 1696, 2174, 121, 2173, 2172, 425, 1762])).
% 1.34/1.16 tff(2182,assumption,(~c1_1(a1315)), introduced(assumption)).
% 1.34/1.16 tff(2183,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2184,plain,
% 1.34/1.16 ((hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2185,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2184])).
% 1.34/1.16 tff(2186,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2185, 2183])).
% 1.34/1.16 tff(2187,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2188,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.34/1.16 tff(2189,plain,
% 1.34/1.16 ($false),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2188, 414, 22, 1696, 1695, 2164, 2182, 1836, 2181, 2171])).
% 1.34/1.16 tff(2190,plain,(c0_1(a1338) | hskp27 | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1315)) | c1_1(a1315) | (~c1_1(a1338)) | (~c3_1(a1338)) | c1_1(a1324) | c0_1(a1315) | (~c2_1(a1338)) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.16 tff(2191,plain,
% 1.34/1.16 (c0_1(a1338)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2190, 2065, 1581, 1580, 2162, 2161, 1664, 1666, 1481, 2160, 1665, 2158, 2157, 2156])).
% 1.34/1.16 tff(2192,plain,
% 1.34/1.16 (hskp17 | (~c0_1(a1338))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1781, 414, 1664, 1665, 1666, 1088])).
% 1.34/1.16 tff(2193,plain,
% 1.34/1.16 (hskp17),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2192, 2191])).
% 1.34/1.16 tff(2194,plain,
% 1.34/1.16 (~c0_1(a1334)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[864, 2193])).
% 1.34/1.16 tff(2195,plain,
% 1.34/1.16 (c3_1(a1334)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[876, 2193])).
% 1.34/1.16 tff(2196,plain,
% 1.34/1.16 (c2_1(a1334)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[887, 2193])).
% 1.34/1.16 tff(2197,plain,
% 1.34/1.16 ($false),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2037, 414, 1664, 1666, 2196, 2195, 2158, 2194, 2157, 2156, 10, 2191])).
% 1.34/1.16 tff(2198,plain,(c0_1(a1339) | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.16 tff(2199,plain,
% 1.34/1.16 (c0_1(a1339)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2198, 415, 23])).
% 1.34/1.16 tff(2200,plain,
% 1.34/1.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2201,plain,
% 1.34/1.16 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2202,plain,
% 1.34/1.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2201])).
% 1.34/1.16 tff(2203,plain,
% 1.34/1.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2202, 2200])).
% 1.34/1.16 tff(2204,plain,
% 1.34/1.16 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2205,plain,
% 1.34/1.16 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 1.34/1.16 tff(2206,plain,
% 1.34/1.16 (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2205, 414, 23, 1013])).
% 1.34/1.16 tff(2207,plain,
% 1.34/1.16 (hskp8),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2206, 1014, 415, 2199])).
% 1.34/1.16 tff(2208,plain,
% 1.34/1.16 (~c3_1(a1319)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1114, 2207])).
% 1.34/1.16 tff(2209,plain,
% 1.34/1.16 (~c0_1(a1319)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1120, 2207])).
% 1.34/1.16 tff(2210,plain,
% 1.34/1.16 (c2_1(a1319)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1214, 2207])).
% 1.34/1.16 tff(2211,plain,
% 1.34/1.16 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2212,plain,
% 1.34/1.16 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2213,plain,
% 1.34/1.16 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2212])).
% 1.34/1.16 tff(2214,plain,
% 1.34/1.16 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2213, 2211])).
% 1.34/1.16 tff(2215,plain,
% 1.34/1.16 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2216,plain,
% 1.34/1.16 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.34/1.16 tff(2217,plain,
% 1.34/1.16 (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2216, 414, 23, 21])).
% 1.34/1.16 tff(2218,plain,
% 1.34/1.16 (hskp29),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2217, 2199, 415, 446])).
% 1.34/1.16 tff(2219,plain,
% 1.34/1.16 (c2_1(a1338)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[535, 2218])).
% 1.34/1.16 tff(2220,plain,
% 1.34/1.16 (c3_1(a1338)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[524, 2218])).
% 1.34/1.16 tff(2221,plain,
% 1.34/1.16 (c1_1(a1338)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[546, 2218])).
% 1.34/1.16 tff(2222,plain,
% 1.34/1.16 (~c0_1(a1338)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2037, 414, 2221, 2220, 1917, 1916, 2210, 1914, 2209, 2208, 10])).
% 1.34/1.16 tff(2223,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2224,plain,
% 1.34/1.16 ((hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2225,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2224])).
% 1.34/1.16 tff(2226,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.34/1.16 tff(2227,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2228,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.34/1.16 tff(2229,plain,
% 1.34/1.16 (hskp4),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2228, 414, 2221, 2220, 2210, 2209, 2208, 1024, 2222])).
% 1.34/1.16 tff(2230,plain,
% 1.34/1.16 (~c1_1(a1312)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[752, 2229])).
% 1.34/1.16 tff(2231,plain,
% 1.34/1.16 (c0_1(a1312)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[763, 2229])).
% 1.34/1.16 tff(2232,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2233,plain,
% 1.34/1.16 (((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2234,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2233])).
% 1.34/1.16 tff(2235,plain,
% 1.34/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.34/1.16 tff(2236,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2237,plain,
% 1.34/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.34/1.16 tff(2238,plain,
% 1.34/1.16 (~c2_1(a1312)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2237, 414, 1917, 1916, 2210, 2231, 1914, 2209, 2208, 2230, 425])).
% 1.34/1.16 tff(2239,plain,
% 1.34/1.16 (~c3_1(a1312)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1174, 2229])).
% 1.34/1.16 tff(2240,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2241,plain,
% 1.34/1.16 ((hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2242,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2241])).
% 1.34/1.16 tff(2243,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2242, 2240])).
% 1.34/1.16 tff(2244,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(2245,plain,
% 1.34/1.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 1.34/1.16 tff(2246,plain,
% 1.34/1.16 (hskp15),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[2245, 414, 415, 2231, 2199, 23, 2230, 2239, 1724])).
% 1.34/1.16 tff(2247,plain,
% 1.34/1.16 (~c3_1(a1331)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1263, 2246])).
% 1.34/1.16 tff(2248,plain,
% 1.34/1.16 (c1_1(a1331)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[1286, 2246])).
% 1.34/1.16 tff(2249,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2250,plain,
% 1.34/1.16 ((hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312))) <=> (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(2251,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[2250])).
% 1.34/1.16 tff(2252,plain,
% 1.34/1.16 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 1.34/1.16 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.34/1.16 tff(2253,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2254,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.34/1.17 tff(2255,plain,
% 1.34/1.17 (~c0_1(a1331)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2254, 414, 22, 2248, 2231, 2247, 2239, 590, 2238])).
% 1.34/1.17 tff(2256,assumption,(~c2_1(a1312)), introduced(assumption)).
% 1.34/1.17 tff(2257,assumption,(~c3_1(a1312)), introduced(assumption)).
% 1.34/1.17 tff(2258,assumption,(hskp22), introduced(assumption)).
% 1.34/1.17 tff(2259,plain,
% 1.34/1.17 (~c3_1(a1356)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[595, 2258])).
% 1.34/1.17 tff(2260,assumption,(c1_1(a1331)), introduced(assumption)).
% 1.34/1.17 tff(2261,plain,
% 1.34/1.17 (c1_1(a1356)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[564, 2258])).
% 1.34/1.17 tff(2262,plain,
% 1.34/1.17 (c0_1(a1356)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[575, 2258])).
% 1.34/1.17 tff(2263,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2264,plain,
% 1.34/1.17 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312)) <=> (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2265,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2264])).
% 1.34/1.17 tff(2266,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2265, 2263])).
% 1.34/1.17 tff(2267,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2268,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 1.34/1.17 tff(2269,plain,
% 1.34/1.17 ($false),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2268, 414, 2262, 2261, 2260, 2259, 1912, 813, 2257, 435, 1911, 2256])).
% 1.34/1.17 tff(2270,plain,((~hskp22) | (~c1_1(a1331)) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | c0_1(a1331) | c2_1(a1312)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.17 tff(2271,plain,
% 1.34/1.17 (~hskp22),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2270, 2248, 2247, 2230, 2239, 2255, 2238])).
% 1.34/1.17 tff(2272,plain,
% 1.34/1.17 (hskp22 | hskp11),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[553, 414, 2221, 2219, 2220, 445])).
% 1.34/1.17 tff(2273,plain,
% 1.34/1.17 (hskp11),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2272, 2271])).
% 1.34/1.17 tff(2274,plain,
% 1.34/1.17 (~c1_1(a1324)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[97, 2273])).
% 1.34/1.17 tff(2275,plain,
% 1.34/1.17 (c0_1(a1324)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[108, 2273])).
% 1.34/1.17 tff(2276,plain,
% 1.34/1.17 (c2_1(a1331)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1275, 2246])).
% 1.34/1.17 tff(2277,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2278,plain,
% 1.34/1.17 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2279,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2278])).
% 1.34/1.17 tff(2280,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2279, 2277])).
% 1.34/1.17 tff(2281,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2282,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 1.34/1.17 tff(2283,plain,
% 1.34/1.17 (~c2_1(a1324)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2282, 414, 1917, 1916, 2276, 2275, 1914, 2247, 2274, 425, 2255])).
% 1.34/1.17 tff(2284,plain,
% 1.34/1.17 (hskp15 | hskp14),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1257, 414, 2174, 2173, 2172, 1003])).
% 1.34/1.17 tff(2285,plain,
% 1.34/1.17 (hskp15),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2284, 700])).
% 1.34/1.17 tff(2286,plain,
% 1.34/1.17 (~c3_1(a1331)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1263, 2285])).
% 1.34/1.17 tff(2287,plain,
% 1.34/1.17 (c2_1(a1331)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1275, 2285])).
% 1.34/1.17 tff(2288,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2289,plain,
% 1.34/1.17 ((hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2290,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2289])).
% 1.34/1.17 tff(2291,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2290, 2288])).
% 1.34/1.17 tff(2292,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2293,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.34/1.17 tff(2294,plain,
% 1.34/1.17 (~c0_1(a1331)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2293, 414, 700, 415, 2287, 2199, 23, 2286, 915])).
% 1.34/1.17 tff(2295,plain,
% 1.34/1.17 (hskp17),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2017, 414, 2221, 2219, 2220, 1028, 1027, 1026, 1088])).
% 1.34/1.17 tff(2296,plain,
% 1.34/1.17 (~c0_1(a1334)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[864, 2295])).
% 1.34/1.17 tff(2297,plain,
% 1.34/1.17 (c3_1(a1334)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[876, 2295])).
% 1.34/1.17 tff(2298,plain,
% 1.34/1.17 (c2_1(a1334)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[887, 2295])).
% 1.34/1.17 tff(2299,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2300,plain,
% 1.34/1.17 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2301,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2300])).
% 1.34/1.17 tff(2302,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2301, 2299])).
% 1.34/1.17 tff(2303,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2304,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 1.34/1.17 tff(2305,plain,
% 1.34/1.17 (~c3_1(a1307)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2304, 414, 1028, 1027, 2298, 2297, 2287, 2296, 2286, 10, 2294])).
% 1.34/1.17 tff(2306,plain,
% 1.34/1.17 (hskp30 | c3_1(a1307)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2051, 446, 414, 1028, 1026, 1870])).
% 1.34/1.17 tff(2307,plain,
% 1.34/1.17 (hskp30),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2306, 2305])).
% 1.34/1.17 tff(2308,plain,
% 1.34/1.17 (c0_1(a1372)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1909, 2307])).
% 1.34/1.17 tff(2309,plain,
% 1.34/1.17 (c1_1(a1372)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1898, 2307])).
% 1.34/1.17 tff(2310,plain,
% 1.34/1.17 (c3_1(a1372)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1887, 2307])).
% 1.34/1.17 tff(2311,plain,
% 1.34/1.17 ($false),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1928, 2310, 2309, 2295, 2294, 2287, 2286, 2308])).
% 1.34/1.17 tff(2312,plain,(hskp14 | c1_1(a1339) | c2_1(a1339) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.17 tff(2313,plain,
% 1.34/1.17 (hskp14),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2312, 2210, 23, 415, 2209, 2208])).
% 1.34/1.17 tff(2314,plain,
% 1.34/1.17 (~c2_1(a1330)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[211, 2313])).
% 1.34/1.17 tff(2315,plain,
% 1.34/1.17 (~c1_1(a1330)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[217, 2313])).
% 1.34/1.17 tff(2316,plain,
% 1.34/1.17 (c0_1(a1330)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[235, 2313])).
% 1.34/1.17 tff(2317,plain,
% 1.34/1.17 (c3_1(a1324)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[119, 2273])).
% 1.34/1.17 tff(2318,plain,
% 1.34/1.17 (hskp3),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1794, 2275, 2220, 2219, 1014, 2317, 2274, 2316, 2315, 2314, 2221])).
% 1.34/1.17 tff(2319,plain,
% 1.34/1.17 (~c1_1(a1311)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[648, 2318])).
% 1.34/1.17 tff(2320,plain,
% 1.34/1.17 (c2_1(a1311)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[659, 2318])).
% 1.34/1.17 tff(2321,plain,
% 1.34/1.17 (c0_1(a1311)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[670, 2318])).
% 1.34/1.17 tff(2322,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2323,plain,
% 1.34/1.17 (((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2324,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2323])).
% 1.34/1.17 tff(2325,plain,
% 1.34/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2324, 2322])).
% 1.34/1.17 tff(2326,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2327,plain,
% 1.34/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.34/1.17 tff(2328,plain,
% 1.34/1.17 ($false),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2327, 414, 2317, 2231, 2321, 2320, 2274, 2239, 2319, 613, 2238, 2283])).
% 1.34/1.17 tff(2329,plain,((~hskp17) | hskp7 | hskp27 | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.17 tff(2330,plain,
% 1.34/1.17 (~hskp17),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2329, 22, 1014, 415, 23])).
% 1.34/1.17 tff(2331,plain,
% 1.34/1.17 (hskp16),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[858, 2330])).
% 1.34/1.17 tff(2332,plain,
% 1.34/1.17 (~c3_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[930, 2331])).
% 1.34/1.17 tff(2333,plain,
% 1.34/1.17 (~c2_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[976, 2331])).
% 1.34/1.17 tff(2334,plain,
% 1.34/1.17 (c1_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[963, 2331])).
% 1.34/1.17 tff(2335,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2336,plain,
% 1.34/1.17 ((hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333))) <=> (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2337,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2336])).
% 1.34/1.17 tff(2338,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2337, 2335])).
% 1.34/1.17 tff(2339,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2340,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.34/1.17 tff(2341,plain,
% 1.34/1.17 (~c0_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2340, 414, 22, 2334, 2333, 2332, 590])).
% 1.34/1.17 tff(2342,plain,
% 1.34/1.17 (hskp17 | (~c0_1(a1338))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1781, 414, 2221, 2219, 2220, 1088])).
% 1.34/1.17 tff(2343,plain,
% 1.34/1.17 (~c0_1(a1338)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2342, 2330])).
% 1.34/1.17 tff(2344,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2345,plain,
% 1.34/1.17 ((hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333)) <=> (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2346,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2345])).
% 1.34/1.17 tff(2347,plain,
% 1.34/1.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.34/1.17 tff(2348,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2349,plain,
% 1.34/1.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.34/1.17 tff(2350,plain,
% 1.34/1.17 (hskp6),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2349, 414, 2221, 2219, 2333, 2332, 1145, 2343, 2341])).
% 1.34/1.17 tff(2351,plain,
% 1.34/1.17 (~c0_1(a1315)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1158, 2350])).
% 1.34/1.17 tff(2352,assumption,(~hskp17), introduced(assumption)).
% 1.34/1.17 tff(2353,plain,
% 1.34/1.17 (hskp16),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[858, 2352])).
% 1.34/1.17 tff(2354,plain,
% 1.34/1.17 (~c3_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[930, 2353])).
% 1.34/1.17 tff(2355,plain,
% 1.34/1.17 (~c2_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[976, 2353])).
% 1.34/1.17 tff(2356,plain,
% 1.34/1.17 (c1_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[963, 2353])).
% 1.34/1.17 tff(2357,plain,
% 1.34/1.17 (~c0_1(a1333)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[2340, 414, 22, 2356, 2355, 2354, 590])).
% 1.34/1.17 tff(2358,plain,
% 1.34/1.17 (hskp6),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1548, 414, 851, 840, 689, 2355, 2354, 1145, 2357])).
% 1.34/1.17 tff(2359,plain,
% 1.34/1.17 (~c0_1(a1315)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1158, 2358])).
% 1.34/1.17 tff(2360,plain,
% 1.34/1.17 (~c1_1(a1315)),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[1236, 2358])).
% 1.34/1.17 tff(2361,plain,
% 1.34/1.17 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2362,plain,
% 1.34/1.17 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315)) <=> (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(2363,plain,
% 1.34/1.17 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315)))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[2362])).
% 1.34/1.17 tff(2364,plain,
% 1.34/1.17 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 1.34/1.17 inference(transitivity,[status(thm)],[2363, 2361])).
% 1.34/1.17 tff(2365,plain,
% 1.34/1.17 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(2366,plain,
% 1.34/1.17 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315)),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 1.34/1.18 tff(2367,plain,
% 1.34/1.18 (c2_1(a1315)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2366, 414, 22, 711, 2359, 2360, 2075])).
% 1.34/1.18 tff(2368,plain,
% 1.34/1.18 (c3_1(a1315)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1203, 2358])).
% 1.34/1.18 tff(2369,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(2370,plain,
% 1.34/1.18 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(2371,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[2370])).
% 1.34/1.18 tff(2372,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.34/1.18 inference(transitivity,[status(thm)],[2371, 2369])).
% 1.34/1.18 tff(2373,plain,
% 1.34/1.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.34/1.18 inference(quant_inst,[status(thm)],[])).
% 1.34/1.18 tff(2374,plain,
% 1.34/1.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 1.34/1.18 tff(2375,plain,
% 1.34/1.18 (~c3_1(a1339)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2374, 414, 22, 2368, 2199, 23, 2360, 1836, 2367])).
% 1.34/1.18 tff(2376,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(2377,plain,
% 1.34/1.18 ((hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339)) <=> (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(2378,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[2377])).
% 1.34/1.18 tff(2379,plain,
% 1.34/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.34/1.18 inference(transitivity,[status(thm)],[2378, 2376])).
% 1.34/1.18 tff(2380,plain,
% 1.34/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))),
% 1.34/1.18 inference(quant_inst,[status(thm)],[])).
% 1.34/1.18 tff(2381,plain,
% 1.34/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.34/1.18 tff(2382,plain,
% 1.34/1.18 (hskp11 | c3_1(a1339)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2381, 414, 415, 2356, 23, 2355, 57, 2357])).
% 1.34/1.18 tff(2383,plain,
% 1.34/1.18 (hskp11),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2382, 2375])).
% 1.34/1.18 tff(2384,plain,
% 1.34/1.18 (~c1_1(a1324)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[97, 2383])).
% 1.34/1.18 tff(2385,plain,
% 1.34/1.18 (~c0_1(a1338)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2342, 2352])).
% 1.34/1.18 tff(2386,plain,
% 1.34/1.18 (c0_1(a1324)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[108, 2383])).
% 1.34/1.18 tff(2387,plain,
% 1.34/1.18 (c3_1(a1324)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[119, 2383])).
% 1.34/1.18 tff(2388,plain,
% 1.34/1.18 ($false),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2190, 2387, 2386, 2172, 2385, 2368, 2360, 2221, 2220, 2384, 2359, 2219, 2174, 2173, 22])).
% 1.34/1.18 tff(2389,plain,(hskp17 | c3_1(a1319) | (~c2_1(a1319)) | c0_1(a1319) | hskp27 | c1_1(a1339) | c2_1(a1339) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.34/1.18 tff(2390,plain,
% 1.34/1.18 (hskp1),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[2389, 2330, 2210, 2209, 22, 415, 23, 2208])).
% 1.34/1.18 tff(2391,plain,
% 1.34/1.18 (~c2_1(a1308)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[991, 2390])).
% 1.34/1.18 tff(2392,plain,
% 1.34/1.18 (c3_1(a1308)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[382, 2390])).
% 1.34/1.18 tff(2393,plain,
% 1.34/1.18 (~c1_1(a1308)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[371, 2390])).
% 1.34/1.18 tff(2394,plain,
% 1.34/1.18 (~hskp3),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1943, 2393, 2314, 446, 2316, 2315, 22, 2392, 2391])).
% 1.34/1.18 tff(2395,plain,
% 1.34/1.18 (hskp21),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1681, 2394, 1014])).
% 1.34/1.18 tff(2396,plain,
% 1.34/1.18 (~c2_1(a1352)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1687, 2395])).
% 1.34/1.18 tff(2397,plain,
% 1.34/1.18 (~c0_1(a1352)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1693, 2395])).
% 1.34/1.18 tff(2398,plain,
% 1.34/1.18 (c3_1(a1352)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[1706, 2395])).
% 1.34/1.18 tff(2399,plain,
% 1.34/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(2400,plain,
% 1.34/1.18 (((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2401,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352))))),
% 1.37/1.18 inference(monotonicity,[status(thm)],[2400])).
% 1.37/1.18 tff(2402,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 1.37/1.18 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.37/1.18 tff(2403,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 1.37/1.18 inference(quant_inst,[status(thm)],[])).
% 1.37/1.18 tff(2404,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.37/1.18 tff(2405,plain,
% 1.37/1.18 (~c3_1(a1339)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2404, 414, 2221, 2220, 2398, 415, 2397, 2396, 2199, 35, 2343])).
% 1.37/1.18 tff(2406,plain,
% 1.37/1.18 (hskp11),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2381, 414, 415, 2334, 23, 2333, 57, 2405, 2341])).
% 1.37/1.18 tff(2407,plain,
% 1.37/1.18 (~c1_1(a1324)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[97, 2406])).
% 1.37/1.18 tff(2408,plain,
% 1.37/1.18 (c3_1(a1324)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[119, 2406])).
% 1.37/1.18 tff(2409,plain,
% 1.37/1.18 (c0_1(a1324)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[108, 2406])).
% 1.37/1.18 tff(2410,plain,
% 1.37/1.18 (c3_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1203, 2350])).
% 1.37/1.18 tff(2411,plain,
% 1.37/1.18 (~c1_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1236, 2350])).
% 1.37/1.18 tff(2412,plain,
% 1.37/1.18 ($false),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2190, 2411, 2410, 2208, 2343, 2409, 2408, 2221, 2220, 2407, 2351, 2219, 2210, 2209, 22])).
% 1.37/1.18 tff(2413,plain,(hskp27 | c1_1(a1339) | c2_1(a1339) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.37/1.18 tff(2414,plain,
% 1.37/1.18 (hskp27),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2413, 1014, 23, 415])).
% 1.37/1.18 tff(2415,plain,
% 1.37/1.18 (c2_1(a1307)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[457, 2414])).
% 1.37/1.18 tff(2416,plain,
% 1.37/1.18 (c1_1(a1307)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[468, 2414])).
% 1.37/1.18 tff(2417,plain,
% 1.37/1.18 (c0_1(a1307)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[479, 2414])).
% 1.37/1.18 tff(2418,plain,
% 1.37/1.18 (hskp17),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2017, 414, 2221, 2219, 2220, 2417, 2416, 2415, 1088])).
% 1.37/1.18 tff(2419,plain,
% 1.37/1.18 (~c0_1(a1334)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[864, 2418])).
% 1.37/1.18 tff(2420,plain,
% 1.37/1.18 (c3_1(a1334)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[876, 2418])).
% 1.37/1.18 tff(2421,plain,
% 1.37/1.18 (c2_1(a1334)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[887, 2418])).
% 1.37/1.18 tff(2422,plain,
% 1.37/1.18 (~c0_1(a1338)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2037, 414, 2221, 2220, 2421, 2420, 2210, 2419, 2209, 2208, 10])).
% 1.37/1.18 tff(2423,plain,
% 1.37/1.18 (~c3_1(a1307)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2044, 414, 2417, 2416, 2421, 2420, 2210, 2419, 2209, 2208, 10])).
% 1.37/1.18 tff(2424,plain,
% 1.37/1.18 (hskp30 | c3_1(a1307)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2051, 446, 414, 2417, 2415, 1870])).
% 1.37/1.18 tff(2425,plain,
% 1.37/1.18 (hskp30),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2424, 2423])).
% 1.37/1.18 tff(2426,plain,
% 1.37/1.18 (c3_1(a1372)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1887, 2425])).
% 1.37/1.18 tff(2427,plain,
% 1.37/1.18 (c1_1(a1372)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1898, 2425])).
% 1.37/1.18 tff(2428,plain,
% 1.37/1.18 (c0_1(a1372)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1909, 2425])).
% 1.37/1.18 tff(2429,plain,
% 1.37/1.18 ($false),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2062, 414, 2428, 2427, 2426, 2219, 2220, 2210, 2209, 2208, 10, 2422])).
% 1.37/1.18 tff(2430,plain,(hskp7 | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.18 tff(2431,plain,
% 1.37/1.18 (hskp7),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2430, 415, 23])).
% 1.37/1.18 tff(2432,plain,
% 1.37/1.18 (~c3_1(a1316)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[305, 2431])).
% 1.37/1.18 tff(2433,plain,
% 1.37/1.18 (~c0_1(a1316)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1416, 2431])).
% 1.37/1.18 tff(2434,plain,
% 1.37/1.18 (~c2_1(a1316)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[299, 2431])).
% 1.37/1.18 tff(2435,plain,
% 1.37/1.18 (~hskp27),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2064, 2434, 2220, 446, 2221, 2219, 2433, 2432])).
% 1.37/1.18 tff(2436,plain,
% 1.37/1.18 (~c1_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1236, 2094])).
% 1.37/1.18 tff(2437,plain,
% 1.37/1.18 (hskp1 | c2_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2366, 414, 22, 2095, 2436, 2075])).
% 1.37/1.18 tff(2438,plain,
% 1.37/1.18 (hskp1),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2437, 2104])).
% 1.37/1.18 tff(2439,plain,
% 1.37/1.18 (~c2_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[991, 2438])).
% 1.37/1.18 tff(2440,plain,
% 1.37/1.18 (hskp14),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[503, 22, 775])).
% 1.37/1.18 tff(2441,plain,
% 1.37/1.18 (c0_1(a1330)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[235, 2440])).
% 1.37/1.18 tff(2442,plain,
% 1.37/1.18 (~c2_1(a1330)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[211, 2440])).
% 1.37/1.18 tff(2443,plain,
% 1.37/1.18 (hskp3),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2154, 1029, 307, 308, 1418, 2442, 2441])).
% 1.37/1.18 tff(2444,plain,
% 1.37/1.18 (~c1_1(a1330)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[217, 2440])).
% 1.37/1.18 tff(2445,plain,
% 1.37/1.18 (c3_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[382, 2438])).
% 1.37/1.18 tff(2446,plain,
% 1.37/1.18 (~c1_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[371, 2438])).
% 1.37/1.18 tff(2447,plain,
% 1.37/1.18 ($false),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1943, 2446, 2445, 2442, 775, 2441, 2444, 22, 2443, 2439])).
% 1.37/1.18 tff(2448,plain,(hskp8 | hskp18 | hskp27 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.18 tff(2449,plain,
% 1.37/1.18 (hskp8),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2448, 446, 2435, 2433, 2434, 2432])).
% 1.37/1.18 tff(2450,plain,
% 1.37/1.18 (~c0_1(a1319)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1120, 2449])).
% 1.37/1.18 tff(2451,plain,
% 1.37/1.18 (c2_1(a1319)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1214, 2449])).
% 1.37/1.18 tff(2452,plain,
% 1.37/1.18 (hskp6),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2093, 414, 851, 840, 689, 2433, 2434, 2432, 1145])).
% 1.37/1.18 tff(2453,plain,
% 1.37/1.18 (~c0_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1158, 2452])).
% 1.37/1.18 tff(2454,plain,
% 1.37/1.18 (~c3_1(a1319)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1114, 2449])).
% 1.37/1.18 tff(2455,plain,
% 1.37/1.18 (~c0_1(a1333)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2340, 414, 2435, 2356, 2355, 2354, 590])).
% 1.37/1.18 tff(2456,plain,
% 1.37/1.18 (hskp1),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2389, 2352, 2451, 2450, 2435, 415, 23, 2454])).
% 1.37/1.18 tff(2457,plain,
% 1.37/1.18 (~c2_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[991, 2456])).
% 1.37/1.18 tff(2458,plain,
% 1.37/1.18 (c3_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[382, 2456])).
% 1.37/1.18 tff(2459,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2460,plain,
% 1.37/1.18 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2461,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333))))),
% 1.37/1.18 inference(monotonicity,[status(thm)],[2460])).
% 1.37/1.18 tff(2462,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.37/1.18 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.37/1.18 tff(2463,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 1.37/1.18 inference(quant_inst,[status(thm)],[])).
% 1.37/1.18 tff(2464,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.37/1.18 tff(2465,plain,
% 1.37/1.18 (c0_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2464, 414, 2356, 2458, 2355, 2354, 2457, 326, 2455])).
% 1.37/1.18 tff(2466,plain,
% 1.37/1.18 (~c1_1(a1308)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[371, 2456])).
% 1.37/1.18 tff(2467,plain,
% 1.37/1.18 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.37/1.18 inference(bind,[status(th)],[])).
% 1.37/1.18 tff(2468,plain,
% 1.37/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(quant_intro,[status(thm)],[2467])).
% 1.37/1.18 tff(2469,plain,
% 1.37/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2470,plain,
% 1.37/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.37/1.18 inference(bind,[status(th)],[])).
% 1.37/1.18 tff(2471,plain,
% 1.37/1.18 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(quant_intro,[status(thm)],[2470])).
% 1.37/1.18 tff(2472,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.37/1.18 tff(2473,plain,
% 1.37/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.37/1.18 tff(2474,plain,
% 1.37/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2473, 2469])).
% 1.37/1.18 tff(2475,plain,(
% 1.37/1.18 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(skolemize,[status(sab)],[2474])).
% 1.37/1.18 tff(2476,plain,
% 1.37/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2475, 2468])).
% 1.37/1.18 tff(2477,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2478,plain,
% 1.37/1.18 ((hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333))) <=> (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2479,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333))))),
% 1.37/1.18 inference(monotonicity,[status(thm)],[2478])).
% 1.37/1.18 tff(2480,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 1.37/1.18 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.37/1.18 tff(2481,plain,
% 1.37/1.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))),
% 1.37/1.18 inference(quant_inst,[status(thm)],[])).
% 1.37/1.18 tff(2482,plain,
% 1.37/1.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.37/1.18 tff(2483,plain,
% 1.37/1.18 (hskp12),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2482, 414, 2221, 2219, 2220, 2356, 2355, 2476, 2455])).
% 1.37/1.18 tff(2484,plain,
% 1.37/1.18 (~c0_1(a1325)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1316, 2483])).
% 1.37/1.18 tff(2485,plain,
% 1.37/1.18 (c3_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1203, 2452])).
% 1.37/1.18 tff(2486,plain,
% 1.37/1.18 (c3_1(a1325)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1327, 2483])).
% 1.37/1.18 tff(2487,plain,
% 1.37/1.18 (c1_1(a1325)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1338, 2483])).
% 1.37/1.18 tff(2488,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2489,plain,
% 1.37/1.18 (((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2490,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 1.37/1.18 inference(monotonicity,[status(thm)],[2489])).
% 1.37/1.18 tff(2491,plain,
% 1.37/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.37/1.18 inference(transitivity,[status(thm)],[2490, 2488])).
% 1.37/1.18 tff(2492,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 1.37/1.18 inference(quant_inst,[status(thm)],[])).
% 1.37/1.18 tff(2493,plain,
% 1.37/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 1.37/1.18 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 1.37/1.18 tff(2494,plain,
% 1.37/1.18 (c2_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[2493, 414, 2487, 2486, 2485, 2458, 2484, 2453, 2466, 35, 2465])).
% 1.37/1.18 tff(2495,plain,
% 1.37/1.18 (~c1_1(a1315)),
% 1.37/1.18 inference(unit_resolution,[status(thm)],[1236, 2452])).
% 1.37/1.18 tff(2496,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2497,plain,
% 1.37/1.18 ((hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.18 inference(rewrite,[status(thm)],[])).
% 1.37/1.18 tff(2498,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 1.37/1.18 inference(monotonicity,[status(thm)],[2497])).
% 1.37/1.18 tff(2499,plain,
% 1.37/1.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.18 inference(transitivity,[status(thm)],[2498, 2496])).
% 1.37/1.18 tff(2500,plain,
% 1.37/1.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2501,plain,
% 1.37/1.19 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 1.37/1.19 tff(2502,plain,
% 1.37/1.19 ((~c0_1(a1308)) | (~c2_1(a1315))),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2501, 414, 2435, 2485, 2458, 2495, 2457, 1836])).
% 1.37/1.19 tff(2503,plain,
% 1.37/1.19 ($false),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2502, 2494, 2465])).
% 1.37/1.19 tff(2504,plain,(hskp17 | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.19 tff(2505,plain,
% 1.37/1.19 (hskp17),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2504, 415, 23])).
% 1.37/1.19 tff(2506,plain,
% 1.37/1.19 (~c0_1(a1334)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[864, 2505])).
% 1.37/1.19 tff(2507,plain,
% 1.37/1.19 (c3_1(a1334)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[876, 2505])).
% 1.37/1.19 tff(2508,plain,
% 1.37/1.19 (c2_1(a1334)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[887, 2505])).
% 1.37/1.19 tff(2509,plain,
% 1.37/1.19 (~c0_1(a1338)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2037, 414, 2221, 2220, 2508, 2507, 2451, 2506, 2450, 2454, 10])).
% 1.37/1.19 tff(2510,plain,
% 1.37/1.19 (hskp4),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2228, 414, 2221, 2220, 2451, 2450, 2454, 1024, 2509])).
% 1.37/1.19 tff(2511,plain,
% 1.37/1.19 (~c3_1(a1312)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1174, 2510])).
% 1.37/1.19 tff(2512,plain,
% 1.37/1.19 (~c1_1(a1312)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[752, 2510])).
% 1.37/1.19 tff(2513,plain,
% 1.37/1.19 (c0_1(a1312)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[763, 2510])).
% 1.37/1.19 tff(2514,plain,
% 1.37/1.19 (hskp15),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2245, 414, 415, 2513, 2199, 23, 2512, 2511, 1724])).
% 1.37/1.19 tff(2515,plain,
% 1.37/1.19 (c1_1(a1331)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1286, 2514])).
% 1.37/1.19 tff(2516,plain,
% 1.37/1.19 (~c3_1(a1331)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1263, 2514])).
% 1.37/1.19 tff(2517,plain,
% 1.37/1.19 (~c2_1(a1312)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2237, 414, 2508, 2507, 2451, 2513, 2506, 2450, 2454, 2512, 425])).
% 1.37/1.19 tff(2518,plain,
% 1.37/1.19 (~c0_1(a1331)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2254, 414, 2435, 2515, 2513, 2516, 2511, 590, 2517])).
% 1.37/1.19 tff(2519,plain,
% 1.37/1.19 (~hskp22),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2270, 2518, 2517, 2512, 2511, 2516, 2515])).
% 1.37/1.19 tff(2520,plain,
% 1.37/1.19 (hskp11),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2272, 2519])).
% 1.37/1.19 tff(2521,plain,
% 1.37/1.19 (~c1_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[97, 2520])).
% 1.37/1.19 tff(2522,plain,
% 1.37/1.19 (c0_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[108, 2520])).
% 1.37/1.19 tff(2523,plain,
% 1.37/1.19 (c3_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[119, 2520])).
% 1.37/1.19 tff(2524,plain,
% 1.37/1.19 ($false),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2190, 2523, 2522, 2485, 2495, 2454, 2509, 2221, 2220, 2521, 2453, 2219, 2451, 2450, 2435])).
% 1.37/1.19 tff(2525,plain,(c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.19 tff(2526,plain,
% 1.37/1.19 (c1_1(a1339)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2525, 23])).
% 1.37/1.19 tff(2527,plain,
% 1.37/1.19 (~hskp13),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[186, 46, 414, 2526, 24, 23])).
% 1.37/1.19 tff(2528,plain,
% 1.37/1.19 (~hskp28),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[292, 2527, 2526, 24, 23, 25, 414])).
% 1.37/1.19 tff(2529,plain,
% 1.37/1.19 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.37/1.19 inference(bind,[status(th)],[])).
% 1.37/1.19 tff(2530,plain,
% 1.37/1.19 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(quant_intro,[status(thm)],[2529])).
% 1.37/1.19 tff(2531,plain,
% 1.37/1.19 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2532,plain,
% 1.37/1.19 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.37/1.19 inference(bind,[status(th)],[])).
% 1.37/1.19 tff(2533,plain,
% 1.37/1.19 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(quant_intro,[status(thm)],[2532])).
% 1.37/1.19 tff(2534,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.37/1.19 tff(2535,plain,
% 1.37/1.19 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 1.37/1.19 tff(2536,plain,
% 1.37/1.19 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2535, 2531])).
% 1.37/1.19 tff(2537,plain,(
% 1.37/1.19 ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(skolemize,[status(sab)],[2536])).
% 1.37/1.19 tff(2538,plain,
% 1.37/1.19 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2537, 2530])).
% 1.37/1.19 tff(2539,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2540,plain,
% 1.37/1.19 ((hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348))) <=> (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2541,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348)))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2540])).
% 1.37/1.19 tff(2542,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2541, 2539])).
% 1.37/1.19 tff(2543,plain,
% 1.37/1.19 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2544,plain,
% 1.37/1.19 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 1.37/1.19 tff(2545,plain,
% 1.37/1.19 (hskp28 | c3_1(a1348)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2544, 414, 851, 689, 2538])).
% 1.37/1.19 tff(2546,plain,
% 1.37/1.19 (c3_1(a1348)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2545, 2528])).
% 1.37/1.19 tff(2547,plain,
% 1.37/1.19 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2548,plain,
% 1.37/1.19 ((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2549,plain,
% 1.37/1.19 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2548])).
% 1.37/1.19 tff(2550,plain,
% 1.37/1.19 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.37/1.19 tff(2551,plain,
% 1.37/1.19 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2552,plain,
% 1.37/1.19 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.37/1.19 tff(2553,plain,
% 1.37/1.19 (hskp22 | hskp11 | (~c3_1(a1348))),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2552, 414, 851, 840, 445])).
% 1.37/1.19 tff(2554,plain,
% 1.37/1.19 (hskp22),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2553, 2546, 46])).
% 1.37/1.19 tff(2555,plain,
% 1.37/1.19 (c1_1(a1356)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[564, 2554])).
% 1.37/1.19 tff(2556,plain,
% 1.37/1.19 (c0_1(a1356)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[575, 2554])).
% 1.37/1.19 tff(2557,plain,
% 1.37/1.19 (~c2_1(a1356)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[579, 414, 2527, 2556, 2555, 45])).
% 1.37/1.19 tff(2558,plain,
% 1.37/1.19 (~c3_1(a1356)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[595, 2554])).
% 1.37/1.19 tff(2559,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2560,plain,
% 1.37/1.19 (((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2561,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356)))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2560])).
% 1.37/1.19 tff(2562,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2561, 2559])).
% 1.37/1.19 tff(2563,plain,
% 1.37/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2564,plain,
% 1.37/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 1.37/1.19 tff(2565,plain,
% 1.37/1.19 ($false),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2564, 414, 2555, 2526, 2558, 24, 23, 326, 25, 2557])).
% 1.37/1.19 tff(2566,plain,(hskp11 | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.19 tff(2567,plain,
% 1.37/1.19 (hskp11),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2566, 25, 23, 24])).
% 1.37/1.19 tff(2568,plain,
% 1.37/1.19 (~c1_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[97, 2567])).
% 1.37/1.19 tff(2569,plain,
% 1.37/1.19 (c3_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[119, 2567])).
% 1.37/1.19 tff(2570,plain,
% 1.37/1.19 (c0_1(a1324)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[108, 2567])).
% 1.37/1.19 tff(2571,plain,
% 1.37/1.19 ($false),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[133, 414, 2526, 2570, 2569, 24, 23, 2568, 35, 25])).
% 1.37/1.19 tff(2572,plain,((~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.19 tff(2573,plain,
% 1.37/1.19 (~c3_1(a1339)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2572, 24, 23])).
% 1.37/1.19 tff(2574,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2575,plain,
% 1.37/1.19 ((hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339))) <=> (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2576,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2575])).
% 1.37/1.19 tff(2577,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.37/1.19 tff(2578,plain,
% 1.37/1.19 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2579,plain,
% 1.37/1.19 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.37/1.19 tff(2580,plain,
% 1.37/1.19 (hskp9 | c3_1(a1339)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2579, 414, 2526, 24, 23, 1498])).
% 1.37/1.19 tff(2581,plain,
% 1.37/1.19 (hskp9),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2580, 2573])).
% 1.37/1.19 tff(2582,plain,
% 1.37/1.19 (c2_1(a1320)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1527, 2581])).
% 1.37/1.19 tff(2583,plain,
% 1.37/1.19 (~c0_1(a1320)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1516, 2581])).
% 1.37/1.19 tff(2584,plain,
% 1.37/1.19 (~c1_1(a1320)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1510, 2581])).
% 1.37/1.19 tff(2585,assumption,(~c3_1(a1320)), introduced(assumption)).
% 1.37/1.19 tff(2586,assumption,(~c1_1(a1320)), introduced(assumption)).
% 1.37/1.19 tff(2587,assumption,(~c0_1(a1320)), introduced(assumption)).
% 1.37/1.19 tff(2588,assumption,(c2_1(a1320)), introduced(assumption)).
% 1.37/1.19 tff(2589,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2590,plain,
% 1.37/1.19 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320)) <=> (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2591,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320)))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2590])).
% 1.37/1.19 tff(2592,plain,
% 1.37/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.37/1.19 tff(2593,plain,
% 1.37/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2594,plain,
% 1.37/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.37/1.19 tff(2595,plain,
% 1.37/1.19 ($false),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2594, 414, 2588, 2587, 2586, 1399, 2585])).
% 1.37/1.19 tff(2596,plain,(c3_1(a1320) | (~c2_1(a1320)) | c0_1(a1320) | c1_1(a1320)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.19 tff(2597,plain,
% 1.37/1.19 (c3_1(a1320)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2596, 2584, 2583, 2582])).
% 1.37/1.19 tff(2598,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2599,plain,
% 1.37/1.19 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2600,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2599])).
% 1.37/1.19 tff(2601,plain,
% 1.37/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2600, 2598])).
% 1.37/1.19 tff(2602,plain,
% 1.37/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2603,plain,
% 1.37/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 1.37/1.19 tff(2604,plain,
% 1.37/1.19 (hskp8),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2603, 414, 2582, 24, 23, 2583, 1069, 2573, 2597])).
% 1.37/1.19 tff(2605,plain,
% 1.37/1.19 (~c3_1(a1319)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1114, 2604])).
% 1.37/1.19 tff(2606,plain,
% 1.37/1.19 (~c0_1(a1319)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1120, 2604])).
% 1.37/1.19 tff(2607,plain,
% 1.37/1.19 (c2_1(a1319)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[1214, 2604])).
% 1.37/1.19 tff(2608,plain,
% 1.37/1.19 (hskp14 | hskp13 | c3_1(a1339) | (~c1_1(a1339))),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[204, 414, 23, 198])).
% 1.37/1.19 tff(2609,plain,
% 1.37/1.19 (c3_1(a1339)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2608, 700, 2526, 269])).
% 1.37/1.19 tff(2610,plain,
% 1.37/1.19 (~hskp28),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[292, 2609, 2526, 24, 23, 269, 414])).
% 1.37/1.19 tff(2611,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2612,plain,
% 1.37/1.19 ((hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319))) <=> (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2613,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319))))),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2612])).
% 1.37/1.19 tff(2614,plain,
% 1.37/1.19 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 1.37/1.19 inference(transitivity,[status(thm)],[2613, 2611])).
% 1.37/1.19 tff(2615,plain,
% 1.37/1.19 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))),
% 1.37/1.19 inference(quant_inst,[status(thm)],[])).
% 1.37/1.19 tff(2616,plain,
% 1.37/1.19 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.37/1.19 tff(2617,plain,
% 1.37/1.19 (hskp28 | c0_1(a1319) | (~c1_1(a1319))),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2616, 414, 2172, 2538])).
% 1.37/1.19 tff(2618,plain,
% 1.37/1.19 (~c1_1(a1319)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2617, 2610, 2173])).
% 1.37/1.19 tff(2619,assumption,(~hskp28), introduced(assumption)).
% 1.37/1.19 tff(2620,plain,
% 1.37/1.19 (hskp1),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[365, 2619, 1014])).
% 1.37/1.19 tff(2621,plain,
% 1.37/1.19 (~c2_1(a1308)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[991, 2620])).
% 1.37/1.19 tff(2622,plain,
% 1.37/1.19 (~c1_1(a1308)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[371, 2620])).
% 1.37/1.19 tff(2623,plain,
% 1.37/1.19 ((hskp28 | hskp25 | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2624,plain,
% 1.37/1.19 (((hskp28 | hskp25) | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2625,plain,
% 1.37/1.19 ((hskp28 | hskp25) <=> (hskp28 | hskp25)),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2626,plain,
% 1.37/1.19 (((hskp28 | hskp25) | hskp14) <=> ((hskp28 | hskp25) | hskp14)),
% 1.37/1.19 inference(monotonicity,[status(thm)],[2625])).
% 1.37/1.19 tff(2627,plain,
% 1.37/1.19 (((hskp28 | hskp25) | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 1.37/1.19 inference(transitivity,[status(thm)],[2626, 2624])).
% 1.37/1.19 tff(2628,axiom,((hskp28 | hskp25) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.37/1.19 tff(2629,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.37/1.19 tff(2630,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2629, 2623])).
% 1.37/1.19 tff(2631,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2630, 2623])).
% 1.37/1.19 tff(2632,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2631, 2623])).
% 1.37/1.19 tff(2633,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2632, 2623])).
% 1.37/1.19 tff(2634,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2633, 2623])).
% 1.37/1.19 tff(2635,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2634, 2623])).
% 1.37/1.19 tff(2636,plain,
% 1.37/1.19 (hskp28 | hskp25 | hskp14),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2635, 2623])).
% 1.37/1.19 tff(2637,plain,
% 1.37/1.19 (hskp25),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2636, 2619, 700])).
% 1.37/1.19 tff(2638,plain,
% 1.37/1.19 (((~hskp25) | (~c3_1(a1394))) <=> ((~hskp25) | (~c3_1(a1394)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2639,plain,
% 1.37/1.19 (((~c3_1(a1394)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1394)))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2640,axiom,((~c3_1(a1394)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.37/1.19 tff(2641,plain,
% 1.37/1.19 ((~hskp25) | (~c3_1(a1394))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.37/1.19 tff(2642,plain,
% 1.37/1.19 ((~hskp25) | (~c3_1(a1394))),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2641, 2638])).
% 1.37/1.19 tff(2643,plain,
% 1.37/1.19 (~c3_1(a1394)),
% 1.37/1.19 inference(unit_resolution,[status(thm)],[2642, 2637])).
% 1.37/1.19 tff(2644,plain,
% 1.37/1.19 (((~hskp25) | c2_1(a1394)) <=> ((~hskp25) | c2_1(a1394))),
% 1.37/1.19 inference(rewrite,[status(thm)],[])).
% 1.37/1.19 tff(2645,axiom,((~hskp25) | c2_1(a1394)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.37/1.19 tff(2646,plain,
% 1.37/1.19 ((~hskp25) | c2_1(a1394)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.37/1.19 tff(2647,plain,
% 1.37/1.19 ((~hskp25) | c2_1(a1394)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2646, 2644])).
% 1.37/1.19 tff(2648,plain,
% 1.37/1.19 ((~hskp25) | c2_1(a1394)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2647, 2644])).
% 1.37/1.19 tff(2649,plain,
% 1.37/1.19 ((~hskp25) | c2_1(a1394)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2648, 2644])).
% 1.37/1.19 tff(2650,plain,
% 1.37/1.19 ((~hskp25) | c2_1(a1394)),
% 1.37/1.19 inference(modus_ponens,[status(thm)],[2649, 2644])).
% 1.37/1.20 tff(2651,plain,
% 1.37/1.20 ((~hskp25) | c2_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2650, 2644])).
% 1.37/1.20 tff(2652,plain,
% 1.37/1.20 ((~hskp25) | c2_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2651, 2644])).
% 1.37/1.20 tff(2653,plain,
% 1.37/1.20 ((~hskp25) | c2_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2652, 2644])).
% 1.37/1.20 tff(2654,plain,
% 1.37/1.20 (c2_1(a1394)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2653, 2637])).
% 1.37/1.20 tff(2655,plain,
% 1.37/1.20 (((~hskp25) | c0_1(a1394)) <=> ((~hskp25) | c0_1(a1394))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2656,axiom,((~hskp25) | c0_1(a1394)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.37/1.20 tff(2657,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 1.37/1.20 tff(2658,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2657, 2655])).
% 1.37/1.20 tff(2659,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2658, 2655])).
% 1.37/1.20 tff(2660,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2659, 2655])).
% 1.37/1.20 tff(2661,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2660, 2655])).
% 1.37/1.20 tff(2662,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2661, 2655])).
% 1.37/1.20 tff(2663,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2662, 2655])).
% 1.37/1.20 tff(2664,plain,
% 1.37/1.20 ((~hskp25) | c0_1(a1394)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2663, 2655])).
% 1.37/1.20 tff(2665,plain,
% 1.37/1.20 (c0_1(a1394)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2664, 2637])).
% 1.37/1.20 tff(2666,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2667,plain,
% 1.37/1.20 ((hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308))) <=> (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2668,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2667])).
% 1.37/1.20 tff(2669,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2668, 2666])).
% 1.37/1.20 tff(2670,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2671,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 1.37/1.20 tff(2672,plain,
% 1.37/1.20 (~c0_1(a1308)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2671, 178, 700, 2665, 2654, 2643, 2622, 2621, 915])).
% 1.37/1.20 tff(2673,plain,
% 1.37/1.20 (c3_1(a1308)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[382, 2620])).
% 1.37/1.20 tff(2674,plain,
% 1.37/1.20 ($false),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[406, 178, 1014, 177, 2673, 23, 2622, 400, 25, 2672])).
% 1.37/1.20 tff(2675,plain,(hskp28 | (~ndr1_0) | hskp7 | (~c1_1(a1339)) | c2_1(a1339) | (~c3_1(a1339)) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.37/1.20 tff(2676,plain,
% 1.37/1.20 (hskp7),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2675, 2610, 2526, 700, 23, 2609, 414])).
% 1.37/1.20 tff(2677,plain,
% 1.37/1.20 (~c3_1(a1316)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[305, 2676])).
% 1.37/1.20 tff(2678,plain,
% 1.37/1.20 (~c0_1(a1316)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1416, 2676])).
% 1.37/1.20 tff(2679,assumption,(~c2_1(a1319)), introduced(assumption)).
% 1.37/1.20 tff(2680,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2681,plain,
% 1.37/1.20 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2682,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2681])).
% 1.37/1.20 tff(2683,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.37/1.20 tff(2684,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2685,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.37/1.20 tff(2686,plain,
% 1.37/1.20 (hskp6),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2685, 414, 851, 840, 2679, 689, 2173, 2172, 1145])).
% 1.37/1.20 tff(2687,plain,
% 1.37/1.20 (~c0_1(a1315)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1158, 2686])).
% 1.37/1.20 tff(2688,plain,
% 1.37/1.20 (c3_1(a1315)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1203, 2686])).
% 1.37/1.20 tff(2689,plain,
% 1.37/1.20 (~hskp8),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1214, 2679])).
% 1.37/1.20 tff(2690,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2691,plain,
% 1.37/1.20 ((hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2692,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2691])).
% 1.37/1.20 tff(2693,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2692, 2690])).
% 1.37/1.20 tff(2694,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2695,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.37/1.20 tff(2696,plain,
% 1.37/1.20 (~c2_1(a1315)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2695, 414, 2689, 2679, 2688, 2173, 2172, 2687, 1069])).
% 1.37/1.20 tff(2697,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2698,plain,
% 1.37/1.20 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2699,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2698])).
% 1.37/1.20 tff(2700,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2699, 2697])).
% 1.37/1.20 tff(2701,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2702,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 1.37/1.20 tff(2703,plain,
% 1.37/1.20 (~c3_1(a1348)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2702, 414, 2689, 840, 2679, 689, 2173, 2172, 1069])).
% 1.37/1.20 tff(2704,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2705,plain,
% 1.37/1.20 ((hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339))) <=> (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2706,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348)))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2705])).
% 1.37/1.20 tff(2707,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2706, 2704])).
% 1.37/1.20 tff(2708,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2709,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 1.37/1.20 tff(2710,plain,
% 1.37/1.20 (hskp9 | c0_1(a1339) | (~c1_1(a1339)) | c3_1(a1348)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2709, 414, 851, 689, 23, 1498])).
% 1.37/1.20 tff(2711,plain,
% 1.37/1.20 (hskp9),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2710, 2703, 2526, 24])).
% 1.37/1.20 tff(2712,plain,
% 1.37/1.20 (~c0_1(a1320)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1516, 2711])).
% 1.37/1.20 tff(2713,plain,
% 1.37/1.20 (c2_1(a1320)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1527, 2711])).
% 1.37/1.20 tff(2714,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2715,plain,
% 1.37/1.20 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2716,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2715])).
% 1.37/1.20 tff(2717,plain,
% 1.37/1.20 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2716, 2714])).
% 1.37/1.20 tff(2718,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2719,plain,
% 1.37/1.20 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 1.37/1.20 tff(2720,plain,
% 1.37/1.20 (~c3_1(a1320)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2719, 414, 2689, 2713, 2679, 2712, 2173, 2172, 1069])).
% 1.37/1.20 tff(2721,plain,
% 1.37/1.20 (~c1_1(a1320)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[1510, 2711])).
% 1.37/1.20 tff(2722,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2723,plain,
% 1.37/1.20 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319)) <=> (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2724,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320)))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2723])).
% 1.37/1.20 tff(2725,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.37/1.20 tff(2726,plain,
% 1.37/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2727,plain,
% 1.37/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320)),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.37/1.20 tff(2728,plain,
% 1.37/1.20 (c1_1(a1319)),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2727, 414, 2713, 2712, 2721, 2173, 2172, 1399, 2720])).
% 1.37/1.20 tff(2729,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2730,plain,
% 1.37/1.20 (((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 1.37/1.20 inference(rewrite,[status(thm)],[])).
% 1.37/1.20 tff(2731,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319))))),
% 1.37/1.20 inference(monotonicity,[status(thm)],[2730])).
% 1.37/1.20 tff(2732,plain,
% 1.37/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 1.37/1.20 inference(transitivity,[status(thm)],[2731, 2729])).
% 1.37/1.20 tff(2733,plain,
% 1.37/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 1.37/1.20 inference(quant_inst,[status(thm)],[])).
% 1.37/1.20 tff(2734,plain,
% 1.37/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319))),
% 1.37/1.20 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 1.37/1.20 tff(2735,plain,
% 1.37/1.20 ($false),
% 1.37/1.20 inference(unit_resolution,[status(thm)],[2734, 414, 2526, 2679, 2688, 24, 23, 2172, 2687, 326, 2728, 2696])).
% 1.37/1.20 tff(2736,plain,(c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2737,plain,
% 1.37/1.21 (c2_1(a1319)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2736, 2173, 23, 2172, 24])).
% 1.37/1.21 tff(2738,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2739,plain,
% 1.37/1.21 (((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316)) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2740,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2739])).
% 1.37/1.21 tff(2741,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2740, 2738])).
% 1.37/1.21 tff(2742,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2743,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.37/1.21 tff(2744,plain,
% 1.37/1.21 (c1_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2743, 414, 2737, 2173, 2172, 2678, 2677, 1399, 2618])).
% 1.37/1.21 tff(2745,plain,
% 1.37/1.21 (~c2_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[299, 2676])).
% 1.37/1.21 tff(2746,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[340, 414, 700, 269, 2745, 2677, 198, 2744])).
% 1.37/1.21 tff(2747,plain,(hskp14 | hskp13 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339) | c0_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2748,plain,
% 1.37/1.21 (hskp14),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2747, 2527, 2173, 2172, 23, 24])).
% 1.37/1.21 tff(2749,plain,
% 1.37/1.21 (~c2_1(a1330)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[211, 2748])).
% 1.37/1.21 tff(2750,plain,
% 1.37/1.21 (~c1_1(a1330)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[217, 2748])).
% 1.37/1.21 tff(2751,plain,
% 1.37/1.21 (c3_1(a1330)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[224, 414, 46, 2526, 24, 23, 2750, 2749, 57])).
% 1.37/1.21 tff(2752,plain,
% 1.37/1.21 (c0_1(a1330)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[235, 2748])).
% 1.37/1.21 tff(2753,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2754,plain,
% 1.37/1.21 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2755,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2754])).
% 1.37/1.21 tff(2756,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2755, 2753])).
% 1.37/1.21 tff(2757,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2758,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 1.37/1.21 tff(2759,plain,
% 1.37/1.21 ((~c3_1(a1339)) | (~c3_1(a1330))),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2758, 414, 2526, 2752, 24, 23, 2750, 35])).
% 1.37/1.21 tff(2760,plain,
% 1.37/1.21 (~c3_1(a1339)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2759, 2751])).
% 1.37/1.21 tff(2761,plain,
% 1.37/1.21 (hskp9),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2580, 2760])).
% 1.37/1.21 tff(2762,plain,
% 1.37/1.21 (c2_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1527, 2761])).
% 1.37/1.21 tff(2763,plain,
% 1.37/1.21 (~c0_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1516, 2761])).
% 1.37/1.21 tff(2764,plain,
% 1.37/1.21 (~c1_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1510, 2761])).
% 1.37/1.21 tff(2765,plain,
% 1.37/1.21 (c3_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2596, 2764, 2763, 2762])).
% 1.37/1.21 tff(2766,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2767,plain,
% 1.37/1.21 ((hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320))) <=> (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2768,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2767])).
% 1.37/1.21 tff(2769,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.37/1.21 tff(2770,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2771,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.37/1.21 tff(2772,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2771, 414, 22, 2752, 2762, 2749, 2764, 1836, 2751, 2765])).
% 1.37/1.21 tff(2773,plain,(hskp11 | hskp27 | c0_1(a1339) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2774,plain,
% 1.37/1.21 (hskp11),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2773, 2173, 24, 23, 22, 2172])).
% 1.37/1.21 tff(2775,plain,
% 1.37/1.21 (~c1_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[97, 2774])).
% 1.37/1.21 tff(2776,plain,
% 1.37/1.21 (c3_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[119, 2774])).
% 1.37/1.21 tff(2777,plain,
% 1.37/1.21 (c0_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[108, 2774])).
% 1.37/1.21 tff(2778,plain,
% 1.37/1.21 (~c3_1(a1339)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[133, 414, 2526, 2777, 2776, 24, 23, 2775, 35])).
% 1.37/1.21 tff(2779,plain,
% 1.37/1.21 (hskp9),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2580, 2778])).
% 1.37/1.21 tff(2780,plain,
% 1.37/1.21 (~c0_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1516, 2779])).
% 1.37/1.21 tff(2781,plain,
% 1.37/1.21 (c2_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1527, 2779])).
% 1.37/1.21 tff(2782,plain,
% 1.37/1.21 (~c1_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1510, 2779])).
% 1.37/1.21 tff(2783,plain,
% 1.37/1.21 (c3_1(a1320)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2596, 2588, 2587, 2586])).
% 1.37/1.21 tff(2784,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2785,plain,
% 1.37/1.21 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2786,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2785])).
% 1.37/1.21 tff(2787,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2786, 2784])).
% 1.37/1.21 tff(2788,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2789,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 1.37/1.21 tff(2790,plain,
% 1.37/1.21 (~c2_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2789, 414, 109, 2588, 2174, 98, 2587, 2173, 2172, 425, 2783])).
% 1.37/1.21 tff(2791,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2792,plain,
% 1.37/1.21 ((hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320))) <=> (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2793,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2792])).
% 1.37/1.21 tff(2794,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2793, 2791])).
% 1.37/1.21 tff(2795,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2796,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 1.37/1.21 tff(2797,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2796, 414, 22, 109, 120, 2588, 2586, 1836, 2783, 2790])).
% 1.37/1.21 tff(2798,plain,((~hskp11) | hskp27 | (~c2_1(a1320)) | c1_1(a1320) | (~c2_1(a1319)) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2799,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2798, 2782, 2781, 22, 2774, 2737, 2780, 2173, 2172])).
% 1.37/1.21 tff(2800,plain,(c0_1(a1319) | hskp27 | c3_1(a1319) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2801,plain,
% 1.37/1.21 (hskp27),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2800, 2605, 2606, 24, 23])).
% 1.37/1.21 tff(2802,plain,
% 1.37/1.21 (c1_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[468, 2801])).
% 1.37/1.21 tff(2803,plain,
% 1.37/1.21 (c0_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[479, 2801])).
% 1.37/1.21 tff(2804,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2805,plain,
% 1.37/1.21 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2806,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2805])).
% 1.37/1.21 tff(2807,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2806, 2804])).
% 1.37/1.21 tff(2808,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2809,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.37/1.21 tff(2810,plain,
% 1.37/1.21 (~c3_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2809, 414, 2803, 2802, 2582, 2607, 2583, 2606, 2605, 10, 2597])).
% 1.37/1.21 tff(2811,plain,
% 1.37/1.21 (hskp13),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[488, 2801])).
% 1.37/1.21 tff(2812,plain,
% 1.37/1.21 (hskp11),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[186, 2811, 414, 2526, 24, 23])).
% 1.37/1.21 tff(2813,plain,
% 1.37/1.21 (~c1_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[97, 2812])).
% 1.37/1.21 tff(2814,plain,
% 1.37/1.21 (c0_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[108, 2812])).
% 1.37/1.21 tff(2815,plain,
% 1.37/1.21 (~c2_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2789, 414, 2814, 2582, 2607, 2813, 2583, 2606, 2605, 425, 2597])).
% 1.37/1.21 tff(2816,plain,
% 1.37/1.21 (c3_1(a1324)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[119, 2812])).
% 1.37/1.21 tff(2817,plain,
% 1.37/1.21 (c2_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[457, 2801])).
% 1.37/1.21 tff(2818,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2819,plain,
% 1.37/1.21 (((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2820,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324))))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2819])).
% 1.37/1.21 tff(2821,plain,
% 1.37/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2820, 2818])).
% 1.37/1.21 tff(2822,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2823,plain,
% 1.37/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324))),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 1.37/1.21 tff(2824,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2823, 414, 2803, 2802, 2817, 2816, 2813, 699, 2815, 2810])).
% 1.37/1.21 tff(2825,plain,(c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2826,plain,
% 1.37/1.21 (c0_1(a1339)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2825, 23])).
% 1.37/1.21 tff(2827,plain,
% 1.37/1.21 (~hskp18),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[79, 2826])).
% 1.37/1.21 tff(2828,plain,
% 1.37/1.21 (hskp7),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1371, 414, 1029, 2441, 2444, 2442, 1013])).
% 1.37/1.21 tff(2829,plain,
% 1.37/1.21 (~c3_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[305, 2828])).
% 1.37/1.21 tff(2830,plain,
% 1.37/1.21 (~c0_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1416, 2828])).
% 1.37/1.21 tff(2831,plain,
% 1.37/1.21 (~c2_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[299, 2828])).
% 1.37/1.21 tff(2832,plain,
% 1.37/1.21 ($false),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2448, 2831, 2830, 775, 1029, 22, 2829])).
% 1.37/1.21 tff(2833,plain,(hskp27 | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.37/1.21 tff(2834,plain,
% 1.37/1.21 (hskp27),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2833, 1029, 775])).
% 1.37/1.21 tff(2835,plain,
% 1.37/1.21 (hskp13),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[488, 2834])).
% 1.37/1.21 tff(2836,plain,
% 1.37/1.21 (~c3_1(a1326)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[163, 2835])).
% 1.37/1.21 tff(2837,plain,
% 1.37/1.21 (~c2_1(a1326)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[169, 2835])).
% 1.37/1.21 tff(2838,assumption,(c3_1(a1307)), introduced(assumption)).
% 1.37/1.21 tff(2839,plain,
% 1.37/1.21 (c2_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[457, 2834])).
% 1.37/1.21 tff(2840,plain,
% 1.37/1.21 (c1_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[468, 2834])).
% 1.37/1.21 tff(2841,plain,
% 1.37/1.21 (c0_1(a1307)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[479, 2834])).
% 1.37/1.21 tff(2842,plain,
% 1.37/1.21 (hskp17 | (~c3_1(a1307))),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1095, 414, 2841, 2840, 2839, 1088])).
% 1.37/1.21 tff(2843,plain,
% 1.37/1.21 (hskp17),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2842, 2838])).
% 1.37/1.21 tff(2844,plain,
% 1.37/1.21 (~c0_1(a1334)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[864, 2843])).
% 1.37/1.21 tff(2845,plain,
% 1.37/1.21 (c3_1(a1334)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[876, 2843])).
% 1.37/1.21 tff(2846,plain,
% 1.37/1.21 (c2_1(a1334)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[887, 2843])).
% 1.37/1.21 tff(2847,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2848,plain,
% 1.37/1.21 ((hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2849,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326)))),
% 1.37/1.21 inference(monotonicity,[status(thm)],[2848])).
% 1.37/1.21 tff(2850,plain,
% 1.37/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 1.37/1.21 inference(transitivity,[status(thm)],[2849, 2847])).
% 1.37/1.21 tff(2851,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 1.37/1.21 inference(quant_inst,[status(thm)],[])).
% 1.37/1.21 tff(2852,plain,
% 1.37/1.21 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326)),
% 1.37/1.21 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 1.37/1.21 tff(2853,plain,
% 1.37/1.21 (c0_1(a1326)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2852, 414, 1029, 2846, 2845, 2844, 2837, 2836, 1069])).
% 1.37/1.21 tff(2854,plain,
% 1.37/1.21 (~c1_1(a1326)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[175, 2835])).
% 1.37/1.21 tff(2855,plain,
% 1.37/1.21 (hskp7 | (~c0_1(a1326))),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[1057, 414, 1029, 2854, 2837, 1013])).
% 1.37/1.21 tff(2856,plain,
% 1.37/1.21 (hskp7),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[2855, 2853])).
% 1.37/1.21 tff(2857,plain,
% 1.37/1.21 (~c3_1(a1316)),
% 1.37/1.21 inference(unit_resolution,[status(thm)],[305, 2856])).
% 1.37/1.21 tff(2858,plain,
% 1.37/1.21 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 1.37/1.21 inference(bind,[status(th)],[])).
% 1.37/1.21 tff(2859,plain,
% 1.37/1.21 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.21 inference(quant_intro,[status(thm)],[2858])).
% 1.37/1.21 tff(2860,plain,
% 1.37/1.21 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.21 inference(rewrite,[status(thm)],[])).
% 1.37/1.21 tff(2861,plain,
% 1.37/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_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) | (~c1_1(U)) | (~c2_1(U)) | (~c3_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) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_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) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_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))) | hskp29) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_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))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.37/1.22 inference(bind,[status(th)],[])).
% 1.37/1.22 tff(2862,plain,
% 1.37/1.22 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.22 inference(quant_intro,[status(thm)],[2861])).
% 1.37/1.22 tff(2863,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))) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.37/1.22 tff(2864,plain,
% 1.37/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.37/1.22 tff(2865,plain,
% 1.37/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2864, 2860])).
% 1.37/1.22 tff(2866,plain,(
% 1.37/1.22 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.22 inference(skolemize,[status(sab)],[2865])).
% 1.37/1.22 tff(2867,plain,
% 1.37/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2866, 2859])).
% 1.37/1.22 tff(2868,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2869,plain,
% 1.37/1.22 ((hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307))) <=> (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2870,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2869])).
% 1.37/1.22 tff(2871,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2870, 2868])).
% 1.37/1.22 tff(2872,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2873,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.37/1.22 tff(2874,plain,
% 1.37/1.22 (hskp29 | (~c3_1(a1307))),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2873, 414, 2841, 2840, 2839, 2867])).
% 1.37/1.22 tff(2875,plain,
% 1.37/1.22 (hskp29),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2874, 2838])).
% 1.37/1.22 tff(2876,plain,
% 1.37/1.22 (c1_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[546, 2875])).
% 1.37/1.22 tff(2877,plain,
% 1.37/1.22 (c2_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[535, 2875])).
% 1.37/1.22 tff(2878,plain,
% 1.37/1.22 (c3_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[524, 2875])).
% 1.37/1.22 tff(2879,plain,
% 1.37/1.22 (~c0_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1416, 2856])).
% 1.37/1.22 tff(2880,plain,
% 1.37/1.22 (~c2_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[299, 2856])).
% 1.37/1.22 tff(2881,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2064, 2880, 2879, 2834, 775, 2878, 2877, 2876, 2857])).
% 1.37/1.22 tff(2882,plain,((~c3_1(a1307)) | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2883,plain,
% 1.37/1.22 (~c3_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2882, 1029, 775])).
% 1.37/1.22 tff(2884,plain,
% 1.37/1.22 (hskp14 | c3_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1047, 414, 1029, 2841, 2840, 1039])).
% 1.37/1.22 tff(2885,plain,
% 1.37/1.22 (hskp14),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2884, 2883])).
% 1.37/1.22 tff(2886,plain,
% 1.37/1.22 (~c2_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[211, 2885])).
% 1.37/1.22 tff(2887,plain,
% 1.37/1.22 (~c1_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[217, 2885])).
% 1.37/1.22 tff(2888,plain,
% 1.37/1.22 (c0_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[235, 2885])).
% 1.37/1.22 tff(2889,plain,
% 1.37/1.22 (hskp7),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1371, 414, 1029, 2888, 2887, 2886, 1013])).
% 1.37/1.22 tff(2890,plain,
% 1.37/1.22 (~c3_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[305, 2889])).
% 1.37/1.22 tff(2891,plain,
% 1.37/1.22 (hskp29),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[513, 775, 414, 2888, 2887, 2886, 21])).
% 1.37/1.22 tff(2892,plain,
% 1.37/1.22 (c1_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[546, 2891])).
% 1.37/1.22 tff(2893,plain,
% 1.37/1.22 (c2_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[535, 2891])).
% 1.37/1.22 tff(2894,plain,
% 1.37/1.22 (c3_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[524, 2891])).
% 1.37/1.22 tff(2895,plain,
% 1.37/1.22 (~c0_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1416, 2889])).
% 1.37/1.22 tff(2896,plain,
% 1.37/1.22 (~c2_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[299, 2889])).
% 1.37/1.22 tff(2897,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2064, 2896, 2895, 2834, 775, 2894, 2893, 2892, 2890])).
% 1.37/1.22 tff(2898,plain,(hskp8 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2899,plain,
% 1.37/1.22 (hskp8),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2898, 2827])).
% 1.37/1.22 tff(2900,plain,
% 1.37/1.22 (~c0_1(a1319)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1120, 2899])).
% 1.37/1.22 tff(2901,plain,
% 1.37/1.22 (~c3_1(a1319)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1114, 2899])).
% 1.37/1.22 tff(2902,assumption,(hskp9), introduced(assumption)).
% 1.37/1.22 tff(2903,plain,
% 1.37/1.22 (c2_1(a1320)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1527, 2902])).
% 1.37/1.22 tff(2904,plain,
% 1.37/1.22 (~c0_1(a1320)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1516, 2902])).
% 1.37/1.22 tff(2905,plain,
% 1.37/1.22 (~c1_1(a1320)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1510, 2902])).
% 1.37/1.22 tff(2906,plain,
% 1.37/1.22 (c3_1(a1320)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2596, 2905, 2904, 2903])).
% 1.37/1.22 tff(2907,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2719, 414, 2689, 2903, 2679, 2904, 2173, 2172, 1069, 2906])).
% 1.37/1.22 tff(2908,plain,((~hskp9) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2909,plain,
% 1.37/1.22 (~hskp9),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2908, 2679, 2173, 2172])).
% 1.37/1.22 tff(2910,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2911,plain,
% 1.37/1.22 ((hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2912,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339)))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2911])).
% 1.37/1.22 tff(2913,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2912, 2910])).
% 1.37/1.22 tff(2914,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2915,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339)),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.37/1.22 tff(2916,plain,
% 1.37/1.22 (hskp9 | c3_1(a1339)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2915, 414, 2679, 2826, 23, 2173, 2172, 2128])).
% 1.37/1.22 tff(2917,plain,
% 1.37/1.22 (c3_1(a1339)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2916, 2909])).
% 1.37/1.22 tff(2918,plain,
% 1.37/1.22 (~c1_1(a1315)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1236, 2686])).
% 1.37/1.22 tff(2919,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2920,plain,
% 1.37/1.22 ((hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315))) <=> (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2921,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315))))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2920])).
% 1.37/1.22 tff(2922,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2921, 2919])).
% 1.37/1.22 tff(2923,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2924,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 1.37/1.22 tff(2925,plain,
% 1.37/1.22 (hskp7 | (~c3_1(a1339))),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2924, 414, 2526, 2688, 23, 2687, 2918, 400])).
% 1.37/1.22 tff(2926,plain,
% 1.37/1.22 (hskp7),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2925, 2917])).
% 1.37/1.22 tff(2927,plain,
% 1.37/1.22 (~c3_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[305, 2926])).
% 1.37/1.22 tff(2928,plain,
% 1.37/1.22 (~c0_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1416, 2926])).
% 1.37/1.22 tff(2929,plain,
% 1.37/1.22 (~c2_1(a1316)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[299, 2926])).
% 1.37/1.22 tff(2930,plain,
% 1.37/1.22 (hskp27),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2448, 2929, 2827, 2689, 2928, 2927])).
% 1.37/1.22 tff(2931,plain,
% 1.37/1.22 (c0_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[479, 2930])).
% 1.37/1.22 tff(2932,plain,
% 1.37/1.22 (c1_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[468, 2930])).
% 1.37/1.22 tff(2933,plain,
% 1.37/1.22 (c2_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[457, 2930])).
% 1.37/1.22 tff(2934,plain,
% 1.37/1.22 (hskp14),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1428, 2933, 2689, 2928, 2932, 2931, 2929, 2927])).
% 1.37/1.22 tff(2935,plain,
% 1.37/1.22 (~c2_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[211, 2934])).
% 1.37/1.22 tff(2936,plain,
% 1.37/1.22 (~c1_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[217, 2934])).
% 1.37/1.22 tff(2937,plain,
% 1.37/1.22 (c0_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[235, 2934])).
% 1.37/1.22 tff(2938,plain,
% 1.37/1.22 (hskp29),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[513, 2827, 414, 2937, 2936, 2935, 21])).
% 1.37/1.22 tff(2939,plain,
% 1.37/1.22 (c2_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[535, 2938])).
% 1.37/1.22 tff(2940,plain,
% 1.37/1.22 (c1_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[546, 2938])).
% 1.37/1.22 tff(2941,plain,
% 1.37/1.22 (c3_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[524, 2938])).
% 1.37/1.22 tff(2942,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2064, 2941, 2940, 2929, 2827, 2930, 2939, 2928, 2927])).
% 1.37/1.22 tff(2943,plain,(c2_1(a1319) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2944,plain,
% 1.37/1.22 (c2_1(a1319)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2943, 2172, 2173, 23])).
% 1.37/1.22 tff(2945,plain,
% 1.37/1.22 (hskp14),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[503, 775, 22])).
% 1.37/1.22 tff(2946,plain,
% 1.37/1.22 (~c2_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[211, 2945])).
% 1.37/1.22 tff(2947,plain,
% 1.37/1.22 (~c1_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[217, 2945])).
% 1.37/1.22 tff(2948,plain,
% 1.37/1.22 (c0_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[235, 2945])).
% 1.37/1.22 tff(2949,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[513, 775, 414, 11, 2948, 2947, 2946, 21])).
% 1.37/1.22 tff(2950,plain,(hskp18 | hskp29 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2951,plain,
% 1.37/1.22 (hskp29),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2950, 22, 2827])).
% 1.37/1.22 tff(2952,plain,
% 1.37/1.22 (c3_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[524, 2951])).
% 1.37/1.22 tff(2953,plain,
% 1.37/1.22 (c2_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[535, 2951])).
% 1.37/1.22 tff(2954,plain,
% 1.37/1.22 (c1_1(a1338)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[546, 2951])).
% 1.37/1.22 tff(2955,plain,
% 1.37/1.22 (hskp22),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[553, 414, 46, 2954, 2953, 2952, 445])).
% 1.37/1.22 tff(2956,plain,
% 1.37/1.22 (~c3_1(a1356)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[595, 2955])).
% 1.37/1.22 tff(2957,plain,
% 1.37/1.22 (c1_1(a1356)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[564, 2955])).
% 1.37/1.22 tff(2958,plain,
% 1.37/1.22 (c0_1(a1356)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[575, 2955])).
% 1.37/1.22 tff(2959,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2960,plain,
% 1.37/1.22 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339))) <=> (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2961,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2960])).
% 1.37/1.22 tff(2962,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2961, 2959])).
% 1.37/1.22 tff(2963,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2964,plain,
% 1.37/1.22 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.37/1.22 tff(2965,plain,
% 1.37/1.22 (c3_1(a1339)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2964, 414, 22, 2958, 2957, 2956, 2826, 23, 590])).
% 1.37/1.22 tff(2966,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2967,plain,
% 1.37/1.22 (((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2968,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2967])).
% 1.37/1.22 tff(2969,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2968, 2966])).
% 1.37/1.22 tff(2970,plain,
% 1.37/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2971,plain,
% 1.37/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 1.37/1.22 tff(2972,plain,
% 1.37/1.22 ((~c3_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2971, 414, 840, 2526, 689, 2826, 2173, 2172, 10])).
% 1.37/1.22 tff(2973,plain,
% 1.37/1.22 (~c3_1(a1348)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2972, 2965, 2944])).
% 1.37/1.22 tff(2974,plain,
% 1.37/1.22 (hskp14),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[503, 22, 2827])).
% 1.37/1.22 tff(2975,plain,
% 1.37/1.22 (~c2_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[211, 2974])).
% 1.37/1.22 tff(2976,plain,
% 1.37/1.22 (c0_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[235, 2974])).
% 1.37/1.22 tff(2977,plain,
% 1.37/1.22 (c3_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[602, 414, 22, 2958, 2957, 2976, 2956, 2975, 590])).
% 1.37/1.22 tff(2978,plain,
% 1.37/1.22 (~c1_1(a1330)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[217, 2974])).
% 1.37/1.22 tff(2979,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2980,plain,
% 1.37/1.22 (((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(rewrite,[status(thm)],[])).
% 1.37/1.22 tff(2981,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 1.37/1.22 inference(monotonicity,[status(thm)],[2980])).
% 1.37/1.22 tff(2982,plain,
% 1.37/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 1.37/1.22 inference(transitivity,[status(thm)],[2981, 2979])).
% 1.37/1.22 tff(2983,plain,
% 1.37/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 1.37/1.22 inference(quant_inst,[status(thm)],[])).
% 1.37/1.22 tff(2984,plain,
% 1.37/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 1.37/1.22 inference(modus_ponens,[status(thm)],[2983, 2982])).
% 1.37/1.22 tff(2985,plain,
% 1.37/1.22 ($false),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2984, 414, 2958, 2957, 851, 840, 2956, 2978, 2975, 699, 2977, 2973])).
% 1.37/1.22 tff(2986,plain,(hskp27 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.37/1.22 tff(2987,plain,
% 1.37/1.22 (hskp27),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2986, 46, 2172, 23, 2173])).
% 1.37/1.22 tff(2988,plain,
% 1.37/1.22 (c2_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[457, 2987])).
% 1.37/1.22 tff(2989,plain,
% 1.37/1.22 (c0_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[479, 2987])).
% 1.37/1.22 tff(2990,assumption,(~c3_1(a1307)), introduced(assumption)).
% 1.37/1.22 tff(2991,plain,
% 1.37/1.22 (hskp30 | c3_1(a1307)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2051, 775, 414, 1041, 1089, 1870])).
% 1.37/1.22 tff(2992,plain,
% 1.37/1.22 (hskp30),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[2991, 2990])).
% 1.37/1.22 tff(2993,plain,
% 1.37/1.22 (c3_1(a1372)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1887, 2992])).
% 1.37/1.22 tff(2994,plain,
% 1.37/1.22 (c1_1(a1372)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1898, 2992])).
% 1.37/1.22 tff(2995,plain,
% 1.37/1.22 (c0_1(a1372)),
% 1.37/1.22 inference(unit_resolution,[status(thm)],[1909, 2992])).
% 1.37/1.22 tff(2996,plain,
% 1.37/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.37/1.23 inference(rewrite,[status(thm)],[])).
% 1.37/1.23 tff(2997,plain,
% 1.37/1.23 ((hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.37/1.23 inference(rewrite,[status(thm)],[])).
% 1.37/1.23 tff(2998,plain,
% 1.37/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 1.37/1.23 inference(monotonicity,[status(thm)],[2997])).
% 1.37/1.23 tff(2999,plain,
% 1.37/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 1.37/1.23 inference(transitivity,[status(thm)],[2998, 2996])).
% 1.37/1.23 tff(3000,plain,
% 1.37/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 1.37/1.23 inference(quant_inst,[status(thm)],[])).
% 1.37/1.23 tff(3001,plain,
% 1.37/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 1.37/1.23 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.37/1.23 tff(3002,plain,
% 1.37/1.23 ($false),
% 1.37/1.23 inference(unit_resolution,[status(thm)],[3001, 414, 46, 2995, 2994, 2993, 1041, 1089, 1169, 2990])).
% 1.37/1.23 tff(3003,plain,(c3_1(a1307) | hskp11 | (~c0_1(a1307)) | (~c2_1(a1307)) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.37/1.23 tff(3004,plain,
% 1.37/1.23 (c3_1(a1307)),
% 1.37/1.23 inference(unit_resolution,[status(thm)],[3003, 46, 2989, 2988, 2827])).
% 1.37/1.23 tff(3005,plain,
% 1.37/1.23 (c1_1(a1307)),
% 1.37/1.23 inference(unit_resolution,[status(thm)],[468, 2987])).
% 1.37/1.23 tff(3006,plain,
% 1.37/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 1.37/1.23 inference(rewrite,[status(thm)],[])).
% 1.37/1.23 tff(3007,plain,
% 1.37/1.23 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 1.37/1.23 inference(rewrite,[status(thm)],[])).
% 1.37/1.23 tff(3008,plain,
% 1.37/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3007])).
% 1.42/1.23 tff(3009,plain,
% 1.42/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3008, 3006])).
% 1.42/1.23 tff(3010,plain,
% 1.42/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3011,plain,
% 1.42/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 1.42/1.23 tff(3012,plain,
% 1.42/1.23 ((~c3_1(a1348)) | (~c3_1(a1307))),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3011, 414, 2989, 3005, 840, 2944, 689, 2173, 2172, 10])).
% 1.42/1.23 tff(3013,plain,
% 1.42/1.23 (~c3_1(a1348)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3012, 3004])).
% 1.42/1.23 tff(3014,plain,
% 1.42/1.23 (hskp17 | (~c3_1(a1307))),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1095, 414, 2989, 3005, 2988, 1088])).
% 1.42/1.23 tff(3015,plain,
% 1.42/1.23 (hskp17),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3014, 3004])).
% 1.42/1.23 tff(3016,plain,
% 1.42/1.23 (~c0_1(a1334)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[864, 3015])).
% 1.42/1.23 tff(3017,plain,
% 1.42/1.23 (c3_1(a1334)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[876, 3015])).
% 1.42/1.23 tff(3018,plain,
% 1.42/1.23 (c2_1(a1334)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[887, 3015])).
% 1.42/1.23 tff(3019,plain,
% 1.42/1.23 ($false),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1106, 414, 2989, 3005, 840, 3018, 3017, 689, 3016, 10, 3013, 3004])).
% 1.42/1.23 tff(3020,plain,(hskp11 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.23 tff(3021,plain,
% 1.42/1.23 (hskp11),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3020, 2172, 2173, 23])).
% 1.42/1.23 tff(3022,plain,
% 1.42/1.23 (~c1_1(a1324)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[97, 3021])).
% 1.42/1.23 tff(3023,plain,
% 1.42/1.23 (c0_1(a1324)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[108, 3021])).
% 1.42/1.23 tff(3024,plain,
% 1.42/1.23 (c3_1(a1324)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[119, 3021])).
% 1.42/1.23 tff(3025,assumption,(~hskp9), introduced(assumption)).
% 1.42/1.23 tff(3026,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3027,plain,
% 1.42/1.23 ((hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3028,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3027])).
% 1.42/1.23 tff(3029,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3028, 3026])).
% 1.42/1.23 tff(3030,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3031,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.42/1.23 tff(3032,plain,
% 1.42/1.23 ($false),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3031, 414, 22, 2526, 2826, 23, 590, 188])).
% 1.42/1.23 tff(3033,plain,(c3_1(a1339) | hskp27 | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.23 tff(3034,plain,
% 1.42/1.23 (c3_1(a1339)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3033, 22, 23])).
% 1.42/1.23 tff(3035,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3036,plain,
% 1.42/1.23 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3037,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3036])).
% 1.42/1.23 tff(3038,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.42/1.23 tff(3039,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3040,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.42/1.23 tff(3041,plain,
% 1.42/1.23 (~c3_1(a1311)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3040, 414, 22, 1818, 2826, 23, 1816, 1836, 3034])).
% 1.42/1.23 tff(3042,plain,
% 1.42/1.23 (hskp30 | c3_1(a1311)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1876, 2827, 414, 1819, 1818, 1870])).
% 1.42/1.23 tff(3043,plain,
% 1.42/1.23 (hskp30),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3042, 3041])).
% 1.42/1.23 tff(3044,plain,
% 1.42/1.23 (c0_1(a1372)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1909, 3043])).
% 1.42/1.23 tff(3045,plain,
% 1.42/1.23 (hskp15),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1849, 414, 2976, 1819, 2978, 2975, 1816, 1724, 3041])).
% 1.42/1.23 tff(3046,plain,
% 1.42/1.23 (~c3_1(a1331)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1263, 3045])).
% 1.42/1.23 tff(3047,plain,
% 1.42/1.23 (c1_1(a1372)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1898, 3043])).
% 1.42/1.23 tff(3048,plain,
% 1.42/1.23 (c3_1(a1372)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1887, 3043])).
% 1.42/1.23 tff(3049,plain,
% 1.42/1.23 (c2_1(a1331)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1275, 3045])).
% 1.42/1.23 tff(3050,plain,
% 1.42/1.23 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.42/1.23 inference(bind,[status(th)],[])).
% 1.42/1.23 tff(3051,plain,
% 1.42/1.23 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(quant_intro,[status(thm)],[3050])).
% 1.42/1.23 tff(3052,plain,
% 1.42/1.23 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3053,plain,
% 1.42/1.23 (^[U: $i] : 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(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)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> ((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.42/1.23 inference(bind,[status(th)],[])).
% 1.42/1.23 tff(3054,plain,
% 1.42/1.23 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(quant_intro,[status(thm)],[3053])).
% 1.42/1.23 tff(3055,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.42/1.23 tff(3056,plain,
% 1.42/1.23 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 1.42/1.23 tff(3057,plain,
% 1.42/1.23 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3056, 3052])).
% 1.42/1.23 tff(3058,plain,(
% 1.42/1.23 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(skolemize,[status(sab)],[3057])).
% 1.42/1.23 tff(3059,plain,
% 1.42/1.23 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3058, 3051])).
% 1.42/1.23 tff(3060,plain,
% 1.42/1.23 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3061,plain,
% 1.42/1.23 ((hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311))) <=> (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3062,plain,
% 1.42/1.23 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3061])).
% 1.42/1.23 tff(3063,plain,
% 1.42/1.23 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3062, 3060])).
% 1.42/1.23 tff(3064,plain,
% 1.42/1.23 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3065,plain,
% 1.42/1.23 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 1.42/1.23 tff(3066,plain,
% 1.42/1.23 (hskp6 | c3_1(a1311)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3065, 414, 3025, 1819, 1818, 3059])).
% 1.42/1.23 tff(3067,plain,
% 1.42/1.23 (hskp6),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3066, 3041])).
% 1.42/1.23 tff(3068,plain,
% 1.42/1.23 (~c0_1(a1315)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1158, 3067])).
% 1.42/1.23 tff(3069,plain,
% 1.42/1.23 (c3_1(a1315)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1203, 3067])).
% 1.42/1.23 tff(3070,plain,
% 1.42/1.23 (~c1_1(a1315)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1236, 3067])).
% 1.42/1.23 tff(3071,plain,
% 1.42/1.23 (c0_1(a1338)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[2190, 3070, 2172, 3023, 3024, 2954, 3069, 2952, 3022, 3068, 2953, 2944, 2173, 22])).
% 1.42/1.23 tff(3072,plain,
% 1.42/1.23 (hskp17 | (~c0_1(a1338))),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1781, 414, 2954, 2953, 2952, 1088])).
% 1.42/1.23 tff(3073,plain,
% 1.42/1.23 (hskp17),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3072, 3071])).
% 1.42/1.23 tff(3074,plain,
% 1.42/1.23 (c0_1(a1331)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1928, 3073, 3049, 3048, 3047, 3046, 3044])).
% 1.42/1.23 tff(3075,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3076,plain,
% 1.42/1.23 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3077,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3076])).
% 1.42/1.23 tff(3078,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3077, 3075])).
% 1.42/1.23 tff(3079,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3080,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 1.42/1.23 tff(3081,plain,
% 1.42/1.23 (hskp27 | (~c3_1(a1339)) | (~c2_1(a1324))),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3080, 414, 3024, 2826, 23, 3022, 1836])).
% 1.42/1.23 tff(3082,plain,
% 1.42/1.23 (~c2_1(a1324)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3081, 3034, 22])).
% 1.42/1.23 tff(3083,plain,
% 1.42/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3084,plain,
% 1.42/1.23 (((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3085,plain,
% 1.42/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3084])).
% 1.42/1.23 tff(3086,plain,
% 1.42/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3085, 3083])).
% 1.42/1.23 tff(3087,plain,
% 1.42/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3088,plain,
% 1.42/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 1.42/1.23 tff(3089,plain,
% 1.42/1.23 (c3_1(a1330)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3088, 414, 2976, 3024, 1819, 1818, 2975, 3022, 1816, 613, 3082])).
% 1.42/1.23 tff(3090,plain,
% 1.42/1.23 (c1_1(a1331)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1286, 3045])).
% 1.42/1.23 tff(3091,plain,
% 1.42/1.23 ($false),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1859, 414, 3090, 3049, 3046, 2978, 2975, 699, 3089, 3074])).
% 1.42/1.23 tff(3092,plain,((~hskp3) | c3_1(a1319) | c0_1(a1319) | hskp27 | hskp9 | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.23 tff(3093,plain,
% 1.42/1.23 (~hskp3),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3092, 3025, 2173, 22, 2172, 23])).
% 1.42/1.23 tff(3094,plain,
% 1.42/1.23 (hskp7),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1794, 3093, 3024, 2953, 3023, 2952, 3022, 2976, 2978, 2975, 2954])).
% 1.42/1.23 tff(3095,plain,
% 1.42/1.23 (~c3_1(a1316)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[305, 3094])).
% 1.42/1.23 tff(3096,plain,
% 1.42/1.23 (~c2_1(a1316)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[299, 3094])).
% 1.42/1.23 tff(3097,plain,
% 1.42/1.23 (~c0_1(a1316)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[1416, 3094])).
% 1.42/1.23 tff(3098,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3099,plain,
% 1.42/1.23 ((hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316))) <=> (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.42/1.23 inference(rewrite,[status(thm)],[])).
% 1.42/1.23 tff(3100,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))))),
% 1.42/1.23 inference(monotonicity,[status(thm)],[3099])).
% 1.42/1.23 tff(3101,plain,
% 1.42/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 1.42/1.23 inference(transitivity,[status(thm)],[3100, 3098])).
% 1.42/1.23 tff(3102,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))),
% 1.42/1.23 inference(quant_inst,[status(thm)],[])).
% 1.42/1.23 tff(3103,plain,
% 1.42/1.23 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))),
% 1.42/1.23 inference(modus_ponens,[status(thm)],[3102, 3101])).
% 1.42/1.23 tff(3104,plain,
% 1.42/1.23 (~c1_1(a1316)),
% 1.42/1.23 inference(unit_resolution,[status(thm)],[3103, 414, 3025, 3097, 3096, 3095, 1498])).
% 1.42/1.24 tff(3105,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3106,plain,
% 1.42/1.24 ((hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3107,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316)))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3106])).
% 1.42/1.24 tff(3108,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3107, 3105])).
% 1.42/1.24 tff(3109,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3110,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316)),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3109, 3108])).
% 1.42/1.24 tff(3111,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3110, 414, 3093, 2826, 23, 3097, 3095, 635, 3034, 3104])).
% 1.42/1.24 tff(3112,plain,(hskp9 | c2_1(a1339) | c0_1(a1319) | hskp27 | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3113,plain,
% 1.42/1.24 (hskp9),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3112, 22, 2173, 23, 2172])).
% 1.42/1.24 tff(3114,plain,
% 1.42/1.24 (~c0_1(a1320)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1516, 3113])).
% 1.42/1.24 tff(3115,plain,
% 1.42/1.24 (c2_1(a1320)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1527, 3113])).
% 1.42/1.24 tff(3116,plain,
% 1.42/1.24 (~c1_1(a1320)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1510, 3113])).
% 1.42/1.24 tff(3117,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[2798, 3116, 3115, 3021, 22, 2944, 2173, 3114, 2172])).
% 1.42/1.24 tff(3118,plain,(hskp27 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3119,plain,
% 1.42/1.24 (hskp27),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3118, 2172, 2173, 23])).
% 1.42/1.24 tff(3120,plain,
% 1.42/1.24 (c2_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[457, 3119])).
% 1.42/1.24 tff(3121,plain,
% 1.42/1.24 (c1_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[468, 3119])).
% 1.42/1.24 tff(3122,plain,
% 1.42/1.24 (c0_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[479, 3119])).
% 1.42/1.24 tff(3123,assumption,(c3_1(a1348)), introduced(assumption)).
% 1.42/1.24 tff(3124,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3125,plain,
% 1.42/1.24 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3126,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3125])).
% 1.42/1.24 tff(3127,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3126, 3124])).
% 1.42/1.24 tff(3128,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3129,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3128, 3127])).
% 1.42/1.24 tff(3130,plain,
% 1.42/1.24 ((~c3_1(a1348)) | (~c2_1(a1324))),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3129, 414, 840, 1696, 2174, 689, 121, 2173, 2172, 425])).
% 1.42/1.24 tff(3131,plain,
% 1.42/1.24 (~c2_1(a1324)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3130, 3123])).
% 1.42/1.24 tff(3132,plain,
% 1.42/1.24 ((~c3_1(a1348)) | (~c3_1(a1307))),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3011, 414, 1041, 1040, 840, 2174, 689, 2173, 2172, 10])).
% 1.42/1.24 tff(3133,plain,
% 1.42/1.24 (~c3_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3132, 3123])).
% 1.42/1.24 tff(3134,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[2823, 414, 1041, 1040, 1089, 1695, 121, 699, 3133, 3131])).
% 1.42/1.24 tff(3135,plain,((~c3_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1324)) | c1_1(a1324) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319) | (~c0_1(a1324))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3136,plain,
% 1.42/1.24 (~c3_1(a1348)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3135, 3122, 3121, 3120, 3024, 3022, 2944, 2173, 2172, 3023])).
% 1.42/1.24 tff(3137,plain,
% 1.42/1.24 (hskp12 | c3_1(a1348)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1994, 414, 3122, 3121, 3120, 851, 689, 1304])).
% 1.42/1.24 tff(3138,plain,
% 1.42/1.24 (hskp12),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3137, 3136])).
% 1.42/1.24 tff(3139,plain,
% 1.42/1.24 (~c0_1(a1325)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1316, 3138])).
% 1.42/1.24 tff(3140,plain,
% 1.42/1.24 (c3_1(a1325)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1327, 3138])).
% 1.42/1.24 tff(3141,plain,
% 1.42/1.24 (c1_1(a1325)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1338, 3138])).
% 1.42/1.24 tff(3142,plain,
% 1.42/1.24 (c2_1(a1325)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1589, 414, 3141, 3140, 3023, 3024, 3139, 3022, 35])).
% 1.42/1.24 tff(3143,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3144,plain,
% 1.42/1.24 ((hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3145,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3144])).
% 1.42/1.24 tff(3146,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3145, 3143])).
% 1.42/1.24 tff(3147,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3148,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 1.42/1.24 tff(3149,plain,
% 1.42/1.24 (hskp17),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3148, 414, 3122, 3121, 3120, 3141, 3140, 1088, 3142])).
% 1.42/1.24 tff(3150,plain,
% 1.42/1.24 (~c0_1(a1334)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[864, 3149])).
% 1.42/1.24 tff(3151,plain,
% 1.42/1.24 (c3_1(a1334)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[876, 3149])).
% 1.42/1.24 tff(3152,plain,
% 1.42/1.24 (c2_1(a1334)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[887, 3149])).
% 1.42/1.24 tff(3153,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3154,plain,
% 1.42/1.24 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3155,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3154])).
% 1.42/1.24 tff(3156,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.42/1.24 tff(3157,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3158,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.42/1.24 tff(3159,plain,
% 1.42/1.24 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3158, 414, 3122, 3121, 840, 3140, 689, 3139, 10, 3136])).
% 1.42/1.24 tff(3160,plain,
% 1.42/1.24 (~c3_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3159, 3142])).
% 1.42/1.24 tff(3161,plain,
% 1.42/1.24 (hskp30 | c3_1(a1307)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[2051, 2827, 414, 3122, 3120, 1870])).
% 1.42/1.24 tff(3162,plain,
% 1.42/1.24 (hskp30),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3161, 3160])).
% 1.42/1.24 tff(3163,plain,
% 1.42/1.24 (c3_1(a1372)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1887, 3162])).
% 1.42/1.24 tff(3164,plain,
% 1.42/1.24 (c1_1(a1372)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1898, 3162])).
% 1.42/1.24 tff(3165,plain,
% 1.42/1.24 (c0_1(a1372)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[1909, 3162])).
% 1.42/1.24 tff(3166,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3167,plain,
% 1.42/1.24 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3168,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3167])).
% 1.42/1.24 tff(3169,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3168, 3166])).
% 1.42/1.24 tff(3170,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3171,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 1.42/1.24 tff(3172,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3171, 414, 3165, 3164, 3163, 3152, 3151, 2944, 3150, 2173, 2172, 10])).
% 1.42/1.24 tff(3173,plain,(c3_1(a1319) | c0_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3174,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3173, 2901, 2900, 23])).
% 1.42/1.24 tff(3175,plain,(c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3176,plain,
% 1.42/1.24 (~hskp18),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[73, 3175])).
% 1.42/1.24 tff(3177,plain,
% 1.42/1.24 (hskp29 | hskp27),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[2950, 3176])).
% 1.42/1.24 tff(3178,plain,
% 1.42/1.24 (hskp29),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3177, 22])).
% 1.42/1.24 tff(3179,plain,
% 1.42/1.24 (c2_1(a1338)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[535, 3178])).
% 1.42/1.24 tff(3180,plain,
% 1.42/1.24 (c1_1(a1338)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[546, 3178])).
% 1.42/1.24 tff(3181,plain,
% 1.42/1.24 (hskp27 | hskp14),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[503, 3176])).
% 1.42/1.24 tff(3182,plain,
% 1.42/1.24 (hskp14),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3181, 22])).
% 1.42/1.24 tff(3183,plain,
% 1.42/1.24 (~c2_1(a1330)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[211, 3182])).
% 1.42/1.24 tff(3184,plain,
% 1.42/1.24 (~c1_1(a1330)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[217, 3182])).
% 1.42/1.24 tff(3185,plain,
% 1.42/1.24 (c0_1(a1330)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[235, 3182])).
% 1.42/1.24 tff(3186,plain,
% 1.42/1.24 (c3_1(a1330)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[602, 414, 22, 2262, 2261, 3185, 2259, 3183, 590])).
% 1.42/1.24 tff(3187,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3188,plain,
% 1.42/1.24 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3189,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3188])).
% 1.42/1.24 tff(3190,plain,
% 1.42/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3189, 3187])).
% 1.42/1.24 tff(3191,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3192,plain,
% 1.42/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3191, 3190])).
% 1.42/1.24 tff(3193,plain,
% 1.42/1.24 ((~c3_1(a1330)) | (~c2_1(a1356))),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3192, 414, 2262, 2261, 2259, 3184, 3183, 699])).
% 1.42/1.24 tff(3194,plain,
% 1.42/1.24 (~c2_1(a1356)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3193, 3186])).
% 1.42/1.24 tff(3195,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3196,plain,
% 1.42/1.24 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356))) <=> (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.42/1.24 inference(rewrite,[status(thm)],[])).
% 1.42/1.24 tff(3197,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356))))),
% 1.42/1.24 inference(monotonicity,[status(thm)],[3196])).
% 1.42/1.24 tff(3198,plain,
% 1.42/1.24 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 1.42/1.24 inference(transitivity,[status(thm)],[3197, 3195])).
% 1.42/1.24 tff(3199,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))),
% 1.42/1.24 inference(quant_inst,[status(thm)],[])).
% 1.42/1.24 tff(3200,plain,
% 1.42/1.24 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356))),
% 1.42/1.24 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 1.42/1.24 tff(3201,plain,
% 1.42/1.24 ($false),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3200, 414, 22, 2262, 2261, 2259, 590, 3194])).
% 1.42/1.24 tff(3202,plain,((~hskp22) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.42/1.24 tff(3203,plain,
% 1.42/1.24 (~hskp22),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3202, 22])).
% 1.42/1.24 tff(3204,plain,
% 1.42/1.24 (c3_1(a1338)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[524, 3178])).
% 1.42/1.24 tff(3205,plain,
% 1.42/1.24 (hskp22 | hskp11),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[553, 414, 3180, 3179, 3204, 445])).
% 1.42/1.24 tff(3206,plain,
% 1.42/1.24 (hskp11),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[3205, 3203])).
% 1.42/1.24 tff(3207,plain,
% 1.42/1.24 (~c1_1(a1324)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[97, 3206])).
% 1.42/1.24 tff(3208,plain,
% 1.42/1.24 (c0_1(a1324)),
% 1.42/1.24 inference(unit_resolution,[status(thm)],[108, 3206])).
% 1.44/1.24 tff(3209,plain,
% 1.44/1.24 (c3_1(a1324)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[119, 3206])).
% 1.44/1.24 tff(3210,assumption,(c0_1(a1338)), introduced(assumption)).
% 1.44/1.24 tff(3211,plain,
% 1.44/1.24 (hskp8),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2898, 3176])).
% 1.44/1.24 tff(3212,plain,
% 1.44/1.24 (~c3_1(a1319)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1114, 3211])).
% 1.44/1.24 tff(3213,plain,
% 1.44/1.24 (~c0_1(a1319)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1120, 3211])).
% 1.44/1.24 tff(3214,plain,
% 1.44/1.24 (hskp17),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1782, 3210])).
% 1.44/1.24 tff(3215,plain,
% 1.44/1.24 (~c0_1(a1334)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[864, 3214])).
% 1.44/1.24 tff(3216,plain,
% 1.44/1.24 (c2_1(a1319)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1214, 3211])).
% 1.44/1.24 tff(3217,plain,
% 1.44/1.24 (c3_1(a1334)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[876, 3214])).
% 1.44/1.24 tff(3218,plain,
% 1.44/1.24 (c2_1(a1334)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[887, 3214])).
% 1.44/1.24 tff(3219,plain,
% 1.44/1.24 ($false),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2037, 414, 1760, 1761, 3218, 3217, 3216, 3215, 3213, 3212, 10, 3210])).
% 1.44/1.24 tff(3220,plain,((~c0_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c2_1(a1338))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.24 tff(3221,plain,
% 1.44/1.24 (~c0_1(a1338)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3220, 3180, 3204, 3179])).
% 1.44/1.24 tff(3222,assumption,(~c1_1(a1311)), introduced(assumption)).
% 1.44/1.24 tff(3223,assumption,(c2_1(a1311)), introduced(assumption)).
% 1.44/1.24 tff(3224,assumption,(c0_1(a1311)), introduced(assumption)).
% 1.44/1.24 tff(3225,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3226,plain,
% 1.44/1.24 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3227,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[3226])).
% 1.44/1.24 tff(3228,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 1.44/1.24 inference(transitivity,[status(thm)],[3227, 3225])).
% 1.44/1.24 tff(3229,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(3230,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 1.44/1.24 tff(3231,plain,
% 1.44/1.24 ($false),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3230, 414, 1775, 1761, 3216, 3224, 3223, 3213, 3212, 3222, 425, 1762])).
% 1.44/1.24 tff(3232,plain,(c0_1(a1338) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1311)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.24 tff(3233,plain,
% 1.44/1.24 ($false),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3232, 1818, 1819, 1761, 1775, 1762, 1816])).
% 1.44/1.24 tff(3234,plain,((~hskp3) | (~c3_1(a1338)) | (~c2_1(a1338)) | c0_1(a1338)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.24 tff(3235,plain,
% 1.44/1.24 (~hskp3),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3234, 3204, 3179, 3221])).
% 1.44/1.24 tff(3236,plain,
% 1.44/1.24 (hskp7),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1794, 3235, 3209, 3179, 3208, 3204, 3207, 3185, 3184, 3183, 3180])).
% 1.44/1.24 tff(3237,plain,
% 1.44/1.24 (~c3_1(a1316)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[305, 3236])).
% 1.44/1.24 tff(3238,plain,
% 1.44/1.24 (~c2_1(a1316)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[299, 3236])).
% 1.44/1.24 tff(3239,plain,
% 1.44/1.24 (~c0_1(a1316)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1416, 3236])).
% 1.44/1.24 tff(3240,plain,
% 1.44/1.24 (hskp6),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2093, 414, 851, 840, 689, 3239, 3238, 3237, 1145])).
% 1.44/1.24 tff(3241,plain,
% 1.44/1.24 (~c0_1(a1315)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1158, 3240])).
% 1.44/1.24 tff(3242,plain,
% 1.44/1.24 (c3_1(a1315)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1203, 3240])).
% 1.44/1.24 tff(3243,plain,
% 1.44/1.24 (~c1_1(a1315)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1236, 3240])).
% 1.44/1.24 tff(3244,plain,
% 1.44/1.24 (c0_1(a1338) | hskp27 | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1315)) | c1_1(a1315) | (~c1_1(a1338)) | (~c3_1(a1338)) | c1_1(a1324) | c0_1(a1315) | (~c2_1(a1338))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2190, 3212, 3216, 3213])).
% 1.44/1.25 tff(3245,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3244, 3243, 3242, 3209, 3208, 3221, 3180, 3204, 3207, 3241, 3179, 22])).
% 1.44/1.25 tff(3246,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3247,plain,
% 1.44/1.25 (hskp13),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[488, 3246])).
% 1.44/1.25 tff(3248,plain,
% 1.44/1.25 (~c2_1(a1326)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[169, 3247])).
% 1.44/1.25 tff(3249,plain,
% 1.44/1.25 (~c1_1(a1326)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[175, 3247])).
% 1.44/1.25 tff(3250,plain,
% 1.44/1.25 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3251,plain,
% 1.44/1.25 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326))) <=> (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3252,plain,
% 1.44/1.25 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3251])).
% 1.44/1.25 tff(3253,plain,
% 1.44/1.25 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3252, 3250])).
% 1.44/1.25 tff(3254,plain,
% 1.44/1.25 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3255,plain,
% 1.44/1.25 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 1.44/1.25 tff(3256,plain,
% 1.44/1.25 (hskp29 | (~c0_1(a1326))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3255, 3176, 414, 3249, 3248, 21])).
% 1.44/1.25 tff(3257,plain,
% 1.44/1.25 (~c0_1(a1326)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3256, 11])).
% 1.44/1.25 tff(3258,plain,
% 1.44/1.25 (~c3_1(a1326)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[163, 3247])).
% 1.44/1.25 tff(3259,plain,
% 1.44/1.25 (hskp6 | c0_1(a1326)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1962, 414, 851, 840, 689, 3248, 3258, 1145])).
% 1.44/1.25 tff(3260,plain,
% 1.44/1.25 (hskp6),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3259, 3257])).
% 1.44/1.25 tff(3261,plain,
% 1.44/1.25 (~c0_1(a1315)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1158, 3260])).
% 1.44/1.25 tff(3262,plain,
% 1.44/1.25 (c3_1(a1315)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1203, 3260])).
% 1.44/1.25 tff(3263,plain,
% 1.44/1.25 (c2_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[457, 3246])).
% 1.44/1.25 tff(3264,plain,
% 1.44/1.25 (c1_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[468, 3246])).
% 1.44/1.25 tff(3265,plain,
% 1.44/1.25 (c0_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[479, 3246])).
% 1.44/1.25 tff(3266,plain,
% 1.44/1.25 (hskp29 | (~c3_1(a1307))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2873, 414, 3265, 3264, 3263, 2867])).
% 1.44/1.25 tff(3267,plain,
% 1.44/1.25 (~c3_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3266, 11])).
% 1.44/1.25 tff(3268,plain,
% 1.44/1.25 (hskp30 | c3_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2051, 3176, 414, 3265, 3263, 1870])).
% 1.44/1.25 tff(3269,plain,
% 1.44/1.25 (hskp30),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3268, 3267])).
% 1.44/1.25 tff(3270,plain,
% 1.44/1.25 (c3_1(a1372)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1887, 3269])).
% 1.44/1.25 tff(3271,plain,
% 1.44/1.25 (c1_1(a1372)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1898, 3269])).
% 1.44/1.25 tff(3272,plain,
% 1.44/1.25 (c0_1(a1372)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1909, 3269])).
% 1.44/1.25 tff(3273,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3274,plain,
% 1.44/1.25 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3275,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3274])).
% 1.44/1.25 tff(3276,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3275, 3273])).
% 1.44/1.25 tff(3277,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3278,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 1.44/1.25 tff(3279,plain,
% 1.44/1.25 (~c2_1(a1315)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3278, 414, 3272, 3271, 3270, 3216, 3262, 3213, 3212, 3261, 10])).
% 1.44/1.25 tff(3280,plain,
% 1.44/1.25 (c3_1(a1307) | hskp11 | (~c0_1(a1307)) | (~c2_1(a1307))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3003, 3176])).
% 1.44/1.25 tff(3281,plain,
% 1.44/1.25 (hskp11),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3280, 3267, 3263, 3265])).
% 1.44/1.25 tff(3282,plain,
% 1.44/1.25 (~c1_1(a1324)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[97, 3281])).
% 1.44/1.25 tff(3283,plain,
% 1.44/1.25 (c0_1(a1324)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[108, 3281])).
% 1.44/1.25 tff(3284,plain,
% 1.44/1.25 (c3_1(a1324)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[119, 3281])).
% 1.44/1.25 tff(3285,plain,
% 1.44/1.25 ((~c3_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1324)) | c1_1(a1324) | (~c0_1(a1324))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3135, 3216, 3212, 3213])).
% 1.44/1.25 tff(3286,plain,
% 1.44/1.25 (~c3_1(a1348)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3285, 3282, 3265, 3264, 3263, 3284, 3283])).
% 1.44/1.25 tff(3287,plain,
% 1.44/1.25 (hskp12 | c3_1(a1348)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1994, 414, 3265, 3264, 3263, 851, 689, 1304])).
% 1.44/1.25 tff(3288,plain,
% 1.44/1.25 (hskp12),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3287, 3286])).
% 1.44/1.25 tff(3289,plain,
% 1.44/1.25 (~c0_1(a1325)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1316, 3288])).
% 1.44/1.25 tff(3290,plain,
% 1.44/1.25 (c3_1(a1325)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1327, 3288])).
% 1.44/1.25 tff(3291,plain,
% 1.44/1.25 (c1_1(a1325)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1338, 3288])).
% 1.44/1.25 tff(3292,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3293,plain,
% 1.44/1.25 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3294,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3293])).
% 1.44/1.25 tff(3295,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3294, 3292])).
% 1.44/1.25 tff(3296,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3297,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 1.44/1.25 tff(3298,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3297, 414, 3291, 3290, 3283, 3284, 3262, 3289, 3282, 3261, 35, 3279])).
% 1.44/1.25 tff(3299,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3300,plain,
% 1.44/1.25 (c2_1(a1338)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[535, 3299])).
% 1.44/1.25 tff(3301,plain,
% 1.44/1.25 (c3_1(a1338)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[524, 3299])).
% 1.44/1.25 tff(3302,plain,
% 1.44/1.25 (c1_1(a1338)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[546, 3299])).
% 1.44/1.25 tff(3303,plain,
% 1.44/1.25 (~c0_1(a1338)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3220, 3302, 3301, 3300])).
% 1.44/1.25 tff(3304,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3305,plain,
% 1.44/1.25 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3306,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3305])).
% 1.44/1.25 tff(3307,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3306, 3304])).
% 1.44/1.25 tff(3308,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3309,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.44/1.25 tff(3310,plain,
% 1.44/1.25 (~c3_1(a1307)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3309, 414, 3300, 3301, 3265, 3264, 3216, 3213, 3212, 10, 3303])).
% 1.44/1.25 tff(3311,plain,
% 1.44/1.25 (hskp11),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3280, 3310, 3263, 3265])).
% 1.44/1.25 tff(3312,plain,
% 1.44/1.25 (c0_1(a1324)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[108, 3311])).
% 1.44/1.25 tff(3313,plain,
% 1.44/1.25 (c3_1(a1324)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[119, 3311])).
% 1.44/1.26 tff(3314,plain,
% 1.44/1.26 (~c1_1(a1324)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[97, 3311])).
% 1.44/1.26 tff(3315,plain,
% 1.44/1.26 (~c3_1(a1348)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3285, 3314, 3265, 3264, 3263, 3313, 3312])).
% 1.44/1.26 tff(3316,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3317,plain,
% 1.44/1.26 (((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3318,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3317])).
% 1.44/1.26 tff(3319,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3318, 3316])).
% 1.44/1.26 tff(3320,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3321,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 1.44/1.26 tff(3322,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3321, 414, 3265, 3264, 851, 689, 3249, 3248, 3258, 435, 3315, 3310])).
% 1.44/1.26 % SZS output end Proof
%------------------------------------------------------------------------------