TSTP Solution File: SYN457-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN457-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 23:55:33 EDT 2022
% Result : Unsatisfiable 8.58s 5.71s
% Output : Proof 9.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN457-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:06:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 8.58/5.71 % SZS status Unsatisfiable
% 8.58/5.71 % SZS output start Proof
% 8.58/5.71 tff(c0_1_type, type, (
% 8.58/5.71 c0_1: $i > $o)).
% 8.58/5.71 tff(c3_1_type, type, (
% 8.58/5.71 c3_1: $i > $o)).
% 8.58/5.71 tff(c1_1_type, type, (
% 8.58/5.71 c1_1: $i > $o)).
% 8.58/5.71 tff(ndr1_0_type, type, (
% 8.58/5.71 ndr1_0: $o)).
% 8.58/5.71 tff(hskp16_type, type, (
% 8.58/5.71 hskp16: $o)).
% 8.58/5.71 tff(hskp17_type, type, (
% 8.58/5.71 hskp17: $o)).
% 8.58/5.71 tff(a1667_type, type, (
% 8.58/5.71 a1667: $i)).
% 8.58/5.71 tff(hskp13_type, type, (
% 8.58/5.71 hskp13: $o)).
% 8.58/5.71 tff(a1654_type, type, (
% 8.58/5.71 a1654: $i)).
% 8.58/5.71 tff(c2_1_type, type, (
% 8.58/5.71 c2_1: $i > $o)).
% 8.58/5.71 tff(a1691_type, type, (
% 8.58/5.71 a1691: $i)).
% 8.58/5.71 tff(hskp26_type, type, (
% 8.58/5.71 hskp26: $o)).
% 8.58/5.71 tff(hskp12_type, type, (
% 8.58/5.71 hskp12: $o)).
% 8.58/5.71 tff(hskp52_type, type, (
% 8.58/5.71 hskp52: $o)).
% 8.58/5.71 tff(hskp7_type, type, (
% 8.58/5.71 hskp7: $o)).
% 8.58/5.71 tff(a1664_type, type, (
% 8.58/5.71 a1664: $i)).
% 8.58/5.71 tff(hskp11_type, type, (
% 8.58/5.71 hskp11: $o)).
% 8.58/5.71 tff(hskp57_type, type, (
% 8.58/5.71 hskp57: $o)).
% 8.58/5.71 tff(a1655_type, type, (
% 8.58/5.71 a1655: $i)).
% 8.58/5.71 tff(a1678_type, type, (
% 8.58/5.71 a1678: $i)).
% 8.58/5.71 tff(a1665_type, type, (
% 8.58/5.71 a1665: $i)).
% 8.58/5.71 tff(a1695_type, type, (
% 8.58/5.71 a1695: $i)).
% 8.58/5.71 tff(a1677_type, type, (
% 8.58/5.71 a1677: $i)).
% 8.58/5.71 tff(hskp29_type, type, (
% 8.58/5.71 hskp29: $o)).
% 8.58/5.71 tff(a1644_type, type, (
% 8.58/5.71 a1644: $i)).
% 8.58/5.71 tff(hskp47_type, type, (
% 8.58/5.71 hskp47: $o)).
% 8.58/5.71 tff(a1656_type, type, (
% 8.58/5.71 a1656: $i)).
% 8.58/5.71 tff(a1715_type, type, (
% 8.58/5.71 a1715: $i)).
% 8.58/5.71 tff(hskp53_type, type, (
% 8.58/5.71 hskp53: $o)).
% 8.58/5.71 tff(hskp23_type, type, (
% 8.58/5.71 hskp23: $o)).
% 8.58/5.71 tff(hskp65_type, type, (
% 8.58/5.71 hskp65: $o)).
% 8.58/5.71 tff(hskp64_type, type, (
% 8.58/5.71 hskp64: $o)).
% 8.58/5.71 tff(a1673_type, type, (
% 8.58/5.71 a1673: $i)).
% 8.58/5.71 tff(hskp60_type, type, (
% 8.58/5.71 hskp60: $o)).
% 8.58/5.71 tff(a1724_type, type, (
% 8.58/5.71 a1724: $i)).
% 8.58/5.71 tff(hskp75_type, type, (
% 8.58/5.71 hskp75: $o)).
% 8.58/5.71 tff(hskp72_type, type, (
% 8.58/5.71 hskp72: $o)).
% 8.58/5.71 tff(a1714_type, type, (
% 8.58/5.71 a1714: $i)).
% 8.58/5.71 tff(hskp37_type, type, (
% 8.58/5.71 hskp37: $o)).
% 8.58/5.71 tff(a1725_type, type, (
% 8.58/5.71 a1725: $i)).
% 8.58/5.71 tff(hskp40_type, type, (
% 8.58/5.71 hskp40: $o)).
% 8.58/5.71 tff(a1637_type, type, (
% 8.58/5.71 a1637: $i)).
% 8.58/5.71 tff(hskp0_type, type, (
% 8.58/5.71 hskp0: $o)).
% 8.58/5.71 tff(a1666_type, type, (
% 8.58/5.71 a1666: $i)).
% 8.58/5.71 tff(a1645_type, type, (
% 8.58/5.71 a1645: $i)).
% 8.58/5.71 tff(hskp2_type, type, (
% 8.58/5.71 hskp2: $o)).
% 8.58/5.71 tff(a1638_type, type, (
% 8.58/5.71 a1638: $i)).
% 8.58/5.71 tff(hskp42_type, type, (
% 8.58/5.71 hskp42: $o)).
% 8.58/5.71 tff(hskp74_type, type, (
% 8.58/5.71 hskp74: $o)).
% 8.58/5.71 tff(hskp38_type, type, (
% 8.58/5.71 hskp38: $o)).
% 8.58/5.71 tff(a1718_type, type, (
% 8.58/5.71 a1718: $i)).
% 8.58/5.71 tff(a1717_type, type, (
% 8.58/5.71 a1717: $i)).
% 8.58/5.71 tff(hskp61_type, type, (
% 8.58/5.71 hskp61: $o)).
% 8.58/5.71 tff(a1674_type, type, (
% 8.58/5.71 a1674: $i)).
% 8.58/5.71 tff(a1709_type, type, (
% 8.58/5.71 a1709: $i)).
% 8.58/5.71 tff(hskp69_type, type, (
% 8.58/5.71 hskp69: $o)).
% 8.58/5.71 tff(a1683_type, type, (
% 8.58/5.71 a1683: $i)).
% 8.58/5.71 tff(hskp21_type, type, (
% 8.58/5.71 hskp21: $o)).
% 8.58/5.71 tff(a1716_type, type, (
% 8.58/5.71 a1716: $i)).
% 8.58/5.71 tff(a1721_type, type, (
% 8.58/5.71 a1721: $i)).
% 8.58/5.71 tff(hskp39_type, type, (
% 8.58/5.71 hskp39: $o)).
% 8.58/5.71 tff(hskp73_type, type, (
% 8.58/5.71 hskp73: $o)).
% 8.58/5.71 tff(a1702_type, type, (
% 8.58/5.71 a1702: $i)).
% 8.58/5.71 tff(hskp67_type, type, (
% 8.58/5.71 hskp67: $o)).
% 8.58/5.71 tff(a1712_type, type, (
% 8.58/5.71 a1712: $i)).
% 8.58/5.71 tff(hskp36_type, type, (
% 8.58/5.71 hskp36: $o)).
% 8.58/5.71 tff(hskp71_type, type, (
% 8.58/5.71 hskp71: $o)).
% 8.58/5.71 tff(a1713_type, type, (
% 8.58/5.71 a1713: $i)).
% 8.58/5.71 tff(a1676_type, type, (
% 8.58/5.71 a1676: $i)).
% 8.58/5.71 tff(hskp63_type, type, (
% 8.58/5.71 hskp63: $o)).
% 8.58/5.71 tff(a1698_type, type, (
% 8.58/5.71 a1698: $i)).
% 8.58/5.71 tff(hskp30_type, type, (
% 8.58/5.71 hskp30: $o)).
% 8.58/5.71 tff(a1710_type, type, (
% 8.58/5.71 a1710: $i)).
% 8.58/5.71 tff(hskp70_type, type, (
% 8.58/5.71 hskp70: $o)).
% 8.58/5.71 tff(a1690_type, type, (
% 8.58/5.71 a1690: $i)).
% 8.58/5.71 tff(hskp25_type, type, (
% 8.58/5.71 hskp25: $o)).
% 8.58/5.71 tff(a1675_type, type, (
% 8.58/5.71 a1675: $i)).
% 8.58/5.71 tff(hskp62_type, type, (
% 8.58/5.71 hskp62: $o)).
% 8.58/5.71 tff(a1704_type, type, (
% 8.58/5.71 a1704: $i)).
% 8.58/5.71 tff(hskp33_type, type, (
% 8.58/5.71 hskp33: $o)).
% 8.58/5.71 tff(hskp59_type, type, (
% 8.58/5.71 hskp59: $o)).
% 8.58/5.71 tff(hskp58_type, type, (
% 8.58/5.71 hskp58: $o)).
% 8.58/5.71 tff(a1668_type, type, (
% 8.58/5.71 a1668: $i)).
% 8.58/5.71 tff(a1669_type, type, (
% 8.58/5.71 a1669: $i)).
% 8.58/5.71 tff(a1639_type, type, (
% 8.58/5.71 a1639: $i)).
% 8.58/5.71 tff(hskp43_type, type, (
% 8.58/5.71 hskp43: $o)).
% 8.58/5.71 tff(hskp44_type, type, (
% 8.58/5.71 hskp44: $o)).
% 8.58/5.71 tff(a1640_type, type, (
% 8.58/5.71 a1640: $i)).
% 8.58/5.71 tff(hskp45_type, type, (
% 8.58/5.71 hskp45: $o)).
% 8.58/5.71 tff(a1641_type, type, (
% 8.58/5.71 a1641: $i)).
% 8.58/5.71 tff(a1684_type, type, (
% 8.58/5.71 a1684: $i)).
% 8.58/5.71 tff(hskp22_type, type, (
% 8.58/5.71 hskp22: $o)).
% 8.58/5.71 tff(a1705_type, type, (
% 8.58/5.71 a1705: $i)).
% 8.58/5.71 tff(hskp34_type, type, (
% 8.58/5.71 hskp34: $o)).
% 8.58/5.71 tff(1,plain,
% 8.58/5.71 (^[U: $i] : refl((hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(2,plain,
% 8.58/5.71 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[1])).
% 8.58/5.71 tff(3,plain,
% 8.58/5.71 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(4,plain,
% 8.58/5.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp17) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(5,plain,
% 8.58/5.71 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp17) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[4])).
% 8.58/5.71 tff(6,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause328')).
% 8.58/5.71 tff(7,plain,
% 8.58/5.71 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[6, 5])).
% 8.58/5.71 tff(8,plain,
% 8.58/5.71 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[7, 3])).
% 8.58/5.71 tff(9,plain,(
% 8.58/5.71 ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(skolemize,[status(sab)],[8])).
% 8.58/5.71 tff(10,plain,
% 8.58/5.71 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[9, 2])).
% 8.58/5.71 tff(11,plain,
% 8.58/5.71 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(12,plain,
% 8.58/5.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[11])).
% 8.58/5.71 tff(13,plain,
% 8.58/5.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(14,plain,
% 8.58/5.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(15,plain,
% 8.58/5.71 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[14])).
% 8.58/5.71 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause356')).
% 8.58/5.71 tff(17,plain,
% 8.58/5.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 8.58/5.71 tff(18,plain,
% 8.58/5.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[17, 13])).
% 8.58/5.71 tff(19,plain,(
% 8.58/5.71 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(skolemize,[status(sab)],[18])).
% 8.58/5.71 tff(20,plain,
% 8.58/5.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[19, 12])).
% 8.58/5.71 tff(21,plain,
% 8.58/5.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(22,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_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) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[21])).
% 8.58/5.71 tff(23,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_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) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(24,plain,
% 8.58/5.71 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c2_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c2_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c2_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(25,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[24])).
% 8.58/5.71 tff(26,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(V)) | c2_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause359')).
% 8.58/5.71 tff(27,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[26, 25])).
% 8.58/5.71 tff(28,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[27, 23])).
% 8.58/5.71 tff(29,plain,(
% 8.58/5.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(skolemize,[status(sab)],[28])).
% 8.58/5.71 tff(30,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[29, 22])).
% 8.58/5.71 tff(31,assumption,(hskp7), introduced(assumption)).
% 8.58/5.71 tff(32,plain,
% 8.58/5.71 (((~hskp7) | c3_1(a1655)) <=> ((~hskp7) | c3_1(a1655))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(33,axiom,((~hskp7) | c3_1(a1655)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 8.58/5.71 tff(34,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[33, 32])).
% 8.58/5.71 tff(35,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[34, 32])).
% 8.58/5.71 tff(36,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[35, 32])).
% 8.58/5.71 tff(37,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[36, 32])).
% 8.58/5.71 tff(38,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[37, 32])).
% 8.58/5.71 tff(39,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[38, 32])).
% 8.58/5.71 tff(40,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[39, 32])).
% 8.58/5.71 tff(41,plain,
% 8.58/5.71 ((~hskp7) | c3_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[40, 32])).
% 8.58/5.71 tff(42,plain,
% 8.58/5.71 (c3_1(a1655)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[41, 31])).
% 8.58/5.71 tff(43,plain,
% 8.58/5.71 (((~hskp7) | (~c2_1(a1655))) <=> ((~hskp7) | (~c2_1(a1655)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(44,plain,
% 8.58/5.71 (((~c2_1(a1655)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1655)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(45,axiom,((~c2_1(a1655)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause297')).
% 8.58/5.71 tff(46,plain,
% 8.58/5.71 ((~hskp7) | (~c2_1(a1655))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[45, 44])).
% 8.58/5.71 tff(47,plain,
% 8.58/5.71 ((~hskp7) | (~c2_1(a1655))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[46, 43])).
% 8.58/5.71 tff(48,plain,
% 8.58/5.71 (~c2_1(a1655)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[47, 31])).
% 8.58/5.71 tff(49,plain,
% 8.58/5.71 (((~hskp7) | c0_1(a1655)) <=> ((~hskp7) | c0_1(a1655))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(50,axiom,((~hskp7) | c0_1(a1655)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 8.58/5.71 tff(51,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[50, 49])).
% 8.58/5.71 tff(52,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[51, 49])).
% 8.58/5.71 tff(53,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[52, 49])).
% 8.58/5.71 tff(54,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[53, 49])).
% 8.58/5.71 tff(55,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[54, 49])).
% 8.58/5.71 tff(56,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[55, 49])).
% 8.58/5.71 tff(57,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[56, 49])).
% 8.58/5.71 tff(58,plain,
% 8.58/5.71 ((~hskp7) | c0_1(a1655)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[57, 49])).
% 8.58/5.71 tff(59,plain,
% 8.58/5.71 (c0_1(a1655)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[58, 31])).
% 8.58/5.71 tff(60,assumption,(hskp57), introduced(assumption)).
% 8.58/5.71 tff(61,plain,
% 8.58/5.71 (((~hskp57) | (~c1_1(a1665))) <=> ((~hskp57) | (~c1_1(a1665)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(62,plain,
% 8.58/5.71 (((~c1_1(a1665)) | (~hskp57)) <=> ((~hskp57) | (~c1_1(a1665)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(63,axiom,((~c1_1(a1665)) | (~hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause209')).
% 8.58/5.71 tff(64,plain,
% 8.58/5.71 ((~hskp57) | (~c1_1(a1665))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[63, 62])).
% 8.58/5.71 tff(65,plain,
% 8.58/5.71 ((~hskp57) | (~c1_1(a1665))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[64, 61])).
% 8.58/5.71 tff(66,plain,
% 8.58/5.71 (~c1_1(a1665)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[65, 60])).
% 8.58/5.71 tff(67,plain,
% 8.58/5.71 (((~hskp57) | c3_1(a1665)) <=> ((~hskp57) | c3_1(a1665))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(68,axiom,((~hskp57) | c3_1(a1665)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 8.58/5.71 tff(69,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[68, 67])).
% 8.58/5.71 tff(70,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[69, 67])).
% 8.58/5.71 tff(71,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[70, 67])).
% 8.58/5.71 tff(72,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[71, 67])).
% 8.58/5.71 tff(73,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[72, 67])).
% 8.58/5.71 tff(74,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[73, 67])).
% 8.58/5.71 tff(75,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[74, 67])).
% 8.58/5.71 tff(76,plain,
% 8.58/5.71 ((~hskp57) | c3_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[75, 67])).
% 8.58/5.71 tff(77,plain,
% 8.58/5.71 (c3_1(a1665)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[76, 60])).
% 8.58/5.71 tff(78,assumption,(c3_1(a1655)), introduced(assumption)).
% 8.58/5.71 tff(79,assumption,(~c2_1(a1655)), introduced(assumption)).
% 8.58/5.71 tff(80,assumption,(c0_1(a1655)), introduced(assumption)).
% 8.58/5.71 tff(81,plain,
% 8.58/5.71 (((~hskp57) | c0_1(a1665)) <=> ((~hskp57) | c0_1(a1665))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(82,axiom,((~hskp57) | c0_1(a1665)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 8.58/5.71 tff(83,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[82, 81])).
% 8.58/5.71 tff(84,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[83, 81])).
% 8.58/5.71 tff(85,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[84, 81])).
% 8.58/5.71 tff(86,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[85, 81])).
% 8.58/5.71 tff(87,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[86, 81])).
% 8.58/5.71 tff(88,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[87, 81])).
% 8.58/5.71 tff(89,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[88, 81])).
% 8.58/5.71 tff(90,plain,
% 8.58/5.71 ((~hskp57) | c0_1(a1665)),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[89, 81])).
% 8.58/5.71 tff(91,plain,
% 8.58/5.71 (c0_1(a1665)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[90, 60])).
% 8.58/5.71 tff(92,assumption,(c3_1(a1678)), introduced(assumption)).
% 8.58/5.71 tff(93,plain,
% 8.58/5.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(94,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[93])).
% 8.58/5.71 tff(95,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(96,plain,
% 8.58/5.71 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 8.58/5.71 inference(bind,[status(th)],[])).
% 8.58/5.71 tff(97,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(quant_intro,[status(thm)],[96])).
% 8.58/5.71 tff(98,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(U)) | c1_1(U)) | c1_1(V)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause363')).
% 8.58/5.71 tff(99,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[98, 97])).
% 8.58/5.71 tff(100,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[99, 95])).
% 8.58/5.71 tff(101,plain,(
% 8.58/5.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(skolemize,[status(sab)],[100])).
% 8.58/5.71 tff(102,plain,
% 8.58/5.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[101, 94])).
% 8.58/5.71 tff(103,assumption,(~c1_1(a1665)), introduced(assumption)).
% 8.58/5.71 tff(104,assumption,(c3_1(a1665)), introduced(assumption)).
% 8.58/5.71 tff(105,assumption,(c0_1(a1665)), introduced(assumption)).
% 8.58/5.71 tff(106,assumption,(hskp16), introduced(assumption)).
% 8.58/5.71 tff(107,plain,
% 8.58/5.71 (((~hskp16) | (~c1_1(a1677))) <=> ((~hskp16) | (~c1_1(a1677)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(108,plain,
% 8.58/5.71 (((~c1_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a1677)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(109,axiom,((~c1_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause280')).
% 8.58/5.71 tff(110,plain,
% 8.58/5.71 ((~hskp16) | (~c1_1(a1677))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[109, 108])).
% 8.58/5.71 tff(111,plain,
% 8.58/5.71 ((~hskp16) | (~c1_1(a1677))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[110, 107])).
% 8.58/5.71 tff(112,plain,
% 8.58/5.71 (~c1_1(a1677)),
% 8.58/5.71 inference(unit_resolution,[status(thm)],[111, 106])).
% 8.58/5.71 tff(113,plain,
% 8.58/5.71 (((~hskp16) | (~c2_1(a1677))) <=> ((~hskp16) | (~c2_1(a1677)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(114,plain,
% 8.58/5.71 (((~c2_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1677)))),
% 8.58/5.71 inference(rewrite,[status(thm)],[])).
% 8.58/5.71 tff(115,axiom,((~c2_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 8.58/5.71 tff(116,plain,
% 8.58/5.71 ((~hskp16) | (~c2_1(a1677))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[115, 114])).
% 8.58/5.71 tff(117,plain,
% 8.58/5.71 ((~hskp16) | (~c2_1(a1677))),
% 8.58/5.71 inference(modus_ponens,[status(thm)],[116, 113])).
% 8.58/5.72 tff(118,plain,
% 8.58/5.72 (~c2_1(a1677)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[117, 106])).
% 8.58/5.72 tff(119,plain,
% 8.58/5.72 (((~hskp16) | (~c0_1(a1677))) <=> ((~hskp16) | (~c0_1(a1677)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(120,plain,
% 8.58/5.72 (((~c0_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1677)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(121,axiom,((~c0_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause278')).
% 8.58/5.72 tff(122,plain,
% 8.58/5.72 ((~hskp16) | (~c0_1(a1677))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[121, 120])).
% 8.58/5.72 tff(123,plain,
% 8.58/5.72 ((~hskp16) | (~c0_1(a1677))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[122, 119])).
% 8.58/5.72 tff(124,plain,
% 8.58/5.72 (~c0_1(a1677)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[123, 106])).
% 8.58/5.72 tff(125,assumption,(c3_1(a1677)), introduced(assumption)).
% 8.58/5.72 tff(126,assumption,(~c1_1(a1677)), introduced(assumption)).
% 8.58/5.72 tff(127,assumption,(~c0_1(a1677)), introduced(assumption)).
% 8.58/5.72 tff(128,plain,
% 8.58/5.72 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 8.58/5.72 inference(bind,[status(th)],[])).
% 8.58/5.72 tff(129,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(quant_intro,[status(thm)],[128])).
% 8.58/5.72 tff(130,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(131,plain,
% 8.58/5.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 8.58/5.72 inference(bind,[status(th)],[])).
% 8.58/5.72 tff(132,plain,
% 8.58/5.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(quant_intro,[status(thm)],[131])).
% 8.58/5.72 tff(133,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause346')).
% 8.58/5.72 tff(134,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[133, 132])).
% 8.58/5.72 tff(135,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[134, 130])).
% 8.58/5.72 tff(136,plain,(
% 8.58/5.72 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(skolemize,[status(sab)],[135])).
% 8.58/5.72 tff(137,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[136, 129])).
% 8.58/5.72 tff(138,assumption,(~hskp29), introduced(assumption)).
% 8.58/5.72 tff(139,assumption,(~hskp52), introduced(assumption)).
% 8.58/5.72 tff(140,plain,
% 8.58/5.72 ((hskp53 | hskp52 | hskp29) <=> (hskp53 | hskp52 | hskp29)),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(141,plain,
% 8.58/5.72 (((hskp29 | hskp52) | hskp53) <=> (hskp53 | hskp52 | hskp29)),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(142,axiom,((hskp29 | hskp52) | hskp53), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 8.58/5.72 tff(143,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[142, 141])).
% 8.58/5.72 tff(144,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[143, 140])).
% 8.58/5.72 tff(145,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[144, 140])).
% 8.58/5.72 tff(146,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[145, 140])).
% 8.58/5.72 tff(147,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[146, 140])).
% 8.58/5.72 tff(148,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[147, 140])).
% 8.58/5.72 tff(149,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[148, 140])).
% 8.58/5.72 tff(150,plain,
% 8.58/5.72 (hskp53 | hskp52 | hskp29),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[149, 140])).
% 8.58/5.72 tff(151,plain,
% 8.58/5.72 (hskp53),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[150, 139, 138])).
% 8.58/5.72 tff(152,plain,
% 8.58/5.72 (((~hskp53) | c0_1(a1656)) <=> ((~hskp53) | c0_1(a1656))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(153,axiom,((~hskp53) | c0_1(a1656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 8.58/5.72 tff(154,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[153, 152])).
% 8.58/5.72 tff(155,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[154, 152])).
% 8.58/5.72 tff(156,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[155, 152])).
% 8.58/5.72 tff(157,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[156, 152])).
% 8.58/5.72 tff(158,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[157, 152])).
% 8.58/5.72 tff(159,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[158, 152])).
% 8.58/5.72 tff(160,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[159, 152])).
% 8.58/5.72 tff(161,plain,
% 8.58/5.72 ((~hskp53) | c0_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[160, 152])).
% 8.58/5.72 tff(162,plain,
% 8.58/5.72 (c0_1(a1656)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[161, 151])).
% 8.58/5.72 tff(163,plain,
% 8.58/5.72 (((~hskp53) | (~c3_1(a1656))) <=> ((~hskp53) | (~c3_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(164,plain,
% 8.58/5.72 (((~c3_1(a1656)) | (~hskp53)) <=> ((~hskp53) | (~c3_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(165,axiom,((~c3_1(a1656)) | (~hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause214')).
% 8.58/5.72 tff(166,plain,
% 8.58/5.72 ((~hskp53) | (~c3_1(a1656))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[165, 164])).
% 8.58/5.72 tff(167,plain,
% 8.58/5.72 ((~hskp53) | (~c3_1(a1656))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[166, 163])).
% 8.58/5.72 tff(168,plain,
% 8.58/5.72 (~c3_1(a1656)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[167, 151])).
% 8.58/5.72 tff(169,plain,
% 8.58/5.72 (((~hskp53) | c2_1(a1656)) <=> ((~hskp53) | c2_1(a1656))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(170,axiom,((~hskp53) | c2_1(a1656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 8.58/5.72 tff(171,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[170, 169])).
% 8.58/5.72 tff(172,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[171, 169])).
% 8.58/5.72 tff(173,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[172, 169])).
% 8.58/5.72 tff(174,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[173, 169])).
% 8.58/5.72 tff(175,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[174, 169])).
% 8.58/5.72 tff(176,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[175, 169])).
% 8.58/5.72 tff(177,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[176, 169])).
% 8.58/5.72 tff(178,plain,
% 8.58/5.72 ((~hskp53) | c2_1(a1656)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[177, 169])).
% 8.58/5.72 tff(179,plain,
% 8.58/5.72 (c2_1(a1656)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[178, 151])).
% 8.58/5.72 tff(180,plain,
% 8.58/5.72 (^[U: $i] : refl((hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 8.58/5.72 inference(bind,[status(th)],[])).
% 8.58/5.72 tff(181,plain,
% 8.58/5.72 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(quant_intro,[status(thm)],[180])).
% 8.58/5.72 tff(182,plain,
% 8.58/5.72 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(183,plain,
% 8.58/5.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp52))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp52) <=> (hskp52 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) <=> (hskp52 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) | hskp7) <=> ((hskp52 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp52 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) | hskp7) <=> (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 8.58/5.72 inference(bind,[status(th)],[])).
% 8.58/5.72 tff(184,plain,
% 8.58/5.72 (![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) | hskp7) <=> ![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(quant_intro,[status(thm)],[183])).
% 8.58/5.72 tff(185,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause324')).
% 8.58/5.72 tff(186,plain,
% 8.58/5.72 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[185, 184])).
% 8.58/5.72 tff(187,plain,
% 8.58/5.72 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[186, 182])).
% 8.58/5.72 tff(188,plain,(
% 8.58/5.72 ![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(skolemize,[status(sab)],[187])).
% 8.58/5.72 tff(189,plain,
% 8.58/5.72 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[188, 181])).
% 8.58/5.72 tff(190,assumption,(~ndr1_0), introduced(assumption)).
% 8.58/5.72 tff(191,plain,
% 8.58/5.72 ((ndr1_0 | (~hskp23)) <=> (ndr1_0 | (~hskp23))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(192,plain,
% 8.58/5.72 (((~hskp23) | ndr1_0) <=> (ndr1_0 | (~hskp23))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(193,axiom,((~hskp23) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 8.58/5.72 tff(194,plain,
% 8.58/5.72 (ndr1_0 | (~hskp23)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[193, 192])).
% 8.58/5.72 tff(195,plain,
% 8.58/5.72 (ndr1_0 | (~hskp23)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[194, 191])).
% 8.58/5.72 tff(196,plain,
% 8.58/5.72 (~hskp23),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[195, 190])).
% 8.58/5.72 tff(197,plain,
% 8.58/5.72 ((ndr1_0 | (~hskp65)) <=> (ndr1_0 | (~hskp65))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(198,plain,
% 8.58/5.72 (((~hskp65) | ndr1_0) <=> (ndr1_0 | (~hskp65))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(199,axiom,((~hskp65) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 8.58/5.72 tff(200,plain,
% 8.58/5.72 (ndr1_0 | (~hskp65)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[199, 198])).
% 8.58/5.72 tff(201,plain,
% 8.58/5.72 (ndr1_0 | (~hskp65)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[200, 197])).
% 8.58/5.72 tff(202,plain,
% 8.58/5.72 (~hskp65),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[201, 190])).
% 8.58/5.72 tff(203,plain,
% 8.58/5.72 ((ndr1_0 | (~hskp64)) <=> (ndr1_0 | (~hskp64))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(204,plain,
% 8.58/5.72 (((~hskp64) | ndr1_0) <=> (ndr1_0 | (~hskp64))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(205,axiom,((~hskp64) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 8.58/5.72 tff(206,plain,
% 8.58/5.72 (ndr1_0 | (~hskp64)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[205, 204])).
% 8.58/5.72 tff(207,plain,
% 8.58/5.72 (ndr1_0 | (~hskp64)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[206, 203])).
% 8.58/5.72 tff(208,plain,
% 8.58/5.72 (~hskp64),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[207, 190])).
% 8.58/5.72 tff(209,plain,
% 8.58/5.72 ((hskp65 | hskp64 | hskp23) <=> (hskp65 | hskp64 | hskp23)),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(210,plain,
% 8.58/5.72 (((hskp23 | hskp64) | hskp65) <=> (hskp65 | hskp64 | hskp23)),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(211,axiom,((hskp23 | hskp64) | hskp65), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 8.58/5.72 tff(212,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[211, 210])).
% 8.58/5.72 tff(213,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[212, 209])).
% 8.58/5.72 tff(214,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[213, 209])).
% 8.58/5.72 tff(215,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[214, 209])).
% 8.58/5.72 tff(216,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[215, 209])).
% 8.58/5.72 tff(217,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[216, 209])).
% 8.58/5.72 tff(218,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[217, 209])).
% 8.58/5.72 tff(219,plain,
% 8.58/5.72 (hskp65 | hskp64 | hskp23),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[218, 209])).
% 8.58/5.72 tff(220,plain,
% 8.58/5.72 ($false),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[219, 208, 202, 196])).
% 8.58/5.72 tff(221,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 8.58/5.72 tff(222,plain,
% 8.58/5.72 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(223,plain,
% 8.58/5.72 ((hskp52 | hskp7 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656))) <=> (hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(224,plain,
% 8.58/5.72 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.58/5.72 inference(monotonicity,[status(thm)],[223])).
% 8.58/5.72 tff(225,plain,
% 8.58/5.72 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(transitivity,[status(thm)],[224, 222])).
% 8.58/5.72 tff(226,plain,
% 8.58/5.72 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))),
% 8.58/5.72 inference(quant_inst,[status(thm)],[])).
% 8.58/5.72 tff(227,plain,
% 8.58/5.72 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[226, 225])).
% 8.58/5.72 tff(228,plain,
% 8.58/5.72 (hskp7),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[227, 221, 139, 179, 162, 168, 189])).
% 8.58/5.72 tff(229,plain,
% 8.58/5.72 (c0_1(a1655)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[58, 228])).
% 8.58/5.72 tff(230,plain,
% 8.58/5.72 (c3_1(a1655)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[41, 228])).
% 8.58/5.72 tff(231,plain,
% 8.58/5.72 (~c2_1(a1655)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[47, 228])).
% 8.58/5.72 tff(232,assumption,(c2_1(a1656)), introduced(assumption)).
% 8.58/5.72 tff(233,assumption,(~c3_1(a1656)), introduced(assumption)).
% 8.58/5.72 tff(234,assumption,(c0_1(a1656)), introduced(assumption)).
% 8.58/5.72 tff(235,assumption,(~c1_1(a1655)), introduced(assumption)).
% 8.58/5.72 tff(236,assumption,(hskp17), introduced(assumption)).
% 8.58/5.72 tff(237,plain,
% 8.58/5.72 (((~hskp17) | (~c1_1(a1678))) <=> ((~hskp17) | (~c1_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(238,plain,
% 8.58/5.72 (((~c1_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(239,axiom,((~c1_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause276')).
% 8.58/5.72 tff(240,plain,
% 8.58/5.72 ((~hskp17) | (~c1_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[239, 238])).
% 8.58/5.72 tff(241,plain,
% 8.58/5.72 ((~hskp17) | (~c1_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[240, 237])).
% 8.58/5.72 tff(242,plain,
% 8.58/5.72 (~c1_1(a1678)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[241, 236])).
% 8.58/5.72 tff(243,plain,
% 8.58/5.72 (((~hskp17) | (~c0_1(a1678))) <=> ((~hskp17) | (~c0_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(244,plain,
% 8.58/5.72 (((~c0_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(245,axiom,((~c0_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause275')).
% 8.58/5.72 tff(246,plain,
% 8.58/5.72 ((~hskp17) | (~c0_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[245, 244])).
% 8.58/5.72 tff(247,plain,
% 8.58/5.72 ((~hskp17) | (~c0_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[246, 243])).
% 8.58/5.72 tff(248,plain,
% 8.58/5.72 (~c0_1(a1678)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[247, 236])).
% 8.58/5.72 tff(249,plain,
% 8.58/5.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(250,plain,
% 8.58/5.72 ((hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))) <=> (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(251,plain,
% 8.58/5.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678))))),
% 8.58/5.72 inference(monotonicity,[status(thm)],[250])).
% 8.58/5.72 tff(252,plain,
% 8.58/5.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678)))),
% 8.58/5.72 inference(transitivity,[status(thm)],[251, 249])).
% 8.58/5.72 tff(253,plain,
% 8.58/5.72 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))),
% 8.58/5.72 inference(quant_inst,[status(thm)],[])).
% 8.58/5.72 tff(254,plain,
% 8.58/5.72 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[253, 252])).
% 8.58/5.72 tff(255,plain,
% 8.58/5.72 (~c3_1(a1678)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[254, 221, 138, 78, 80, 248, 242, 137, 235])).
% 8.58/5.72 tff(256,plain,
% 8.58/5.72 (((~hskp17) | (~c2_1(a1678))) <=> ((~hskp17) | (~c2_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(257,plain,
% 8.58/5.72 (((~c2_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1678)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(258,axiom,((~c2_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause277')).
% 8.58/5.72 tff(259,plain,
% 8.58/5.72 ((~hskp17) | (~c2_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[258, 257])).
% 8.58/5.72 tff(260,plain,
% 8.58/5.72 ((~hskp17) | (~c2_1(a1678))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[259, 256])).
% 8.58/5.72 tff(261,plain,
% 8.58/5.72 (~c2_1(a1678)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[260, 236])).
% 8.58/5.72 tff(262,plain,
% 8.58/5.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(263,plain,
% 8.58/5.72 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678)) <=> (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(264,plain,
% 8.58/5.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.58/5.72 inference(monotonicity,[status(thm)],[263])).
% 8.58/5.72 tff(265,plain,
% 8.58/5.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.72 inference(transitivity,[status(thm)],[264, 262])).
% 8.58/5.72 tff(266,plain,
% 8.58/5.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))),
% 8.58/5.72 inference(quant_inst,[status(thm)],[])).
% 8.58/5.72 tff(267,plain,
% 8.58/5.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[266, 265])).
% 8.58/5.72 tff(268,plain,
% 8.58/5.72 ($false),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[267, 221, 232, 234, 233, 248, 242, 261, 30, 255])).
% 8.58/5.72 tff(269,plain,((~hskp17) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | hskp29 | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 8.58/5.72 tff(270,plain,
% 8.58/5.72 (~hskp17),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[269, 235, 234, 233, 138, 78, 80, 232])).
% 8.58/5.72 tff(271,assumption,(~hskp17), introduced(assumption)).
% 8.58/5.72 tff(272,assumption,(~hskp16), introduced(assumption)).
% 8.58/5.72 tff(273,plain,
% 8.58/5.72 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(274,plain,
% 8.58/5.72 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655))) <=> (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(275,plain,
% 8.58/5.72 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655)))),
% 8.58/5.72 inference(monotonicity,[status(thm)],[274])).
% 8.58/5.72 tff(276,plain,
% 8.58/5.72 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655))),
% 8.58/5.72 inference(transitivity,[status(thm)],[275, 273])).
% 8.58/5.72 tff(277,plain,
% 8.58/5.72 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))),
% 8.58/5.72 inference(quant_inst,[status(thm)],[])).
% 8.58/5.72 tff(278,plain,
% 8.58/5.72 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655)),
% 8.58/5.72 inference(modus_ponens,[status(thm)],[277, 276])).
% 8.58/5.72 tff(279,plain,
% 8.58/5.72 (hskp17 | hskp16 | c1_1(a1655)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[278, 221, 78, 80, 10])).
% 8.58/5.72 tff(280,plain,
% 8.58/5.72 (c1_1(a1655)),
% 8.58/5.72 inference(unit_resolution,[status(thm)],[279, 272, 271])).
% 8.58/5.72 tff(281,plain,
% 8.58/5.72 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 8.58/5.72 inference(bind,[status(th)],[])).
% 8.58/5.72 tff(282,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.72 inference(quant_intro,[status(thm)],[281])).
% 8.58/5.72 tff(283,plain,
% 8.58/5.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.72 inference(rewrite,[status(thm)],[])).
% 8.58/5.72 tff(284,plain,
% 8.58/5.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> (((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))))), rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(285,plain,
% 8.58/5.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[284])).
% 8.58/5.73 tff(286,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause357')).
% 8.58/5.73 tff(287,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[286, 285])).
% 8.58/5.73 tff(288,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[287, 283])).
% 8.58/5.73 tff(289,plain,(
% 8.58/5.73 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.73 inference(skolemize,[status(sab)],[288])).
% 8.58/5.73 tff(290,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[289, 282])).
% 8.58/5.73 tff(291,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(292,plain,
% 8.58/5.73 ((hskp13 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | c2_1(a1655) | (~c3_1(a1655)) | (~c1_1(a1655))) <=> (hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(293,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | c2_1(a1655) | (~c3_1(a1655)) | (~c1_1(a1655)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655))))),
% 8.58/5.73 inference(monotonicity,[status(thm)],[292])).
% 8.58/5.73 tff(294,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | c2_1(a1655) | (~c3_1(a1655)) | (~c1_1(a1655)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)))),
% 8.58/5.73 inference(transitivity,[status(thm)],[293, 291])).
% 8.58/5.73 tff(295,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | c2_1(a1655) | (~c3_1(a1655)) | (~c1_1(a1655)))),
% 8.58/5.73 inference(quant_inst,[status(thm)],[])).
% 8.58/5.73 tff(296,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[295, 294])).
% 8.58/5.73 tff(297,plain,
% 8.58/5.73 (hskp13 | (~c1_1(a1655))),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[296, 221, 78, 80, 79, 290])).
% 8.58/5.73 tff(298,plain,
% 8.58/5.73 (hskp13),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[297, 280])).
% 8.58/5.73 tff(299,plain,
% 8.58/5.73 (((~hskp13) | (~c1_1(a1667))) <=> ((~hskp13) | (~c1_1(a1667)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(300,plain,
% 8.58/5.73 (((~c1_1(a1667)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1667)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(301,axiom,((~c1_1(a1667)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 8.58/5.73 tff(302,plain,
% 8.58/5.73 ((~hskp13) | (~c1_1(a1667))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[301, 300])).
% 8.58/5.73 tff(303,plain,
% 8.58/5.73 ((~hskp13) | (~c1_1(a1667))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[302, 299])).
% 8.58/5.73 tff(304,plain,
% 8.58/5.73 (~c1_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[303, 298])).
% 8.58/5.73 tff(305,plain,
% 8.58/5.73 (((~hskp13) | c3_1(a1667)) <=> ((~hskp13) | c3_1(a1667))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(306,axiom,((~hskp13) | c3_1(a1667)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 8.58/5.73 tff(307,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[306, 305])).
% 8.58/5.73 tff(308,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[307, 305])).
% 8.58/5.73 tff(309,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[308, 305])).
% 8.58/5.73 tff(310,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[309, 305])).
% 8.58/5.73 tff(311,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[310, 305])).
% 8.58/5.73 tff(312,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[311, 305])).
% 8.58/5.73 tff(313,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[312, 305])).
% 8.58/5.73 tff(314,plain,
% 8.58/5.73 ((~hskp13) | c3_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[313, 305])).
% 8.58/5.73 tff(315,plain,
% 8.58/5.73 (c3_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[314, 298])).
% 8.58/5.73 tff(316,plain,
% 8.58/5.73 (((~hskp13) | c0_1(a1667)) <=> ((~hskp13) | c0_1(a1667))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(317,axiom,((~hskp13) | c0_1(a1667)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 8.58/5.73 tff(318,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[317, 316])).
% 8.58/5.73 tff(319,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[318, 316])).
% 8.58/5.73 tff(320,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[319, 316])).
% 8.58/5.73 tff(321,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[320, 316])).
% 8.58/5.73 tff(322,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[321, 316])).
% 8.58/5.73 tff(323,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[322, 316])).
% 8.58/5.73 tff(324,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[323, 316])).
% 8.58/5.73 tff(325,plain,
% 8.58/5.73 ((~hskp13) | c0_1(a1667)),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[324, 316])).
% 8.58/5.73 tff(326,plain,
% 8.58/5.73 (c0_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[325, 298])).
% 8.58/5.73 tff(327,plain,
% 8.58/5.73 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(328,plain,
% 8.58/5.73 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667))) <=> (hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(329,plain,
% 8.58/5.73 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667))))),
% 8.58/5.73 inference(monotonicity,[status(thm)],[328])).
% 8.58/5.73 tff(330,plain,
% 8.58/5.73 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.58/5.73 inference(transitivity,[status(thm)],[329, 327])).
% 8.58/5.73 tff(331,plain,
% 8.58/5.73 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.58/5.73 inference(quant_inst,[status(thm)],[])).
% 8.58/5.73 tff(332,plain,
% 8.58/5.73 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[331, 330])).
% 8.58/5.73 tff(333,plain,
% 8.58/5.73 ($false),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[332, 221, 271, 272, 326, 315, 304, 10])).
% 8.58/5.73 tff(334,plain,(hskp16 | hskp17 | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 8.58/5.73 tff(335,plain,
% 8.58/5.73 (hskp16),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[334, 270, 78, 80, 79])).
% 8.58/5.73 tff(336,plain,
% 8.58/5.73 (~c1_1(a1677)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[111, 335])).
% 8.58/5.73 tff(337,plain,
% 8.58/5.73 (~c2_1(a1677)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[117, 335])).
% 8.58/5.73 tff(338,plain,
% 8.58/5.73 (~c0_1(a1677)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[123, 335])).
% 8.58/5.73 tff(339,assumption,(~c3_1(a1677)), introduced(assumption)).
% 8.58/5.73 tff(340,assumption,(~c2_1(a1677)), introduced(assumption)).
% 8.58/5.73 tff(341,plain,
% 8.58/5.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(342,plain,
% 8.58/5.73 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677)) <=> (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(343,plain,
% 8.58/5.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.58/5.73 inference(monotonicity,[status(thm)],[342])).
% 8.58/5.73 tff(344,plain,
% 8.58/5.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.58/5.73 inference(transitivity,[status(thm)],[343, 341])).
% 8.58/5.73 tff(345,plain,
% 8.58/5.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))),
% 8.58/5.73 inference(quant_inst,[status(thm)],[])).
% 8.58/5.73 tff(346,plain,
% 8.58/5.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[345, 344])).
% 8.58/5.73 tff(347,plain,
% 8.58/5.73 ($false),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[346, 221, 232, 234, 233, 127, 340, 126, 30, 339])).
% 8.58/5.73 tff(348,plain,(c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677)), inference(lemma,lemma(discharge,[]))).
% 8.58/5.73 tff(349,plain,
% 8.58/5.73 (c3_1(a1677)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[348, 338, 232, 233, 234, 337, 336])).
% 8.58/5.73 tff(350,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(351,plain,
% 8.58/5.73 ((hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))) <=> (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(352,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677))))),
% 8.58/5.73 inference(monotonicity,[status(thm)],[351])).
% 8.58/5.73 tff(353,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)))),
% 8.58/5.73 inference(transitivity,[status(thm)],[352, 350])).
% 8.58/5.73 tff(354,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 8.58/5.73 inference(quant_inst,[status(thm)],[])).
% 8.58/5.73 tff(355,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[354, 353])).
% 8.58/5.73 tff(356,plain,
% 8.58/5.73 ($false),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[355, 221, 138, 78, 80, 338, 336, 137, 235, 349])).
% 8.58/5.73 tff(357,plain,(c1_1(a1655) | hskp29 | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c2_1(a1656)) | c3_1(a1656) | (~c0_1(a1656)) | c2_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 8.58/5.73 tff(358,plain,
% 8.58/5.73 (c1_1(a1655)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[357, 231, 230, 229, 179, 168, 162, 138])).
% 8.58/5.73 tff(359,plain,
% 8.58/5.73 (hskp13),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[296, 221, 230, 229, 231, 290, 358])).
% 8.58/5.73 tff(360,plain,
% 8.58/5.73 (~c1_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[303, 359])).
% 8.58/5.73 tff(361,plain,
% 8.58/5.73 (c3_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[314, 359])).
% 8.58/5.73 tff(362,plain,
% 8.58/5.73 (c0_1(a1667)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[325, 359])).
% 8.58/5.73 tff(363,assumption,(~c3_1(a1715)), introduced(assumption)).
% 8.58/5.73 tff(364,assumption,(c2_1(a1715)), introduced(assumption)).
% 8.58/5.73 tff(365,assumption,(~c1_1(a1715)), introduced(assumption)).
% 8.58/5.73 tff(366,plain,
% 8.58/5.73 (c3_1(a1677)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[348, 124, 234, 233, 232, 118, 112])).
% 8.58/5.73 tff(367,plain,
% 8.58/5.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(368,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[367])).
% 8.58/5.73 tff(369,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(370,plain,
% 8.58/5.73 (^[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) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(371,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[370])).
% 8.58/5.73 tff(372,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause362')).
% 8.58/5.73 tff(373,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[372, 371])).
% 8.58/5.73 tff(374,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[373, 369])).
% 8.58/5.73 tff(375,plain,(
% 8.58/5.73 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(skolemize,[status(sab)],[374])).
% 8.58/5.73 tff(376,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[375, 368])).
% 8.58/5.73 tff(377,plain,
% 8.58/5.73 (^[V: $i, U: $i] : refl((hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(378,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[377])).
% 8.58/5.73 tff(379,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(380,plain,
% 8.58/5.73 (^[V: $i, U: $i] : 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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp60) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp60))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp60) <=> (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp60) <=> (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(381,plain,
% 8.58/5.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp60) <=> ![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[380])).
% 8.58/5.73 tff(382,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause337')).
% 8.58/5.73 tff(383,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[382, 381])).
% 8.58/5.73 tff(384,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[383, 379])).
% 8.58/5.73 tff(385,plain,(
% 8.58/5.73 ![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(skolemize,[status(sab)],[384])).
% 8.58/5.73 tff(386,plain,
% 8.58/5.73 (![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[385, 378])).
% 8.58/5.73 tff(387,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(388,plain,
% 8.58/5.73 ((hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))) <=> (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(389,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677))))),
% 8.58/5.73 inference(monotonicity,[status(thm)],[388])).
% 8.58/5.73 tff(390,plain,
% 8.58/5.73 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)))),
% 8.58/5.73 inference(transitivity,[status(thm)],[389, 387])).
% 8.58/5.73 tff(391,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 8.58/5.73 inference(quant_inst,[status(thm)],[])).
% 8.58/5.73 tff(392,plain,
% 8.58/5.73 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[391, 390])).
% 8.58/5.73 tff(393,plain,
% 8.58/5.73 (hskp60 | (~c3_1(a1677))),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[392, 221, 365, 363, 364, 124, 112, 386])).
% 8.58/5.73 tff(394,plain,
% 8.58/5.73 (hskp60),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[393, 366])).
% 8.58/5.73 tff(395,plain,
% 8.58/5.73 (((~hskp60) | (~c1_1(a1673))) <=> ((~hskp60) | (~c1_1(a1673)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(396,plain,
% 8.58/5.73 (((~c1_1(a1673)) | (~hskp60)) <=> ((~hskp60) | (~c1_1(a1673)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(397,axiom,((~c1_1(a1673)) | (~hskp60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 8.58/5.73 tff(398,plain,
% 8.58/5.73 ((~hskp60) | (~c1_1(a1673))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[397, 396])).
% 8.58/5.73 tff(399,plain,
% 8.58/5.73 ((~hskp60) | (~c1_1(a1673))),
% 8.58/5.73 inference(modus_ponens,[status(thm)],[398, 395])).
% 8.58/5.73 tff(400,plain,
% 8.58/5.73 (~c1_1(a1673)),
% 8.58/5.73 inference(unit_resolution,[status(thm)],[399, 394])).
% 8.58/5.73 tff(401,plain,
% 8.58/5.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 8.58/5.73 inference(bind,[status(th)],[])).
% 8.58/5.73 tff(402,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.73 inference(quant_intro,[status(thm)],[401])).
% 8.58/5.73 tff(403,plain,
% 8.58/5.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.73 inference(rewrite,[status(thm)],[])).
% 8.58/5.73 tff(404,plain,
% 8.58/5.73 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 8.58/5.74 inference(bind,[status(th)],[])).
% 8.58/5.74 tff(405,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.74 inference(quant_intro,[status(thm)],[404])).
% 8.58/5.74 tff(406,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause360')).
% 8.58/5.74 tff(407,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[406, 405])).
% 8.58/5.74 tff(408,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[407, 403])).
% 8.58/5.74 tff(409,plain,(
% 8.58/5.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.74 inference(skolemize,[status(sab)],[408])).
% 8.58/5.74 tff(410,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[409, 402])).
% 8.58/5.74 tff(411,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(412,plain,
% 8.58/5.74 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(413,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656))))),
% 8.58/5.74 inference(monotonicity,[status(thm)],[412])).
% 8.58/5.74 tff(414,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.58/5.74 inference(transitivity,[status(thm)],[413, 411])).
% 8.58/5.74 tff(415,plain,
% 8.58/5.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.58/5.74 inference(quant_inst,[status(thm)],[])).
% 8.58/5.74 tff(416,plain,
% 8.58/5.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1656) | (~c0_1(a1656))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[415, 414])).
% 8.58/5.74 tff(417,plain,
% 8.58/5.74 ((~c3_1(a1677)) | c1_1(a1656)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[416, 221, 234, 78, 80, 233, 124, 118, 79, 410])).
% 8.58/5.74 tff(418,plain,
% 8.58/5.74 (c1_1(a1656)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[417, 366])).
% 8.58/5.74 tff(419,plain,
% 8.58/5.74 (^[V: $i, U: $i] : refl((hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 8.58/5.74 inference(bind,[status(th)],[])).
% 8.58/5.74 tff(420,plain,
% 8.58/5.74 (![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(quant_intro,[status(thm)],[419])).
% 8.58/5.74 tff(421,plain,
% 8.58/5.74 (![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(422,plain,
% 8.58/5.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp75) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp75))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp75) <=> (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp75) <=> (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 8.58/5.74 inference(bind,[status(th)],[])).
% 8.58/5.74 tff(423,plain,
% 8.58/5.74 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp75) <=> ![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(quant_intro,[status(thm)],[422])).
% 8.58/5.74 tff(424,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp75)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause348')).
% 8.58/5.74 tff(425,plain,
% 8.58/5.74 (![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[424, 423])).
% 8.58/5.74 tff(426,plain,
% 8.58/5.74 (![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[425, 421])).
% 8.58/5.74 tff(427,plain,(
% 8.58/5.74 ![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(skolemize,[status(sab)],[426])).
% 8.58/5.74 tff(428,plain,
% 8.58/5.74 (![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[427, 420])).
% 8.58/5.74 tff(429,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(430,plain,
% 8.58/5.74 ((hskp75 | (~ndr1_0) | c2_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656))) <=> (hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(431,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656))))),
% 8.58/5.74 inference(monotonicity,[status(thm)],[430])).
% 8.58/5.74 tff(432,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.58/5.74 inference(transitivity,[status(thm)],[431, 429])).
% 8.58/5.74 tff(433,plain,
% 8.58/5.74 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))),
% 8.58/5.74 inference(quant_inst,[status(thm)],[])).
% 8.58/5.74 tff(434,plain,
% 8.58/5.74 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1656) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[433, 432])).
% 8.58/5.74 tff(435,plain,
% 8.58/5.74 (hskp75 | (~c3_1(a1677)) | (~c1_1(a1656))),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[434, 221, 232, 233, 118, 112, 428])).
% 8.58/5.74 tff(436,plain,
% 8.58/5.74 (hskp75),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[435, 418, 366])).
% 8.58/5.74 tff(437,plain,
% 8.58/5.74 (((~hskp75) | (~c2_1(a1724))) <=> ((~hskp75) | (~c2_1(a1724)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(438,plain,
% 8.58/5.74 (((~c2_1(a1724)) | (~hskp75)) <=> ((~hskp75) | (~c2_1(a1724)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(439,axiom,((~c2_1(a1724)) | (~hskp75)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 8.58/5.74 tff(440,plain,
% 8.58/5.74 ((~hskp75) | (~c2_1(a1724))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[439, 438])).
% 8.58/5.74 tff(441,plain,
% 8.58/5.74 ((~hskp75) | (~c2_1(a1724))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[440, 437])).
% 8.58/5.74 tff(442,plain,
% 8.58/5.74 (~c2_1(a1724)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[441, 436])).
% 8.58/5.74 tff(443,plain,
% 8.58/5.74 (((~hskp60) | c2_1(a1673)) <=> ((~hskp60) | c2_1(a1673))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(444,axiom,((~hskp60) | c2_1(a1673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 8.58/5.74 tff(445,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[444, 443])).
% 8.58/5.74 tff(446,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[445, 443])).
% 8.58/5.74 tff(447,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[446, 443])).
% 8.58/5.74 tff(448,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[447, 443])).
% 8.58/5.74 tff(449,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[448, 443])).
% 8.58/5.74 tff(450,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[449, 443])).
% 8.58/5.74 tff(451,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[450, 443])).
% 8.58/5.74 tff(452,plain,
% 8.58/5.74 ((~hskp60) | c2_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[451, 443])).
% 8.58/5.74 tff(453,plain,
% 8.58/5.74 (c2_1(a1673)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[452, 394])).
% 8.58/5.74 tff(454,plain,
% 8.58/5.74 (((~hskp60) | c3_1(a1673)) <=> ((~hskp60) | c3_1(a1673))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(455,axiom,((~hskp60) | c3_1(a1673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 8.58/5.74 tff(456,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[455, 454])).
% 8.58/5.74 tff(457,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[456, 454])).
% 8.58/5.74 tff(458,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[457, 454])).
% 8.58/5.74 tff(459,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[458, 454])).
% 8.58/5.74 tff(460,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[459, 454])).
% 8.58/5.74 tff(461,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[460, 454])).
% 8.58/5.74 tff(462,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[461, 454])).
% 8.58/5.74 tff(463,plain,
% 8.58/5.74 ((~hskp60) | c3_1(a1673)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[462, 454])).
% 8.58/5.74 tff(464,plain,
% 8.58/5.74 (c3_1(a1673)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[463, 394])).
% 8.58/5.74 tff(465,plain,
% 8.58/5.74 (((~hskp75) | c3_1(a1724)) <=> ((~hskp75) | c3_1(a1724))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(466,axiom,((~hskp75) | c3_1(a1724)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 8.58/5.74 tff(467,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[466, 465])).
% 8.58/5.74 tff(468,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[467, 465])).
% 8.58/5.74 tff(469,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[468, 465])).
% 8.58/5.74 tff(470,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[469, 465])).
% 8.58/5.74 tff(471,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[470, 465])).
% 8.58/5.74 tff(472,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[471, 465])).
% 8.58/5.74 tff(473,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[472, 465])).
% 8.58/5.74 tff(474,plain,
% 8.58/5.74 ((~hskp75) | c3_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[473, 465])).
% 8.58/5.74 tff(475,plain,
% 8.58/5.74 (c3_1(a1724)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[474, 436])).
% 8.58/5.74 tff(476,plain,
% 8.58/5.74 (((~hskp75) | c0_1(a1724)) <=> ((~hskp75) | c0_1(a1724))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(477,axiom,((~hskp75) | c0_1(a1724)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 8.58/5.74 tff(478,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[477, 476])).
% 8.58/5.74 tff(479,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[478, 476])).
% 8.58/5.74 tff(480,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[479, 476])).
% 8.58/5.74 tff(481,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[480, 476])).
% 8.58/5.74 tff(482,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[481, 476])).
% 8.58/5.74 tff(483,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[482, 476])).
% 8.58/5.74 tff(484,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[483, 476])).
% 8.58/5.74 tff(485,plain,
% 8.58/5.74 ((~hskp75) | c0_1(a1724)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[484, 476])).
% 8.58/5.74 tff(486,plain,
% 8.58/5.74 (c0_1(a1724)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[485, 436])).
% 8.58/5.74 tff(487,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(488,plain,
% 8.58/5.74 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(489,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.58/5.74 inference(monotonicity,[status(thm)],[488])).
% 8.58/5.74 tff(490,plain,
% 8.58/5.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.58/5.74 inference(transitivity,[status(thm)],[489, 487])).
% 8.58/5.74 tff(491,plain,
% 8.58/5.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.58/5.74 inference(quant_inst,[status(thm)],[])).
% 8.58/5.74 tff(492,plain,
% 8.58/5.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[491, 490])).
% 8.58/5.74 tff(493,plain,
% 8.58/5.74 ($false),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[492, 221, 486, 475, 464, 453, 442, 400, 124, 118, 376, 366])).
% 8.58/5.74 tff(494,plain,((~hskp16) | (~c2_1(a1656)) | c3_1(a1656) | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~c0_1(a1656)) | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 8.58/5.74 tff(495,plain,
% 8.58/5.74 (~hskp16),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[494, 179, 168, 365, 363, 364, 162, 230, 229, 231])).
% 8.58/5.74 tff(496,plain,
% 8.58/5.74 (hskp17),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[334, 495, 230, 229, 231])).
% 8.58/5.74 tff(497,plain,
% 8.58/5.74 (c1_1(a1655)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[269, 496, 162, 168, 138, 230, 229, 179])).
% 8.58/5.74 tff(498,plain,
% 8.58/5.74 (hskp13 | (~c1_1(a1655))),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[296, 221, 230, 229, 231, 290])).
% 8.58/5.74 tff(499,plain,
% 8.58/5.74 (hskp13),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[498, 497])).
% 8.58/5.74 tff(500,plain,
% 8.58/5.74 (~c1_1(a1667)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[303, 499])).
% 8.58/5.74 tff(501,plain,
% 8.58/5.74 (~c1_1(a1678)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[241, 496])).
% 8.58/5.74 tff(502,plain,
% 8.58/5.74 (~c0_1(a1678)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[247, 496])).
% 8.58/5.74 tff(503,plain,
% 8.58/5.74 (c3_1(a1667)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[314, 499])).
% 8.58/5.74 tff(504,plain,
% 8.58/5.74 (c0_1(a1667)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[325, 499])).
% 8.58/5.74 tff(505,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(506,plain,
% 8.58/5.74 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))) <=> (hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(507,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678))))),
% 8.58/5.74 inference(monotonicity,[status(thm)],[506])).
% 8.58/5.74 tff(508,plain,
% 8.58/5.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)))),
% 8.58/5.74 inference(transitivity,[status(thm)],[507, 505])).
% 8.58/5.74 tff(509,plain,
% 8.58/5.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))),
% 8.58/5.74 inference(quant_inst,[status(thm)],[])).
% 8.58/5.74 tff(510,plain,
% 8.58/5.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[509, 508])).
% 8.58/5.74 tff(511,plain,
% 8.58/5.74 (~c3_1(a1678)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[510, 221, 138, 504, 503, 502, 501, 500, 137])).
% 8.58/5.74 tff(512,plain,
% 8.58/5.74 (~c2_1(a1678)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[260, 496])).
% 8.58/5.74 tff(513,plain,
% 8.58/5.74 ($false),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[267, 221, 179, 162, 168, 502, 501, 512, 30, 511])).
% 8.58/5.74 tff(514,plain,(hskp52 | hskp29 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.74 tff(515,plain,
% 8.58/5.74 (hskp52),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[514, 365, 138, 363, 364])).
% 8.58/5.74 tff(516,plain,
% 8.58/5.74 (((~hskp52) | c0_1(a1654)) <=> ((~hskp52) | c0_1(a1654))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(517,axiom,((~hskp52) | c0_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 8.58/5.74 tff(518,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[517, 516])).
% 8.58/5.74 tff(519,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[518, 516])).
% 8.58/5.74 tff(520,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[519, 516])).
% 8.58/5.74 tff(521,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[520, 516])).
% 8.58/5.74 tff(522,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[521, 516])).
% 8.58/5.74 tff(523,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[522, 516])).
% 8.58/5.74 tff(524,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[523, 516])).
% 8.58/5.74 tff(525,plain,
% 8.58/5.74 ((~hskp52) | c0_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[524, 516])).
% 8.58/5.74 tff(526,plain,
% 8.58/5.74 (c0_1(a1654)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[525, 515])).
% 8.58/5.74 tff(527,plain,
% 8.58/5.74 (((~hskp52) | c3_1(a1654)) <=> ((~hskp52) | c3_1(a1654))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(528,axiom,((~hskp52) | c3_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 8.58/5.74 tff(529,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[528, 527])).
% 8.58/5.74 tff(530,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[529, 527])).
% 8.58/5.74 tff(531,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[530, 527])).
% 8.58/5.74 tff(532,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[531, 527])).
% 8.58/5.74 tff(533,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[532, 527])).
% 8.58/5.74 tff(534,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[533, 527])).
% 8.58/5.74 tff(535,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[534, 527])).
% 8.58/5.74 tff(536,plain,
% 8.58/5.74 ((~hskp52) | c3_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[535, 527])).
% 8.58/5.74 tff(537,plain,
% 8.58/5.74 (c3_1(a1654)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[536, 515])).
% 8.58/5.74 tff(538,plain,
% 8.58/5.74 (((~hskp52) | c2_1(a1654)) <=> ((~hskp52) | c2_1(a1654))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(539,axiom,((~hskp52) | c2_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 8.58/5.74 tff(540,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[539, 538])).
% 8.58/5.74 tff(541,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[540, 538])).
% 8.58/5.74 tff(542,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[541, 538])).
% 8.58/5.74 tff(543,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[542, 538])).
% 8.58/5.74 tff(544,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[543, 538])).
% 8.58/5.74 tff(545,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[544, 538])).
% 8.58/5.74 tff(546,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[545, 538])).
% 8.58/5.74 tff(547,plain,
% 8.58/5.74 ((~hskp52) | c2_1(a1654)),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[546, 538])).
% 8.58/5.74 tff(548,plain,
% 8.58/5.74 (c2_1(a1654)),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[547, 515])).
% 8.58/5.74 tff(549,plain,
% 8.58/5.74 (((~hskp72) | (~c2_1(a1715))) <=> ((~hskp72) | (~c2_1(a1715)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(550,plain,
% 8.58/5.74 (((~c2_1(a1715)) | (~hskp72)) <=> ((~hskp72) | (~c2_1(a1715)))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(551,axiom,((~c2_1(a1715)) | (~hskp72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 8.58/5.74 tff(552,plain,
% 8.58/5.74 ((~hskp72) | (~c2_1(a1715))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[551, 550])).
% 8.58/5.74 tff(553,plain,
% 8.58/5.74 ((~hskp72) | (~c2_1(a1715))),
% 8.58/5.74 inference(modus_ponens,[status(thm)],[552, 549])).
% 8.58/5.74 tff(554,plain,
% 8.58/5.74 (~hskp72),
% 8.58/5.74 inference(unit_resolution,[status(thm)],[553, 364])).
% 8.58/5.74 tff(555,assumption,(~c3_1(a1678)), introduced(assumption)).
% 8.58/5.74 tff(556,plain,
% 8.58/5.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 8.58/5.74 inference(bind,[status(th)],[])).
% 8.58/5.74 tff(557,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.74 inference(quant_intro,[status(thm)],[556])).
% 8.58/5.74 tff(558,plain,
% 8.58/5.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.74 inference(rewrite,[status(thm)],[])).
% 8.58/5.74 tff(559,plain,
% 8.58/5.74 (^[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))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 8.58/5.75 inference(bind,[status(th)],[])).
% 8.58/5.75 tff(560,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.75 inference(quant_intro,[status(thm)],[559])).
% 8.58/5.75 tff(561,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c2_1(W)) | c3_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause361')).
% 8.58/5.75 tff(562,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[561, 560])).
% 8.58/5.75 tff(563,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[562, 558])).
% 8.58/5.75 tff(564,plain,(
% 8.58/5.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.75 inference(skolemize,[status(sab)],[563])).
% 8.58/5.75 tff(565,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[564, 557])).
% 8.58/5.75 tff(566,assumption,(~c2_1(a1678)), introduced(assumption)).
% 8.58/5.75 tff(567,assumption,(~c0_1(a1678)), introduced(assumption)).
% 8.58/5.75 tff(568,plain,
% 8.58/5.75 (^[U: $i] : refl((hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) <=> (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)))),
% 8.58/5.75 inference(bind,[status(th)],[])).
% 8.58/5.75 tff(569,plain,
% 8.58/5.75 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) <=> ![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(quant_intro,[status(thm)],[568])).
% 8.58/5.75 tff(570,plain,
% 8.58/5.75 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) <=> ![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(571,plain,
% 8.58/5.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c3_1(U)) | c0_1(U)))), rewrite((((~ndr1_0) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U)))), (((((~ndr1_0) | c3_1(U)) | c0_1(U)) | 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) | c0_1(U) | c3_1(U) | c2_1(U))), (((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)))), ((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) | hskp37))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) | hskp37) <=> (hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))), ((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) <=> (hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)))), (((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) | hskp72) <=> ((hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) | hskp72))), rewrite(((hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U)) | hskp72) <=> (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))), (((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) | hskp72) <=> (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))))),
% 8.58/5.75 inference(bind,[status(th)],[])).
% 8.58/5.75 tff(572,plain,
% 8.58/5.75 (![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) | hskp72) <=> ![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(quant_intro,[status(thm)],[571])).
% 8.58/5.75 tff(573,axiom,(![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) | hskp72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause314')).
% 8.58/5.75 tff(574,plain,
% 8.58/5.75 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[573, 572])).
% 8.58/5.75 tff(575,plain,
% 8.58/5.75 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[574, 570])).
% 8.58/5.75 tff(576,plain,(
% 8.58/5.75 ![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(skolemize,[status(sab)],[575])).
% 8.58/5.75 tff(577,plain,
% 8.58/5.75 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[576, 569])).
% 8.58/5.75 tff(578,assumption,(~hskp72), introduced(assumption)).
% 8.58/5.75 tff(579,plain,
% 8.58/5.75 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(580,plain,
% 8.58/5.75 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1678) | c3_1(a1678) | c2_1(a1678)) <=> (hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(581,plain,
% 8.58/5.75 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1678) | c3_1(a1678) | c2_1(a1678))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678)))),
% 8.58/5.75 inference(monotonicity,[status(thm)],[580])).
% 8.58/5.75 tff(582,plain,
% 8.58/5.75 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1678) | c3_1(a1678) | c2_1(a1678))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678))),
% 8.58/5.75 inference(transitivity,[status(thm)],[581, 579])).
% 8.58/5.75 tff(583,plain,
% 8.58/5.75 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1678) | c3_1(a1678) | c2_1(a1678))),
% 8.58/5.75 inference(quant_inst,[status(thm)],[])).
% 8.58/5.75 tff(584,plain,
% 8.58/5.75 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[583, 582])).
% 8.58/5.75 tff(585,plain,
% 8.58/5.75 (hskp37 | c3_1(a1678)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[584, 221, 578, 567, 566, 577])).
% 8.58/5.75 tff(586,plain,
% 8.58/5.75 (hskp37),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[585, 555])).
% 8.58/5.75 tff(587,plain,
% 8.58/5.75 (((~hskp37) | (~c1_1(a1714))) <=> ((~hskp37) | (~c1_1(a1714)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(588,plain,
% 8.58/5.75 (((~c1_1(a1714)) | (~hskp37)) <=> ((~hskp37) | (~c1_1(a1714)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(589,axiom,((~c1_1(a1714)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 8.58/5.75 tff(590,plain,
% 8.58/5.75 ((~hskp37) | (~c1_1(a1714))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[589, 588])).
% 8.58/5.75 tff(591,plain,
% 8.58/5.75 ((~hskp37) | (~c1_1(a1714))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[590, 587])).
% 8.58/5.75 tff(592,plain,
% 8.58/5.75 (~c1_1(a1714)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[591, 586])).
% 8.58/5.75 tff(593,plain,
% 8.58/5.75 (((~hskp37) | c0_1(a1714)) <=> ((~hskp37) | c0_1(a1714))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(594,axiom,((~hskp37) | c0_1(a1714)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 8.58/5.75 tff(595,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[594, 593])).
% 8.58/5.75 tff(596,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[595, 593])).
% 8.58/5.75 tff(597,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[596, 593])).
% 8.58/5.75 tff(598,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[597, 593])).
% 8.58/5.75 tff(599,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[598, 593])).
% 8.58/5.75 tff(600,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[599, 593])).
% 8.58/5.75 tff(601,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[600, 593])).
% 8.58/5.75 tff(602,plain,
% 8.58/5.75 ((~hskp37) | c0_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[601, 593])).
% 8.58/5.75 tff(603,plain,
% 8.58/5.75 (c0_1(a1714)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[602, 586])).
% 8.58/5.75 tff(604,plain,
% 8.58/5.75 (((~hskp37) | c2_1(a1714)) <=> ((~hskp37) | c2_1(a1714))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(605,axiom,((~hskp37) | c2_1(a1714)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 8.58/5.75 tff(606,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[605, 604])).
% 8.58/5.75 tff(607,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[606, 604])).
% 8.58/5.75 tff(608,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[607, 604])).
% 8.58/5.75 tff(609,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[608, 604])).
% 8.58/5.75 tff(610,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[609, 604])).
% 8.58/5.75 tff(611,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[610, 604])).
% 8.58/5.75 tff(612,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[611, 604])).
% 8.58/5.75 tff(613,plain,
% 8.58/5.75 ((~hskp37) | c2_1(a1714)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[612, 604])).
% 8.58/5.75 tff(614,plain,
% 8.58/5.75 (c2_1(a1714)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[613, 586])).
% 8.58/5.75 tff(615,assumption,(c3_1(a1654)), introduced(assumption)).
% 8.58/5.75 tff(616,assumption,(c2_1(a1654)), introduced(assumption)).
% 8.58/5.75 tff(617,assumption,(c0_1(a1654)), introduced(assumption)).
% 8.58/5.75 tff(618,plain,
% 8.58/5.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(619,plain,
% 8.58/5.75 (((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1678) | c2_1(a1678) | c0_1(a1678)) <=> (c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(620,plain,
% 8.58/5.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1678) | c2_1(a1678) | c0_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.58/5.75 inference(monotonicity,[status(thm)],[619])).
% 8.58/5.75 tff(621,plain,
% 8.58/5.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1678) | c2_1(a1678) | c0_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(transitivity,[status(thm)],[620, 618])).
% 8.58/5.75 tff(622,plain,
% 8.58/5.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1678) | c2_1(a1678) | c0_1(a1678))),
% 8.58/5.75 inference(quant_inst,[status(thm)],[])).
% 8.58/5.75 tff(623,plain,
% 8.58/5.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[622, 621])).
% 8.58/5.75 tff(624,plain,
% 8.58/5.75 ($false),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[623, 221, 617, 616, 615, 614, 603, 592, 567, 566, 565, 555])).
% 8.58/5.75 tff(625,plain,(c3_1(a1678) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c0_1(a1678) | c2_1(a1678) | hskp72), inference(lemma,lemma(discharge,[]))).
% 8.58/5.75 tff(626,plain,
% 8.58/5.75 (c3_1(a1678)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[625, 248, 554, 548, 537, 261, 526])).
% 8.58/5.75 tff(627,assumption,(~c1_1(a1654)), introduced(assumption)).
% 8.58/5.75 tff(628,assumption,(~c1_1(a1678)), introduced(assumption)).
% 8.58/5.75 tff(629,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(630,plain,
% 8.58/5.75 ((hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))) <=> (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(631,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.58/5.75 inference(monotonicity,[status(thm)],[630])).
% 8.58/5.75 tff(632,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.75 inference(transitivity,[status(thm)],[631, 629])).
% 8.58/5.75 tff(633,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))),
% 8.58/5.75 inference(quant_inst,[status(thm)],[])).
% 8.58/5.75 tff(634,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[633, 632])).
% 8.58/5.75 tff(635,plain,
% 8.58/5.75 ($false),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[634, 221, 138, 617, 615, 567, 628, 137, 627, 92])).
% 8.58/5.75 tff(636,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.75 tff(637,plain,
% 8.58/5.75 (c1_1(a1654)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[636, 248, 526, 537, 138, 242, 626])).
% 8.58/5.75 tff(638,plain,
% 8.58/5.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 8.58/5.75 inference(bind,[status(th)],[])).
% 8.58/5.75 tff(639,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_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) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(quant_intro,[status(thm)],[638])).
% 8.58/5.75 tff(640,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_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) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(641,plain,
% 8.58/5.75 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 8.58/5.75 inference(bind,[status(th)],[])).
% 8.58/5.75 tff(642,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(quant_intro,[status(thm)],[641])).
% 8.58/5.75 tff(643,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause364')).
% 8.58/5.75 tff(644,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[643, 642])).
% 8.58/5.75 tff(645,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[644, 640])).
% 8.58/5.75 tff(646,plain,(
% 8.58/5.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(skolemize,[status(sab)],[645])).
% 8.58/5.75 tff(647,plain,
% 8.58/5.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[646, 639])).
% 8.58/5.75 tff(648,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(649,plain,
% 8.58/5.75 ((hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))) <=> (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(650,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678))))),
% 8.58/5.75 inference(monotonicity,[status(thm)],[649])).
% 8.58/5.75 tff(651,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)))),
% 8.58/5.75 inference(transitivity,[status(thm)],[650, 648])).
% 8.58/5.75 tff(652,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))),
% 8.58/5.75 inference(quant_inst,[status(thm)],[])).
% 8.58/5.75 tff(653,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[652, 651])).
% 8.58/5.75 tff(654,plain,
% 8.58/5.75 (hskp60),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[653, 221, 365, 363, 364, 248, 242, 386, 626])).
% 8.58/5.75 tff(655,plain,
% 8.58/5.75 (~c1_1(a1673)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[399, 654])).
% 8.58/5.75 tff(656,plain,
% 8.58/5.75 (c2_1(a1673)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[452, 654])).
% 8.58/5.75 tff(657,plain,
% 8.58/5.75 (c3_1(a1673)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[463, 654])).
% 8.58/5.75 tff(658,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(659,plain,
% 8.58/5.75 ((hskp26 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(660,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.58/5.75 inference(monotonicity,[status(thm)],[659])).
% 8.58/5.75 tff(661,plain,
% 8.58/5.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.75 inference(transitivity,[status(thm)],[660, 658])).
% 8.58/5.75 tff(662,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.58/5.75 inference(quant_inst,[status(thm)],[])).
% 8.58/5.75 tff(663,plain,
% 8.58/5.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[662, 661])).
% 8.58/5.75 tff(664,plain,
% 8.58/5.75 (hskp26),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[663, 221, 657, 656, 526, 548, 537, 655, 20])).
% 8.58/5.75 tff(665,plain,
% 8.58/5.75 (((~hskp26) | (~c2_1(a1691))) <=> ((~hskp26) | (~c2_1(a1691)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(666,plain,
% 8.58/5.75 (((~c2_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1691)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(667,axiom,((~c2_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause256')).
% 8.58/5.75 tff(668,plain,
% 8.58/5.75 ((~hskp26) | (~c2_1(a1691))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[667, 666])).
% 8.58/5.75 tff(669,plain,
% 8.58/5.75 ((~hskp26) | (~c2_1(a1691))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[668, 665])).
% 8.58/5.75 tff(670,plain,
% 8.58/5.75 (~c2_1(a1691)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[669, 664])).
% 8.58/5.75 tff(671,plain,
% 8.58/5.75 (((~hskp26) | (~c1_1(a1691))) <=> ((~hskp26) | (~c1_1(a1691)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(672,plain,
% 8.58/5.75 (((~c1_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a1691)))),
% 8.58/5.75 inference(rewrite,[status(thm)],[])).
% 8.58/5.75 tff(673,axiom,((~c1_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause255')).
% 8.58/5.75 tff(674,plain,
% 8.58/5.75 ((~hskp26) | (~c1_1(a1691))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[673, 672])).
% 8.58/5.75 tff(675,plain,
% 8.58/5.75 ((~hskp26) | (~c1_1(a1691))),
% 8.58/5.75 inference(modus_ponens,[status(thm)],[674, 671])).
% 8.58/5.75 tff(676,plain,
% 8.58/5.75 (~c1_1(a1691)),
% 8.58/5.75 inference(unit_resolution,[status(thm)],[675, 664])).
% 8.58/5.75 tff(677,plain,
% 8.58/5.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(678,plain,
% 8.58/5.76 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1678) | c2_1(a1678) | (~c3_1(a1678))) <=> (c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(679,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1678) | c2_1(a1678) | (~c3_1(a1678)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[678])).
% 8.58/5.76 tff(680,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1678) | c2_1(a1678) | (~c3_1(a1678)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(transitivity,[status(thm)],[679, 677])).
% 8.58/5.76 tff(681,plain,
% 8.58/5.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1678) | c2_1(a1678) | (~c3_1(a1678)))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(682,plain,
% 8.58/5.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[681, 680])).
% 8.58/5.76 tff(683,plain,
% 8.58/5.76 ((~c0_1(a1691)) | (~c1_1(a1654))),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[682, 221, 526, 537, 676, 670, 242, 261, 647, 626])).
% 8.58/5.76 tff(684,plain,
% 8.58/5.76 (~c0_1(a1691)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[683, 637])).
% 8.58/5.76 tff(685,plain,
% 8.58/5.76 (((~hskp26) | (~c3_1(a1691))) <=> ((~hskp26) | (~c3_1(a1691)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(686,plain,
% 8.58/5.76 (((~c3_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a1691)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(687,axiom,((~c3_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause254')).
% 8.58/5.76 tff(688,plain,
% 8.58/5.76 ((~hskp26) | (~c3_1(a1691))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[687, 686])).
% 8.58/5.76 tff(689,plain,
% 8.58/5.76 ((~hskp26) | (~c3_1(a1691))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[688, 685])).
% 8.58/5.76 tff(690,plain,
% 8.58/5.76 (~c3_1(a1691)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[689, 664])).
% 8.58/5.76 tff(691,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(692,plain,
% 8.58/5.76 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1691) | c3_1(a1691) | c2_1(a1691)) <=> (hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(693,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1691) | c3_1(a1691) | c2_1(a1691))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691)))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[692])).
% 8.58/5.76 tff(694,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1691) | c3_1(a1691) | c2_1(a1691))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691))),
% 8.58/5.76 inference(transitivity,[status(thm)],[693, 691])).
% 8.58/5.76 tff(695,plain,
% 8.58/5.76 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1691) | c3_1(a1691) | c2_1(a1691))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(696,plain,
% 8.58/5.76 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[695, 694])).
% 8.58/5.76 tff(697,plain,
% 8.58/5.76 (hskp37 | c0_1(a1691)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[696, 221, 554, 690, 670, 577])).
% 8.58/5.76 tff(698,plain,
% 8.58/5.76 (hskp37),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[697, 684])).
% 8.58/5.76 tff(699,plain,
% 8.58/5.76 (~c1_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[591, 698])).
% 8.58/5.76 tff(700,plain,
% 8.58/5.76 (c0_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[602, 698])).
% 8.58/5.76 tff(701,plain,
% 8.58/5.76 (c2_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[613, 698])).
% 8.58/5.76 tff(702,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(703,plain,
% 8.58/5.76 (((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691)) <=> (c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(704,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[703])).
% 8.58/5.76 tff(705,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.76 inference(transitivity,[status(thm)],[704, 702])).
% 8.58/5.76 tff(706,plain,
% 8.58/5.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(707,plain,
% 8.58/5.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[706, 705])).
% 8.58/5.76 tff(708,plain,
% 8.58/5.76 ($false),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[707, 221, 526, 548, 537, 701, 700, 699, 690, 670, 565, 684])).
% 8.58/5.76 tff(709,plain,((~hskp17) | hskp29 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.76 tff(710,plain,
% 8.58/5.76 (~hskp17),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[709, 365, 138, 363, 364])).
% 8.58/5.76 tff(711,plain,
% 8.58/5.76 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(712,plain,
% 8.58/5.76 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654))) <=> (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(713,plain,
% 8.58/5.76 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[712])).
% 8.58/5.76 tff(714,plain,
% 8.58/5.76 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.76 inference(transitivity,[status(thm)],[713, 711])).
% 8.58/5.76 tff(715,plain,
% 8.58/5.76 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(716,plain,
% 8.58/5.76 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[715, 714])).
% 8.58/5.76 tff(717,plain,
% 8.58/5.76 (hskp17 | hskp16 | c1_1(a1654)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[716, 221, 617, 615, 10])).
% 8.58/5.76 tff(718,plain,
% 8.58/5.76 (c1_1(a1654)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[717, 271, 272])).
% 8.58/5.76 tff(719,plain,
% 8.58/5.76 (^[V: $i, U: $i] : refl((hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 8.58/5.76 inference(bind,[status(th)],[])).
% 8.58/5.76 tff(720,plain,
% 8.58/5.76 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(quant_intro,[status(thm)],[719])).
% 8.58/5.76 tff(721,plain,
% 8.58/5.76 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(722,plain,
% 8.58/5.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp40) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp40))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp40) <=> (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp40) <=> (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 8.58/5.76 inference(bind,[status(th)],[])).
% 8.58/5.76 tff(723,plain,
% 8.58/5.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp40) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(quant_intro,[status(thm)],[722])).
% 8.58/5.76 tff(724,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause354')).
% 8.58/5.76 tff(725,plain,
% 8.58/5.76 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[724, 723])).
% 8.58/5.76 tff(726,plain,
% 8.58/5.76 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[725, 721])).
% 8.58/5.76 tff(727,plain,(
% 8.58/5.76 ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(skolemize,[status(sab)],[726])).
% 8.58/5.76 tff(728,plain,
% 8.58/5.76 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[727, 720])).
% 8.58/5.76 tff(729,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(730,plain,
% 8.58/5.76 ((hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715))) <=> (hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(731,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[730])).
% 8.58/5.76 tff(732,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(transitivity,[status(thm)],[731, 729])).
% 8.58/5.76 tff(733,plain,
% 8.58/5.76 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1715) | c1_1(a1715) | (~c2_1(a1715)))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(734,plain,
% 8.58/5.76 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[733, 732])).
% 8.58/5.76 tff(735,plain,
% 8.58/5.76 (hskp40 | (~c1_1(a1654))),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[734, 221, 365, 363, 617, 615, 364, 728])).
% 8.58/5.76 tff(736,plain,
% 8.58/5.76 (hskp40),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[735, 718])).
% 8.58/5.76 tff(737,plain,
% 8.58/5.76 (((~hskp40) | (~c2_1(a1725))) <=> ((~hskp40) | (~c2_1(a1725)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(738,plain,
% 8.58/5.76 (((~c2_1(a1725)) | (~hskp40)) <=> ((~hskp40) | (~c2_1(a1725)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(739,axiom,((~c2_1(a1725)) | (~hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 8.58/5.76 tff(740,plain,
% 8.58/5.76 ((~hskp40) | (~c2_1(a1725))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[739, 738])).
% 8.58/5.76 tff(741,plain,
% 8.58/5.76 ((~hskp40) | (~c2_1(a1725))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[740, 737])).
% 8.58/5.76 tff(742,plain,
% 8.58/5.76 (~c2_1(a1725)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[741, 736])).
% 8.58/5.76 tff(743,plain,
% 8.58/5.76 (((~hskp40) | c3_1(a1725)) <=> ((~hskp40) | c3_1(a1725))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(744,axiom,((~hskp40) | c3_1(a1725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 8.58/5.76 tff(745,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[744, 743])).
% 8.58/5.76 tff(746,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[745, 743])).
% 8.58/5.76 tff(747,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[746, 743])).
% 8.58/5.76 tff(748,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[747, 743])).
% 8.58/5.76 tff(749,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[748, 743])).
% 8.58/5.76 tff(750,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[749, 743])).
% 8.58/5.76 tff(751,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[750, 743])).
% 8.58/5.76 tff(752,plain,
% 8.58/5.76 ((~hskp40) | c3_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[751, 743])).
% 8.58/5.76 tff(753,plain,
% 8.58/5.76 (c3_1(a1725)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[752, 736])).
% 8.58/5.76 tff(754,plain,
% 8.58/5.76 (((~hskp40) | c1_1(a1725)) <=> ((~hskp40) | c1_1(a1725))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(755,axiom,((~hskp40) | c1_1(a1725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 8.58/5.76 tff(756,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[755, 754])).
% 8.58/5.76 tff(757,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[756, 754])).
% 8.58/5.76 tff(758,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[757, 754])).
% 8.58/5.76 tff(759,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[758, 754])).
% 8.58/5.76 tff(760,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[759, 754])).
% 8.58/5.76 tff(761,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[760, 754])).
% 8.58/5.76 tff(762,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[761, 754])).
% 8.58/5.76 tff(763,plain,
% 8.58/5.76 ((~hskp40) | c1_1(a1725)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[762, 754])).
% 8.58/5.76 tff(764,plain,
% 8.58/5.76 (c1_1(a1725)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[763, 736])).
% 8.58/5.76 tff(765,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(766,plain,
% 8.58/5.76 ((hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725))) <=> (hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(767,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[766])).
% 8.58/5.76 tff(768,plain,
% 8.58/5.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.76 inference(transitivity,[status(thm)],[767, 765])).
% 8.58/5.76 tff(769,plain,
% 8.58/5.76 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(770,plain,
% 8.58/5.76 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[769, 768])).
% 8.58/5.76 tff(771,plain,
% 8.58/5.76 (hskp13),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[770, 221, 617, 615, 764, 753, 742, 290, 718])).
% 8.58/5.76 tff(772,plain,
% 8.58/5.76 (~c1_1(a1667)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[303, 771])).
% 8.58/5.76 tff(773,plain,
% 8.58/5.76 (c3_1(a1667)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[314, 771])).
% 8.58/5.76 tff(774,plain,
% 8.58/5.76 (c0_1(a1667)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[325, 771])).
% 8.58/5.76 tff(775,plain,
% 8.58/5.76 ($false),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[332, 221, 271, 272, 774, 773, 772, 10])).
% 8.58/5.76 tff(776,plain,(hskp17 | hskp16 | (~c0_1(a1654)) | (~c3_1(a1654)) | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.76 tff(777,plain,
% 8.58/5.76 (hskp16),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[776, 710, 526, 537, 365, 363, 364])).
% 8.58/5.76 tff(778,plain,
% 8.58/5.76 (~c2_1(a1677)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[117, 777])).
% 8.58/5.76 tff(779,plain,
% 8.58/5.76 (~c0_1(a1677)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[123, 777])).
% 8.58/5.76 tff(780,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(781,plain,
% 8.58/5.76 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1677) | c3_1(a1677) | c2_1(a1677)) <=> (hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(782,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1677) | c3_1(a1677) | c2_1(a1677))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677)))),
% 8.58/5.76 inference(monotonicity,[status(thm)],[781])).
% 8.58/5.76 tff(783,plain,
% 8.58/5.76 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1677) | c3_1(a1677) | c2_1(a1677))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677))),
% 8.58/5.76 inference(transitivity,[status(thm)],[782, 780])).
% 8.58/5.76 tff(784,plain,
% 8.58/5.76 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1677) | c3_1(a1677) | c2_1(a1677))),
% 8.58/5.76 inference(quant_inst,[status(thm)],[])).
% 8.58/5.76 tff(785,plain,
% 8.58/5.76 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677)),
% 8.58/5.76 inference(modus_ponens,[status(thm)],[784, 783])).
% 8.58/5.76 tff(786,plain,
% 8.58/5.76 (hskp37 | c3_1(a1677)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[785, 221, 578, 127, 340, 577])).
% 8.58/5.76 tff(787,plain,
% 8.58/5.76 (hskp37),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[786, 339])).
% 8.58/5.76 tff(788,plain,
% 8.58/5.76 (~c1_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[591, 787])).
% 8.58/5.76 tff(789,plain,
% 8.58/5.76 (c0_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[602, 787])).
% 8.58/5.76 tff(790,plain,
% 8.58/5.76 (c2_1(a1714)),
% 8.58/5.76 inference(unit_resolution,[status(thm)],[613, 787])).
% 8.58/5.76 tff(791,plain,
% 8.58/5.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.76 inference(rewrite,[status(thm)],[])).
% 8.58/5.76 tff(792,plain,
% 8.58/5.76 (((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1677) | c2_1(a1677) | c0_1(a1677)) <=> (c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(793,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1677) | c2_1(a1677) | c0_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[792])).
% 8.58/5.77 tff(794,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1677) | c2_1(a1677) | c0_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.77 inference(transitivity,[status(thm)],[793, 791])).
% 8.58/5.77 tff(795,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1677) | c2_1(a1677) | c0_1(a1677))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(796,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[795, 794])).
% 8.58/5.77 tff(797,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[796, 221, 617, 616, 615, 790, 789, 788, 127, 340, 565, 339])).
% 8.58/5.77 tff(798,plain,(c3_1(a1677) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c0_1(a1677) | c2_1(a1677) | hskp72), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(799,plain,
% 8.58/5.77 (c3_1(a1677)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[798, 779, 554, 537, 548, 778, 526])).
% 8.58/5.77 tff(800,plain,
% 8.58/5.77 (~c1_1(a1677)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[111, 777])).
% 8.58/5.77 tff(801,plain,
% 8.58/5.77 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(802,plain,
% 8.58/5.77 ((hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))) <=> (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(803,plain,
% 8.58/5.77 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[802])).
% 8.58/5.77 tff(804,plain,
% 8.58/5.77 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.58/5.77 inference(transitivity,[status(thm)],[803, 801])).
% 8.58/5.77 tff(805,plain,
% 8.58/5.77 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(806,plain,
% 8.58/5.77 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[805, 804])).
% 8.58/5.77 tff(807,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[806, 221, 138, 617, 615, 127, 126, 137, 627, 125])).
% 8.58/5.77 tff(808,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(809,plain,
% 8.58/5.77 (c1_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[808, 526, 138, 537, 779, 800, 799])).
% 8.58/5.77 tff(810,plain,
% 8.58/5.77 (hskp60),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[392, 221, 365, 363, 364, 779, 800, 386, 799])).
% 8.58/5.77 tff(811,plain,
% 8.58/5.77 (~c1_1(a1673)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[399, 810])).
% 8.58/5.77 tff(812,plain,
% 8.58/5.77 (c2_1(a1673)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[452, 810])).
% 8.58/5.77 tff(813,plain,
% 8.58/5.77 (c3_1(a1673)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[463, 810])).
% 8.58/5.77 tff(814,plain,
% 8.58/5.77 (hskp26),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[663, 221, 813, 812, 526, 548, 537, 811, 20])).
% 8.58/5.77 tff(815,plain,
% 8.58/5.77 (~c2_1(a1691)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[669, 814])).
% 8.58/5.77 tff(816,plain,
% 8.58/5.77 (~c1_1(a1691)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[675, 814])).
% 8.58/5.77 tff(817,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(818,plain,
% 8.58/5.77 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1677) | c2_1(a1677) | (~c3_1(a1677))) <=> (c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(819,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1677) | c2_1(a1677) | (~c3_1(a1677)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[818])).
% 8.58/5.77 tff(820,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1677) | c2_1(a1677) | (~c3_1(a1677)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.77 inference(transitivity,[status(thm)],[819, 817])).
% 8.58/5.77 tff(821,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1677) | c2_1(a1677) | (~c3_1(a1677)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(822,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[821, 820])).
% 8.58/5.77 tff(823,plain,
% 8.58/5.77 ((~c0_1(a1691)) | (~c1_1(a1654))),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[822, 221, 526, 537, 816, 815, 778, 800, 647, 799])).
% 8.58/5.77 tff(824,plain,
% 8.58/5.77 (~c0_1(a1691)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[823, 809])).
% 8.58/5.77 tff(825,plain,
% 8.58/5.77 (~c3_1(a1691)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[689, 814])).
% 8.58/5.77 tff(826,plain,
% 8.58/5.77 (hskp37 | c0_1(a1691)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[696, 221, 554, 825, 815, 577])).
% 8.58/5.77 tff(827,plain,
% 8.58/5.77 (hskp37),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[826, 824])).
% 8.58/5.77 tff(828,plain,
% 8.58/5.77 (~c1_1(a1714)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[591, 827])).
% 8.58/5.77 tff(829,plain,
% 8.58/5.77 (c0_1(a1714)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[602, 827])).
% 8.58/5.77 tff(830,plain,
% 8.58/5.77 (c2_1(a1714)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[613, 827])).
% 8.58/5.77 tff(831,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[707, 221, 526, 548, 537, 830, 829, 828, 825, 815, 565, 824])).
% 8.58/5.77 tff(832,plain,(c1_1(a1715) | hskp29 | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(833,plain,
% 8.58/5.77 (c1_1(a1715)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[832, 363, 138, 364])).
% 8.58/5.77 tff(834,assumption,(c1_1(a1715)), introduced(assumption)).
% 8.58/5.77 tff(835,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(836,plain,
% 8.58/5.77 (((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715))) <=> (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(837,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715))))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[836])).
% 8.58/5.77 tff(838,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(transitivity,[status(thm)],[837, 835])).
% 8.58/5.77 tff(839,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(840,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[839, 838])).
% 8.58/5.77 tff(841,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[840, 221, 834, 363, 78, 80, 364, 127, 126, 102, 235, 125])).
% 8.58/5.77 tff(842,plain,(c1_1(a1655) | (~c1_1(a1715)) | c3_1(a1715) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(843,plain,
% 8.58/5.77 (c1_1(a1655)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[842, 124, 363, 78, 80, 364, 834, 112, 366])).
% 8.58/5.77 tff(844,plain,
% 8.58/5.77 (hskp13),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[297, 843])).
% 8.58/5.77 tff(845,plain,
% 8.58/5.77 (~c1_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[303, 844])).
% 8.58/5.77 tff(846,plain,
% 8.58/5.77 (c3_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[314, 844])).
% 8.58/5.77 tff(847,plain,
% 8.58/5.77 (c0_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[325, 844])).
% 8.58/5.77 tff(848,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(849,plain,
% 8.58/5.77 (((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715))) <=> (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(850,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715))))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[849])).
% 8.58/5.77 tff(851,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(transitivity,[status(thm)],[850, 848])).
% 8.58/5.77 tff(852,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(853,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[852, 851])).
% 8.58/5.77 tff(854,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[853, 221, 834, 363, 847, 846, 364, 124, 112, 845, 102, 366])).
% 8.58/5.77 tff(855,plain,((~hskp16) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715)) | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1655) | (~c0_1(a1656)) | c3_1(a1656) | (~c2_1(a1656))), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(856,plain,
% 8.58/5.77 (~hskp16),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[855, 230, 363, 364, 833, 229, 231, 162, 168, 179])).
% 8.58/5.77 tff(857,plain,
% 8.58/5.77 (hskp17),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[334, 856, 230, 229, 231])).
% 8.58/5.77 tff(858,plain,
% 8.58/5.77 (c1_1(a1655)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[269, 857, 162, 168, 138, 230, 229, 179])).
% 8.58/5.77 tff(859,plain,
% 8.58/5.77 (hskp13),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[498, 858])).
% 8.58/5.77 tff(860,plain,
% 8.58/5.77 (~c1_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[303, 859])).
% 8.58/5.77 tff(861,plain,
% 8.58/5.77 (~c1_1(a1678)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[241, 857])).
% 8.58/5.77 tff(862,plain,
% 8.58/5.77 (~c0_1(a1678)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[247, 857])).
% 8.58/5.77 tff(863,plain,
% 8.58/5.77 (c3_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[314, 859])).
% 8.58/5.77 tff(864,plain,
% 8.58/5.77 (c0_1(a1667)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[325, 859])).
% 8.58/5.77 tff(865,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(866,plain,
% 8.58/5.77 (((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715))) <=> (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(867,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715))))),
% 8.58/5.77 inference(monotonicity,[status(thm)],[866])).
% 8.58/5.77 tff(868,plain,
% 8.58/5.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(transitivity,[status(thm)],[867, 865])).
% 8.58/5.77 tff(869,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1715) | (~c2_1(a1715)) | (~c1_1(a1715)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(870,plain,
% 8.58/5.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[869, 868])).
% 8.58/5.77 tff(871,plain,
% 8.58/5.77 (~c3_1(a1678)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[870, 221, 833, 363, 864, 863, 364, 862, 861, 860, 102])).
% 8.58/5.77 tff(872,plain,
% 8.58/5.77 (~c2_1(a1678)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[260, 857])).
% 8.58/5.77 tff(873,plain,
% 8.58/5.77 ($false),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[267, 221, 179, 162, 168, 862, 861, 872, 30, 871])).
% 8.58/5.77 tff(874,plain,(hskp52 | c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.58/5.77 tff(875,plain,
% 8.58/5.77 (hskp52),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[874, 363, 364, 138])).
% 8.58/5.77 tff(876,plain,
% 8.58/5.77 (c0_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[525, 875])).
% 8.58/5.77 tff(877,plain,
% 8.58/5.77 (c3_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[536, 875])).
% 8.58/5.77 tff(878,plain,
% 8.58/5.77 (c2_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[547, 875])).
% 8.58/5.77 tff(879,plain,
% 8.58/5.77 (c3_1(a1678)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[625, 261, 554, 878, 877, 248, 876])).
% 8.58/5.77 tff(880,plain,
% 8.58/5.77 (c1_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[636, 879, 876, 877, 138, 248, 242])).
% 8.58/5.77 tff(881,assumption,(hskp52), introduced(assumption)).
% 8.58/5.77 tff(882,assumption,(c1_1(a1654)), introduced(assumption)).
% 8.58/5.77 tff(883,assumption,(~hskp13), introduced(assumption)).
% 8.58/5.77 tff(884,plain,
% 8.58/5.77 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))),
% 8.58/5.77 inference(bind,[status(th)],[])).
% 8.58/5.77 tff(885,plain,
% 8.58/5.77 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(quant_intro,[status(thm)],[884])).
% 8.58/5.77 tff(886,plain,
% 8.58/5.77 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(887,plain,
% 8.58/5.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))))),
% 8.58/5.77 inference(bind,[status(th)],[])).
% 8.58/5.77 tff(888,plain,
% 8.58/5.77 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(quant_intro,[status(thm)],[887])).
% 8.58/5.77 tff(889,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause332')).
% 8.58/5.77 tff(890,plain,
% 8.58/5.77 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[889, 888])).
% 8.58/5.77 tff(891,plain,
% 8.58/5.77 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[890, 886])).
% 8.58/5.77 tff(892,plain,(
% 8.58/5.77 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(skolemize,[status(sab)],[891])).
% 8.58/5.77 tff(893,plain,
% 8.58/5.77 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[892, 885])).
% 8.58/5.77 tff(894,plain,
% 8.58/5.77 (c3_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[536, 881])).
% 8.58/5.77 tff(895,plain,
% 8.58/5.77 (c2_1(a1654)),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[547, 881])).
% 8.58/5.77 tff(896,plain,
% 8.58/5.77 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(897,plain,
% 8.58/5.77 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.58/5.77 inference(quant_inst,[status(thm)],[])).
% 8.58/5.77 tff(898,plain,
% 8.58/5.77 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[897, 896])).
% 8.58/5.77 tff(899,plain,
% 8.58/5.77 (hskp13 | hskp12 | (~c1_1(a1654))),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[898, 221, 895, 894, 893])).
% 8.58/5.77 tff(900,plain,
% 8.58/5.77 (hskp12),
% 8.58/5.77 inference(unit_resolution,[status(thm)],[899, 883, 882])).
% 8.58/5.77 tff(901,plain,
% 8.58/5.77 (((~hskp12) | (~c1_1(a1666))) <=> ((~hskp12) | (~c1_1(a1666)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(902,plain,
% 8.58/5.77 (((~c1_1(a1666)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a1666)))),
% 8.58/5.77 inference(rewrite,[status(thm)],[])).
% 8.58/5.77 tff(903,axiom,((~c1_1(a1666)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 8.58/5.77 tff(904,plain,
% 8.58/5.77 ((~hskp12) | (~c1_1(a1666))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[903, 902])).
% 8.58/5.77 tff(905,plain,
% 8.58/5.77 ((~hskp12) | (~c1_1(a1666))),
% 8.58/5.77 inference(modus_ponens,[status(thm)],[904, 901])).
% 8.58/5.78 tff(906,plain,
% 8.58/5.78 (~c1_1(a1666)),
% 8.58/5.78 inference(unit_resolution,[status(thm)],[905, 900])).
% 8.58/5.78 tff(907,plain,
% 8.58/5.78 (((~hskp12) | c3_1(a1666)) <=> ((~hskp12) | c3_1(a1666))),
% 8.58/5.78 inference(rewrite,[status(thm)],[])).
% 8.58/5.78 tff(908,axiom,((~hskp12) | c3_1(a1666)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 8.58/5.78 tff(909,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[908, 907])).
% 8.58/5.78 tff(910,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[909, 907])).
% 8.58/5.78 tff(911,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[910, 907])).
% 8.58/5.78 tff(912,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[911, 907])).
% 8.58/5.78 tff(913,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[912, 907])).
% 8.58/5.78 tff(914,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[913, 907])).
% 8.58/5.78 tff(915,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[914, 907])).
% 8.58/5.78 tff(916,plain,
% 8.58/5.78 ((~hskp12) | c3_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[915, 907])).
% 8.58/5.78 tff(917,plain,
% 8.58/5.78 (c3_1(a1666)),
% 8.58/5.78 inference(unit_resolution,[status(thm)],[916, 900])).
% 8.58/5.78 tff(918,plain,
% 8.58/5.78 (((~hskp12) | c2_1(a1666)) <=> ((~hskp12) | c2_1(a1666))),
% 8.58/5.78 inference(rewrite,[status(thm)],[])).
% 8.58/5.78 tff(919,axiom,((~hskp12) | c2_1(a1666)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 8.58/5.78 tff(920,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[919, 918])).
% 8.58/5.78 tff(921,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[920, 918])).
% 8.58/5.78 tff(922,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[921, 918])).
% 8.58/5.78 tff(923,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[922, 918])).
% 8.58/5.78 tff(924,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[923, 918])).
% 8.58/5.78 tff(925,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[924, 918])).
% 8.58/5.78 tff(926,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[925, 918])).
% 8.58/5.78 tff(927,plain,
% 8.58/5.78 ((~hskp12) | c2_1(a1666)),
% 8.58/5.78 inference(modus_ponens,[status(thm)],[926, 918])).
% 8.58/5.78 tff(928,plain,
% 8.58/5.78 (c2_1(a1666)),
% 8.58/5.78 inference(unit_resolution,[status(thm)],[927, 900])).
% 8.58/5.78 tff(929,plain,
% 8.58/5.78 (c0_1(a1654)),
% 8.58/5.78 inference(unit_resolution,[status(thm)],[525, 881])).
% 8.58/5.78 tff(930,plain,
% 8.58/5.78 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.78 inference(rewrite,[status(thm)],[])).
% 8.58/5.78 tff(931,plain,
% 8.58/5.78 ((hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.58/5.78 inference(rewrite,[status(thm)],[])).
% 8.58/5.78 tff(932,plain,
% 8.58/5.78 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.58/5.78 inference(monotonicity,[status(thm)],[931])).
% 8.58/5.78 tff(933,plain,
% 8.58/5.78 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.66/5.78 inference(transitivity,[status(thm)],[932, 930])).
% 8.66/5.78 tff(934,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.66/5.78 inference(quant_inst,[status(thm)],[])).
% 8.66/5.78 tff(935,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[934, 933])).
% 8.66/5.78 tff(936,plain,
% 8.66/5.78 (hskp26),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[935, 221, 929, 895, 894, 928, 917, 906, 20])).
% 8.66/5.78 tff(937,plain,
% 8.66/5.78 (~c2_1(a1691)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[669, 936])).
% 8.66/5.78 tff(938,plain,
% 8.66/5.78 (~c1_1(a1691)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[675, 936])).
% 8.66/5.78 tff(939,plain,
% 8.66/5.78 (~c3_1(a1691)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[689, 936])).
% 8.66/5.78 tff(940,assumption,(c0_1(a1691)), introduced(assumption)).
% 8.66/5.78 tff(941,plain,
% 8.66/5.78 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 8.66/5.78 inference(bind,[status(th)],[])).
% 8.66/5.78 tff(942,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(quant_intro,[status(thm)],[941])).
% 8.66/5.78 tff(943,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(944,plain,
% 8.66/5.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 8.66/5.78 inference(bind,[status(th)],[])).
% 8.66/5.78 tff(945,plain,
% 8.66/5.78 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(quant_intro,[status(thm)],[944])).
% 8.66/5.78 tff(946,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause358')).
% 8.66/5.78 tff(947,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[946, 945])).
% 8.66/5.78 tff(948,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[947, 943])).
% 8.66/5.78 tff(949,plain,(
% 8.66/5.78 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(skolemize,[status(sab)],[948])).
% 8.66/5.78 tff(950,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[949, 942])).
% 8.66/5.78 tff(951,plain,
% 8.66/5.78 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 8.66/5.78 inference(bind,[status(th)],[])).
% 8.66/5.78 tff(952,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(quant_intro,[status(thm)],[951])).
% 8.66/5.78 tff(953,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(954,plain,
% 8.66/5.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 8.66/5.78 inference(bind,[status(th)],[])).
% 8.66/5.78 tff(955,plain,
% 8.66/5.78 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(quant_intro,[status(thm)],[954])).
% 8.66/5.78 tff(956,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c3_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause344')).
% 8.66/5.78 tff(957,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[956, 955])).
% 8.66/5.78 tff(958,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[957, 953])).
% 8.66/5.78 tff(959,plain,(
% 8.66/5.78 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(skolemize,[status(sab)],[958])).
% 8.66/5.78 tff(960,plain,
% 8.66/5.78 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[959, 952])).
% 8.66/5.78 tff(961,assumption,(~c1_1(a1691)), introduced(assumption)).
% 8.66/5.78 tff(962,assumption,(~c3_1(a1691)), introduced(assumption)).
% 8.66/5.78 tff(963,assumption,(~hskp0), introduced(assumption)).
% 8.66/5.78 tff(964,assumption,(~c2_1(a1691)), introduced(assumption)).
% 8.66/5.78 tff(965,assumption,(hskp38), introduced(assumption)).
% 8.66/5.78 tff(966,plain,
% 8.66/5.78 (((~hskp38) | (~c2_1(a1718))) <=> ((~hskp38) | (~c2_1(a1718)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(967,plain,
% 8.66/5.78 (((~c2_1(a1718)) | (~hskp38)) <=> ((~hskp38) | (~c2_1(a1718)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(968,axiom,((~c2_1(a1718)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause231')).
% 8.66/5.78 tff(969,plain,
% 8.66/5.78 ((~hskp38) | (~c2_1(a1718))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[968, 967])).
% 8.66/5.78 tff(970,plain,
% 8.66/5.78 ((~hskp38) | (~c2_1(a1718))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[969, 966])).
% 8.66/5.78 tff(971,plain,
% 8.66/5.78 (~c2_1(a1718)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[970, 965])).
% 8.66/5.78 tff(972,plain,
% 8.66/5.78 (((~hskp38) | c3_1(a1718)) <=> ((~hskp38) | c3_1(a1718))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(973,axiom,((~hskp38) | c3_1(a1718)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 8.66/5.78 tff(974,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[973, 972])).
% 8.66/5.78 tff(975,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[974, 972])).
% 8.66/5.78 tff(976,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[975, 972])).
% 8.66/5.78 tff(977,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[976, 972])).
% 8.66/5.78 tff(978,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[977, 972])).
% 8.66/5.78 tff(979,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[978, 972])).
% 8.66/5.78 tff(980,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[979, 972])).
% 8.66/5.78 tff(981,plain,
% 8.66/5.78 ((~hskp38) | c3_1(a1718)),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[980, 972])).
% 8.66/5.78 tff(982,plain,
% 8.66/5.78 (c3_1(a1718)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[981, 965])).
% 8.66/5.78 tff(983,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(984,plain,
% 8.66/5.78 ((hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(985,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))))),
% 8.66/5.78 inference(monotonicity,[status(thm)],[984])).
% 8.66/5.78 tff(986,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(transitivity,[status(thm)],[985, 983])).
% 8.66/5.78 tff(987,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.66/5.78 inference(quant_inst,[status(thm)],[])).
% 8.66/5.78 tff(988,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[987, 986])).
% 8.66/5.78 tff(989,plain,
% 8.66/5.78 (~c1_1(a1718)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[988, 221, 963, 617, 616, 982, 971, 950, 882])).
% 8.66/5.78 tff(990,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(991,plain,
% 8.66/5.78 ((hskp75 | (~ndr1_0) | c2_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c3_1(a1715) | (~c1_1(a1715)) | (~c2_1(a1715))) <=> (hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(992,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c3_1(a1715) | (~c1_1(a1715)) | (~c2_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))))),
% 8.66/5.78 inference(monotonicity,[status(thm)],[991])).
% 8.66/5.78 tff(993,plain,
% 8.66/5.78 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c3_1(a1715) | (~c1_1(a1715)) | (~c2_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.66/5.78 inference(transitivity,[status(thm)],[992, 990])).
% 8.66/5.78 tff(994,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c3_1(a1715) | (~c1_1(a1715)) | (~c2_1(a1715)))),
% 8.66/5.78 inference(quant_inst,[status(thm)],[])).
% 8.66/5.78 tff(995,plain,
% 8.66/5.78 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1715) | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[994, 993])).
% 8.66/5.78 tff(996,plain,
% 8.66/5.78 (hskp75),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[995, 221, 834, 363, 982, 364, 971, 428, 989])).
% 8.66/5.78 tff(997,plain,
% 8.66/5.78 (~c2_1(a1724)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[441, 996])).
% 8.66/5.78 tff(998,plain,
% 8.66/5.78 (c0_1(a1724)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[485, 996])).
% 8.66/5.78 tff(999,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(1000,plain,
% 8.66/5.78 (((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718))) <=> (c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(1001,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.66/5.78 inference(monotonicity,[status(thm)],[1000])).
% 8.66/5.78 tff(1002,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.66/5.78 inference(transitivity,[status(thm)],[1001, 999])).
% 8.66/5.78 tff(1003,plain,
% 8.66/5.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))),
% 8.66/5.78 inference(quant_inst,[status(thm)],[])).
% 8.66/5.78 tff(1004,plain,
% 8.66/5.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c2_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.66/5.78 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 8.66/5.78 tff(1005,plain,
% 8.66/5.78 (c1_1(a1724)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[1004, 221, 998, 617, 615, 982, 997, 971, 647, 882, 989])).
% 8.66/5.78 tff(1006,plain,
% 8.66/5.78 (c3_1(a1724)),
% 8.66/5.78 inference(unit_resolution,[status(thm)],[474, 996])).
% 8.66/5.78 tff(1007,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(1008,plain,
% 8.66/5.78 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718))) <=> (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.66/5.78 inference(rewrite,[status(thm)],[])).
% 8.66/5.78 tff(1009,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))))),
% 8.66/5.78 inference(monotonicity,[status(thm)],[1008])).
% 8.66/5.78 tff(1010,plain,
% 8.66/5.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.66/5.79 inference(transitivity,[status(thm)],[1009, 1007])).
% 8.66/5.79 tff(1011,plain,
% 8.66/5.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))),
% 8.66/5.79 inference(quant_inst,[status(thm)],[])).
% 8.66/5.79 tff(1012,plain,
% 8.66/5.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 8.66/5.79 tff(1013,plain,
% 8.66/5.79 ($false),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1012, 221, 998, 1006, 982, 971, 961, 964, 647, 1005, 989, 940])).
% 8.66/5.79 tff(1014,plain,((~hskp38) | c1_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715)) | hskp0 | (~c2_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.66/5.79 tff(1015,plain,
% 8.66/5.79 (~hskp38),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1014, 963, 964, 940, 929, 894, 882, 834, 363, 364, 961, 895])).
% 8.66/5.79 tff(1016,plain,
% 8.66/5.79 (^[U: $i] : refl((hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 8.66/5.79 inference(bind,[status(th)],[])).
% 8.66/5.79 tff(1017,plain,
% 8.66/5.79 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(quant_intro,[status(thm)],[1016])).
% 8.66/5.79 tff(1018,plain,
% 8.66/5.79 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1019,plain,
% 8.66/5.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) <=> (((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp74))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp74) <=> (hskp74 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) <=> (hskp74 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) | hskp38) <=> ((hskp74 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp38))), rewrite(((hskp74 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp38) <=> (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) | hskp38) <=> (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 8.66/5.79 inference(bind,[status(th)],[])).
% 8.66/5.79 tff(1020,plain,
% 8.66/5.79 (![U: $i] : ((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) | hskp38) <=> ![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(quant_intro,[status(thm)],[1019])).
% 8.66/5.79 tff(1021,axiom,(![U: $i] : ((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause333')).
% 8.66/5.79 tff(1022,plain,
% 8.66/5.79 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 8.66/5.79 tff(1023,plain,
% 8.66/5.79 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1022, 1018])).
% 8.66/5.79 tff(1024,plain,(
% 8.66/5.79 ![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(skolemize,[status(sab)],[1023])).
% 8.66/5.79 tff(1025,plain,
% 8.66/5.79 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1024, 1017])).
% 8.66/5.79 tff(1026,assumption,(~hskp38), introduced(assumption)).
% 8.66/5.79 tff(1027,assumption,(~hskp74), introduced(assumption)).
% 8.66/5.79 tff(1028,plain,
% 8.66/5.79 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1029,plain,
% 8.66/5.79 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.66/5.79 inference(quant_inst,[status(thm)],[])).
% 8.66/5.79 tff(1030,plain,
% 8.66/5.79 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 8.66/5.79 tff(1031,plain,
% 8.66/5.79 ($false),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1030, 221, 1027, 1026, 929, 895, 894, 1025])).
% 8.66/5.79 tff(1032,plain,((~hskp52) | hskp74 | hskp38), inference(lemma,lemma(discharge,[]))).
% 8.66/5.79 tff(1033,plain,
% 8.66/5.79 (hskp74),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1032, 1015, 881])).
% 8.66/5.79 tff(1034,plain,
% 8.66/5.79 (^[U: $i] : refl((hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 8.66/5.79 inference(bind,[status(th)],[])).
% 8.66/5.79 tff(1035,plain,
% 8.66/5.79 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(quant_intro,[status(thm)],[1034])).
% 8.66/5.79 tff(1036,plain,
% 8.66/5.79 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1037,plain,
% 8.66/5.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp42) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp42))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp42) <=> (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp42) <=> (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 8.66/5.79 inference(bind,[status(th)],[])).
% 8.66/5.79 tff(1038,plain,
% 8.66/5.79 (![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp42) <=> ![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(quant_intro,[status(thm)],[1037])).
% 8.66/5.79 tff(1039,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause322')).
% 8.66/5.79 tff(1040,plain,
% 8.66/5.79 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 8.66/5.79 tff(1041,plain,
% 8.66/5.79 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1040, 1036])).
% 8.66/5.79 tff(1042,plain,(
% 8.66/5.79 ![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(skolemize,[status(sab)],[1041])).
% 8.66/5.79 tff(1043,plain,
% 8.66/5.79 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1042, 1035])).
% 8.66/5.79 tff(1044,assumption,(hskp74), introduced(assumption)).
% 8.66/5.79 tff(1045,plain,
% 8.66/5.79 (((~hskp74) | (~c3_1(a1717))) <=> ((~hskp74) | (~c3_1(a1717)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1046,plain,
% 8.66/5.79 (((~c3_1(a1717)) | (~hskp74)) <=> ((~hskp74) | (~c3_1(a1717)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1047,axiom,((~c3_1(a1717)) | (~hskp74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 8.66/5.79 tff(1048,plain,
% 8.66/5.79 ((~hskp74) | (~c3_1(a1717))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 8.66/5.79 tff(1049,plain,
% 8.66/5.79 ((~hskp74) | (~c3_1(a1717))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1048, 1045])).
% 8.66/5.79 tff(1050,plain,
% 8.66/5.79 (~c3_1(a1717)),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1049, 1044])).
% 8.66/5.79 tff(1051,plain,
% 8.66/5.79 (((~hskp74) | c2_1(a1717)) <=> ((~hskp74) | c2_1(a1717))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1052,axiom,((~hskp74) | c2_1(a1717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 8.66/5.79 tff(1053,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 8.66/5.79 tff(1054,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1053, 1051])).
% 8.66/5.79 tff(1055,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1054, 1051])).
% 8.66/5.79 tff(1056,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 8.66/5.79 tff(1057,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1056, 1051])).
% 8.66/5.79 tff(1058,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1057, 1051])).
% 8.66/5.79 tff(1059,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1058, 1051])).
% 8.66/5.79 tff(1060,plain,
% 8.66/5.79 ((~hskp74) | c2_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1059, 1051])).
% 8.66/5.79 tff(1061,plain,
% 8.66/5.79 (c2_1(a1717)),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1060, 1044])).
% 8.66/5.79 tff(1062,plain,
% 8.66/5.79 (((~hskp74) | c0_1(a1717)) <=> ((~hskp74) | c0_1(a1717))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1063,axiom,((~hskp74) | c0_1(a1717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 8.66/5.79 tff(1064,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 8.66/5.79 tff(1065,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1064, 1062])).
% 8.66/5.79 tff(1066,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1065, 1062])).
% 8.66/5.79 tff(1067,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1066, 1062])).
% 8.66/5.79 tff(1068,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1067, 1062])).
% 8.66/5.79 tff(1069,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1068, 1062])).
% 8.66/5.79 tff(1070,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1069, 1062])).
% 8.66/5.79 tff(1071,plain,
% 8.66/5.79 ((~hskp74) | c0_1(a1717)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1070, 1062])).
% 8.66/5.79 tff(1072,plain,
% 8.66/5.79 (c0_1(a1717)),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1071, 1044])).
% 8.66/5.79 tff(1073,assumption,(~hskp42), introduced(assumption)).
% 8.66/5.79 tff(1074,plain,
% 8.66/5.79 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1075,plain,
% 8.66/5.79 ((hskp42 | hskp0 | (~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717))) <=> (hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1076,plain,
% 8.66/5.79 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717))))),
% 8.66/5.79 inference(monotonicity,[status(thm)],[1075])).
% 8.66/5.79 tff(1077,plain,
% 8.66/5.79 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.66/5.79 inference(transitivity,[status(thm)],[1076, 1074])).
% 8.66/5.79 tff(1078,plain,
% 8.66/5.79 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)))),
% 8.66/5.79 inference(quant_inst,[status(thm)],[])).
% 8.66/5.79 tff(1079,plain,
% 8.66/5.79 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 8.66/5.79 tff(1080,plain,
% 8.66/5.79 ($false),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1079, 221, 1073, 963, 1072, 1061, 1050, 1043])).
% 8.66/5.79 tff(1081,plain,((~hskp74) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.66/5.79 tff(1082,plain,
% 8.66/5.79 (hskp42),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1081, 1033, 963])).
% 8.66/5.79 tff(1083,plain,
% 8.66/5.79 (((~hskp42) | (~c3_1(a1638))) <=> ((~hskp42) | (~c3_1(a1638)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1084,plain,
% 8.66/5.79 (((~c3_1(a1638)) | (~hskp42)) <=> ((~hskp42) | (~c3_1(a1638)))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1085,axiom,((~c3_1(a1638)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause226')).
% 8.66/5.79 tff(1086,plain,
% 8.66/5.79 ((~hskp42) | (~c3_1(a1638))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 8.66/5.79 tff(1087,plain,
% 8.66/5.79 ((~hskp42) | (~c3_1(a1638))),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1086, 1083])).
% 8.66/5.79 tff(1088,plain,
% 8.66/5.79 (~c3_1(a1638)),
% 8.66/5.79 inference(unit_resolution,[status(thm)],[1087, 1082])).
% 8.66/5.79 tff(1089,plain,
% 8.66/5.79 (((~hskp42) | c0_1(a1638)) <=> ((~hskp42) | c0_1(a1638))),
% 8.66/5.79 inference(rewrite,[status(thm)],[])).
% 8.66/5.79 tff(1090,axiom,((~hskp42) | c0_1(a1638)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 8.66/5.79 tff(1091,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 8.66/5.79 tff(1092,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1091, 1089])).
% 8.66/5.79 tff(1093,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 8.66/5.79 tff(1094,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 8.66/5.79 tff(1095,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1094, 1089])).
% 8.66/5.79 tff(1096,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1095, 1089])).
% 8.66/5.79 tff(1097,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.66/5.79 inference(modus_ponens,[status(thm)],[1096, 1089])).
% 8.66/5.79 tff(1098,plain,
% 8.66/5.79 ((~hskp42) | c0_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1097, 1089])).
% 8.67/5.79 tff(1099,plain,
% 8.67/5.79 (c0_1(a1638)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1098, 1082])).
% 8.67/5.79 tff(1100,plain,
% 8.67/5.79 (((~hskp42) | c1_1(a1638)) <=> ((~hskp42) | c1_1(a1638))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1101,axiom,((~hskp42) | c1_1(a1638)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 8.67/5.79 tff(1102,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 8.67/5.79 tff(1103,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1102, 1100])).
% 8.67/5.79 tff(1104,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1103, 1100])).
% 8.67/5.79 tff(1105,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 8.67/5.79 tff(1106,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1105, 1100])).
% 8.67/5.79 tff(1107,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1106, 1100])).
% 8.67/5.79 tff(1108,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1107, 1100])).
% 8.67/5.79 tff(1109,plain,
% 8.67/5.79 ((~hskp42) | c1_1(a1638)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1108, 1100])).
% 8.67/5.79 tff(1110,plain,
% 8.67/5.79 (c1_1(a1638)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1109, 1082])).
% 8.67/5.79 tff(1111,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1112,plain,
% 8.67/5.79 ((hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691))) <=> (hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1113,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.67/5.79 inference(monotonicity,[status(thm)],[1112])).
% 8.67/5.79 tff(1114,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.67/5.79 inference(transitivity,[status(thm)],[1113, 1111])).
% 8.67/5.79 tff(1115,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))),
% 8.67/5.79 inference(quant_inst,[status(thm)],[])).
% 8.67/5.79 tff(1116,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1638) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 8.67/5.79 tff(1117,plain,
% 8.67/5.79 (hskp2),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1116, 221, 1110, 1099, 1088, 962, 961, 960, 940])).
% 8.67/5.79 tff(1118,plain,
% 8.67/5.79 (((~hskp2) | (~c0_1(a1645))) <=> ((~hskp2) | (~c0_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1119,plain,
% 8.67/5.79 (((~c0_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1120,axiom,((~c0_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause308')).
% 8.67/5.79 tff(1121,plain,
% 8.67/5.79 ((~hskp2) | (~c0_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 8.67/5.79 tff(1122,plain,
% 8.67/5.79 ((~hskp2) | (~c0_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1121, 1118])).
% 8.67/5.79 tff(1123,plain,
% 8.67/5.79 (~c0_1(a1645)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1122, 1117])).
% 8.67/5.79 tff(1124,plain,
% 8.67/5.79 (((~hskp2) | (~c1_1(a1645))) <=> ((~hskp2) | (~c1_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1125,plain,
% 8.67/5.79 (((~c1_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1126,axiom,((~c1_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause307')).
% 8.67/5.79 tff(1127,plain,
% 8.67/5.79 ((~hskp2) | (~c1_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 8.67/5.79 tff(1128,plain,
% 8.67/5.79 ((~hskp2) | (~c1_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1127, 1124])).
% 8.67/5.79 tff(1129,plain,
% 8.67/5.79 (~c1_1(a1645)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1128, 1117])).
% 8.67/5.79 tff(1130,plain,
% 8.67/5.79 (~c3_1(a1717)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1049, 1033])).
% 8.67/5.79 tff(1131,plain,
% 8.67/5.79 (c2_1(a1717)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1060, 1033])).
% 8.67/5.79 tff(1132,plain,
% 8.67/5.79 (c0_1(a1717)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1071, 1033])).
% 8.67/5.79 tff(1133,plain,
% 8.67/5.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1134,plain,
% 8.67/5.79 (((~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1135,plain,
% 8.67/5.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717))))),
% 8.67/5.79 inference(monotonicity,[status(thm)],[1134])).
% 8.67/5.79 tff(1136,plain,
% 8.67/5.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717)))),
% 8.67/5.79 inference(transitivity,[status(thm)],[1135, 1133])).
% 8.67/5.79 tff(1137,plain,
% 8.67/5.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1717) | (~c0_1(a1717)) | (~c2_1(a1717)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.67/5.79 inference(quant_inst,[status(thm)],[])).
% 8.67/5.79 tff(1138,plain,
% 8.67/5.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1717) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1717)) | (~c0_1(a1717))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 8.67/5.79 tff(1139,plain,
% 8.67/5.79 (c2_1(a1645)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1138, 221, 1132, 1131, 1130, 962, 961, 964, 1129, 1123, 30])).
% 8.67/5.79 tff(1140,plain,
% 8.67/5.79 (((~hskp2) | (~c3_1(a1645))) <=> ((~hskp2) | (~c3_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1141,plain,
% 8.67/5.79 (((~c3_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1645)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1142,axiom,((~c3_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause309')).
% 8.67/5.79 tff(1143,plain,
% 8.67/5.79 ((~hskp2) | (~c3_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 8.67/5.79 tff(1144,plain,
% 8.67/5.79 ((~hskp2) | (~c3_1(a1645))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1143, 1140])).
% 8.67/5.79 tff(1145,plain,
% 8.67/5.79 (~c3_1(a1645)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1144, 1117])).
% 8.67/5.79 tff(1146,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1147,plain,
% 8.67/5.79 ((hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645))) <=> (hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1148,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.67/5.79 inference(monotonicity,[status(thm)],[1147])).
% 8.67/5.79 tff(1149,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(transitivity,[status(thm)],[1148, 1146])).
% 8.67/5.79 tff(1150,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))),
% 8.67/5.79 inference(quant_inst,[status(thm)],[])).
% 8.67/5.79 tff(1151,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 8.67/5.79 tff(1152,plain,
% 8.67/5.79 (hskp40),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1151, 221, 929, 894, 1129, 1145, 728, 882, 1139])).
% 8.67/5.79 tff(1153,plain,
% 8.67/5.79 (~c2_1(a1725)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[741, 1152])).
% 8.67/5.79 tff(1154,plain,
% 8.67/5.79 (c3_1(a1725)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[752, 1152])).
% 8.67/5.79 tff(1155,plain,
% 8.67/5.79 (c1_1(a1725)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[763, 1152])).
% 8.67/5.79 tff(1156,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1157,plain,
% 8.67/5.79 ((hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1158,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))))),
% 8.67/5.79 inference(monotonicity,[status(thm)],[1157])).
% 8.67/5.79 tff(1159,plain,
% 8.67/5.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.79 inference(transitivity,[status(thm)],[1158, 1156])).
% 8.67/5.79 tff(1160,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.67/5.79 inference(quant_inst,[status(thm)],[])).
% 8.67/5.79 tff(1161,plain,
% 8.67/5.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 8.67/5.79 tff(1162,plain,
% 8.67/5.79 ($false),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1161, 221, 963, 929, 895, 1155, 1154, 1153, 950, 882])).
% 8.67/5.79 tff(1163,plain,(hskp0 | (~c1_1(a1654)) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.67/5.79 tff(1164,plain,
% 8.67/5.79 (hskp0),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1163, 940, 939, 938, 937, 882, 881, 834, 363, 364])).
% 8.67/5.79 tff(1165,plain,
% 8.67/5.79 (((~hskp0) | (~c2_1(a1637))) <=> ((~hskp0) | (~c2_1(a1637)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1166,plain,
% 8.67/5.79 (((~c2_1(a1637)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1637)))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1167,axiom,((~c2_1(a1637)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause312')).
% 8.67/5.79 tff(1168,plain,
% 8.67/5.79 ((~hskp0) | (~c2_1(a1637))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 8.67/5.79 tff(1169,plain,
% 8.67/5.79 ((~hskp0) | (~c2_1(a1637))),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 8.67/5.79 tff(1170,plain,
% 8.67/5.79 (~c2_1(a1637)),
% 8.67/5.79 inference(unit_resolution,[status(thm)],[1169, 1164])).
% 8.67/5.79 tff(1171,plain,
% 8.67/5.79 (((~hskp0) | c0_1(a1637)) <=> ((~hskp0) | c0_1(a1637))),
% 8.67/5.79 inference(rewrite,[status(thm)],[])).
% 8.67/5.79 tff(1172,axiom,((~hskp0) | c0_1(a1637)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 8.67/5.79 tff(1173,plain,
% 8.67/5.79 ((~hskp0) | c0_1(a1637)),
% 8.67/5.79 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 8.67/5.80 tff(1174,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1173, 1171])).
% 8.67/5.80 tff(1175,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1174, 1171])).
% 8.67/5.80 tff(1176,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 8.67/5.80 tff(1177,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1176, 1171])).
% 8.67/5.80 tff(1178,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1177, 1171])).
% 8.67/5.80 tff(1179,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1178, 1171])).
% 8.67/5.80 tff(1180,plain,
% 8.67/5.80 ((~hskp0) | c0_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1179, 1171])).
% 8.67/5.80 tff(1181,plain,
% 8.67/5.80 (c0_1(a1637)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1180, 1164])).
% 8.67/5.80 tff(1182,assumption,(hskp61), introduced(assumption)).
% 8.67/5.80 tff(1183,plain,
% 8.67/5.80 (((~hskp61) | (~c2_1(a1674))) <=> ((~hskp61) | (~c2_1(a1674)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1184,plain,
% 8.67/5.80 (((~c2_1(a1674)) | (~hskp61)) <=> ((~hskp61) | (~c2_1(a1674)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1185,axiom,((~c2_1(a1674)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 8.67/5.80 tff(1186,plain,
% 8.67/5.80 ((~hskp61) | (~c2_1(a1674))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 8.67/5.80 tff(1187,plain,
% 8.67/5.80 ((~hskp61) | (~c2_1(a1674))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1186, 1183])).
% 8.67/5.80 tff(1188,plain,
% 8.67/5.80 (~c2_1(a1674)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1187, 1182])).
% 8.67/5.80 tff(1189,plain,
% 8.67/5.80 (((~hskp61) | (~c1_1(a1674))) <=> ((~hskp61) | (~c1_1(a1674)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1190,plain,
% 8.67/5.80 (((~c1_1(a1674)) | (~hskp61)) <=> ((~hskp61) | (~c1_1(a1674)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1191,axiom,((~c1_1(a1674)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 8.67/5.80 tff(1192,plain,
% 8.67/5.80 ((~hskp61) | (~c1_1(a1674))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 8.67/5.80 tff(1193,plain,
% 8.67/5.80 ((~hskp61) | (~c1_1(a1674))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1192, 1189])).
% 8.67/5.80 tff(1194,plain,
% 8.67/5.80 (~c1_1(a1674)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1193, 1182])).
% 8.67/5.80 tff(1195,plain,
% 8.67/5.80 (((~hskp61) | c3_1(a1674)) <=> ((~hskp61) | c3_1(a1674))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1196,axiom,((~hskp61) | c3_1(a1674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 8.67/5.80 tff(1197,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 8.67/5.80 tff(1198,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1197, 1195])).
% 8.67/5.80 tff(1199,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1198, 1195])).
% 8.67/5.80 tff(1200,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 8.67/5.80 tff(1201,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1200, 1195])).
% 8.67/5.80 tff(1202,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1201, 1195])).
% 8.67/5.80 tff(1203,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1202, 1195])).
% 8.67/5.80 tff(1204,plain,
% 8.67/5.80 ((~hskp61) | c3_1(a1674)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1203, 1195])).
% 8.67/5.80 tff(1205,plain,
% 8.67/5.80 (c3_1(a1674)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1204, 1182])).
% 8.67/5.80 tff(1206,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1207,plain,
% 8.67/5.80 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1208,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.67/5.80 inference(monotonicity,[status(thm)],[1207])).
% 8.67/5.80 tff(1209,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.67/5.80 inference(transitivity,[status(thm)],[1208, 1206])).
% 8.67/5.80 tff(1210,plain,
% 8.67/5.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.67/5.80 inference(quant_inst,[status(thm)],[])).
% 8.67/5.80 tff(1211,plain,
% 8.67/5.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 8.67/5.80 tff(1212,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1211, 221, 1205, 617, 615, 1194, 1188, 961, 964, 647, 882, 940])).
% 8.67/5.80 tff(1213,plain,((~hskp61) | (~c0_1(a1654)) | (~c3_1(a1654)) | c1_1(a1691) | c2_1(a1691) | (~c1_1(a1654)) | (~c0_1(a1691))), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1214,plain,
% 8.67/5.80 (~hskp61),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1213, 940, 894, 938, 937, 882, 929])).
% 8.67/5.80 tff(1215,plain,
% 8.67/5.80 (((~hskp0) | c1_1(a1637)) <=> ((~hskp0) | c1_1(a1637))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1216,axiom,((~hskp0) | c1_1(a1637)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 8.67/5.80 tff(1217,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 8.67/5.80 tff(1218,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1217, 1215])).
% 8.67/5.80 tff(1219,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1218, 1215])).
% 8.67/5.80 tff(1220,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 8.67/5.80 tff(1221,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1220, 1215])).
% 8.67/5.80 tff(1222,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1221, 1215])).
% 8.67/5.80 tff(1223,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1222, 1215])).
% 8.67/5.80 tff(1224,plain,
% 8.67/5.80 ((~hskp0) | c1_1(a1637)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1223, 1215])).
% 8.67/5.80 tff(1225,plain,
% 8.67/5.80 (c1_1(a1637)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1224, 1164])).
% 8.67/5.80 tff(1226,assumption,(c3_1(a1637)), introduced(assumption)).
% 8.67/5.80 tff(1227,assumption,(~c2_1(a1637)), introduced(assumption)).
% 8.67/5.80 tff(1228,assumption,(c0_1(a1637)), introduced(assumption)).
% 8.67/5.80 tff(1229,assumption,(c1_1(a1637)), introduced(assumption)).
% 8.67/5.80 tff(1230,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1231,plain,
% 8.67/5.80 ((hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1232,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637))))),
% 8.67/5.80 inference(monotonicity,[status(thm)],[1231])).
% 8.67/5.80 tff(1233,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(transitivity,[status(thm)],[1232, 1230])).
% 8.67/5.80 tff(1234,plain,
% 8.67/5.80 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 8.67/5.80 inference(quant_inst,[status(thm)],[])).
% 8.67/5.80 tff(1235,plain,
% 8.67/5.80 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 8.67/5.80 tff(1236,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1235, 221, 883, 1229, 1228, 1227, 290, 1226])).
% 8.67/5.80 tff(1237,plain,((~c3_1(a1637)) | hskp13 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1238,plain,
% 8.67/5.80 (~c3_1(a1637)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1237, 1225, 883, 1181, 1170])).
% 8.67/5.80 tff(1239,assumption,(~c3_1(a1637)), introduced(assumption)).
% 8.67/5.80 tff(1240,plain,
% 8.67/5.80 (^[V: $i, U: $i] : refl((hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 8.67/5.80 inference(bind,[status(th)],[])).
% 8.67/5.80 tff(1241,plain,
% 8.67/5.80 (![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(quant_intro,[status(thm)],[1240])).
% 8.67/5.80 tff(1242,plain,
% 8.67/5.80 (![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1243,plain,
% 8.67/5.80 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp61) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp61))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp61) <=> (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp61) <=> (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 8.67/5.80 inference(bind,[status(th)],[])).
% 8.67/5.80 tff(1244,plain,
% 8.67/5.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp61) <=> ![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(quant_intro,[status(thm)],[1243])).
% 8.67/5.80 tff(1245,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause347')).
% 8.67/5.80 tff(1246,plain,
% 8.67/5.80 (![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 8.67/5.80 tff(1247,plain,
% 8.67/5.80 (![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1246, 1242])).
% 8.67/5.80 tff(1248,plain,(
% 8.67/5.80 ![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(skolemize,[status(sab)],[1247])).
% 8.67/5.80 tff(1249,plain,
% 8.67/5.80 (![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1248, 1241])).
% 8.67/5.80 tff(1250,assumption,(~hskp61), introduced(assumption)).
% 8.67/5.80 tff(1251,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1252,plain,
% 8.67/5.80 ((hskp61 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))) <=> (hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1253,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))))),
% 8.67/5.80 inference(monotonicity,[status(thm)],[1252])).
% 8.67/5.80 tff(1254,plain,
% 8.67/5.80 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(transitivity,[status(thm)],[1253, 1251])).
% 8.67/5.80 tff(1255,plain,
% 8.67/5.80 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.67/5.80 inference(quant_inst,[status(thm)],[])).
% 8.67/5.80 tff(1256,plain,
% 8.67/5.80 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 8.67/5.80 tff(1257,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1256, 221, 1250, 1229, 1228, 1227, 1249, 1239])).
% 8.67/5.80 tff(1258,plain,(c3_1(a1637) | hskp61 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1259,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1258, 1238, 1225, 1214, 1181, 1170])).
% 8.67/5.80 tff(1260,plain,((~c0_1(a1691)) | hskp13 | (~c1_1(a1654)) | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1261,plain,
% 8.67/5.80 (~c0_1(a1691)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1260, 883, 882, 881, 834, 363, 364])).
% 8.67/5.80 tff(1262,plain,
% 8.67/5.80 (hskp37 | c0_1(a1691)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[696, 221, 554, 939, 937, 577])).
% 8.67/5.80 tff(1263,plain,
% 8.67/5.80 (hskp37),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1262, 1261])).
% 8.67/5.80 tff(1264,plain,
% 8.67/5.80 (~c1_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[591, 1263])).
% 8.67/5.80 tff(1265,plain,
% 8.67/5.80 (c0_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[602, 1263])).
% 8.67/5.80 tff(1266,plain,
% 8.67/5.80 (c2_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[613, 1263])).
% 8.67/5.80 tff(1267,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[707, 221, 929, 895, 894, 1266, 1265, 1264, 939, 937, 565, 1261])).
% 8.67/5.80 tff(1268,plain,(hskp13 | (~c1_1(a1654)) | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1269,plain,
% 8.67/5.80 (hskp13),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1268, 880, 875, 833, 363, 364])).
% 8.67/5.80 tff(1270,plain,
% 8.67/5.80 (~c1_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[303, 1269])).
% 8.67/5.80 tff(1271,plain,
% 8.67/5.80 (c3_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[314, 1269])).
% 8.67/5.80 tff(1272,plain,
% 8.67/5.80 (c0_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[325, 1269])).
% 8.67/5.80 tff(1273,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[870, 221, 833, 363, 1272, 1271, 364, 248, 242, 1270, 102, 879])).
% 8.67/5.80 tff(1274,plain,((~hskp17) | c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1275,plain,
% 8.67/5.80 (~hskp17),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1274, 363, 364, 138])).
% 8.67/5.80 tff(1276,plain,
% 8.67/5.80 (hskp17 | hskp16 | c1_1(a1654)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[716, 221, 929, 894, 10])).
% 8.67/5.80 tff(1277,plain,
% 8.67/5.80 (c1_1(a1654)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1276, 271, 272])).
% 8.67/5.80 tff(1278,plain,
% 8.67/5.80 (hskp13),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1268, 1277, 881, 834, 363, 364])).
% 8.67/5.80 tff(1279,plain,
% 8.67/5.80 (~c1_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[303, 1278])).
% 8.67/5.80 tff(1280,plain,
% 8.67/5.80 (c3_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[314, 1278])).
% 8.67/5.80 tff(1281,plain,
% 8.67/5.80 (c0_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[325, 1278])).
% 8.67/5.80 tff(1282,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[332, 221, 271, 272, 1281, 1280, 1279, 10])).
% 8.67/5.80 tff(1283,plain,(hskp17 | hskp16 | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1284,plain,
% 8.67/5.80 (hskp16),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1283, 1275, 875, 833, 363, 364])).
% 8.67/5.80 tff(1285,plain,
% 8.67/5.80 (~c0_1(a1677)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[123, 1284])).
% 8.67/5.80 tff(1286,plain,
% 8.67/5.80 (~c2_1(a1677)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[117, 1284])).
% 8.67/5.80 tff(1287,plain,
% 8.67/5.80 (c3_1(a1677)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[798, 1286, 554, 877, 878, 1285, 876])).
% 8.67/5.80 tff(1288,plain,
% 8.67/5.80 (~c1_1(a1677)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[111, 1284])).
% 8.67/5.80 tff(1289,plain,
% 8.67/5.80 (c1_1(a1654)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[808, 1287, 138, 877, 876, 1288, 1285])).
% 8.67/5.80 tff(1290,plain,
% 8.67/5.80 (hskp13),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1268, 1289, 875, 833, 363, 364])).
% 8.67/5.80 tff(1291,plain,
% 8.67/5.80 (~c1_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[303, 1290])).
% 8.67/5.80 tff(1292,plain,
% 8.67/5.80 (c3_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[314, 1290])).
% 8.67/5.80 tff(1293,plain,
% 8.67/5.80 (c0_1(a1667)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[325, 1290])).
% 8.67/5.80 tff(1294,plain,
% 8.67/5.80 ($false),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[853, 221, 833, 363, 1293, 1292, 364, 1285, 1288, 1291, 102, 1287])).
% 8.67/5.80 tff(1295,plain,(c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.67/5.80 tff(1296,plain,
% 8.67/5.80 (~c2_1(a1715)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1295, 363, 138])).
% 8.67/5.80 tff(1297,assumption,(~c0_1(a1715)), introduced(assumption)).
% 8.67/5.80 tff(1298,plain,
% 8.67/5.80 (((~hskp72) | c3_1(a1715)) <=> ((~hskp72) | c3_1(a1715))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1299,axiom,((~hskp72) | c3_1(a1715)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 8.67/5.80 tff(1300,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 8.67/5.80 tff(1301,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1300, 1298])).
% 8.67/5.80 tff(1302,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1301, 1298])).
% 8.67/5.80 tff(1303,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1302, 1298])).
% 8.67/5.80 tff(1304,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1303, 1298])).
% 8.67/5.80 tff(1305,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1304, 1298])).
% 8.67/5.80 tff(1306,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1305, 1298])).
% 8.67/5.80 tff(1307,plain,
% 8.67/5.80 ((~hskp72) | c3_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1306, 1298])).
% 8.67/5.80 tff(1308,plain,
% 8.67/5.80 (~hskp72),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1307, 363])).
% 8.67/5.80 tff(1309,assumption,(~c2_1(a1715)), introduced(assumption)).
% 8.67/5.80 tff(1310,plain,
% 8.67/5.80 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1311,plain,
% 8.67/5.80 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1715) | c3_1(a1715) | c2_1(a1715)) <=> (hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1312,plain,
% 8.67/5.80 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1715) | c3_1(a1715) | c2_1(a1715))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715)))),
% 8.67/5.80 inference(monotonicity,[status(thm)],[1311])).
% 8.67/5.80 tff(1313,plain,
% 8.67/5.80 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1715) | c3_1(a1715) | c2_1(a1715))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715))),
% 8.67/5.80 inference(transitivity,[status(thm)],[1312, 1310])).
% 8.67/5.80 tff(1314,plain,
% 8.67/5.80 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1715) | c3_1(a1715) | c2_1(a1715))),
% 8.67/5.80 inference(quant_inst,[status(thm)],[])).
% 8.67/5.80 tff(1315,plain,
% 8.67/5.80 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715)),
% 8.67/5.80 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 8.67/5.80 tff(1316,plain,
% 8.67/5.80 (hskp72 | hskp37 | c3_1(a1715)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1315, 221, 1309, 577, 1297])).
% 8.67/5.80 tff(1317,plain,
% 8.67/5.80 (hskp37),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[1316, 1308, 363])).
% 8.67/5.80 tff(1318,plain,
% 8.67/5.80 (~c1_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[591, 1317])).
% 8.67/5.80 tff(1319,plain,
% 8.67/5.80 (c0_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[602, 1317])).
% 8.67/5.80 tff(1320,plain,
% 8.67/5.80 (c2_1(a1714)),
% 8.67/5.80 inference(unit_resolution,[status(thm)],[613, 1317])).
% 8.67/5.80 tff(1321,assumption,(c3_1(a1714)), introduced(assumption)).
% 8.67/5.80 tff(1322,assumption,(~c1_1(a1714)), introduced(assumption)).
% 8.67/5.80 tff(1323,assumption,(c0_1(a1714)), introduced(assumption)).
% 8.67/5.80 tff(1324,assumption,(c2_1(a1714)), introduced(assumption)).
% 8.67/5.80 tff(1325,assumption,(ndr1_0), introduced(assumption)).
% 8.67/5.80 tff(1326,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1327,plain,
% 8.67/5.80 (((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715)) <=> (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.80 inference(rewrite,[status(thm)],[])).
% 8.67/5.80 tff(1328,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.67/5.80 inference(monotonicity,[status(thm)],[1327])).
% 8.67/5.80 tff(1329,plain,
% 8.67/5.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.81 inference(transitivity,[status(thm)],[1328, 1326])).
% 8.67/5.81 tff(1330,plain,
% 8.67/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))),
% 8.67/5.81 inference(quant_inst,[status(thm)],[])).
% 8.67/5.81 tff(1331,plain,
% 8.67/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.67/5.81 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 8.67/5.81 tff(1332,plain,
% 8.67/5.81 ($false),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1331, 1325, 363, 1324, 1323, 1309, 1322, 565, 1297, 1321])).
% 8.67/5.81 tff(1333,plain,((~c3_1(a1714)) | (~ndr1_0) | c3_1(a1715) | (~c2_1(a1714)) | (~c0_1(a1714)) | c2_1(a1715) | c1_1(a1714) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.67/5.81 tff(1334,plain,
% 8.67/5.81 ((~c3_1(a1714)) | c3_1(a1715) | (~c2_1(a1714)) | (~c0_1(a1714)) | c2_1(a1715) | c1_1(a1714) | c0_1(a1715)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1333, 221])).
% 8.67/5.81 tff(1335,plain,
% 8.67/5.81 (~c3_1(a1714)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1334, 1320, 1297, 363, 1319, 1309, 1318])).
% 8.67/5.81 tff(1336,plain,
% 8.67/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.81 inference(rewrite,[status(thm)],[])).
% 8.67/5.81 tff(1337,plain,
% 8.67/5.81 (((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.81 inference(rewrite,[status(thm)],[])).
% 8.67/5.81 tff(1338,plain,
% 8.67/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.67/5.81 inference(monotonicity,[status(thm)],[1337])).
% 8.67/5.81 tff(1339,plain,
% 8.67/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.67/5.81 inference(transitivity,[status(thm)],[1338, 1336])).
% 8.67/5.81 tff(1340,plain,
% 8.67/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.67/5.81 inference(quant_inst,[status(thm)],[])).
% 8.67/5.81 tff(1341,plain,
% 8.67/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.67/5.81 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 8.67/5.81 tff(1342,plain,
% 8.67/5.81 (c1_1(a1715)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1341, 221, 363, 1320, 1319, 1309, 30, 1297, 1335])).
% 8.67/5.81 tff(1343,plain,
% 8.67/5.81 (hskp72 | hskp37 | c3_1(a1715) | c0_1(a1715)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1315, 221, 1309, 577])).
% 8.67/5.81 tff(1344,plain,
% 8.67/5.81 (hskp37),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1343, 1297, 363, 1308])).
% 8.67/5.81 tff(1345,assumption,(~hskp21), introduced(assumption)).
% 8.67/5.81 tff(1346,plain,
% 8.67/5.81 (c2_1(a1714)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[613, 1344])).
% 8.67/5.81 tff(1347,plain,
% 8.67/5.81 (c0_1(a1714)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[602, 1344])).
% 8.67/5.81 tff(1348,plain,
% 8.67/5.81 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 8.67/5.81 inference(bind,[status(th)],[])).
% 8.67/5.81 tff(1349,plain,
% 8.67/5.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(quant_intro,[status(thm)],[1348])).
% 8.67/5.81 tff(1350,plain,
% 8.67/5.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(rewrite,[status(thm)],[])).
% 8.67/5.81 tff(1351,plain,
% 8.67/5.81 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 8.67/5.81 inference(bind,[status(th)],[])).
% 8.67/5.81 tff(1352,plain,
% 8.67/5.81 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(quant_intro,[status(thm)],[1351])).
% 8.67/5.81 tff(1353,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause338')).
% 8.67/5.81 tff(1354,plain,
% 8.67/5.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 8.67/5.81 tff(1355,plain,
% 8.67/5.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(modus_ponens,[status(thm)],[1354, 1350])).
% 8.67/5.81 tff(1356,plain,(
% 8.67/5.81 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(skolemize,[status(sab)],[1355])).
% 8.67/5.81 tff(1357,plain,
% 8.67/5.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.67/5.81 inference(modus_ponens,[status(thm)],[1356, 1349])).
% 8.67/5.81 tff(1358,plain,
% 8.67/5.81 (~c3_1(a1714)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1333, 1297, 1325, 363, 1323, 1309, 1322, 1324])).
% 8.67/5.81 tff(1359,plain,
% 8.67/5.81 (c1_1(a1715)),
% 8.67/5.81 inference(unit_resolution,[status(thm)],[1341, 1325, 363, 1324, 1323, 1309, 30, 1297, 1358])).
% 8.67/5.81 tff(1360,plain,
% 8.67/5.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.67/5.81 inference(rewrite,[status(thm)],[])).
% 8.67/5.81 tff(1361,plain,
% 8.67/5.81 ((hskp21 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.67/5.81 inference(rewrite,[status(thm)],[])).
% 8.67/5.81 tff(1362,plain,
% 8.67/5.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715))))),
% 8.67/5.81 inference(monotonicity,[status(thm)],[1361])).
% 8.67/5.81 tff(1363,plain,
% 8.67/5.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.67/5.81 inference(transitivity,[status(thm)],[1362, 1360])).
% 8.67/5.81 tff(1364,plain,
% 8.67/5.81 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.67/5.81 inference(quant_inst,[status(thm)],[])).
% 8.69/5.81 tff(1365,plain,
% 8.69/5.81 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 8.69/5.81 tff(1366,plain,
% 8.69/5.81 ($false),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1365, 1325, 1345, 1359, 363, 1309, 1357, 1297])).
% 8.69/5.81 tff(1367,plain,(c0_1(a1715) | (~ndr1_0) | hskp21 | c3_1(a1715) | c2_1(a1715) | (~c2_1(a1714)) | (~c0_1(a1714)) | c1_1(a1714)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.81 tff(1368,plain,
% 8.69/5.81 ($false),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1367, 1347, 1346, 1345, 363, 1309, 1322, 1297, 221])).
% 8.69/5.81 tff(1369,plain,(c0_1(a1715) | hskp21 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.81 tff(1370,plain,
% 8.69/5.81 (c1_1(a1714)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1369, 1297, 363, 1309, 1345])).
% 8.69/5.81 tff(1371,plain,
% 8.69/5.81 ($false),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[591, 1370, 1344])).
% 8.69/5.81 tff(1372,plain,(c0_1(a1715) | c3_1(a1715) | c2_1(a1715) | hskp21), inference(lemma,lemma(discharge,[]))).
% 8.69/5.81 tff(1373,plain,
% 8.69/5.81 (hskp21),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1372, 363, 1297, 1309])).
% 8.69/5.81 tff(1374,plain,
% 8.69/5.81 (((~hskp21) | c2_1(a1683)) <=> ((~hskp21) | c2_1(a1683))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1375,axiom,((~hskp21) | c2_1(a1683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 8.69/5.81 tff(1376,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 8.69/5.81 tff(1377,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1376, 1374])).
% 8.69/5.81 tff(1378,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1377, 1374])).
% 8.69/5.81 tff(1379,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1378, 1374])).
% 8.69/5.81 tff(1380,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1379, 1374])).
% 8.69/5.81 tff(1381,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1380, 1374])).
% 8.69/5.81 tff(1382,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1381, 1374])).
% 8.69/5.81 tff(1383,plain,
% 8.69/5.81 ((~hskp21) | c2_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1382, 1374])).
% 8.69/5.81 tff(1384,plain,
% 8.69/5.81 (c2_1(a1683)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1383, 1373])).
% 8.69/5.81 tff(1385,plain,
% 8.69/5.81 (((~hskp21) | c3_1(a1683)) <=> ((~hskp21) | c3_1(a1683))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1386,axiom,((~hskp21) | c3_1(a1683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 8.69/5.81 tff(1387,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 8.69/5.81 tff(1388,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1387, 1385])).
% 8.69/5.81 tff(1389,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1388, 1385])).
% 8.69/5.81 tff(1390,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1389, 1385])).
% 8.69/5.81 tff(1391,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1390, 1385])).
% 8.69/5.81 tff(1392,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1391, 1385])).
% 8.69/5.81 tff(1393,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1392, 1385])).
% 8.69/5.81 tff(1394,plain,
% 8.69/5.81 ((~hskp21) | c3_1(a1683)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1393, 1385])).
% 8.69/5.81 tff(1395,plain,
% 8.69/5.81 (c3_1(a1683)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1394, 1373])).
% 8.69/5.81 tff(1396,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1397,plain,
% 8.69/5.81 (((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715)) <=> (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1398,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.69/5.81 inference(monotonicity,[status(thm)],[1397])).
% 8.69/5.81 tff(1399,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.81 inference(transitivity,[status(thm)],[1398, 1396])).
% 8.69/5.81 tff(1400,plain,
% 8.69/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))),
% 8.69/5.81 inference(quant_inst,[status(thm)],[])).
% 8.69/5.81 tff(1401,plain,
% 8.69/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | c0_1(a1715) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 8.69/5.81 tff(1402,plain,
% 8.69/5.81 (~c0_1(a1683)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1401, 221, 363, 1320, 1319, 1395, 1384, 1309, 1318, 565, 1297])).
% 8.69/5.81 tff(1403,plain,
% 8.69/5.81 (^[V: $i, U: $i] : refl((hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 8.69/5.81 inference(bind,[status(th)],[])).
% 8.69/5.81 tff(1404,plain,
% 8.69/5.81 (![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(quant_intro,[status(thm)],[1403])).
% 8.69/5.81 tff(1405,plain,
% 8.69/5.81 (![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1406,plain,
% 8.69/5.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp69) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp69))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp69) <=> (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp69) <=> (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 8.69/5.81 inference(bind,[status(th)],[])).
% 8.69/5.81 tff(1407,plain,
% 8.69/5.81 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp69) <=> ![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(quant_intro,[status(thm)],[1406])).
% 8.69/5.81 tff(1408,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp69)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause341')).
% 8.69/5.81 tff(1409,plain,
% 8.69/5.81 (![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 8.69/5.81 tff(1410,plain,
% 8.69/5.81 (![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1409, 1405])).
% 8.69/5.81 tff(1411,plain,(
% 8.69/5.81 ![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(skolemize,[status(sab)],[1410])).
% 8.69/5.81 tff(1412,plain,
% 8.69/5.81 (![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1411, 1404])).
% 8.69/5.81 tff(1413,plain,
% 8.69/5.81 (((~hskp21) | (~c1_1(a1683))) <=> ((~hskp21) | (~c1_1(a1683)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1414,plain,
% 8.69/5.81 (((~c1_1(a1683)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1683)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1415,axiom,((~c1_1(a1683)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 8.69/5.81 tff(1416,plain,
% 8.69/5.81 ((~hskp21) | (~c1_1(a1683))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 8.69/5.81 tff(1417,plain,
% 8.69/5.81 ((~hskp21) | (~c1_1(a1683))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1416, 1413])).
% 8.69/5.81 tff(1418,plain,
% 8.69/5.81 (~c1_1(a1683)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1417, 1373])).
% 8.69/5.81 tff(1419,plain,
% 8.69/5.81 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1420,plain,
% 8.69/5.81 ((hskp69 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1421,plain,
% 8.69/5.81 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715))))),
% 8.69/5.81 inference(monotonicity,[status(thm)],[1420])).
% 8.69/5.81 tff(1422,plain,
% 8.69/5.81 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715)))),
% 8.69/5.81 inference(transitivity,[status(thm)],[1421, 1419])).
% 8.69/5.81 tff(1423,plain,
% 8.69/5.81 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.81 inference(quant_inst,[status(thm)],[])).
% 8.69/5.81 tff(1424,plain,
% 8.69/5.81 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c1_1(a1715))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 8.69/5.81 tff(1425,plain,
% 8.69/5.81 (hskp69 | (~c1_1(a1715))),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1424, 221, 363, 1395, 1309, 1418, 1412, 1402])).
% 8.69/5.81 tff(1426,plain,
% 8.69/5.81 (hskp69),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1425, 1342])).
% 8.69/5.81 tff(1427,plain,
% 8.69/5.81 (((~hskp69) | (~c1_1(a1709))) <=> ((~hskp69) | (~c1_1(a1709)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1428,plain,
% 8.69/5.81 (((~c1_1(a1709)) | (~hskp69)) <=> ((~hskp69) | (~c1_1(a1709)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1429,axiom,((~c1_1(a1709)) | (~hskp69)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 8.69/5.81 tff(1430,plain,
% 8.69/5.81 ((~hskp69) | (~c1_1(a1709))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 8.69/5.81 tff(1431,plain,
% 8.69/5.81 ((~hskp69) | (~c1_1(a1709))),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1430, 1427])).
% 8.69/5.81 tff(1432,plain,
% 8.69/5.81 (~c1_1(a1709)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1431, 1426])).
% 8.69/5.81 tff(1433,plain,
% 8.69/5.81 (((~hskp69) | c3_1(a1709)) <=> ((~hskp69) | c3_1(a1709))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1434,axiom,((~hskp69) | c3_1(a1709)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 8.69/5.81 tff(1435,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 8.69/5.81 tff(1436,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1435, 1433])).
% 8.69/5.81 tff(1437,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1436, 1433])).
% 8.69/5.81 tff(1438,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1437, 1433])).
% 8.69/5.81 tff(1439,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1438, 1433])).
% 8.69/5.81 tff(1440,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1439, 1433])).
% 8.69/5.81 tff(1441,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1440, 1433])).
% 8.69/5.81 tff(1442,plain,
% 8.69/5.81 ((~hskp69) | c3_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1441, 1433])).
% 8.69/5.81 tff(1443,plain,
% 8.69/5.81 (c3_1(a1709)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1442, 1426])).
% 8.69/5.81 tff(1444,plain,
% 8.69/5.81 (((~hskp69) | c0_1(a1709)) <=> ((~hskp69) | c0_1(a1709))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1445,axiom,((~hskp69) | c0_1(a1709)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 8.69/5.81 tff(1446,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 8.69/5.81 tff(1447,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1446, 1444])).
% 8.69/5.81 tff(1448,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1447, 1444])).
% 8.69/5.81 tff(1449,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1448, 1444])).
% 8.69/5.81 tff(1450,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1449, 1444])).
% 8.69/5.81 tff(1451,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1450, 1444])).
% 8.69/5.81 tff(1452,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1451, 1444])).
% 8.69/5.81 tff(1453,plain,
% 8.69/5.81 ((~hskp69) | c0_1(a1709)),
% 8.69/5.81 inference(modus_ponens,[status(thm)],[1452, 1444])).
% 8.69/5.81 tff(1454,plain,
% 8.69/5.81 (c0_1(a1709)),
% 8.69/5.81 inference(unit_resolution,[status(thm)],[1453, 1426])).
% 8.69/5.81 tff(1455,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1456,plain,
% 8.69/5.81 (((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715)) <=> (c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.81 inference(rewrite,[status(thm)],[])).
% 8.69/5.81 tff(1457,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709))))),
% 8.69/5.81 inference(monotonicity,[status(thm)],[1456])).
% 8.69/5.81 tff(1458,plain,
% 8.69/5.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.81 inference(transitivity,[status(thm)],[1457, 1455])).
% 8.69/5.81 tff(1459,plain,
% 8.69/5.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1460,plain,
% 8.69/5.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 8.69/5.82 tff(1461,plain,
% 8.69/5.82 (~c2_1(a1709)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1460, 221, 363, 1454, 1443, 1309, 1432, 565, 1297])).
% 8.69/5.82 tff(1462,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1463,plain,
% 8.69/5.82 ((hskp60 | (~ndr1_0) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683))) <=> (hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1464,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714))))),
% 8.69/5.82 inference(monotonicity,[status(thm)],[1463])).
% 8.69/5.82 tff(1465,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.69/5.82 inference(transitivity,[status(thm)],[1464, 1462])).
% 8.69/5.82 tff(1466,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1467,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 8.69/5.82 tff(1468,plain,
% 8.69/5.82 (hskp60),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1467, 221, 1320, 1395, 1318, 1418, 386, 1335, 1402])).
% 8.69/5.82 tff(1469,plain,
% 8.69/5.82 (~c1_1(a1673)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[399, 1468])).
% 8.69/5.82 tff(1470,plain,
% 8.69/5.82 (c2_1(a1673)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[452, 1468])).
% 8.69/5.82 tff(1471,plain,
% 8.69/5.82 (c3_1(a1673)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[463, 1468])).
% 8.69/5.82 tff(1472,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1473,plain,
% 8.69/5.82 (((~ndr1_0) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1673)) | (~c0_1(a1673)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715)) <=> (c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1474,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1673)) | (~c0_1(a1673)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673))))),
% 8.69/5.82 inference(monotonicity,[status(thm)],[1473])).
% 8.69/5.82 tff(1475,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1673)) | (~c0_1(a1673)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.82 inference(transitivity,[status(thm)],[1474, 1472])).
% 8.69/5.82 tff(1476,plain,
% 8.69/5.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1673)) | (~c0_1(a1673)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1477,plain,
% 8.69/5.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 8.69/5.82 tff(1478,plain,
% 8.69/5.82 (~c0_1(a1673)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1477, 221, 363, 1471, 1470, 1309, 1469, 565, 1297])).
% 8.69/5.82 tff(1479,plain,
% 8.69/5.82 (^[V: $i, U: $i] : refl((hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1480,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(quant_intro,[status(thm)],[1479])).
% 8.69/5.82 tff(1481,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1482,plain,
% 8.69/5.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp39) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp39))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1483,plain,
% 8.69/5.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp39) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(quant_intro,[status(thm)],[1482])).
% 8.69/5.82 tff(1484,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause353')).
% 8.69/5.82 tff(1485,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 8.69/5.82 tff(1486,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1485, 1481])).
% 8.69/5.82 tff(1487,plain,(
% 8.69/5.82 ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(skolemize,[status(sab)],[1486])).
% 8.69/5.82 tff(1488,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1487, 1480])).
% 8.69/5.82 tff(1489,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1490,plain,
% 8.69/5.82 ((hskp39 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1491,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)))),
% 8.69/5.82 inference(monotonicity,[status(thm)],[1490])).
% 8.69/5.82 tff(1492,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.82 inference(transitivity,[status(thm)],[1491, 1489])).
% 8.69/5.82 tff(1493,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1494,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | (~ndr1_0) | (~c3_1(a1673)) | c0_1(a1673) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 8.69/5.82 tff(1495,plain,
% 8.69/5.82 (hskp39),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1494, 221, 1454, 1443, 1471, 1470, 1488, 1478, 1461])).
% 8.69/5.82 tff(1496,plain,
% 8.69/5.82 (((~hskp39) | (~c0_1(a1721))) <=> ((~hskp39) | (~c0_1(a1721)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1497,plain,
% 8.69/5.82 (((~c0_1(a1721)) | (~hskp39)) <=> ((~hskp39) | (~c0_1(a1721)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1498,axiom,((~c0_1(a1721)) | (~hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause230')).
% 8.69/5.82 tff(1499,plain,
% 8.69/5.82 ((~hskp39) | (~c0_1(a1721))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 8.69/5.82 tff(1500,plain,
% 8.69/5.82 ((~hskp39) | (~c0_1(a1721))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1499, 1496])).
% 8.69/5.82 tff(1501,plain,
% 8.69/5.82 (~c0_1(a1721)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1500, 1495])).
% 8.69/5.82 tff(1502,plain,
% 8.69/5.82 (((~hskp39) | (~c1_1(a1721))) <=> ((~hskp39) | (~c1_1(a1721)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1503,plain,
% 8.69/5.82 (((~c1_1(a1721)) | (~hskp39)) <=> ((~hskp39) | (~c1_1(a1721)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1504,axiom,((~c1_1(a1721)) | (~hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause229')).
% 8.69/5.82 tff(1505,plain,
% 8.69/5.82 ((~hskp39) | (~c1_1(a1721))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 8.69/5.82 tff(1506,plain,
% 8.69/5.82 ((~hskp39) | (~c1_1(a1721))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1505, 1502])).
% 8.69/5.82 tff(1507,plain,
% 8.69/5.82 (~c1_1(a1721)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1506, 1495])).
% 8.69/5.82 tff(1508,plain,
% 8.69/5.82 (^[V: $i, U: $i] : refl((hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1509,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(quant_intro,[status(thm)],[1508])).
% 8.69/5.82 tff(1510,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1511,plain,
% 8.69/5.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp67) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp67))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp67) <=> (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp67) <=> (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1512,plain,
% 8.69/5.82 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp67) <=> ![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(quant_intro,[status(thm)],[1511])).
% 8.69/5.82 tff(1513,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp67)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause349')).
% 8.69/5.82 tff(1514,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 8.69/5.82 tff(1515,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1514, 1510])).
% 8.69/5.82 tff(1516,plain,(
% 8.69/5.82 ![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(skolemize,[status(sab)],[1515])).
% 8.69/5.82 tff(1517,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1516, 1509])).
% 8.69/5.82 tff(1518,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1519,plain,
% 8.69/5.82 ((hskp67 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1520,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.82 inference(monotonicity,[status(thm)],[1519])).
% 8.69/5.82 tff(1521,plain,
% 8.69/5.82 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.82 inference(transitivity,[status(thm)],[1520, 1518])).
% 8.69/5.82 tff(1522,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1523,plain,
% 8.69/5.82 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1709) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 8.69/5.82 tff(1524,plain,
% 8.69/5.82 (hskp67),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1523, 221, 1454, 1443, 1471, 1470, 1432, 1469, 1517])).
% 8.69/5.82 tff(1525,plain,
% 8.69/5.82 (((~hskp67) | c3_1(a1702)) <=> ((~hskp67) | c3_1(a1702))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1526,axiom,((~hskp67) | c3_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 8.69/5.82 tff(1527,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 8.69/5.82 tff(1528,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1527, 1525])).
% 8.69/5.82 tff(1529,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1528, 1525])).
% 8.69/5.82 tff(1530,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1529, 1525])).
% 8.69/5.82 tff(1531,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1530, 1525])).
% 8.69/5.82 tff(1532,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1531, 1525])).
% 8.69/5.82 tff(1533,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1532, 1525])).
% 8.69/5.82 tff(1534,plain,
% 8.69/5.82 ((~hskp67) | c3_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1533, 1525])).
% 8.69/5.82 tff(1535,plain,
% 8.69/5.82 (c3_1(a1702)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1534, 1524])).
% 8.69/5.82 tff(1536,plain,
% 8.69/5.82 (((~hskp67) | c1_1(a1702)) <=> ((~hskp67) | c1_1(a1702))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1537,axiom,((~hskp67) | c1_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 8.69/5.82 tff(1538,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 8.69/5.82 tff(1539,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1538, 1536])).
% 8.69/5.82 tff(1540,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1539, 1536])).
% 8.69/5.82 tff(1541,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1540, 1536])).
% 8.69/5.82 tff(1542,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1541, 1536])).
% 8.69/5.82 tff(1543,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1542, 1536])).
% 8.69/5.82 tff(1544,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1543, 1536])).
% 8.69/5.82 tff(1545,plain,
% 8.69/5.82 ((~hskp67) | c1_1(a1702)),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1544, 1536])).
% 8.69/5.82 tff(1546,plain,
% 8.69/5.82 (c1_1(a1702)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1545, 1524])).
% 8.69/5.82 tff(1547,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1548,plain,
% 8.69/5.82 (((~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c0_1(a1709)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1709) | c2_1(a1709) | (~c3_1(a1709))) <=> (c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1549,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c0_1(a1709)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1709) | c2_1(a1709) | (~c3_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))))),
% 8.69/5.82 inference(monotonicity,[status(thm)],[1548])).
% 8.69/5.82 tff(1550,plain,
% 8.69/5.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c0_1(a1709)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1709) | c2_1(a1709) | (~c3_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.69/5.82 inference(transitivity,[status(thm)],[1549, 1547])).
% 8.69/5.82 tff(1551,plain,
% 8.69/5.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c0_1(a1709)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1709) | c2_1(a1709) | (~c3_1(a1709)))),
% 8.69/5.82 inference(quant_inst,[status(thm)],[])).
% 8.69/5.82 tff(1552,plain,
% 8.69/5.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))),
% 8.69/5.82 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 8.69/5.82 tff(1553,plain,
% 8.69/5.82 (~c0_1(a1702)),
% 8.69/5.82 inference(unit_resolution,[status(thm)],[1552, 221, 1454, 1443, 1546, 1535, 1432, 647, 1461])).
% 8.69/5.82 tff(1554,plain,
% 8.69/5.82 (^[V: $i, U: $i] : refl((hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1555,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.82 inference(quant_intro,[status(thm)],[1554])).
% 8.69/5.82 tff(1556,plain,
% 8.69/5.82 (![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.82 inference(rewrite,[status(thm)],[])).
% 8.69/5.82 tff(1557,plain,
% 8.69/5.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp73) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp73))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp73) <=> (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp73) <=> (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 8.69/5.82 inference(bind,[status(th)],[])).
% 8.69/5.82 tff(1558,plain,
% 8.69/5.82 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp73) <=> ![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.83 inference(quant_intro,[status(thm)],[1557])).
% 8.69/5.83 tff(1559,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause351')).
% 8.69/5.83 tff(1560,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 8.69/5.83 tff(1561,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1560, 1556])).
% 8.69/5.83 tff(1562,plain,(
% 8.69/5.83 ![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.83 inference(skolemize,[status(sab)],[1561])).
% 8.69/5.83 tff(1563,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1562, 1555])).
% 8.69/5.83 tff(1564,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1565,plain,
% 8.69/5.83 ((hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702))) <=> (hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1566,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)))),
% 8.69/5.83 inference(monotonicity,[status(thm)],[1565])).
% 8.69/5.83 tff(1567,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.69/5.83 inference(transitivity,[status(thm)],[1566, 1564])).
% 8.69/5.83 tff(1568,plain,
% 8.69/5.83 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 8.69/5.83 inference(quant_inst,[status(thm)],[])).
% 8.69/5.83 tff(1569,plain,
% 8.69/5.83 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 8.69/5.83 tff(1570,plain,
% 8.69/5.83 (hskp73),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1569, 221, 1546, 1535, 1471, 1470, 1469, 1563, 1553])).
% 8.69/5.83 tff(1571,plain,
% 8.69/5.83 (((~hskp73) | (~c3_1(a1716))) <=> ((~hskp73) | (~c3_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1572,plain,
% 8.69/5.83 (((~c3_1(a1716)) | (~hskp73)) <=> ((~hskp73) | (~c3_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1573,axiom,((~c3_1(a1716)) | (~hskp73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 8.69/5.83 tff(1574,plain,
% 8.69/5.83 ((~hskp73) | (~c3_1(a1716))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 8.69/5.83 tff(1575,plain,
% 8.69/5.83 ((~hskp73) | (~c3_1(a1716))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1574, 1571])).
% 8.69/5.83 tff(1576,plain,
% 8.69/5.83 (~c3_1(a1716)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1575, 1570])).
% 8.69/5.83 tff(1577,plain,
% 8.69/5.83 (((~hskp39) | c3_1(a1721)) <=> ((~hskp39) | c3_1(a1721))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1578,axiom,((~hskp39) | c3_1(a1721)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 8.69/5.83 tff(1579,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 8.69/5.83 tff(1580,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1579, 1577])).
% 8.69/5.83 tff(1581,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1580, 1577])).
% 8.69/5.83 tff(1582,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1581, 1577])).
% 8.69/5.83 tff(1583,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1582, 1577])).
% 8.69/5.83 tff(1584,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1583, 1577])).
% 8.69/5.83 tff(1585,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1584, 1577])).
% 8.69/5.83 tff(1586,plain,
% 8.69/5.83 ((~hskp39) | c3_1(a1721)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1585, 1577])).
% 8.69/5.83 tff(1587,plain,
% 8.69/5.83 (c3_1(a1721)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1586, 1495])).
% 8.69/5.83 tff(1588,plain,
% 8.69/5.83 (((~hskp73) | c2_1(a1716)) <=> ((~hskp73) | c2_1(a1716))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1589,axiom,((~hskp73) | c2_1(a1716)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 8.69/5.83 tff(1590,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 8.69/5.83 tff(1591,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1590, 1588])).
% 8.69/5.83 tff(1592,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1591, 1588])).
% 8.69/5.83 tff(1593,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1592, 1588])).
% 8.69/5.83 tff(1594,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1593, 1588])).
% 8.69/5.83 tff(1595,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1594, 1588])).
% 8.69/5.83 tff(1596,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1595, 1588])).
% 8.69/5.83 tff(1597,plain,
% 8.69/5.83 ((~hskp73) | c2_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1596, 1588])).
% 8.69/5.83 tff(1598,plain,
% 8.69/5.83 (c2_1(a1716)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1597, 1570])).
% 8.69/5.83 tff(1599,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1600,plain,
% 8.69/5.83 (((~ndr1_0) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716))) <=> (c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1601,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.69/5.83 inference(monotonicity,[status(thm)],[1600])).
% 8.69/5.83 tff(1602,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.69/5.83 inference(transitivity,[status(thm)],[1601, 1599])).
% 8.69/5.83 tff(1603,plain,
% 8.69/5.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.69/5.83 inference(quant_inst,[status(thm)],[])).
% 8.69/5.83 tff(1604,plain,
% 8.69/5.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1709) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 8.69/5.83 tff(1605,plain,
% 8.69/5.83 (~c1_1(a1716)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1604, 221, 1598, 1454, 1443, 1587, 1576, 1432, 1507, 1501, 102])).
% 8.69/5.83 tff(1606,plain,
% 8.69/5.83 (((~hskp73) | c0_1(a1716)) <=> ((~hskp73) | c0_1(a1716))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1607,axiom,((~hskp73) | c0_1(a1716)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 8.69/5.83 tff(1608,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 8.69/5.83 tff(1609,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1608, 1606])).
% 8.69/5.83 tff(1610,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1609, 1606])).
% 8.69/5.83 tff(1611,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1610, 1606])).
% 8.69/5.83 tff(1612,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1611, 1606])).
% 8.69/5.83 tff(1613,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1612, 1606])).
% 8.69/5.83 tff(1614,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1613, 1606])).
% 8.69/5.83 tff(1615,plain,
% 8.69/5.83 ((~hskp73) | c0_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1614, 1606])).
% 8.69/5.83 tff(1616,plain,
% 8.69/5.83 (c0_1(a1716)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1615, 1570])).
% 8.69/5.83 tff(1617,assumption,(~c1_1(a1716)), introduced(assumption)).
% 8.69/5.83 tff(1618,plain,
% 8.69/5.83 (^[V: $i, U: $i] : refl((hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 8.69/5.83 inference(bind,[status(th)],[])).
% 8.69/5.83 tff(1619,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(quant_intro,[status(thm)],[1618])).
% 8.69/5.83 tff(1620,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1621,plain,
% 8.69/5.83 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp57) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp57))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp57) <=> (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp57) <=> (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 8.69/5.83 inference(bind,[status(th)],[])).
% 8.69/5.83 tff(1622,plain,
% 8.69/5.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp57) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(quant_intro,[status(thm)],[1621])).
% 8.69/5.83 tff(1623,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause342')).
% 8.69/5.83 tff(1624,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 8.69/5.83 tff(1625,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1624, 1620])).
% 8.69/5.83 tff(1626,plain,(
% 8.69/5.83 ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(skolemize,[status(sab)],[1625])).
% 8.69/5.83 tff(1627,plain,
% 8.69/5.83 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1626, 1619])).
% 8.69/5.83 tff(1628,assumption,(~hskp57), introduced(assumption)).
% 8.69/5.83 tff(1629,assumption,(~c2_1(a1709)), introduced(assumption)).
% 8.69/5.83 tff(1630,plain,
% 8.69/5.83 (^[U: $i] : refl((hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 8.69/5.83 inference(bind,[status(th)],[])).
% 8.69/5.83 tff(1631,plain,
% 8.69/5.83 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(quant_intro,[status(thm)],[1630])).
% 8.69/5.83 tff(1632,plain,
% 8.69/5.83 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1633,plain,
% 8.69/5.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp57) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp57))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp57) <=> (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp57) <=> (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 8.69/5.83 inference(bind,[status(th)],[])).
% 8.69/5.83 tff(1634,plain,
% 8.69/5.83 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp57) <=> ![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(quant_intro,[status(thm)],[1633])).
% 8.69/5.83 tff(1635,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause326')).
% 8.69/5.83 tff(1636,plain,
% 8.69/5.83 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 8.69/5.83 tff(1637,plain,
% 8.69/5.83 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1636, 1632])).
% 8.69/5.83 tff(1638,plain,(
% 8.69/5.83 ![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(skolemize,[status(sab)],[1637])).
% 8.69/5.83 tff(1639,plain,
% 8.69/5.83 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1638, 1631])).
% 8.69/5.83 tff(1640,assumption,(c3_1(a1709)), introduced(assumption)).
% 8.69/5.83 tff(1641,assumption,(c0_1(a1709)), introduced(assumption)).
% 8.69/5.83 tff(1642,plain,
% 8.69/5.83 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1643,plain,
% 8.69/5.83 ((hskp57 | hskp11 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709))) <=> (hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1644,plain,
% 8.69/5.83 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)))),
% 8.69/5.83 inference(monotonicity,[status(thm)],[1643])).
% 8.69/5.83 tff(1645,plain,
% 8.69/5.83 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.83 inference(transitivity,[status(thm)],[1644, 1642])).
% 8.69/5.83 tff(1646,plain,
% 8.69/5.83 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.83 inference(quant_inst,[status(thm)],[])).
% 8.69/5.83 tff(1647,plain,
% 8.69/5.83 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 8.69/5.83 tff(1648,plain,
% 8.69/5.83 (hskp57 | hskp11),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1647, 221, 1641, 1640, 1639, 1629])).
% 8.69/5.83 tff(1649,plain,
% 8.69/5.83 (hskp11),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1648, 1628])).
% 8.69/5.83 tff(1650,plain,
% 8.69/5.83 (((~hskp11) | (~c2_1(a1664))) <=> ((~hskp11) | (~c2_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1651,plain,
% 8.69/5.83 (((~c2_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1652,axiom,((~c2_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause287')).
% 8.69/5.83 tff(1653,plain,
% 8.69/5.83 ((~hskp11) | (~c2_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 8.69/5.83 tff(1654,plain,
% 8.69/5.83 ((~hskp11) | (~c2_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1653, 1650])).
% 8.69/5.83 tff(1655,plain,
% 8.69/5.83 (~c2_1(a1664)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1654, 1649])).
% 8.69/5.83 tff(1656,plain,
% 8.69/5.83 (((~hskp11) | (~c3_1(a1664))) <=> ((~hskp11) | (~c3_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1657,plain,
% 8.69/5.83 (((~c3_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1658,axiom,((~c3_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 8.69/5.83 tff(1659,plain,
% 8.69/5.83 ((~hskp11) | (~c3_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 8.69/5.83 tff(1660,plain,
% 8.69/5.83 ((~hskp11) | (~c3_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1659, 1656])).
% 8.69/5.83 tff(1661,plain,
% 8.69/5.83 (~c3_1(a1664)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1660, 1649])).
% 8.69/5.83 tff(1662,assumption,(~c3_1(a1716)), introduced(assumption)).
% 8.69/5.83 tff(1663,assumption,(c2_1(a1716)), introduced(assumption)).
% 8.69/5.83 tff(1664,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1665,plain,
% 8.69/5.83 ((hskp57 | (~ndr1_0) | c3_1(a1664) | c2_1(a1664) | (~c0_1(a1664)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716))) <=> (hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1666,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1664) | c2_1(a1664) | (~c0_1(a1664)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.69/5.83 inference(monotonicity,[status(thm)],[1665])).
% 8.69/5.83 tff(1667,plain,
% 8.69/5.83 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1664) | c2_1(a1664) | (~c0_1(a1664)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.69/5.83 inference(transitivity,[status(thm)],[1666, 1664])).
% 8.69/5.83 tff(1668,plain,
% 8.69/5.83 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1664) | c2_1(a1664) | (~c0_1(a1664)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))),
% 8.69/5.83 inference(quant_inst,[status(thm)],[])).
% 8.69/5.83 tff(1669,plain,
% 8.69/5.83 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 8.69/5.83 tff(1670,plain,
% 8.69/5.83 (~c0_1(a1664)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1669, 221, 1628, 1663, 1662, 1661, 1655, 1627, 1617])).
% 8.69/5.83 tff(1671,plain,
% 8.69/5.83 (((~hskp11) | (~c1_1(a1664))) <=> ((~hskp11) | (~c1_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1672,plain,
% 8.69/5.83 (((~c1_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a1664)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1673,axiom,((~c1_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 8.69/5.83 tff(1674,plain,
% 8.69/5.83 ((~hskp11) | (~c1_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 8.69/5.83 tff(1675,plain,
% 8.69/5.83 ((~hskp11) | (~c1_1(a1664))),
% 8.69/5.83 inference(modus_ponens,[status(thm)],[1674, 1671])).
% 8.69/5.83 tff(1676,plain,
% 8.69/5.83 (~c1_1(a1664)),
% 8.69/5.83 inference(unit_resolution,[status(thm)],[1675, 1649])).
% 8.69/5.83 tff(1677,assumption,(c0_1(a1716)), introduced(assumption)).
% 8.69/5.83 tff(1678,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1679,plain,
% 8.69/5.83 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1664) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664)) <=> (c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.83 inference(rewrite,[status(thm)],[])).
% 8.69/5.83 tff(1680,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1664) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.69/5.83 inference(monotonicity,[status(thm)],[1679])).
% 8.69/5.83 tff(1681,plain,
% 8.69/5.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1664) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.83 inference(transitivity,[status(thm)],[1680, 1678])).
% 8.69/5.83 tff(1682,plain,
% 8.69/5.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1664) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1683,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 8.69/5.84 tff(1684,plain,
% 8.69/5.84 ($false),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1683, 221, 1663, 1677, 1662, 1661, 1655, 1676, 30, 1670])).
% 8.69/5.84 tff(1685,plain,(hskp57 | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1709)) | (~c3_1(a1709)) | c2_1(a1709)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.84 tff(1686,plain,
% 8.69/5.84 (hskp57),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1685, 1598, 1616, 1576, 1605, 1454, 1443, 1461])).
% 8.69/5.84 tff(1687,plain,
% 8.69/5.84 (~c1_1(a1665)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[65, 1686])).
% 8.69/5.84 tff(1688,plain,
% 8.69/5.84 (c3_1(a1665)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[76, 1686])).
% 8.69/5.84 tff(1689,plain,
% 8.69/5.84 (c0_1(a1665)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[90, 1686])).
% 8.69/5.84 tff(1690,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1691,plain,
% 8.69/5.84 (((~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)) | c1_1(a1665) | (~c2_1(a1665)) | (~c0_1(a1665)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715)) <=> (c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1692,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)) | c1_1(a1665) | (~c2_1(a1665)) | (~c0_1(a1665)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1691])).
% 8.69/5.84 tff(1693,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)) | c1_1(a1665) | (~c2_1(a1665)) | (~c0_1(a1665)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1692, 1690])).
% 8.69/5.84 tff(1694,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)) | c1_1(a1665) | (~c2_1(a1665)) | (~c0_1(a1665)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1715))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1695,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 8.69/5.84 tff(1696,plain,
% 8.69/5.84 (~c2_1(a1665)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1695, 221, 363, 1689, 1688, 1309, 1687, 565, 1297])).
% 8.69/5.84 tff(1697,assumption,(~c1_1(a1673)), introduced(assumption)).
% 8.69/5.84 tff(1698,assumption,(hskp71), introduced(assumption)).
% 8.69/5.84 tff(1699,plain,
% 8.69/5.84 (((~hskp71) | (~c2_1(a1713))) <=> ((~hskp71) | (~c2_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1700,plain,
% 8.69/5.84 (((~c2_1(a1713)) | (~hskp71)) <=> ((~hskp71) | (~c2_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1701,axiom,((~c2_1(a1713)) | (~hskp71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 8.69/5.84 tff(1702,plain,
% 8.69/5.84 ((~hskp71) | (~c2_1(a1713))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 8.69/5.84 tff(1703,plain,
% 8.69/5.84 ((~hskp71) | (~c2_1(a1713))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1702, 1699])).
% 8.69/5.84 tff(1704,plain,
% 8.69/5.84 (~c2_1(a1713)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1703, 1698])).
% 8.69/5.84 tff(1705,assumption,(c2_1(a1673)), introduced(assumption)).
% 8.69/5.84 tff(1706,assumption,(c3_1(a1673)), introduced(assumption)).
% 8.69/5.84 tff(1707,plain,
% 8.69/5.84 (((~hskp71) | c0_1(a1713)) <=> ((~hskp71) | c0_1(a1713))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1708,axiom,((~hskp71) | c0_1(a1713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 8.69/5.84 tff(1709,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 8.69/5.84 tff(1710,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1709, 1707])).
% 8.69/5.84 tff(1711,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1710, 1707])).
% 8.69/5.84 tff(1712,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1711, 1707])).
% 8.69/5.84 tff(1713,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1712, 1707])).
% 8.69/5.84 tff(1714,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1713, 1707])).
% 8.69/5.84 tff(1715,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1714, 1707])).
% 8.69/5.84 tff(1716,plain,
% 8.69/5.84 ((~hskp71) | c0_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1715, 1707])).
% 8.69/5.84 tff(1717,plain,
% 8.69/5.84 (c0_1(a1713)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1716, 1698])).
% 8.69/5.84 tff(1718,plain,
% 8.69/5.84 (((~hskp71) | c3_1(a1713)) <=> ((~hskp71) | c3_1(a1713))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1719,axiom,((~hskp71) | c3_1(a1713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 8.69/5.84 tff(1720,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 8.69/5.84 tff(1721,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1720, 1718])).
% 8.69/5.84 tff(1722,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1721, 1718])).
% 8.69/5.84 tff(1723,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1722, 1718])).
% 8.69/5.84 tff(1724,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1723, 1718])).
% 8.69/5.84 tff(1725,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1724, 1718])).
% 8.69/5.84 tff(1726,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1725, 1718])).
% 8.69/5.84 tff(1727,plain,
% 8.69/5.84 ((~hskp71) | c3_1(a1713)),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1726, 1718])).
% 8.69/5.84 tff(1728,plain,
% 8.69/5.84 (c3_1(a1713)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1727, 1698])).
% 8.69/5.84 tff(1729,assumption,(~c2_1(a1713)), introduced(assumption)).
% 8.69/5.84 tff(1730,assumption,(c0_1(a1713)), introduced(assumption)).
% 8.69/5.84 tff(1731,assumption,(c3_1(a1713)), introduced(assumption)).
% 8.69/5.84 tff(1732,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1733,plain,
% 8.69/5.84 (((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1734,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1733])).
% 8.69/5.84 tff(1735,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1734, 1732])).
% 8.69/5.84 tff(1736,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1737,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 8.69/5.84 tff(1738,plain,
% 8.69/5.84 (~c3_1(a1678)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1737, 221, 1731, 1730, 1706, 1705, 1729, 1697, 248, 261, 376])).
% 8.69/5.84 tff(1739,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1740,plain,
% 8.69/5.84 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678)) <=> (c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1741,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1740])).
% 8.69/5.84 tff(1742,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1741, 1739])).
% 8.69/5.84 tff(1743,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1744,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 8.69/5.84 tff(1745,plain,
% 8.69/5.84 ($false),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1744, 221, 1663, 1677, 1662, 248, 242, 261, 30, 1738])).
% 8.69/5.84 tff(1746,plain,((~hskp17) | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | (~c3_1(a1713)) | (~c0_1(a1713)) | (~c3_1(a1673)) | (~c2_1(a1673)) | c2_1(a1713) | c1_1(a1673)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.84 tff(1747,plain,
% 8.69/5.84 (~hskp17),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1746, 1728, 1677, 1662, 1663, 1717, 1706, 1705, 1704, 1697])).
% 8.69/5.84 tff(1748,assumption,(~c1_1(a1709)), introduced(assumption)).
% 8.69/5.84 tff(1749,plain,
% 8.69/5.84 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1750,plain,
% 8.69/5.84 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709))) <=> (hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1751,plain,
% 8.69/5.84 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1750])).
% 8.69/5.84 tff(1752,plain,
% 8.69/5.84 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1751, 1749])).
% 8.69/5.84 tff(1753,plain,
% 8.69/5.84 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1754,plain,
% 8.69/5.84 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 8.69/5.84 tff(1755,plain,
% 8.69/5.84 (hskp17 | hskp16),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1754, 221, 1641, 1640, 1748, 10])).
% 8.69/5.84 tff(1756,plain,
% 8.69/5.84 (hskp16),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1755, 1747])).
% 8.69/5.84 tff(1757,plain,
% 8.69/5.84 (~c2_1(a1677)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[117, 1756])).
% 8.69/5.84 tff(1758,plain,
% 8.69/5.84 (~c0_1(a1677)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[123, 1756])).
% 8.69/5.84 tff(1759,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1760,plain,
% 8.69/5.84 (((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1761,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1760])).
% 8.69/5.84 tff(1762,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1761, 1759])).
% 8.69/5.84 tff(1763,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1713) | (~c3_1(a1713)) | (~c0_1(a1713)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1764,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1713) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1713)) | (~c0_1(a1713))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 8.69/5.84 tff(1765,plain,
% 8.69/5.84 (~c3_1(a1677)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1764, 221, 1728, 1717, 1706, 1705, 1704, 1697, 1758, 1757, 376])).
% 8.69/5.84 tff(1766,plain,
% 8.69/5.84 (~c1_1(a1677)),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[111, 1756])).
% 8.69/5.84 tff(1767,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1768,plain,
% 8.69/5.84 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677)) <=> (c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1769,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1768])).
% 8.69/5.84 tff(1770,plain,
% 8.69/5.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1769, 1767])).
% 8.69/5.84 tff(1771,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1772,plain,
% 8.69/5.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 8.69/5.84 tff(1773,plain,
% 8.69/5.84 ($false),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1772, 221, 1663, 1677, 1662, 1758, 1757, 1766, 30, 1765])).
% 8.69/5.84 tff(1774,plain,((~hskp71) | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c0_1(a1709)) | (~c3_1(a1709)) | c1_1(a1709)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.84 tff(1775,plain,
% 8.69/5.84 (~hskp71),
% 8.69/5.84 inference(unit_resolution,[status(thm)],[1774, 1598, 1616, 1576, 1471, 1470, 1469, 1454, 1443, 1432])).
% 8.69/5.84 tff(1776,plain,
% 8.69/5.84 (^[U: $i] : refl((hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 8.69/5.84 inference(bind,[status(th)],[])).
% 8.69/5.84 tff(1777,plain,
% 8.69/5.84 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(quant_intro,[status(thm)],[1776])).
% 8.69/5.84 tff(1778,plain,
% 8.69/5.84 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1779,plain,
% 8.69/5.84 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp71) <=> ((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp71))), rewrite(((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp71) <=> (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp71) <=> (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 8.69/5.84 inference(bind,[status(th)],[])).
% 8.69/5.84 tff(1780,plain,
% 8.69/5.84 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp71) <=> ![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(quant_intro,[status(thm)],[1779])).
% 8.69/5.84 tff(1781,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause320')).
% 8.69/5.84 tff(1782,plain,
% 8.69/5.84 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 8.69/5.84 tff(1783,plain,
% 8.69/5.84 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1782, 1778])).
% 8.69/5.84 tff(1784,plain,(
% 8.69/5.84 ![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(skolemize,[status(sab)],[1783])).
% 8.69/5.84 tff(1785,plain,
% 8.69/5.84 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1784, 1777])).
% 8.69/5.84 tff(1786,plain,
% 8.69/5.84 (((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1787,plain,
% 8.69/5.84 ((hskp71 | hskp36 | (~ndr1_0) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.84 inference(rewrite,[status(thm)],[])).
% 8.69/5.84 tff(1788,plain,
% 8.69/5.84 (((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp71 | hskp36 | (~ndr1_0) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715))))),
% 8.69/5.84 inference(monotonicity,[status(thm)],[1787])).
% 8.69/5.84 tff(1789,plain,
% 8.69/5.84 (((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp71 | hskp36 | (~ndr1_0) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.84 inference(transitivity,[status(thm)],[1788, 1786])).
% 8.69/5.84 tff(1790,plain,
% 8.69/5.84 ((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp71 | hskp36 | (~ndr1_0) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.84 inference(quant_inst,[status(thm)],[])).
% 8.69/5.84 tff(1791,plain,
% 8.69/5.84 ((~![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp71 | hskp36 | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715))),
% 8.69/5.84 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 8.69/5.84 tff(1792,plain,
% 8.69/5.84 (hskp71 | hskp36 | (~c1_1(a1715))),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1791, 221, 1309, 1785, 1297])).
% 8.69/5.85 tff(1793,plain,
% 8.69/5.85 (hskp36),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1792, 1775, 1342])).
% 8.69/5.85 tff(1794,plain,
% 8.69/5.85 (((~hskp36) | (~c0_1(a1712))) <=> ((~hskp36) | (~c0_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1795,plain,
% 8.69/5.85 (((~c0_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c0_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1796,axiom,((~c0_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 8.69/5.85 tff(1797,plain,
% 8.69/5.85 ((~hskp36) | (~c0_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 8.69/5.85 tff(1798,plain,
% 8.69/5.85 ((~hskp36) | (~c0_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1797, 1794])).
% 8.69/5.85 tff(1799,plain,
% 8.69/5.85 (~c0_1(a1712)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1798, 1793])).
% 8.69/5.85 tff(1800,plain,
% 8.69/5.85 (((~hskp36) | (~c2_1(a1712))) <=> ((~hskp36) | (~c2_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1801,plain,
% 8.69/5.85 (((~c2_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c2_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1802,axiom,((~c2_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause234')).
% 8.69/5.85 tff(1803,plain,
% 8.69/5.85 ((~hskp36) | (~c2_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 8.69/5.85 tff(1804,plain,
% 8.69/5.85 ((~hskp36) | (~c2_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1803, 1800])).
% 8.69/5.85 tff(1805,plain,
% 8.69/5.85 (~c2_1(a1712)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1804, 1793])).
% 8.69/5.85 tff(1806,plain,
% 8.69/5.85 (((~hskp36) | (~c1_1(a1712))) <=> ((~hskp36) | (~c1_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1807,plain,
% 8.69/5.85 (((~c1_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c1_1(a1712)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1808,axiom,((~c1_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 8.69/5.85 tff(1809,plain,
% 8.69/5.85 ((~hskp36) | (~c1_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 8.69/5.85 tff(1810,plain,
% 8.69/5.85 ((~hskp36) | (~c1_1(a1712))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1809, 1806])).
% 8.69/5.85 tff(1811,plain,
% 8.69/5.85 (~c1_1(a1712)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1810, 1793])).
% 8.69/5.85 tff(1812,assumption,(~c2_1(a1712)), introduced(assumption)).
% 8.69/5.85 tff(1813,assumption,(~c2_1(a1665)), introduced(assumption)).
% 8.69/5.85 tff(1814,assumption,(~c0_1(a1712)), introduced(assumption)).
% 8.69/5.85 tff(1815,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1816,plain,
% 8.69/5.85 (((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1712) | c2_1(a1712) | (~c3_1(a1712)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1817,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1712) | c2_1(a1712) | (~c3_1(a1712)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1816])).
% 8.69/5.85 tff(1818,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1712) | c2_1(a1712) | (~c3_1(a1712)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1817, 1815])).
% 8.69/5.85 tff(1819,plain,
% 8.69/5.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1712) | c2_1(a1712) | (~c3_1(a1712)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1820,plain,
% 8.69/5.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1673) | c2_1(a1712) | c0_1(a1712) | (~ndr1_0) | (~c3_1(a1712)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 8.69/5.85 tff(1821,plain,
% 8.69/5.85 (c2_1(a1712) | (~c3_1(a1712))),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1820, 221, 1706, 1705, 105, 104, 1697, 1814, 376, 1813])).
% 8.69/5.85 tff(1822,plain,
% 8.69/5.85 (~c3_1(a1712)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1821, 1812])).
% 8.69/5.85 tff(1823,assumption,(~c1_1(a1712)), introduced(assumption)).
% 8.69/5.85 tff(1824,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1825,plain,
% 8.69/5.85 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1712) | c2_1(a1712) | c1_1(a1712) | c3_1(a1712) | c1_1(a1712) | c2_1(a1712)) <=> (c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1826,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1712) | c2_1(a1712) | c1_1(a1712) | c3_1(a1712) | c1_1(a1712) | c2_1(a1712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1825])).
% 8.69/5.85 tff(1827,plain,
% 8.69/5.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1712) | c2_1(a1712) | c1_1(a1712) | c3_1(a1712) | c1_1(a1712) | c2_1(a1712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1826, 1824])).
% 8.69/5.85 tff(1828,plain,
% 8.69/5.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1712) | c2_1(a1712) | c1_1(a1712) | c3_1(a1712) | c1_1(a1712) | c2_1(a1712))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1829,plain,
% 8.69/5.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 8.69/5.85 tff(1830,plain,
% 8.69/5.85 ($false),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1829, 221, 1663, 1677, 1662, 1812, 1814, 1823, 30, 1822])).
% 8.69/5.85 tff(1831,plain,(c2_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | c0_1(a1712) | c1_1(a1712) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1673) | c2_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.85 tff(1832,plain,
% 8.69/5.85 ($false),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1831, 1811, 1805, 1616, 1576, 1799, 1598, 1471, 1470, 1689, 1688, 1469, 1696])).
% 8.69/5.85 tff(1833,plain,(c3_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.85 tff(1834,plain,
% 8.69/5.85 (c0_1(a1715)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1833, 1296, 363])).
% 8.69/5.85 tff(1835,assumption,(c0_1(a1715)), introduced(assumption)).
% 8.69/5.85 tff(1836,assumption,(c1_1(a1655)), introduced(assumption)).
% 8.69/5.85 tff(1837,plain,
% 8.69/5.85 (hskp13),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[297, 1836])).
% 8.69/5.85 tff(1838,plain,
% 8.69/5.85 (~c1_1(a1667)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[303, 1837])).
% 8.69/5.85 tff(1839,plain,
% 8.69/5.85 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))),
% 8.69/5.85 inference(bind,[status(th)],[])).
% 8.69/5.85 tff(1840,plain,
% 8.69/5.85 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(quant_intro,[status(thm)],[1839])).
% 8.69/5.85 tff(1841,plain,
% 8.69/5.85 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1842,plain,
% 8.69/5.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | hskp47) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp47))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))))),
% 8.69/5.85 inference(bind,[status(th)],[])).
% 8.69/5.85 tff(1843,plain,
% 8.69/5.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(quant_intro,[status(thm)],[1842])).
% 8.69/5.85 tff(1844,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause352')).
% 8.69/5.85 tff(1845,plain,
% 8.69/5.85 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 8.69/5.85 tff(1846,plain,
% 8.69/5.85 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1845, 1841])).
% 8.69/5.85 tff(1847,plain,(
% 8.69/5.85 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(skolemize,[status(sab)],[1846])).
% 8.69/5.85 tff(1848,plain,
% 8.69/5.85 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1847, 1840])).
% 8.69/5.85 tff(1849,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1850,plain,
% 8.69/5.85 ((hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655))) <=> (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1851,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1850])).
% 8.69/5.85 tff(1852,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1851, 1849])).
% 8.69/5.85 tff(1853,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1854,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 8.69/5.85 tff(1855,plain,
% 8.69/5.85 (hskp47 | (~c1_1(a1655))),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1854, 221, 363, 78, 80, 1309, 1848, 1835])).
% 8.69/5.85 tff(1856,plain,
% 8.69/5.85 (hskp47),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1855, 1836])).
% 8.69/5.85 tff(1857,plain,
% 8.69/5.85 (((~hskp47) | (~c0_1(a1644))) <=> ((~hskp47) | (~c0_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1858,plain,
% 8.69/5.85 (((~c0_1(a1644)) | (~hskp47)) <=> ((~hskp47) | (~c0_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1859,axiom,((~c0_1(a1644)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause220')).
% 8.69/5.85 tff(1860,plain,
% 8.69/5.85 ((~hskp47) | (~c0_1(a1644))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 8.69/5.85 tff(1861,plain,
% 8.69/5.85 ((~hskp47) | (~c0_1(a1644))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1860, 1857])).
% 8.69/5.85 tff(1862,plain,
% 8.69/5.85 (~c0_1(a1644)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1861, 1856])).
% 8.69/5.85 tff(1863,plain,
% 8.69/5.85 (((~hskp47) | (~c1_1(a1644))) <=> ((~hskp47) | (~c1_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1864,plain,
% 8.69/5.85 (((~c1_1(a1644)) | (~hskp47)) <=> ((~hskp47) | (~c1_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1865,axiom,((~c1_1(a1644)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 8.69/5.85 tff(1866,plain,
% 8.69/5.85 ((~hskp47) | (~c1_1(a1644))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 8.69/5.85 tff(1867,plain,
% 8.69/5.85 ((~hskp47) | (~c1_1(a1644))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1866, 1863])).
% 8.69/5.85 tff(1868,plain,
% 8.69/5.85 (~c1_1(a1644)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1867, 1856])).
% 8.69/5.85 tff(1869,plain,
% 8.69/5.85 (c3_1(a1667)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[314, 1837])).
% 8.69/5.85 tff(1870,plain,
% 8.69/5.85 (c0_1(a1667)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[325, 1837])).
% 8.69/5.85 tff(1871,plain,
% 8.69/5.85 (((~hskp47) | c3_1(a1644)) <=> ((~hskp47) | c3_1(a1644))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1872,axiom,((~hskp47) | c3_1(a1644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 8.69/5.85 tff(1873,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 8.69/5.85 tff(1874,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1873, 1871])).
% 8.69/5.85 tff(1875,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1874, 1871])).
% 8.69/5.85 tff(1876,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1875, 1871])).
% 8.69/5.85 tff(1877,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1876, 1871])).
% 8.69/5.85 tff(1878,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1877, 1871])).
% 8.69/5.85 tff(1879,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1878, 1871])).
% 8.69/5.85 tff(1880,plain,
% 8.69/5.85 ((~hskp47) | c3_1(a1644)),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1879, 1871])).
% 8.69/5.85 tff(1881,plain,
% 8.69/5.85 (c3_1(a1644)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1880, 1856])).
% 8.69/5.85 tff(1882,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1883,plain,
% 8.69/5.85 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644))) <=> (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1884,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1883])).
% 8.69/5.85 tff(1885,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1884, 1882])).
% 8.69/5.85 tff(1886,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1887,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 8.69/5.85 tff(1888,plain,
% 8.69/5.85 ($false),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1887, 221, 138, 1881, 1870, 1869, 1868, 1862, 1838, 137])).
% 8.69/5.85 tff(1889,plain,((~c1_1(a1655)) | hskp29 | c3_1(a1715) | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.85 tff(1890,plain,
% 8.69/5.85 (~c1_1(a1655)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1889, 230, 363, 138, 229, 1309, 1835, 231])).
% 8.69/5.85 tff(1891,plain,
% 8.69/5.85 (~hskp17),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[269, 179, 162, 168, 138, 230, 229, 1890])).
% 8.69/5.85 tff(1892,plain,
% 8.69/5.85 (hskp17 | hskp16 | c1_1(a1655)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[278, 221, 230, 229, 10])).
% 8.69/5.85 tff(1893,plain,
% 8.69/5.85 (hskp16),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1892, 1891, 1890])).
% 8.69/5.85 tff(1894,plain,
% 8.69/5.85 (~c1_1(a1677)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[111, 1893])).
% 8.69/5.85 tff(1895,plain,
% 8.69/5.85 (~c0_1(a1677)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[123, 1893])).
% 8.69/5.85 tff(1896,plain,
% 8.69/5.85 (~c3_1(a1677)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[355, 221, 138, 230, 229, 1895, 1894, 137, 1890])).
% 8.69/5.85 tff(1897,plain,
% 8.69/5.85 (~c2_1(a1677)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[117, 1893])).
% 8.69/5.85 tff(1898,plain,
% 8.69/5.85 ($false),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[346, 221, 179, 162, 168, 1895, 1897, 1894, 30, 1896])).
% 8.69/5.85 tff(1899,plain,(hskp52 | hskp29 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.69/5.85 tff(1900,plain,
% 8.69/5.85 (hskp52),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1899, 1296, 138, 363, 1834])).
% 8.69/5.85 tff(1901,plain,
% 8.69/5.85 (hskp52),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1899, 363, 138, 1309, 1835])).
% 8.69/5.85 tff(1902,plain,
% 8.69/5.85 (c0_1(a1654)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[525, 1901])).
% 8.69/5.85 tff(1903,plain,
% 8.69/5.85 (c3_1(a1654)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[536, 1901])).
% 8.69/5.85 tff(1904,plain,
% 8.69/5.85 (c2_1(a1654)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[547, 1901])).
% 8.69/5.85 tff(1905,plain,
% 8.69/5.85 (c3_1(a1677)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[798, 124, 616, 615, 617, 118, 1308])).
% 8.69/5.85 tff(1906,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1907,plain,
% 8.69/5.85 ((hskp69 | (~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1908,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1907])).
% 8.69/5.85 tff(1909,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1908, 1906])).
% 8.69/5.85 tff(1910,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1911,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c1_1(a1715))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 8.69/5.85 tff(1912,plain,
% 8.69/5.85 (hskp69 | (~c3_1(a1677))),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1911, 221, 834, 363, 1309, 124, 112, 1412])).
% 8.69/5.85 tff(1913,plain,
% 8.69/5.85 (hskp69),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1912, 1905])).
% 8.69/5.85 tff(1914,plain,
% 8.69/5.85 (~c1_1(a1709)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1431, 1913])).
% 8.69/5.85 tff(1915,plain,
% 8.69/5.85 (c3_1(a1709)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1442, 1913])).
% 8.69/5.85 tff(1916,plain,
% 8.69/5.85 (c0_1(a1709)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1453, 1913])).
% 8.69/5.85 tff(1917,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1918,plain,
% 8.69/5.85 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))) <=> (hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1919,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1918])).
% 8.69/5.85 tff(1920,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.85 inference(transitivity,[status(thm)],[1919, 1917])).
% 8.69/5.85 tff(1921,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 8.69/5.85 inference(quant_inst,[status(thm)],[])).
% 8.69/5.85 tff(1922,plain,
% 8.69/5.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.85 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 8.69/5.85 tff(1923,plain,
% 8.69/5.85 ($false),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1922, 221, 138, 1916, 1915, 1914, 124, 112, 137, 1905])).
% 8.69/5.85 tff(1924,plain,((~hskp16) | hskp29 | (~c1_1(a1715)) | c3_1(a1715) | c2_1(a1715) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c0_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.69/5.85 tff(1925,plain,
% 8.69/5.85 (~hskp16),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1924, 363, 834, 138, 1309, 1904, 1903, 1902])).
% 8.69/5.85 tff(1926,plain,
% 8.69/5.85 (hskp17 | hskp16 | c1_1(a1654)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[716, 221, 1902, 1903, 10])).
% 8.69/5.85 tff(1927,plain,
% 8.69/5.85 (c1_1(a1654)),
% 8.69/5.85 inference(unit_resolution,[status(thm)],[1926, 272, 271])).
% 8.69/5.85 tff(1928,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1929,plain,
% 8.69/5.85 ((hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654))) <=> (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.85 inference(rewrite,[status(thm)],[])).
% 8.69/5.85 tff(1930,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.69/5.85 inference(monotonicity,[status(thm)],[1929])).
% 8.69/5.85 tff(1931,plain,
% 8.69/5.85 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1930, 1928])).
% 8.69/5.86 tff(1932,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1933,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 8.69/5.86 tff(1934,plain,
% 8.69/5.86 (hskp47 | (~c1_1(a1654))),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1933, 221, 363, 1902, 1903, 1309, 1848, 1835])).
% 8.69/5.86 tff(1935,plain,
% 8.69/5.86 (hskp47),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1934, 1927])).
% 8.69/5.86 tff(1936,plain,
% 8.69/5.86 (~c0_1(a1644)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1861, 1935])).
% 8.69/5.86 tff(1937,plain,
% 8.69/5.86 (~c1_1(a1644)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1867, 1935])).
% 8.69/5.86 tff(1938,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1939,plain,
% 8.69/5.86 ((hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1715) | (~c1_1(a1715)) | (~c0_1(a1715))) <=> (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1940,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1715) | (~c1_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715))))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1939])).
% 8.69/5.86 tff(1941,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1715) | (~c1_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1940, 1938])).
% 8.69/5.86 tff(1942,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1715) | (~c1_1(a1715)) | (~c0_1(a1715)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1943,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 8.69/5.86 tff(1944,plain,
% 8.69/5.86 (hskp61),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1943, 221, 834, 363, 1309, 1249, 1835])).
% 8.69/5.86 tff(1945,plain,
% 8.69/5.86 (~c1_1(a1674)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1193, 1944])).
% 8.69/5.86 tff(1946,plain,
% 8.69/5.86 (c3_1(a1674)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1204, 1944])).
% 8.69/5.86 tff(1947,plain,
% 8.69/5.86 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1948,plain,
% 8.69/5.86 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674))) <=> (hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1949,plain,
% 8.69/5.86 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674))))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1948])).
% 8.69/5.86 tff(1950,plain,
% 8.69/5.86 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1949, 1947])).
% 8.69/5.86 tff(1951,plain,
% 8.69/5.86 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1952,plain,
% 8.69/5.86 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 8.69/5.86 tff(1953,plain,
% 8.69/5.86 (hskp17 | hskp16 | (~c0_1(a1674))),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1952, 221, 1946, 1945, 10])).
% 8.69/5.86 tff(1954,plain,
% 8.69/5.86 (~c0_1(a1674)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1953, 272, 271])).
% 8.69/5.86 tff(1955,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1956,plain,
% 8.69/5.86 ((hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1957,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674)))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1956])).
% 8.69/5.86 tff(1958,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1957, 1955])).
% 8.69/5.86 tff(1959,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1960,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c1_1(a1674) | (~ndr1_0) | (~c1_1(a1715)) | (~c3_1(a1674)) | c0_1(a1674)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 8.69/5.86 tff(1961,plain,
% 8.69/5.86 (hskp69),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1960, 221, 834, 363, 1946, 1309, 1945, 1412, 1954])).
% 8.69/5.86 tff(1962,plain,
% 8.69/5.86 (~c1_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1431, 1961])).
% 8.69/5.86 tff(1963,plain,
% 8.69/5.86 (c3_1(a1644)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1880, 1935])).
% 8.69/5.86 tff(1964,plain,
% 8.69/5.86 (c3_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1442, 1961])).
% 8.69/5.86 tff(1965,plain,
% 8.69/5.86 (c0_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1453, 1961])).
% 8.69/5.86 tff(1966,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1967,plain,
% 8.69/5.86 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644))) <=> (hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1968,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1967])).
% 8.69/5.86 tff(1969,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1968, 1966])).
% 8.69/5.86 tff(1970,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1971,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 8.69/5.86 tff(1972,plain,
% 8.69/5.86 ($false),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1971, 221, 138, 1965, 1964, 1963, 1962, 1937, 1936, 137])).
% 8.69/5.86 tff(1973,plain,(hskp16 | hskp29 | (~c1_1(a1715)) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 8.69/5.86 tff(1974,plain,
% 8.69/5.86 (hskp17),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1973, 1925, 834, 363, 1309, 1835, 138])).
% 8.69/5.86 tff(1975,plain,
% 8.69/5.86 (~c2_1(a1678)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[260, 1974])).
% 8.69/5.86 tff(1976,plain,
% 8.69/5.86 (~c0_1(a1678)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[247, 1974])).
% 8.69/5.86 tff(1977,plain,
% 8.69/5.86 (c3_1(a1678)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[625, 1902, 1904, 1903, 1976, 1975, 1308])).
% 8.69/5.86 tff(1978,plain,
% 8.69/5.86 (~c1_1(a1678)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[241, 1974])).
% 8.69/5.86 tff(1979,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1980,plain,
% 8.69/5.86 ((hskp69 | (~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1981,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715))))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1980])).
% 8.69/5.86 tff(1982,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1981, 1979])).
% 8.69/5.86 tff(1983,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c3_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1984,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c3_1(a1715) | c2_1(a1715) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c1_1(a1715))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 8.69/5.86 tff(1985,plain,
% 8.69/5.86 (hskp69 | (~c3_1(a1678))),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1984, 221, 834, 363, 1309, 1976, 1978, 1412])).
% 8.69/5.86 tff(1986,plain,
% 8.69/5.86 (hskp69),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1985, 1977])).
% 8.69/5.86 tff(1987,plain,
% 8.69/5.86 (~c1_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1431, 1986])).
% 8.69/5.86 tff(1988,plain,
% 8.69/5.86 (c3_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1442, 1986])).
% 8.69/5.86 tff(1989,plain,
% 8.69/5.86 (c0_1(a1709)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1453, 1986])).
% 8.69/5.86 tff(1990,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1991,plain,
% 8.69/5.86 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))) <=> (hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(1992,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[1991])).
% 8.69/5.86 tff(1993,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.86 inference(transitivity,[status(thm)],[1992, 1990])).
% 8.69/5.86 tff(1994,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(1995,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 8.69/5.86 tff(1996,plain,
% 8.69/5.86 ($false),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1995, 221, 138, 1989, 1988, 1987, 1976, 1978, 137, 1977])).
% 8.69/5.86 tff(1997,plain,(c3_1(a1715) | hskp29 | (~c1_1(a1715)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.69/5.86 tff(1998,plain,
% 8.69/5.86 (~c1_1(a1715)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1997, 1296, 138, 363, 1834])).
% 8.69/5.86 tff(1999,plain,
% 8.69/5.86 (c2_1(a1654)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[547, 1900])).
% 8.69/5.86 tff(2000,plain,
% 8.69/5.86 (c3_1(a1654)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[536, 1900])).
% 8.69/5.86 tff(2001,plain,
% 8.69/5.86 (c0_1(a1654)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[525, 1900])).
% 8.69/5.86 tff(2002,plain,
% 8.69/5.86 (^[V: $i, U: $i] : refl((hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 8.69/5.86 inference(bind,[status(th)],[])).
% 8.69/5.86 tff(2003,plain,
% 8.69/5.86 (![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(quant_intro,[status(thm)],[2002])).
% 8.69/5.86 tff(2004,plain,
% 8.69/5.86 (![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2005,plain,
% 8.69/5.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> (((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))))), rewrite((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp63) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp63))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp63) <=> (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp63) <=> (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 8.69/5.86 inference(bind,[status(th)],[])).
% 8.69/5.86 tff(2006,plain,
% 8.69/5.86 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp63) <=> ![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(quant_intro,[status(thm)],[2005])).
% 8.69/5.86 tff(2007,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause355')).
% 8.69/5.86 tff(2008,plain,
% 8.69/5.86 (![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 8.69/5.86 tff(2009,plain,
% 8.69/5.86 (![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2008, 2004])).
% 8.69/5.86 tff(2010,plain,(
% 8.69/5.86 ![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(skolemize,[status(sab)],[2009])).
% 8.69/5.86 tff(2011,plain,
% 8.69/5.86 (![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2010, 2003])).
% 8.69/5.86 tff(2012,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2013,plain,
% 8.69/5.86 ((hskp67 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654))) <=> (hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2014,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.69/5.86 inference(monotonicity,[status(thm)],[2013])).
% 8.69/5.86 tff(2015,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.86 inference(transitivity,[status(thm)],[2014, 2012])).
% 8.69/5.86 tff(2016,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))),
% 8.69/5.86 inference(quant_inst,[status(thm)],[])).
% 8.69/5.86 tff(2017,plain,
% 8.69/5.86 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 8.69/5.86 tff(2018,plain,
% 8.69/5.86 (hskp67),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[2017, 221, 617, 616, 615, 1517, 627])).
% 8.69/5.86 tff(2019,plain,
% 8.69/5.86 (c3_1(a1702)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1534, 2018])).
% 8.69/5.86 tff(2020,plain,
% 8.69/5.86 (((~hskp67) | c2_1(a1702)) <=> ((~hskp67) | c2_1(a1702))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2021,axiom,((~hskp67) | c2_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 8.69/5.86 tff(2022,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 8.69/5.86 tff(2023,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2022, 2020])).
% 8.69/5.86 tff(2024,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2023, 2020])).
% 8.69/5.86 tff(2025,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2024, 2020])).
% 8.69/5.86 tff(2026,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2025, 2020])).
% 8.69/5.86 tff(2027,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2026, 2020])).
% 8.69/5.86 tff(2028,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2027, 2020])).
% 8.69/5.86 tff(2029,plain,
% 8.69/5.86 ((~hskp67) | c2_1(a1702)),
% 8.69/5.86 inference(modus_ponens,[status(thm)],[2028, 2020])).
% 8.69/5.86 tff(2030,plain,
% 8.69/5.86 (c2_1(a1702)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[2029, 2018])).
% 8.69/5.86 tff(2031,plain,
% 8.69/5.86 (c1_1(a1702)),
% 8.69/5.86 inference(unit_resolution,[status(thm)],[1545, 2018])).
% 8.69/5.86 tff(2032,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2033,plain,
% 8.69/5.86 ((hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654))) <=> (hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.69/5.86 inference(rewrite,[status(thm)],[])).
% 8.69/5.86 tff(2034,plain,
% 8.69/5.86 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))))),
% 8.69/5.87 inference(monotonicity,[status(thm)],[2033])).
% 8.69/5.87 tff(2035,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.69/5.87 inference(transitivity,[status(thm)],[2034, 2032])).
% 8.69/5.87 tff(2036,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))),
% 8.69/5.87 inference(quant_inst,[status(thm)],[])).
% 8.69/5.87 tff(2037,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 8.69/5.87 tff(2038,plain,
% 8.69/5.87 (hskp63),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2037, 221, 2031, 2030, 2019, 617, 615, 2011, 627])).
% 8.69/5.87 tff(2039,plain,
% 8.69/5.87 (((~hskp63) | (~c0_1(a1676))) <=> ((~hskp63) | (~c0_1(a1676)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2040,plain,
% 8.69/5.87 (((~c0_1(a1676)) | (~hskp63)) <=> ((~hskp63) | (~c0_1(a1676)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2041,axiom,((~c0_1(a1676)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 8.69/5.87 tff(2042,plain,
% 8.69/5.87 ((~hskp63) | (~c0_1(a1676))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 8.69/5.87 tff(2043,plain,
% 8.69/5.87 ((~hskp63) | (~c0_1(a1676))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2042, 2039])).
% 8.69/5.87 tff(2044,plain,
% 8.69/5.87 (~c0_1(a1676)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2043, 2038])).
% 8.69/5.87 tff(2045,plain,
% 8.69/5.87 (((~hskp63) | c3_1(a1676)) <=> ((~hskp63) | c3_1(a1676))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2046,axiom,((~hskp63) | c3_1(a1676)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 8.69/5.87 tff(2047,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 8.69/5.87 tff(2048,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2047, 2045])).
% 8.69/5.87 tff(2049,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2048, 2045])).
% 8.69/5.87 tff(2050,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2049, 2045])).
% 8.69/5.87 tff(2051,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2050, 2045])).
% 8.69/5.87 tff(2052,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2051, 2045])).
% 8.69/5.87 tff(2053,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2052, 2045])).
% 8.69/5.87 tff(2054,plain,
% 8.69/5.87 ((~hskp63) | c3_1(a1676)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2053, 2045])).
% 8.69/5.87 tff(2055,plain,
% 8.69/5.87 (c3_1(a1676)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2054, 2038])).
% 8.69/5.87 tff(2056,assumption,(~hskp75), introduced(assumption)).
% 8.69/5.87 tff(2057,assumption,(~c2_1(a1716)), introduced(assumption)).
% 8.69/5.87 tff(2058,assumption,(hskp29), introduced(assumption)).
% 8.69/5.87 tff(2059,plain,
% 8.69/5.87 (((~hskp29) | (~c3_1(a1695))) <=> ((~hskp29) | (~c3_1(a1695)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2060,plain,
% 8.69/5.87 (((~c3_1(a1695)) | (~hskp29)) <=> ((~hskp29) | (~c3_1(a1695)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2061,axiom,((~c3_1(a1695)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause248')).
% 8.69/5.87 tff(2062,plain,
% 8.69/5.87 ((~hskp29) | (~c3_1(a1695))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 8.69/5.87 tff(2063,plain,
% 8.69/5.87 ((~hskp29) | (~c3_1(a1695))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2062, 2059])).
% 8.69/5.87 tff(2064,plain,
% 8.69/5.87 (~c3_1(a1695)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2063, 2058])).
% 8.69/5.87 tff(2065,plain,
% 8.69/5.87 (((~hskp29) | c0_1(a1695)) <=> ((~hskp29) | c0_1(a1695))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2066,axiom,((~hskp29) | c0_1(a1695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 8.69/5.87 tff(2067,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 8.69/5.87 tff(2068,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2067, 2065])).
% 8.69/5.87 tff(2069,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2068, 2065])).
% 8.69/5.87 tff(2070,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2069, 2065])).
% 8.69/5.87 tff(2071,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2070, 2065])).
% 8.69/5.87 tff(2072,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2071, 2065])).
% 8.69/5.87 tff(2073,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2072, 2065])).
% 8.69/5.87 tff(2074,plain,
% 8.69/5.87 ((~hskp29) | c0_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2073, 2065])).
% 8.69/5.87 tff(2075,plain,
% 8.69/5.87 (c0_1(a1695)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2074, 2058])).
% 8.69/5.87 tff(2076,plain,
% 8.69/5.87 (((~hskp29) | c2_1(a1695)) <=> ((~hskp29) | c2_1(a1695))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2077,axiom,((~hskp29) | c2_1(a1695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 8.69/5.87 tff(2078,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 8.69/5.87 tff(2079,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2078, 2076])).
% 8.69/5.87 tff(2080,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2079, 2076])).
% 8.69/5.87 tff(2081,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2080, 2076])).
% 8.69/5.87 tff(2082,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2081, 2076])).
% 8.69/5.87 tff(2083,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2082, 2076])).
% 8.69/5.87 tff(2084,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2083, 2076])).
% 8.69/5.87 tff(2085,plain,
% 8.69/5.87 ((~hskp29) | c2_1(a1695)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2084, 2076])).
% 8.69/5.87 tff(2086,plain,
% 8.69/5.87 (c2_1(a1695)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2085, 2058])).
% 8.69/5.87 tff(2087,plain,
% 8.69/5.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2088,plain,
% 8.69/5.87 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2089,plain,
% 8.69/5.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716)))),
% 8.69/5.87 inference(monotonicity,[status(thm)],[2088])).
% 8.69/5.87 tff(2090,plain,
% 8.69/5.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716))),
% 8.69/5.87 inference(transitivity,[status(thm)],[2089, 2087])).
% 8.69/5.87 tff(2091,plain,
% 8.69/5.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.69/5.87 inference(quant_inst,[status(thm)],[])).
% 8.69/5.87 tff(2092,plain,
% 8.69/5.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 8.69/5.87 tff(2093,plain,
% 8.69/5.87 ($false),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2092, 221, 2057, 365, 2086, 2075, 1662, 1309, 2064, 30, 1297, 1617])).
% 8.69/5.87 tff(2094,plain,((~hskp29) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.87 tff(2095,plain,
% 8.69/5.87 (~hskp29),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2094, 1617, 365, 1662, 1309, 1297, 2057])).
% 8.69/5.87 tff(2096,plain,
% 8.69/5.87 (c3_1(a1715)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[1833, 1309, 1297])).
% 8.69/5.87 tff(2097,assumption,(~c0_1(a1716)), introduced(assumption)).
% 8.69/5.87 tff(2098,plain,
% 8.69/5.87 (~hskp73),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[1615, 2097])).
% 8.69/5.87 tff(2099,assumption,(hskp21), introduced(assumption)).
% 8.69/5.87 tff(2100,plain,
% 8.69/5.87 (~c1_1(a1683)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[1417, 2099])).
% 8.69/5.87 tff(2101,plain,
% 8.69/5.87 (c2_1(a1683)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[1383, 2099])).
% 8.69/5.87 tff(2102,plain,
% 8.69/5.87 (c3_1(a1683)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[1394, 2099])).
% 8.69/5.87 tff(2103,assumption,(c3_1(a1715)), introduced(assumption)).
% 8.69/5.87 tff(2104,assumption,(~hskp73), introduced(assumption)).
% 8.69/5.87 tff(2105,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2106,plain,
% 8.69/5.87 ((hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2107,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715))))),
% 8.69/5.87 inference(monotonicity,[status(thm)],[2106])).
% 8.69/5.87 tff(2108,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.87 inference(transitivity,[status(thm)],[2107, 2105])).
% 8.69/5.87 tff(2109,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.69/5.87 inference(quant_inst,[status(thm)],[])).
% 8.69/5.87 tff(2110,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 8.69/5.87 tff(2111,plain,
% 8.69/5.87 ($false),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2110, 221, 2104, 834, 2103, 2102, 2101, 2100, 1563, 1297])).
% 8.69/5.87 tff(2112,plain,((~hskp21) | hskp73 | (~c1_1(a1715)) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.87 tff(2113,plain,
% 8.69/5.87 (~hskp21),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2112, 834, 2098, 2096, 1297])).
% 8.69/5.87 tff(2114,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2115,plain,
% 8.69/5.87 ((hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2116,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716))))),
% 8.69/5.87 inference(monotonicity,[status(thm)],[2115])).
% 8.69/5.87 tff(2117,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716)))),
% 8.69/5.87 inference(transitivity,[status(thm)],[2116, 2114])).
% 8.69/5.87 tff(2118,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.87 inference(quant_inst,[status(thm)],[])).
% 8.69/5.87 tff(2119,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | (~c1_1(a1716))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 8.69/5.87 tff(2120,plain,
% 8.69/5.87 (hskp21 | c2_1(a1716) | (~c1_1(a1715)) | (~c1_1(a1716))),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2119, 221, 1662, 1309, 1357, 1297])).
% 8.69/5.87 tff(2121,plain,
% 8.69/5.87 (~c1_1(a1716)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2120, 2113, 2057, 834])).
% 8.69/5.87 tff(2122,plain,
% 8.69/5.87 (^[V: $i, U: $i] : refl((hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 8.69/5.87 inference(bind,[status(th)],[])).
% 8.69/5.87 tff(2123,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(quant_intro,[status(thm)],[2122])).
% 8.69/5.87 tff(2124,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2125,plain,
% 8.69/5.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(V) | c2_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) | hskp70) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp70))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp70) <=> (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) | hskp70) <=> (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 8.69/5.87 inference(bind,[status(th)],[])).
% 8.69/5.87 tff(2126,plain,
% 8.69/5.87 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) | hskp70) <=> ![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(quant_intro,[status(thm)],[2125])).
% 8.69/5.87 tff(2127,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c2_1(V)) | c0_1(V)) | c3_1(V)) | c1_1(U)) | c0_1(U)) | hskp70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause336')).
% 8.69/5.87 tff(2128,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 8.69/5.87 tff(2129,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2128, 2124])).
% 8.69/5.87 tff(2130,plain,(
% 8.69/5.87 ![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(skolemize,[status(sab)],[2129])).
% 8.69/5.87 tff(2131,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2130, 2123])).
% 8.69/5.87 tff(2132,plain,
% 8.69/5.87 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))),
% 8.69/5.87 inference(bind,[status(th)],[])).
% 8.69/5.87 tff(2133,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(quant_intro,[status(thm)],[2132])).
% 8.69/5.87 tff(2134,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2135,plain,
% 8.69/5.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c0_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)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp25) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp25))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))))),
% 8.69/5.87 inference(bind,[status(th)],[])).
% 8.69/5.87 tff(2136,plain,
% 8.69/5.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(quant_intro,[status(thm)],[2135])).
% 8.69/5.87 tff(2137,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause340')).
% 8.69/5.87 tff(2138,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 8.69/5.87 tff(2139,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2138, 2134])).
% 8.69/5.87 tff(2140,plain,(
% 8.69/5.87 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(skolemize,[status(sab)],[2139])).
% 8.69/5.87 tff(2141,plain,
% 8.69/5.87 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2140, 2133])).
% 8.69/5.87 tff(2142,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2143,plain,
% 8.69/5.87 ((hskp25 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | c3_1(a1716) | c0_1(a1716) | c1_1(a1716)) <=> (hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2144,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp25 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | c3_1(a1716) | c0_1(a1716) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716)))),
% 8.69/5.87 inference(monotonicity,[status(thm)],[2143])).
% 8.69/5.87 tff(2145,plain,
% 8.69/5.87 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp25 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | c3_1(a1716) | c0_1(a1716) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716))),
% 8.69/5.87 inference(transitivity,[status(thm)],[2144, 2142])).
% 8.69/5.87 tff(2146,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp25 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | c3_1(a1716) | c0_1(a1716) | c1_1(a1716))),
% 8.69/5.87 inference(quant_inst,[status(thm)],[])).
% 8.69/5.87 tff(2147,plain,
% 8.69/5.87 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp25 | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | c1_1(a1716)),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 8.69/5.87 tff(2148,plain,
% 8.69/5.87 (hskp25 | c0_1(a1716) | (~c1_1(a1715)) | c1_1(a1716)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2147, 221, 2096, 1662, 2141, 1297])).
% 8.69/5.87 tff(2149,plain,
% 8.69/5.87 (hskp25),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2148, 2121, 2097, 834])).
% 8.69/5.87 tff(2150,plain,
% 8.69/5.87 (((~hskp25) | (~c1_1(a1690))) <=> ((~hskp25) | (~c1_1(a1690)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2151,plain,
% 8.69/5.87 (((~c1_1(a1690)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a1690)))),
% 8.69/5.87 inference(rewrite,[status(thm)],[])).
% 8.69/5.87 tff(2152,axiom,((~c1_1(a1690)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 8.69/5.87 tff(2153,plain,
% 8.69/5.87 ((~hskp25) | (~c1_1(a1690))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 8.69/5.87 tff(2154,plain,
% 8.69/5.87 ((~hskp25) | (~c1_1(a1690))),
% 8.69/5.87 inference(modus_ponens,[status(thm)],[2153, 2150])).
% 8.69/5.87 tff(2155,plain,
% 8.69/5.87 (~c1_1(a1690)),
% 8.69/5.87 inference(unit_resolution,[status(thm)],[2154, 2149])).
% 8.69/5.88 tff(2156,plain,
% 8.69/5.88 (((~hskp25) | (~c0_1(a1690))) <=> ((~hskp25) | (~c0_1(a1690)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2157,plain,
% 8.69/5.88 (((~c0_1(a1690)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1690)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2158,axiom,((~c0_1(a1690)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause257')).
% 8.69/5.88 tff(2159,plain,
% 8.69/5.88 ((~hskp25) | (~c0_1(a1690))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 8.69/5.88 tff(2160,plain,
% 8.69/5.88 ((~hskp25) | (~c0_1(a1690))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2159, 2156])).
% 8.69/5.88 tff(2161,plain,
% 8.69/5.88 (~c0_1(a1690)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2160, 2149])).
% 8.69/5.88 tff(2162,plain,
% 8.69/5.88 (((~hskp25) | c2_1(a1690)) <=> ((~hskp25) | c2_1(a1690))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2163,axiom,((~hskp25) | c2_1(a1690)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 8.69/5.88 tff(2164,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 8.69/5.88 tff(2165,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2164, 2162])).
% 8.69/5.88 tff(2166,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2165, 2162])).
% 8.69/5.88 tff(2167,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2166, 2162])).
% 8.69/5.88 tff(2168,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2167, 2162])).
% 8.69/5.88 tff(2169,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2168, 2162])).
% 8.69/5.88 tff(2170,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2169, 2162])).
% 8.69/5.88 tff(2171,plain,
% 8.69/5.88 ((~hskp25) | c2_1(a1690)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2170, 2162])).
% 8.69/5.88 tff(2172,plain,
% 8.69/5.88 (c2_1(a1690)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2171, 2149])).
% 8.69/5.88 tff(2173,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690)))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2174,plain,
% 8.69/5.88 ((hskp70 | (~ndr1_0) | c0_1(a1690) | c1_1(a1690) | (~c2_1(a1690)) | c3_1(a1716) | c0_1(a1716) | c2_1(a1716)) <=> (hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2175,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1690) | c1_1(a1690) | (~c2_1(a1690)) | c3_1(a1716) | c0_1(a1716) | c2_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2174])).
% 8.69/5.88 tff(2176,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1690) | c1_1(a1690) | (~c2_1(a1690)) | c3_1(a1716) | c0_1(a1716) | c2_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690)))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2175, 2173])).
% 8.69/5.88 tff(2177,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1690) | c1_1(a1690) | (~c2_1(a1690)) | c3_1(a1716) | c0_1(a1716) | c2_1(a1716))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2178,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c0_1(a1690) | c1_1(a1690) | (~ndr1_0) | (~c2_1(a1690))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2177, 2176])).
% 8.69/5.88 tff(2179,plain,
% 8.69/5.88 (hskp70),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2178, 221, 2057, 2097, 2172, 1662, 2161, 2155, 2131])).
% 8.69/5.88 tff(2180,plain,
% 8.69/5.88 (((~hskp70) | (~c3_1(a1710))) <=> ((~hskp70) | (~c3_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2181,plain,
% 8.69/5.88 (((~c3_1(a1710)) | (~hskp70)) <=> ((~hskp70) | (~c3_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2182,axiom,((~c3_1(a1710)) | (~hskp70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 8.69/5.88 tff(2183,plain,
% 8.69/5.88 ((~hskp70) | (~c3_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 8.69/5.88 tff(2184,plain,
% 8.69/5.88 ((~hskp70) | (~c3_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2183, 2180])).
% 8.69/5.88 tff(2185,plain,
% 8.69/5.88 (~c3_1(a1710)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2184, 2179])).
% 8.69/5.88 tff(2186,plain,
% 8.69/5.88 (((~hskp70) | (~c0_1(a1710))) <=> ((~hskp70) | (~c0_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2187,plain,
% 8.69/5.88 (((~c0_1(a1710)) | (~hskp70)) <=> ((~hskp70) | (~c0_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2188,axiom,((~c0_1(a1710)) | (~hskp70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 8.69/5.88 tff(2189,plain,
% 8.69/5.88 ((~hskp70) | (~c0_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 8.69/5.88 tff(2190,plain,
% 8.69/5.88 ((~hskp70) | (~c0_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2189, 2186])).
% 8.69/5.88 tff(2191,plain,
% 8.69/5.88 (~c0_1(a1710)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2190, 2179])).
% 8.69/5.88 tff(2192,plain,
% 8.69/5.88 (((~hskp70) | c1_1(a1710)) <=> ((~hskp70) | c1_1(a1710))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2193,axiom,((~hskp70) | c1_1(a1710)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 8.69/5.88 tff(2194,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 8.69/5.88 tff(2195,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2194, 2192])).
% 8.69/5.88 tff(2196,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2195, 2192])).
% 8.69/5.88 tff(2197,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2196, 2192])).
% 8.69/5.88 tff(2198,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2197, 2192])).
% 8.69/5.88 tff(2199,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2198, 2192])).
% 8.69/5.88 tff(2200,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2199, 2192])).
% 8.69/5.88 tff(2201,plain,
% 8.69/5.88 ((~hskp70) | c1_1(a1710)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2200, 2192])).
% 8.69/5.88 tff(2202,plain,
% 8.69/5.88 (c1_1(a1710)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2201, 2179])).
% 8.69/5.88 tff(2203,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2204,plain,
% 8.69/5.88 ((hskp21 | (~ndr1_0) | c3_1(a1710) | c2_1(a1710) | (~c1_1(a1710)) | c0_1(a1710) | c2_1(a1710) | (~c1_1(a1710))) <=> (hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2205,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1710) | c2_1(a1710) | (~c1_1(a1710)) | c0_1(a1710) | c2_1(a1710) | (~c1_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2204])).
% 8.69/5.88 tff(2206,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1710) | c2_1(a1710) | (~c1_1(a1710)) | c0_1(a1710) | c2_1(a1710) | (~c1_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710)))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2205, 2203])).
% 8.69/5.88 tff(2207,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1710) | c2_1(a1710) | (~c1_1(a1710)) | c0_1(a1710) | c2_1(a1710) | (~c1_1(a1710)))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2208,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 8.69/5.88 tff(2209,plain,
% 8.69/5.88 (c2_1(a1710)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2208, 221, 2113, 2202, 2191, 2185, 1357])).
% 8.69/5.88 tff(2210,plain,
% 8.69/5.88 (^[U: $i] : refl((hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 8.69/5.88 inference(bind,[status(th)],[])).
% 8.69/5.88 tff(2211,plain,
% 8.69/5.88 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(quant_intro,[status(thm)],[2210])).
% 8.69/5.88 tff(2212,plain,
% 8.69/5.88 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2213,plain,
% 8.69/5.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp61))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp61) <=> (hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) <=> (hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) | hskp62) <=> ((hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp62))), rewrite(((hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp62) <=> (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) | hskp62) <=> (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 8.69/5.88 inference(bind,[status(th)],[])).
% 8.69/5.88 tff(2214,plain,
% 8.69/5.88 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) | hskp62) <=> ![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(quant_intro,[status(thm)],[2213])).
% 8.69/5.88 tff(2215,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) | hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause327')).
% 8.69/5.88 tff(2216,plain,
% 8.69/5.88 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 8.69/5.88 tff(2217,plain,
% 8.69/5.88 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2216, 2212])).
% 8.69/5.88 tff(2218,plain,(
% 8.69/5.88 ![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(skolemize,[status(sab)],[2217])).
% 8.69/5.88 tff(2219,plain,
% 8.69/5.88 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2218, 2211])).
% 8.69/5.88 tff(2220,plain,
% 8.69/5.88 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2221,plain,
% 8.69/5.88 ((hskp62 | hskp61 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2222,plain,
% 8.69/5.88 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2221])).
% 8.69/5.88 tff(2223,plain,
% 8.69/5.88 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2222, 2220])).
% 8.69/5.88 tff(2224,plain,
% 8.69/5.88 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2225,plain,
% 8.69/5.88 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 8.69/5.88 tff(2226,plain,
% 8.69/5.88 (hskp62 | hskp61 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2225, 221, 2219, 1297])).
% 8.69/5.88 tff(2227,plain,
% 8.69/5.88 (hskp62),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2226, 1250, 2103, 834])).
% 8.69/5.88 tff(2228,plain,
% 8.69/5.88 (((~hskp62) | c0_1(a1675)) <=> ((~hskp62) | c0_1(a1675))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2229,axiom,((~hskp62) | c0_1(a1675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 8.69/5.88 tff(2230,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 8.69/5.88 tff(2231,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2230, 2228])).
% 8.69/5.88 tff(2232,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2231, 2228])).
% 8.69/5.88 tff(2233,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2232, 2228])).
% 8.69/5.88 tff(2234,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2233, 2228])).
% 8.69/5.88 tff(2235,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2234, 2228])).
% 8.69/5.88 tff(2236,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2235, 2228])).
% 8.69/5.88 tff(2237,plain,
% 8.69/5.88 ((~hskp62) | c0_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2236, 2228])).
% 8.69/5.88 tff(2238,plain,
% 8.69/5.88 (c0_1(a1675)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2237, 2227])).
% 8.69/5.88 tff(2239,plain,
% 8.69/5.88 (((~hskp62) | c1_1(a1675)) <=> ((~hskp62) | c1_1(a1675))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2240,axiom,((~hskp62) | c1_1(a1675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 8.69/5.88 tff(2241,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2240, 2239])).
% 8.69/5.88 tff(2242,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2241, 2239])).
% 8.69/5.88 tff(2243,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2242, 2239])).
% 8.69/5.88 tff(2244,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2243, 2239])).
% 8.69/5.88 tff(2245,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2244, 2239])).
% 8.69/5.88 tff(2246,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2245, 2239])).
% 8.69/5.88 tff(2247,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2246, 2239])).
% 8.69/5.88 tff(2248,plain,
% 8.69/5.88 ((~hskp62) | c1_1(a1675)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2247, 2239])).
% 8.69/5.88 tff(2249,plain,
% 8.69/5.88 (c1_1(a1675)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2248, 2227])).
% 8.69/5.88 tff(2250,plain,
% 8.69/5.88 (((~hskp62) | (~c3_1(a1675))) <=> ((~hskp62) | (~c3_1(a1675)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2251,plain,
% 8.69/5.88 (((~c3_1(a1675)) | (~hskp62)) <=> ((~hskp62) | (~c3_1(a1675)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2252,axiom,((~c3_1(a1675)) | (~hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 8.69/5.88 tff(2253,plain,
% 8.69/5.88 ((~hskp62) | (~c3_1(a1675))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 8.69/5.88 tff(2254,plain,
% 8.69/5.88 ((~hskp62) | (~c3_1(a1675))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2253, 2250])).
% 8.69/5.88 tff(2255,plain,
% 8.69/5.88 (~c3_1(a1675)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2254, 2227])).
% 8.69/5.88 tff(2256,assumption,(~c2_1(a1675)), introduced(assumption)).
% 8.69/5.88 tff(2257,assumption,(~c3_1(a1675)), introduced(assumption)).
% 8.69/5.88 tff(2258,assumption,(c0_1(a1675)), introduced(assumption)).
% 8.69/5.88 tff(2259,assumption,(c1_1(a1675)), introduced(assumption)).
% 8.69/5.88 tff(2260,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2261,plain,
% 8.69/5.88 ((hskp61 | (~ndr1_0) | c3_1(a1675) | c2_1(a1675) | (~c0_1(a1675)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))) <=> (hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2262,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1675) | c2_1(a1675) | (~c0_1(a1675)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2261])).
% 8.69/5.88 tff(2263,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1675) | c2_1(a1675) | (~c0_1(a1675)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2262, 2260])).
% 8.69/5.88 tff(2264,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1675) | c2_1(a1675) | (~c0_1(a1675)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2265,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 8.69/5.88 tff(2266,plain,
% 8.69/5.88 ($false),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2265, 221, 1250, 2259, 2258, 2257, 1249, 2256])).
% 8.69/5.88 tff(2267,plain,(c2_1(a1675) | hskp61 | (~c1_1(a1675)) | (~c0_1(a1675)) | c3_1(a1675)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.88 tff(2268,plain,
% 8.69/5.88 (c2_1(a1675)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2267, 2255, 2249, 2238, 1250])).
% 8.69/5.88 tff(2269,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2270,plain,
% 8.69/5.88 (((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2271,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716)))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2270])).
% 8.69/5.88 tff(2272,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2271, 2269])).
% 8.69/5.88 tff(2273,plain,
% 8.69/5.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2274,plain,
% 8.69/5.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 8.69/5.88 tff(2275,plain,
% 8.69/5.88 ($false),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2274, 221, 2057, 2097, 2238, 1662, 2255, 30, 1617, 2268])).
% 8.69/5.88 tff(2276,plain,(hskp61 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1716) | (~c3_1(a1715)) | (~c1_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.88 tff(2277,plain,
% 8.69/5.88 (hskp61),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2276, 2121, 2097, 1662, 2057, 2096, 834, 1297])).
% 8.69/5.88 tff(2278,plain,
% 8.69/5.88 (~c2_1(a1674)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[1187, 2277])).
% 8.69/5.88 tff(2279,plain,
% 8.69/5.88 (~c1_1(a1674)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[1193, 2277])).
% 8.69/5.88 tff(2280,plain,
% 8.69/5.88 (c3_1(a1674)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[1204, 2277])).
% 8.69/5.88 tff(2281,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2282,plain,
% 8.69/5.88 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1710) | (~c1_1(a1710)) | (~c2_1(a1710))) <=> (hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2283,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1710) | (~c1_1(a1710)) | (~c2_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2282])).
% 8.69/5.88 tff(2284,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1710) | (~c1_1(a1710)) | (~c2_1(a1710)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2283, 2281])).
% 8.69/5.88 tff(2285,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1710) | (~c1_1(a1710)) | (~c2_1(a1710)))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2286,plain,
% 8.69/5.88 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1710) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1710)) | (~c1_1(a1710))),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 8.69/5.88 tff(2287,plain,
% 8.69/5.88 (hskp75),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2286, 221, 2202, 2280, 2185, 2279, 2278, 428, 2209])).
% 8.69/5.88 tff(2288,plain,
% 8.69/5.88 (~c2_1(a1724)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[441, 2287])).
% 8.69/5.88 tff(2289,plain,
% 8.69/5.88 (c3_1(a1724)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[474, 2287])).
% 8.69/5.88 tff(2290,plain,
% 8.69/5.88 (c0_1(a1724)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[485, 2287])).
% 8.69/5.88 tff(2291,assumption,(c2_1(a1710)), introduced(assumption)).
% 8.69/5.88 tff(2292,assumption,(~c0_1(a1674)), introduced(assumption)).
% 8.69/5.88 tff(2293,assumption,(c0_1(a1724)), introduced(assumption)).
% 8.69/5.88 tff(2294,assumption,(~c1_1(a1674)), introduced(assumption)).
% 8.69/5.88 tff(2295,assumption,(~c3_1(a1710)), introduced(assumption)).
% 8.69/5.88 tff(2296,assumption,(c3_1(a1674)), introduced(assumption)).
% 8.69/5.88 tff(2297,assumption,(c1_1(a1710)), introduced(assumption)).
% 8.69/5.88 tff(2298,assumption,(c3_1(a1724)), introduced(assumption)).
% 8.69/5.88 tff(2299,assumption,(~c1_1(a1724)), introduced(assumption)).
% 8.69/5.88 tff(2300,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2301,plain,
% 8.69/5.88 (((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710))) <=> (c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2302,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2301])).
% 8.69/5.88 tff(2303,plain,
% 8.69/5.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.69/5.88 inference(transitivity,[status(thm)],[2302, 2300])).
% 8.69/5.88 tff(2304,plain,
% 8.69/5.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.88 inference(quant_inst,[status(thm)],[])).
% 8.69/5.88 tff(2305,plain,
% 8.69/5.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 8.69/5.88 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 8.69/5.88 tff(2306,plain,
% 8.69/5.88 ($false),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2305, 221, 2293, 2298, 2297, 2296, 2295, 2294, 102, 2292, 2291, 2299])).
% 8.69/5.88 tff(2307,plain,(c0_1(a1674) | (~c0_1(a1724)) | (~c3_1(a1724)) | (~c1_1(a1710)) | (~c3_1(a1674)) | c3_1(a1710) | c1_1(a1674) | (~c2_1(a1710)) | c1_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.88 tff(2308,plain,
% 8.69/5.88 (c1_1(a1724)),
% 8.69/5.88 inference(unit_resolution,[status(thm)],[2307, 2292, 2298, 2297, 2296, 2295, 2294, 2291, 2293])).
% 8.69/5.88 tff(2309,assumption,(~c2_1(a1724)), introduced(assumption)).
% 8.69/5.88 tff(2310,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2311,plain,
% 8.69/5.88 ((hskp13 | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724))) <=> (hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.88 inference(rewrite,[status(thm)],[])).
% 8.69/5.88 tff(2312,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))))),
% 8.69/5.88 inference(monotonicity,[status(thm)],[2311])).
% 8.69/5.88 tff(2313,plain,
% 8.69/5.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2312, 2310])).
% 8.69/5.89 tff(2314,plain,
% 8.69/5.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2315,plain,
% 8.69/5.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 8.69/5.89 tff(2316,plain,
% 8.69/5.89 (hskp13 | (~c1_1(a1724))),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2315, 221, 2293, 2298, 2309, 290])).
% 8.69/5.89 tff(2317,plain,
% 8.69/5.89 (hskp13),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2316, 2308])).
% 8.69/5.89 tff(2318,plain,
% 8.69/5.89 (~c1_1(a1667)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[303, 2317])).
% 8.69/5.89 tff(2319,plain,
% 8.69/5.89 (c3_1(a1667)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[314, 2317])).
% 8.69/5.89 tff(2320,plain,
% 8.69/5.89 (c0_1(a1667)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[325, 2317])).
% 8.69/5.89 tff(2321,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2322,plain,
% 8.69/5.89 (((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710))) <=> (c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2323,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710))))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2322])).
% 8.69/5.89 tff(2324,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2323, 2321])).
% 8.69/5.89 tff(2325,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2326,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710))),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 8.69/5.89 tff(2327,plain,
% 8.69/5.89 ($false),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2326, 221, 2297, 2296, 2320, 2319, 2295, 2294, 2318, 102, 2292, 2291])).
% 8.69/5.89 tff(2328,plain,(c0_1(a1674) | (~c1_1(a1710)) | (~c3_1(a1674)) | c3_1(a1710) | c1_1(a1674) | (~c2_1(a1710)) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.89 tff(2329,plain,
% 8.69/5.89 (c0_1(a1674)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2328, 2202, 2280, 2185, 2279, 2209, 2290, 2289, 2288])).
% 8.69/5.89 tff(2330,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2331,plain,
% 8.69/5.89 (((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2332,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2331])).
% 8.69/5.89 tff(2333,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724)))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2332, 2330])).
% 8.69/5.89 tff(2334,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c0_1(a1724)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2335,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 8.69/5.89 tff(2336,plain,
% 8.69/5.89 ((~c0_1(a1674)) | (~c1_1(a1724))),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2335, 221, 2290, 2289, 2280, 2279, 2278, 647])).
% 8.69/5.89 tff(2337,plain,
% 8.69/5.89 (~c1_1(a1724)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2336, 2329])).
% 8.69/5.89 tff(2338,assumption,(~c2_1(a1674)), introduced(assumption)).
% 8.69/5.89 tff(2339,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2340,plain,
% 8.69/5.89 (((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2341,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2340])).
% 8.69/5.89 tff(2342,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2341, 2339])).
% 8.69/5.89 tff(2343,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2344,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 8.69/5.89 tff(2345,plain,
% 8.69/5.89 (~c1_1(a1654)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2344, 221, 2293, 2296, 929, 894, 2309, 2294, 2338, 647, 2299])).
% 8.69/5.89 tff(2346,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2347,plain,
% 8.69/5.89 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654))) <=> (c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2348,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2347])).
% 8.69/5.89 tff(2349,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2348, 2346])).
% 8.69/5.89 tff(2350,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2351,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 8.69/5.89 tff(2352,plain,
% 8.69/5.89 ($false),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2351, 221, 2293, 2298, 2096, 895, 894, 2309, 1309, 376, 1297, 2345])).
% 8.69/5.89 tff(2353,plain,((~hskp52) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724) | c2_1(a1715) | c0_1(a1715) | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | c1_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.89 tff(2354,plain,
% 8.69/5.89 (~hskp52),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2353, 2290, 2289, 2288, 1309, 1297, 2280, 2279, 2278, 2337])).
% 8.69/5.89 tff(2355,assumption,(hskp53), introduced(assumption)).
% 8.69/5.89 tff(2356,plain,
% 8.69/5.89 (~c3_1(a1656)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[167, 2355])).
% 8.69/5.89 tff(2357,plain,
% 8.69/5.89 (c0_1(a1656)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[161, 2355])).
% 8.69/5.89 tff(2358,plain,
% 8.69/5.89 (c2_1(a1656)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[178, 2355])).
% 8.69/5.89 tff(2359,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2360,plain,
% 8.69/5.89 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2361,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716)))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2360])).
% 8.69/5.89 tff(2362,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2361, 2359])).
% 8.69/5.89 tff(2363,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2364,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716)),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 8.69/5.89 tff(2365,plain,
% 8.69/5.89 ($false),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2364, 221, 2057, 2097, 2358, 2357, 1662, 2356, 30, 1617])).
% 8.69/5.89 tff(2366,plain,((~hskp53) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.89 tff(2367,plain,
% 8.69/5.89 (~hskp53),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2366, 2121, 2097, 1662, 2057])).
% 8.69/5.89 tff(2368,plain,
% 8.69/5.89 (hskp29),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[150, 2367, 2354])).
% 8.69/5.89 tff(2369,plain,
% 8.69/5.89 (~c3_1(a1695)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2063, 2368])).
% 8.69/5.89 tff(2370,plain,
% 8.69/5.89 (c0_1(a1695)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2074, 2368])).
% 8.69/5.89 tff(2371,plain,
% 8.69/5.89 (c2_1(a1695)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2085, 2368])).
% 8.69/5.89 tff(2372,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2373,plain,
% 8.69/5.89 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2374,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716)))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2373])).
% 8.69/5.89 tff(2375,plain,
% 8.69/5.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2374, 2372])).
% 8.69/5.89 tff(2376,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2377,plain,
% 8.69/5.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716)),
% 8.69/5.89 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 8.69/5.89 tff(2378,plain,
% 8.69/5.89 ($false),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2377, 221, 2057, 2097, 2371, 2370, 1662, 2369, 30, 2121])).
% 8.69/5.89 tff(2379,plain,((~c1_1(a1715)) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.89 tff(2380,plain,
% 8.69/5.89 (~c1_1(a1715)),
% 8.69/5.89 inference(unit_resolution,[status(thm)],[2379, 2057, 2097, 1662, 1309, 1297])).
% 8.69/5.89 tff(2381,assumption,(~hskp69), introduced(assumption)).
% 8.69/5.89 tff(2382,plain,
% 8.69/5.89 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2383,plain,
% 8.69/5.89 ((hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716))) <=> (hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)))),
% 8.69/5.89 inference(rewrite,[status(thm)],[])).
% 8.69/5.89 tff(2384,plain,
% 8.69/5.89 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716))))),
% 8.69/5.89 inference(monotonicity,[status(thm)],[2383])).
% 8.69/5.89 tff(2385,plain,
% 8.69/5.89 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)))),
% 8.69/5.89 inference(transitivity,[status(thm)],[2384, 2382])).
% 8.69/5.89 tff(2386,plain,
% 8.69/5.89 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))),
% 8.69/5.89 inference(quant_inst,[status(thm)],[])).
% 8.69/5.89 tff(2387,plain,
% 8.69/5.89 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716))),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 8.69/5.90 tff(2388,plain,
% 8.69/5.90 (hskp69 | c2_1(a1716) | c1_1(a1715) | (~c1_1(a1716))),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2387, 221, 2103, 1662, 1412, 1297])).
% 8.69/5.90 tff(2389,plain,
% 8.69/5.90 (~c1_1(a1716)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2388, 365, 2057, 2381])).
% 8.69/5.90 tff(2390,plain,
% 8.69/5.90 (((~hskp72) | c1_1(a1715)) <=> ((~hskp72) | c1_1(a1715))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2391,axiom,((~hskp72) | c1_1(a1715)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 8.69/5.90 tff(2392,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 8.69/5.90 tff(2393,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2392, 2390])).
% 8.69/5.90 tff(2394,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2393, 2390])).
% 8.69/5.90 tff(2395,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2394, 2390])).
% 8.69/5.90 tff(2396,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2395, 2390])).
% 8.69/5.90 tff(2397,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2396, 2390])).
% 8.69/5.90 tff(2398,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2397, 2390])).
% 8.69/5.90 tff(2399,plain,
% 8.69/5.90 ((~hskp72) | c1_1(a1715)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2398, 2390])).
% 8.69/5.90 tff(2400,plain,
% 8.69/5.90 (~hskp72),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2399, 365])).
% 8.69/5.90 tff(2401,plain,
% 8.69/5.90 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2402,plain,
% 8.69/5.90 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1716) | c3_1(a1716) | c2_1(a1716)) <=> (hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2403,plain,
% 8.69/5.90 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1716) | c3_1(a1716) | c2_1(a1716))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0)))),
% 8.69/5.90 inference(monotonicity,[status(thm)],[2402])).
% 8.69/5.90 tff(2404,plain,
% 8.69/5.90 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1716) | c3_1(a1716) | c2_1(a1716))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0))),
% 8.69/5.90 inference(transitivity,[status(thm)],[2403, 2401])).
% 8.69/5.90 tff(2405,plain,
% 8.69/5.90 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1716) | c3_1(a1716) | c2_1(a1716))),
% 8.69/5.90 inference(quant_inst,[status(thm)],[])).
% 8.69/5.90 tff(2406,plain,
% 8.69/5.90 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 8.69/5.90 tff(2407,plain,
% 8.69/5.90 (hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2406, 221, 1662, 577])).
% 8.69/5.90 tff(2408,plain,
% 8.69/5.90 (hskp37),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2407, 2400, 2057, 2097])).
% 8.69/5.90 tff(2409,plain,
% 8.69/5.90 (c0_1(a1714)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[602, 2408])).
% 8.69/5.90 tff(2410,plain,
% 8.69/5.90 (c2_1(a1714)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[613, 2408])).
% 8.69/5.90 tff(2411,assumption,(~c3_1(a1714)), introduced(assumption)).
% 8.69/5.90 tff(2412,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2413,plain,
% 8.69/5.90 (((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2414,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716)))),
% 8.69/5.90 inference(monotonicity,[status(thm)],[2413])).
% 8.69/5.90 tff(2415,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716))),
% 8.69/5.90 inference(transitivity,[status(thm)],[2414, 2412])).
% 8.69/5.90 tff(2416,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c0_1(a1716) | c2_1(a1716) | c1_1(a1716) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.69/5.90 inference(quant_inst,[status(thm)],[])).
% 8.69/5.90 tff(2417,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716)),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 8.69/5.90 tff(2418,plain,
% 8.69/5.90 ($false),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2417, 221, 2057, 2097, 1324, 1323, 1662, 30, 2411, 1617])).
% 8.69/5.90 tff(2419,plain,(c3_1(a1714) | c2_1(a1716) | c0_1(a1716) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.90 tff(2420,plain,
% 8.69/5.90 (c3_1(a1714)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2419, 2410, 2097, 2057, 2409, 1662, 2389])).
% 8.69/5.90 tff(2421,plain,
% 8.69/5.90 (~c1_1(a1714)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[591, 2408])).
% 8.69/5.90 tff(2422,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2423,plain,
% 8.69/5.90 (((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2424,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.69/5.90 inference(monotonicity,[status(thm)],[2423])).
% 8.69/5.90 tff(2425,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.69/5.90 inference(transitivity,[status(thm)],[2424, 2422])).
% 8.69/5.90 tff(2426,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))),
% 8.69/5.90 inference(quant_inst,[status(thm)],[])).
% 8.69/5.90 tff(2427,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 8.69/5.90 tff(2428,plain,
% 8.69/5.90 ($false),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2427, 221, 2057, 2097, 2410, 2409, 1662, 2421, 565, 2420])).
% 8.69/5.90 tff(2429,plain,(c1_1(a1715) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | hskp69 | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.69/5.90 tff(2430,plain,
% 8.69/5.90 (hskp69),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2429, 2380, 2097, 1662, 2057, 2096, 1297])).
% 8.69/5.90 tff(2431,plain,
% 8.69/5.90 (~c1_1(a1709)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[1431, 2430])).
% 8.69/5.90 tff(2432,plain,
% 8.69/5.90 (c3_1(a1709)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[1442, 2430])).
% 8.69/5.90 tff(2433,plain,
% 8.69/5.90 (c0_1(a1709)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[1453, 2430])).
% 8.69/5.90 tff(2434,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2435,plain,
% 8.69/5.90 (((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2436,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709))))),
% 8.69/5.90 inference(monotonicity,[status(thm)],[2435])).
% 8.69/5.90 tff(2437,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)))),
% 8.69/5.90 inference(transitivity,[status(thm)],[2436, 2434])).
% 8.69/5.90 tff(2438,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709)) | c1_1(a1709) | (~c2_1(a1709)) | (~c0_1(a1709)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))),
% 8.69/5.90 inference(quant_inst,[status(thm)],[])).
% 8.69/5.90 tff(2439,plain,
% 8.69/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709))),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 8.69/5.90 tff(2440,plain,
% 8.69/5.90 (~c2_1(a1709)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2439, 221, 2057, 2097, 2433, 2432, 1662, 2431, 565])).
% 8.69/5.90 tff(2441,plain,
% 8.69/5.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2442,plain,
% 8.69/5.90 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2443,plain,
% 8.69/5.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.69/5.90 inference(monotonicity,[status(thm)],[2442])).
% 8.69/5.90 tff(2444,plain,
% 8.69/5.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.69/5.90 inference(transitivity,[status(thm)],[2443, 2441])).
% 8.69/5.90 tff(2445,plain,
% 8.69/5.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.69/5.90 inference(quant_inst,[status(thm)],[])).
% 8.69/5.90 tff(2446,plain,
% 8.69/5.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.69/5.90 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 8.69/5.90 tff(2447,plain,
% 8.69/5.90 (hskp29),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2446, 221, 2380, 2096, 2433, 2432, 2431, 137, 1297])).
% 8.69/5.90 tff(2448,plain,
% 8.69/5.90 (~c3_1(a1695)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2063, 2447])).
% 8.69/5.90 tff(2449,plain,
% 8.69/5.90 (c0_1(a1695)),
% 8.69/5.90 inference(unit_resolution,[status(thm)],[2074, 2447])).
% 8.69/5.90 tff(2450,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2451,plain,
% 8.69/5.90 (((~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.69/5.90 inference(rewrite,[status(thm)],[])).
% 8.69/5.90 tff(2452,plain,
% 8.69/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)))),
% 8.78/5.90 inference(monotonicity,[status(thm)],[2451])).
% 8.78/5.90 tff(2453,plain,
% 8.78/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709))),
% 8.78/5.90 inference(transitivity,[status(thm)],[2452, 2450])).
% 8.78/5.90 tff(2454,plain,
% 8.78/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.78/5.90 inference(quant_inst,[status(thm)],[])).
% 8.78/5.90 tff(2455,plain,
% 8.78/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709)),
% 8.78/5.90 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 8.78/5.90 tff(2456,plain,
% 8.78/5.90 (c1_1(a1695)),
% 8.78/5.90 inference(unit_resolution,[status(thm)],[2455, 221, 2096, 2433, 2432, 2449, 1309, 2448, 410, 1297, 2440])).
% 8.78/5.90 tff(2457,plain,
% 8.78/5.90 (c2_1(a1695)),
% 8.78/5.90 inference(unit_resolution,[status(thm)],[2085, 2447])).
% 8.78/5.90 tff(2458,plain,
% 8.78/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.78/5.90 inference(rewrite,[status(thm)],[])).
% 8.78/5.90 tff(2459,plain,
% 8.78/5.90 (((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.78/5.90 inference(rewrite,[status(thm)],[])).
% 8.78/5.90 tff(2460,plain,
% 8.78/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.78/5.90 inference(monotonicity,[status(thm)],[2459])).
% 8.78/5.90 tff(2461,plain,
% 8.78/5.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.78/5.90 inference(transitivity,[status(thm)],[2460, 2458])).
% 8.78/5.90 tff(2462,plain,
% 8.78/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.78/5.90 inference(quant_inst,[status(thm)],[])).
% 8.78/5.90 tff(2463,plain,
% 8.78/5.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.78/5.90 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 8.78/5.90 tff(2464,plain,
% 8.78/5.90 ($false),
% 8.78/5.90 inference(unit_resolution,[status(thm)],[2463, 221, 2380, 2096, 2433, 2432, 2457, 2431, 2448, 102, 1297, 2456])).
% 8.78/5.90 tff(2465,plain,(c2_1(a1716) | c0_1(a1715) | c2_1(a1715) | c0_1(a1716) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.90 tff(2466,plain,
% 8.78/5.90 (c2_1(a1716)),
% 8.78/5.90 inference(unit_resolution,[status(thm)],[2465, 2097, 1309, 1297, 1662])).
% 8.78/5.90 tff(2467,plain,
% 8.78/5.90 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.90 inference(rewrite,[status(thm)],[])).
% 8.78/5.90 tff(2468,plain,
% 8.78/5.90 ((hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716))) <=> (hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.90 inference(rewrite,[status(thm)],[])).
% 8.78/5.90 tff(2469,plain,
% 8.78/5.90 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2468])).
% 8.78/5.91 tff(2470,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2469, 2467])).
% 8.78/5.91 tff(2471,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2472,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 8.78/5.91 tff(2473,plain,
% 8.78/5.91 (hskp75 | c1_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2472, 221, 2096, 1662, 1309, 428])).
% 8.78/5.91 tff(2474,plain,
% 8.78/5.91 (~c1_1(a1716)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2473, 365, 1663, 2056])).
% 8.78/5.91 tff(2475,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2476,plain,
% 8.78/5.91 ((hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2477,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2476])).
% 8.78/5.91 tff(2478,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2477, 2475])).
% 8.78/5.91 tff(2479,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2480,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 8.78/5.91 tff(2481,plain,
% 8.78/5.91 (hskp60 | c1_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2480, 221, 2096, 1662, 386, 1297])).
% 8.78/5.91 tff(2482,plain,
% 8.78/5.91 (hskp60),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2481, 365, 1663, 2474])).
% 8.78/5.91 tff(2483,plain,
% 8.78/5.91 (~c1_1(a1673)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[399, 2482])).
% 8.78/5.91 tff(2484,plain,
% 8.78/5.91 (c2_1(a1673)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[452, 2482])).
% 8.78/5.91 tff(2485,plain,
% 8.78/5.91 (c3_1(a1673)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[463, 2482])).
% 8.78/5.91 tff(2486,assumption,(hskp30), introduced(assumption)).
% 8.78/5.91 tff(2487,plain,
% 8.78/5.91 (((~hskp30) | (~c0_1(a1698))) <=> ((~hskp30) | (~c0_1(a1698)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2488,plain,
% 8.78/5.91 (((~c0_1(a1698)) | (~hskp30)) <=> ((~hskp30) | (~c0_1(a1698)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2489,axiom,((~c0_1(a1698)) | (~hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 8.78/5.91 tff(2490,plain,
% 8.78/5.91 ((~hskp30) | (~c0_1(a1698))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 8.78/5.91 tff(2491,plain,
% 8.78/5.91 ((~hskp30) | (~c0_1(a1698))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2490, 2487])).
% 8.78/5.91 tff(2492,plain,
% 8.78/5.91 (~c0_1(a1698)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2491, 2486])).
% 8.78/5.91 tff(2493,plain,
% 8.78/5.91 (((~hskp30) | c3_1(a1698)) <=> ((~hskp30) | c3_1(a1698))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2494,axiom,((~hskp30) | c3_1(a1698)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 8.78/5.91 tff(2495,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 8.78/5.91 tff(2496,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2495, 2493])).
% 8.78/5.91 tff(2497,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2496, 2493])).
% 8.78/5.91 tff(2498,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2497, 2493])).
% 8.78/5.91 tff(2499,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2498, 2493])).
% 8.78/5.91 tff(2500,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2499, 2493])).
% 8.78/5.91 tff(2501,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2500, 2493])).
% 8.78/5.91 tff(2502,plain,
% 8.78/5.91 ((~hskp30) | c3_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2501, 2493])).
% 8.78/5.91 tff(2503,plain,
% 8.78/5.91 (c3_1(a1698)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2502, 2486])).
% 8.78/5.91 tff(2504,plain,
% 8.78/5.91 (((~hskp30) | c1_1(a1698)) <=> ((~hskp30) | c1_1(a1698))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2505,axiom,((~hskp30) | c1_1(a1698)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 8.78/5.91 tff(2506,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 8.78/5.91 tff(2507,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2506, 2504])).
% 8.78/5.91 tff(2508,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2507, 2504])).
% 8.78/5.91 tff(2509,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2508, 2504])).
% 8.78/5.91 tff(2510,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2509, 2504])).
% 8.78/5.91 tff(2511,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2510, 2504])).
% 8.78/5.91 tff(2512,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2511, 2504])).
% 8.78/5.91 tff(2513,plain,
% 8.78/5.91 ((~hskp30) | c1_1(a1698)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2512, 2504])).
% 8.78/5.91 tff(2514,plain,
% 8.78/5.91 (c1_1(a1698)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2513, 2486])).
% 8.78/5.91 tff(2515,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2516,plain,
% 8.78/5.91 ((hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698))) <=> (hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2517,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673))))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2516])).
% 8.78/5.91 tff(2518,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2517, 2515])).
% 8.78/5.91 tff(2519,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2520,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 8.78/5.91 tff(2521,plain,
% 8.78/5.91 ($false),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2520, 221, 2104, 1706, 1705, 2514, 2503, 1697, 2492, 1563])).
% 8.78/5.91 tff(2522,plain,((~hskp30) | hskp73 | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.91 tff(2523,plain,
% 8.78/5.91 (~hskp30),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2522, 2485, 2104, 2484, 2483])).
% 8.78/5.91 tff(2524,plain,
% 8.78/5.91 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 8.78/5.91 inference(bind,[status(th)],[])).
% 8.78/5.91 tff(2525,plain,
% 8.78/5.91 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(quant_intro,[status(thm)],[2524])).
% 8.78/5.91 tff(2526,plain,
% 8.78/5.91 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2527,plain,
% 8.78/5.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | hskp30) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp30))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 8.78/5.91 inference(bind,[status(th)],[])).
% 8.78/5.91 tff(2528,plain,
% 8.78/5.91 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(quant_intro,[status(thm)],[2527])).
% 8.78/5.91 tff(2529,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c0_1(U)) | c1_1(U)) | c2_1(V)) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause345')).
% 8.78/5.91 tff(2530,plain,
% 8.78/5.91 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 8.78/5.91 tff(2531,plain,
% 8.78/5.91 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2530, 2526])).
% 8.78/5.91 tff(2532,plain,(
% 8.78/5.91 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(skolemize,[status(sab)],[2531])).
% 8.78/5.91 tff(2533,plain,
% 8.78/5.91 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2532, 2525])).
% 8.78/5.91 tff(2534,assumption,(hskp0), introduced(assumption)).
% 8.78/5.91 tff(2535,plain,
% 8.78/5.91 (~c2_1(a1637)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1169, 2534])).
% 8.78/5.91 tff(2536,plain,
% 8.78/5.91 (c0_1(a1637)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1180, 2534])).
% 8.78/5.91 tff(2537,plain,
% 8.78/5.91 (c1_1(a1637)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1224, 2534])).
% 8.78/5.91 tff(2538,assumption,(~hskp30), introduced(assumption)).
% 8.78/5.91 tff(2539,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2540,plain,
% 8.78/5.91 ((hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))) <=> (hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2541,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2540])).
% 8.78/5.91 tff(2542,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2541, 2539])).
% 8.78/5.91 tff(2543,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2544,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 8.78/5.91 tff(2545,plain,
% 8.78/5.91 ($false),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2544, 221, 2538, 365, 2103, 2537, 2536, 2535, 2533, 1297])).
% 8.78/5.91 tff(2546,plain,((~hskp0) | hskp30 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.91 tff(2547,plain,
% 8.78/5.91 (~hskp0),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2546, 2523, 365, 2096, 1297])).
% 8.78/5.91 tff(2548,assumption,(hskp42), introduced(assumption)).
% 8.78/5.91 tff(2549,plain,
% 8.78/5.91 (~c3_1(a1638)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1087, 2548])).
% 8.78/5.91 tff(2550,plain,
% 8.78/5.91 (c1_1(a1638)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1109, 2548])).
% 8.78/5.91 tff(2551,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2552,plain,
% 8.78/5.91 ((hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638))) <=> (hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2553,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638))))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2552])).
% 8.78/5.91 tff(2554,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2553, 2551])).
% 8.78/5.91 tff(2555,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2556,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1715) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2555, 2554])).
% 8.78/5.91 tff(2557,plain,
% 8.78/5.91 (~c2_1(a1638)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2556, 2056, 221, 365, 2096, 2550, 1309, 2549, 428])).
% 8.78/5.91 tff(2558,plain,
% 8.78/5.91 (c0_1(a1638)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1098, 2548])).
% 8.78/5.91 tff(2559,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2560,plain,
% 8.78/5.91 ((hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))) <=> (hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2561,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2560])).
% 8.78/5.91 tff(2562,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2561, 2559])).
% 8.78/5.91 tff(2563,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2564,plain,
% 8.78/5.91 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 8.78/5.91 tff(2565,plain,
% 8.78/5.91 ($false),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2564, 221, 2538, 365, 2096, 2550, 2558, 2533, 1297, 2557])).
% 8.78/5.91 tff(2566,plain,((~hskp42) | hskp30 | c1_1(a1715) | c0_1(a1715) | hskp75 | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.91 tff(2567,plain,
% 8.78/5.91 (~hskp42),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2566, 2523, 365, 1297, 2056, 1309])).
% 8.78/5.91 tff(2568,plain,
% 8.78/5.91 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2569,plain,
% 8.78/5.91 ((hskp42 | hskp0 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695))) <=> (hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2570,plain,
% 8.78/5.91 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.78/5.91 inference(monotonicity,[status(thm)],[2569])).
% 8.78/5.91 tff(2571,plain,
% 8.78/5.91 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.78/5.91 inference(transitivity,[status(thm)],[2570, 2568])).
% 8.78/5.91 tff(2572,plain,
% 8.78/5.91 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))),
% 8.78/5.91 inference(quant_inst,[status(thm)],[])).
% 8.78/5.91 tff(2573,plain,
% 8.78/5.91 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 8.78/5.91 tff(2574,plain,
% 8.78/5.91 ($false),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2573, 221, 1073, 963, 2086, 2075, 2064, 1043])).
% 8.78/5.91 tff(2575,plain,((~hskp29) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.78/5.91 tff(2576,plain,
% 8.78/5.91 (~hskp29),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2575, 2567, 2547])).
% 8.78/5.91 tff(2577,plain,
% 8.78/5.91 (~hskp74),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1081, 963, 1073])).
% 8.78/5.91 tff(2578,plain,
% 8.78/5.91 (hskp38),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[1032, 2577, 881])).
% 8.78/5.91 tff(2579,plain,
% 8.78/5.91 (((~hskp38) | (~c0_1(a1718))) <=> ((~hskp38) | (~c0_1(a1718)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2580,plain,
% 8.78/5.91 (((~c0_1(a1718)) | (~hskp38)) <=> ((~hskp38) | (~c0_1(a1718)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2581,axiom,((~c0_1(a1718)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 8.78/5.91 tff(2582,plain,
% 8.78/5.91 ((~hskp38) | (~c0_1(a1718))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 8.78/5.91 tff(2583,plain,
% 8.78/5.91 ((~hskp38) | (~c0_1(a1718))),
% 8.78/5.91 inference(modus_ponens,[status(thm)],[2582, 2579])).
% 8.78/5.91 tff(2584,plain,
% 8.78/5.91 (~c0_1(a1718)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[2583, 2578])).
% 8.78/5.91 tff(2585,plain,
% 8.78/5.91 (c3_1(a1718)),
% 8.78/5.91 inference(unit_resolution,[status(thm)],[981, 2578])).
% 8.78/5.91 tff(2586,plain,
% 8.78/5.91 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.91 inference(rewrite,[status(thm)],[])).
% 8.78/5.91 tff(2587,plain,
% 8.78/5.92 ((hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718))) <=> (hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2588,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2587])).
% 8.78/5.92 tff(2589,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2588, 2586])).
% 8.78/5.92 tff(2590,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2591,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2590, 2589])).
% 8.78/5.92 tff(2592,plain,
% 8.78/5.92 (~c1_1(a1718)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2591, 221, 2104, 1706, 1705, 2585, 1697, 2584, 1563])).
% 8.78/5.92 tff(2593,assumption,(~c1_1(a1718)), introduced(assumption)).
% 8.78/5.92 tff(2594,assumption,(~c0_1(a1718)), introduced(assumption)).
% 8.78/5.92 tff(2595,assumption,(c3_1(a1718)), introduced(assumption)).
% 8.78/5.92 tff(2596,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2597,plain,
% 8.78/5.92 ((hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718))) <=> (hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2598,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2597])).
% 8.78/5.92 tff(2599,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2598, 2596])).
% 8.78/5.92 tff(2600,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2601,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 8.78/5.92 tff(2602,plain,
% 8.78/5.92 ($false),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2601, 221, 138, 617, 615, 2595, 2594, 137, 627, 2593])).
% 8.78/5.92 tff(2603,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c3_1(a1718)) | c0_1(a1718) | c1_1(a1718)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.92 tff(2604,plain,
% 8.78/5.92 (c1_1(a1654)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2603, 2585, 929, 894, 138, 2584, 2592])).
% 8.78/5.92 tff(2605,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2606,plain,
% 8.78/5.92 ((hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716))) <=> (hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2607,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2606])).
% 8.78/5.92 tff(2608,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2607, 2605])).
% 8.78/5.92 tff(2609,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp40 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2610,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 8.78/5.92 tff(2611,plain,
% 8.78/5.92 (hskp40 | (~c1_1(a1654))),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2610, 221, 1663, 929, 894, 1662, 728, 1617])).
% 8.78/5.92 tff(2612,plain,
% 8.78/5.92 (hskp40),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2611, 2604])).
% 8.78/5.92 tff(2613,plain,
% 8.78/5.92 (~c2_1(a1725)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[741, 2612])).
% 8.78/5.92 tff(2614,plain,
% 8.78/5.92 (c3_1(a1725)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[752, 2612])).
% 8.78/5.92 tff(2615,plain,
% 8.78/5.92 (c1_1(a1725)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[763, 2612])).
% 8.78/5.92 tff(2616,plain,
% 8.78/5.92 ($false),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[1161, 221, 963, 929, 895, 2615, 2614, 2613, 950, 2604])).
% 8.78/5.92 tff(2617,plain,(hskp0 | (~c2_1(a1716)) | c3_1(a1716) | c1_1(a1716) | hskp29 | hskp73 | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~hskp52) | hskp42), inference(lemma,lemma(discharge,[]))).
% 8.78/5.92 tff(2618,plain,
% 8.78/5.92 (~hskp52),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2617, 1073, 1662, 1617, 963, 2104, 1706, 1705, 1697, 138, 1663])).
% 8.78/5.92 tff(2619,plain,
% 8.78/5.92 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2620,plain,
% 8.78/5.92 ((hskp42 | hskp0 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656))) <=> (hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2621,plain,
% 8.78/5.92 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2620])).
% 8.78/5.92 tff(2622,plain,
% 8.78/5.92 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2621, 2619])).
% 8.78/5.92 tff(2623,plain,
% 8.78/5.92 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2624,plain,
% 8.78/5.92 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 8.78/5.92 tff(2625,plain,
% 8.78/5.92 ($false),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2624, 221, 1073, 963, 2358, 2357, 2356, 1043])).
% 8.78/5.92 tff(2626,plain,((~hskp53) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.78/5.92 tff(2627,plain,
% 8.78/5.92 (~hskp53),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2626, 1073, 963])).
% 8.78/5.92 tff(2628,plain,
% 8.78/5.92 ($false),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[150, 2627, 2618, 138])).
% 8.78/5.92 tff(2629,plain,(hskp42 | hskp29 | hskp0 | c3_1(a1716) | c1_1(a1716) | hskp73 | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.78/5.92 tff(2630,plain,
% 8.78/5.92 ($false),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2629, 2576, 2567, 2547, 1662, 2474, 2104, 2485, 2484, 2483, 1663])).
% 8.78/5.92 tff(2631,plain,(c1_1(a1715) | c3_1(a1716) | hskp73 | (~c2_1(a1716)) | c0_1(a1715) | hskp75 | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.92 tff(2632,plain,
% 8.78/5.92 (c1_1(a1715)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2631, 2056, 2104, 1663, 1297, 1662, 1309])).
% 8.78/5.92 tff(2633,plain,
% 8.78/5.92 (c3_1(a1637)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[1258, 1250, 1229, 1228, 1227])).
% 8.78/5.92 tff(2634,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2635,plain,
% 8.78/5.92 ((hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2636,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2635])).
% 8.78/5.92 tff(2637,plain,
% 8.78/5.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2636, 2634])).
% 8.78/5.92 tff(2638,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c1_1(a1637)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2639,plain,
% 8.78/5.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 8.78/5.92 tff(2640,plain,
% 8.78/5.92 (hskp13),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2639, 221, 834, 2103, 1229, 1228, 1309, 290, 2633])).
% 8.78/5.92 tff(2641,plain,
% 8.78/5.92 (~c1_1(a1667)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[303, 2640])).
% 8.78/5.92 tff(2642,plain,
% 8.78/5.92 (^[U: $i] : refl((hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 8.78/5.92 inference(bind,[status(th)],[])).
% 8.78/5.92 tff(2643,plain,
% 8.78/5.92 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(quant_intro,[status(thm)],[2642])).
% 8.78/5.92 tff(2644,plain,
% 8.78/5.92 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2645,plain,
% 8.78/5.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp61))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp61) <=> (hskp61 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) <=> (hskp61 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) | hskp33) <=> ((hskp61 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp33))), rewrite(((hskp61 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp33) <=> (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) | hskp33) <=> (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 8.78/5.92 inference(bind,[status(th)],[])).
% 8.78/5.92 tff(2646,plain,
% 8.78/5.92 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) | hskp33) <=> ![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(quant_intro,[status(thm)],[2645])).
% 8.78/5.92 tff(2647,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause330')).
% 8.78/5.92 tff(2648,plain,
% 8.78/5.92 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 8.78/5.92 tff(2649,plain,
% 8.78/5.92 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2648, 2644])).
% 8.78/5.92 tff(2650,plain,(
% 8.78/5.92 ![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(skolemize,[status(sab)],[2649])).
% 8.78/5.92 tff(2651,plain,
% 8.78/5.92 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2650, 2643])).
% 8.78/5.92 tff(2652,plain,
% 8.78/5.92 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2653,plain,
% 8.78/5.92 ((hskp61 | hskp33 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637))) <=> (hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2654,plain,
% 8.78/5.92 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2653])).
% 8.78/5.92 tff(2655,plain,
% 8.78/5.92 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2654, 2652])).
% 8.78/5.92 tff(2656,plain,
% 8.78/5.92 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2657,plain,
% 8.78/5.92 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 8.78/5.92 tff(2658,plain,
% 8.78/5.92 (hskp61 | hskp33 | (~c3_1(a1637))),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2657, 221, 1228, 1227, 2651])).
% 8.78/5.92 tff(2659,plain,
% 8.78/5.92 (hskp33),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2658, 2633, 1250])).
% 8.78/5.92 tff(2660,plain,
% 8.78/5.92 (((~hskp33) | (~c2_1(a1704))) <=> ((~hskp33) | (~c2_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2661,plain,
% 8.78/5.92 (((~c2_1(a1704)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2662,axiom,((~c2_1(a1704)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 8.78/5.92 tff(2663,plain,
% 8.78/5.92 ((~hskp33) | (~c2_1(a1704))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2662, 2661])).
% 8.78/5.92 tff(2664,plain,
% 8.78/5.92 ((~hskp33) | (~c2_1(a1704))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2663, 2660])).
% 8.78/5.92 tff(2665,plain,
% 8.78/5.92 (~c2_1(a1704)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2664, 2659])).
% 8.78/5.92 tff(2666,plain,
% 8.78/5.92 (((~hskp33) | (~c0_1(a1704))) <=> ((~hskp33) | (~c0_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2667,plain,
% 8.78/5.92 (((~c0_1(a1704)) | (~hskp33)) <=> ((~hskp33) | (~c0_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2668,axiom,((~c0_1(a1704)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 8.78/5.92 tff(2669,plain,
% 8.78/5.92 ((~hskp33) | (~c0_1(a1704))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 8.78/5.92 tff(2670,plain,
% 8.78/5.92 ((~hskp33) | (~c0_1(a1704))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2669, 2666])).
% 8.78/5.92 tff(2671,plain,
% 8.78/5.92 (~c0_1(a1704)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2670, 2659])).
% 8.78/5.92 tff(2672,plain,
% 8.78/5.92 (c3_1(a1667)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[314, 2640])).
% 8.78/5.92 tff(2673,plain,
% 8.78/5.92 (((~hskp33) | c3_1(a1704)) <=> ((~hskp33) | c3_1(a1704))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2674,axiom,((~hskp33) | c3_1(a1704)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 8.78/5.92 tff(2675,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 8.78/5.92 tff(2676,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2675, 2673])).
% 8.78/5.92 tff(2677,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2676, 2673])).
% 8.78/5.92 tff(2678,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2677, 2673])).
% 8.78/5.92 tff(2679,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2678, 2673])).
% 8.78/5.92 tff(2680,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2679, 2673])).
% 8.78/5.92 tff(2681,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2680, 2673])).
% 8.78/5.92 tff(2682,plain,
% 8.78/5.92 ((~hskp33) | c3_1(a1704)),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2681, 2673])).
% 8.78/5.92 tff(2683,plain,
% 8.78/5.92 (c3_1(a1704)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2682, 2659])).
% 8.78/5.92 tff(2684,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2685,plain,
% 8.78/5.92 (((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667))) <=> (c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2686,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2685])).
% 8.78/5.92 tff(2687,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2686, 2684])).
% 8.78/5.92 tff(2688,plain,
% 8.78/5.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2689,plain,
% 8.78/5.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704))),
% 8.78/5.92 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 8.78/5.92 tff(2690,plain,
% 8.78/5.92 (~c2_1(a1667)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[2689, 221, 2683, 2672, 1228, 2671, 2665, 2641, 1227, 376, 2633])).
% 8.78/5.92 tff(2691,plain,
% 8.78/5.92 (c0_1(a1667)),
% 8.78/5.92 inference(unit_resolution,[status(thm)],[325, 2640])).
% 8.78/5.92 tff(2692,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2693,plain,
% 8.78/5.92 (((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667))) <=> (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)))),
% 8.78/5.92 inference(rewrite,[status(thm)],[])).
% 8.78/5.92 tff(2694,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667))))),
% 8.78/5.92 inference(monotonicity,[status(thm)],[2693])).
% 8.78/5.92 tff(2695,plain,
% 8.78/5.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)))),
% 8.78/5.92 inference(transitivity,[status(thm)],[2694, 2692])).
% 8.78/5.92 tff(2696,plain,
% 8.78/5.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))),
% 8.78/5.92 inference(quant_inst,[status(thm)],[])).
% 8.78/5.92 tff(2697,plain,
% 8.78/5.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 8.78/5.93 tff(2698,plain,
% 8.78/5.93 ($false),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2697, 221, 2691, 2672, 1229, 1228, 2641, 647, 2633, 2690])).
% 8.78/5.93 tff(2699,plain,(hskp61 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1715)) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.93 tff(2700,plain,
% 8.78/5.93 (hskp61),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2699, 2537, 2536, 2535, 2632, 2096, 1309])).
% 8.78/5.93 tff(2701,plain,
% 8.78/5.93 (~c2_1(a1674)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1187, 2700])).
% 8.78/5.93 tff(2702,plain,
% 8.78/5.93 (~c1_1(a1674)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1193, 2700])).
% 8.78/5.93 tff(2703,plain,
% 8.78/5.93 (c3_1(a1674)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1204, 2700])).
% 8.78/5.93 tff(2704,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2705,plain,
% 8.78/5.93 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716))) <=> (hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2706,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2705])).
% 8.78/5.93 tff(2707,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2706, 2704])).
% 8.78/5.93 tff(2708,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1716) | (~c1_1(a1716)) | (~c2_1(a1716)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2709,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 8.78/5.93 tff(2710,plain,
% 8.78/5.93 (~c1_1(a1716)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2709, 2056, 221, 1663, 2703, 1662, 2702, 2701, 428])).
% 8.78/5.93 tff(2711,assumption,(~hskp60), introduced(assumption)).
% 8.78/5.93 tff(2712,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2713,plain,
% 8.78/5.93 ((hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674))) <=> (hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2714,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2713])).
% 8.78/5.93 tff(2715,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2714, 2712])).
% 8.78/5.93 tff(2716,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2717,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 8.78/5.93 tff(2718,plain,
% 8.78/5.93 ($false),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2717, 221, 2711, 1663, 2296, 1662, 2294, 386, 2292, 1617])).
% 8.78/5.93 tff(2719,plain,(c0_1(a1674) | hskp60 | (~c2_1(a1716)) | (~c3_1(a1674)) | c3_1(a1716) | c1_1(a1674) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.93 tff(2720,plain,
% 8.78/5.93 (hskp60),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2719, 2292, 1663, 2296, 1662, 2294, 1617])).
% 8.78/5.93 tff(2721,plain,
% 8.78/5.93 (~c1_1(a1673)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[399, 2720])).
% 8.78/5.93 tff(2722,plain,
% 8.78/5.93 (c3_1(a1673)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[463, 2720])).
% 8.78/5.93 tff(2723,plain,
% 8.78/5.93 (c2_1(a1673)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[452, 2720])).
% 8.78/5.93 tff(2724,plain,
% 8.78/5.93 (~hskp30),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2522, 2723, 2104, 2722, 2721])).
% 8.78/5.93 tff(2725,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2726,plain,
% 8.78/5.93 ((hskp30 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))) <=> (hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2727,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2726])).
% 8.78/5.93 tff(2728,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2727, 2725])).
% 8.78/5.93 tff(2729,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2730,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2729, 2728])).
% 8.78/5.93 tff(2731,plain,
% 8.78/5.93 ($false),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2730, 221, 2724, 2296, 1229, 1228, 2294, 1227, 2533, 2292])).
% 8.78/5.93 tff(2732,plain,(c0_1(a1674) | (~c3_1(a1674)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1674) | c2_1(a1637) | hskp73 | (~c2_1(a1716)) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.93 tff(2733,plain,
% 8.78/5.93 (c0_1(a1674)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2732, 2703, 2537, 2536, 2702, 2535, 2104, 1663, 1662, 2710])).
% 8.78/5.93 tff(2734,assumption,(c0_1(a1674)), introduced(assumption)).
% 8.78/5.93 tff(2735,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2736,plain,
% 8.78/5.93 (((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2737,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2736])).
% 8.78/5.93 tff(2738,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2737, 2735])).
% 8.78/5.93 tff(2739,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2740,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1674)) | (~c0_1(a1674))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 8.78/5.93 tff(2741,plain,
% 8.78/5.93 (c1_1(a1656)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2740, 221, 2096, 2296, 2357, 1309, 2338, 2356, 410, 1297, 2734])).
% 8.78/5.93 tff(2742,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2743,plain,
% 8.78/5.93 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656))) <=> (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2744,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2743])).
% 8.78/5.93 tff(2745,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2744, 2742])).
% 8.78/5.93 tff(2746,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1656) | (~c1_1(a1656)) | (~c2_1(a1656)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2747,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 8.78/5.93 tff(2748,plain,
% 8.78/5.93 ($false),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2747, 2056, 221, 2296, 2358, 2294, 2338, 2356, 428, 2741])).
% 8.78/5.93 tff(2749,plain,((~hskp53) | hskp75 | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | c2_1(a1715) | c0_1(a1715) | (~c0_1(a1674))), inference(lemma,lemma(discharge,[]))).
% 8.78/5.93 tff(2750,plain,
% 8.78/5.93 (~hskp53),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2749, 2734, 2296, 2294, 2338, 1309, 1297, 2056])).
% 8.78/5.93 tff(2751,plain,
% 8.78/5.93 (hskp52),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[150, 138, 2750])).
% 8.78/5.93 tff(2752,plain,
% 8.78/5.93 (c0_1(a1654)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[525, 2751])).
% 8.78/5.93 tff(2753,plain,
% 8.78/5.93 (hskp52),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[150, 2750, 138])).
% 8.78/5.93 tff(2754,plain,
% 8.78/5.93 (hskp74),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1032, 2753, 1026])).
% 8.78/5.93 tff(2755,plain,
% 8.78/5.93 (~c3_1(a1717)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1049, 2754])).
% 8.78/5.93 tff(2756,plain,
% 8.78/5.93 (c0_1(a1717)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1071, 2754])).
% 8.78/5.93 tff(2757,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2758,plain,
% 8.78/5.93 (((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1717) | c1_1(a1717) | (~c0_1(a1717))) <=> (c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2759,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1717) | c1_1(a1717) | (~c0_1(a1717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2758])).
% 8.78/5.93 tff(2760,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1717) | c1_1(a1717) | (~c0_1(a1717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2759, 2757])).
% 8.78/5.93 tff(2761,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1717) | c1_1(a1717) | (~c0_1(a1717)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2762,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1717) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1717) | (~c0_1(a1717))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 8.78/5.93 tff(2763,plain,
% 8.78/5.93 (c1_1(a1717)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2762, 221, 2756, 2096, 2296, 2755, 1309, 2338, 410, 1297, 2734])).
% 8.78/5.93 tff(2764,plain,
% 8.78/5.93 (c2_1(a1717)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[1060, 2754])).
% 8.78/5.93 tff(2765,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2766,plain,
% 8.78/5.93 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1717) | (~c1_1(a1717)) | (~c2_1(a1717))) <=> (hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2767,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1717) | (~c1_1(a1717)) | (~c2_1(a1717)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2766])).
% 8.78/5.93 tff(2768,plain,
% 8.78/5.93 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1717) | (~c1_1(a1717)) | (~c2_1(a1717)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2767, 2765])).
% 8.78/5.93 tff(2769,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1717) | (~c1_1(a1717)) | (~c2_1(a1717)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2770,plain,
% 8.78/5.93 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 8.78/5.93 tff(2771,plain,
% 8.78/5.93 ($false),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2770, 2056, 221, 2764, 2296, 2755, 2294, 2338, 428, 2763])).
% 8.78/5.93 tff(2772,plain,((~c0_1(a1674)) | hskp75 | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | c2_1(a1715) | c0_1(a1715) | hskp38 | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.78/5.93 tff(2773,plain,
% 8.78/5.93 (hskp38),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2772, 138, 2296, 2294, 2338, 1309, 1297, 2056, 2734])).
% 8.78/5.93 tff(2774,plain,
% 8.78/5.93 (~c0_1(a1718)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2583, 2773])).
% 8.78/5.93 tff(2775,plain,
% 8.78/5.93 (~c2_1(a1718)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[970, 2773])).
% 8.78/5.93 tff(2776,plain,
% 8.78/5.93 (c2_1(a1654)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[547, 2751])).
% 8.78/5.93 tff(2777,plain,
% 8.78/5.93 (c3_1(a1718)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[981, 2773])).
% 8.78/5.93 tff(2778,plain,
% 8.78/5.93 (c3_1(a1654)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[536, 2751])).
% 8.78/5.93 tff(2779,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2780,plain,
% 8.78/5.93 (((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2781,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2780])).
% 8.78/5.93 tff(2782,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.93 inference(transitivity,[status(thm)],[2781, 2779])).
% 8.78/5.93 tff(2783,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.78/5.93 inference(quant_inst,[status(thm)],[])).
% 8.78/5.93 tff(2784,plain,
% 8.78/5.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.78/5.93 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 8.78/5.93 tff(2785,plain,
% 8.78/5.93 ((~c0_1(a1674)) | (~c1_1(a1654))),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2784, 221, 2296, 617, 615, 2294, 2338, 647])).
% 8.78/5.93 tff(2786,plain,
% 8.78/5.93 (~c1_1(a1654)),
% 8.78/5.93 inference(unit_resolution,[status(thm)],[2785, 2734])).
% 8.78/5.93 tff(2787,assumption,(~c2_1(a1718)), introduced(assumption)).
% 8.78/5.93 tff(2788,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2789,plain,
% 8.78/5.93 (((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1718) | c2_1(a1718) | (~c3_1(a1718)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654))) <=> (c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.93 inference(rewrite,[status(thm)],[])).
% 8.78/5.93 tff(2790,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1718) | c2_1(a1718) | (~c3_1(a1718)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.78/5.93 inference(monotonicity,[status(thm)],[2789])).
% 8.78/5.93 tff(2791,plain,
% 8.78/5.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1718) | c2_1(a1718) | (~c3_1(a1718)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2790, 2788])).
% 8.78/5.94 tff(2792,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1718) | c2_1(a1718) | (~c3_1(a1718)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2793,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 8.78/5.94 tff(2794,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2793, 221, 2296, 616, 615, 2595, 2338, 2787, 2594, 376, 2734, 2786])).
% 8.78/5.94 tff(2795,plain,((~c0_1(a1674)) | (~c3_1(a1674)) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c3_1(a1718)) | c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~c0_1(a1654)) | c1_1(a1674)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2796,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2795, 2778, 2777, 2296, 2734, 2776, 2338, 2775, 2774, 2752, 2294])).
% 8.78/5.94 tff(2797,plain,(hskp29 | (~c3_1(a1674)) | (~c0_1(a1674)) | c2_1(a1674) | c1_1(a1674) | c2_1(a1715) | c0_1(a1715) | hskp75), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2798,plain,
% 8.78/5.94 (hskp29),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2797, 2703, 2733, 2701, 2702, 1309, 1297, 2056])).
% 8.78/5.94 tff(2799,plain,
% 8.78/5.94 (~c3_1(a1695)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2063, 2798])).
% 8.78/5.94 tff(2800,plain,
% 8.78/5.94 (c0_1(a1695)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2074, 2798])).
% 8.78/5.94 tff(2801,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2802,plain,
% 8.78/5.94 (((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2803,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2802])).
% 8.78/5.94 tff(2804,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2803, 2801])).
% 8.78/5.94 tff(2805,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2806,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 8.78/5.94 tff(2807,plain,
% 8.78/5.94 (c1_1(a1695)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2806, 221, 2096, 2703, 2800, 1309, 2701, 2799, 410, 1297, 2733])).
% 8.78/5.94 tff(2808,plain,
% 8.78/5.94 (c2_1(a1695)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2085, 2798])).
% 8.78/5.94 tff(2809,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2810,plain,
% 8.78/5.94 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695))) <=> (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2811,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2810])).
% 8.78/5.94 tff(2812,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2811, 2809])).
% 8.78/5.94 tff(2813,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2814,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 8.78/5.94 tff(2815,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2814, 2056, 221, 2703, 2808, 2702, 2701, 2799, 428, 2807])).
% 8.78/5.94 tff(2816,plain,((~hskp0) | hskp75 | c2_1(a1715) | c0_1(a1715) | hskp73 | (~c2_1(a1716)) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2817,plain,
% 8.78/5.94 (~hskp0),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2816, 2056, 1309, 1297, 2104, 1663, 1662])).
% 8.78/5.94 tff(2818,plain,
% 8.78/5.94 (hskp62),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2226, 1250, 2096, 834])).
% 8.78/5.94 tff(2819,plain,
% 8.78/5.94 (c0_1(a1675)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2237, 2818])).
% 8.78/5.94 tff(2820,plain,
% 8.78/5.94 (c1_1(a1675)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2248, 2818])).
% 8.78/5.94 tff(2821,plain,
% 8.78/5.94 (~c3_1(a1675)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2254, 2818])).
% 8.78/5.94 tff(2822,plain,
% 8.78/5.94 (c2_1(a1675)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2267, 2821, 2820, 2819, 1250])).
% 8.78/5.94 tff(2823,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2824,plain,
% 8.78/5.94 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2825,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2824])).
% 8.78/5.94 tff(2826,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2825, 2823])).
% 8.78/5.94 tff(2827,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2828,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 8.78/5.94 tff(2829,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2828, 221, 963, 834, 2096, 2820, 2819, 1309, 950, 2822])).
% 8.78/5.94 tff(2830,plain,(hskp61 | hskp0 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2831,plain,
% 8.78/5.94 (hskp61),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2830, 963, 2632, 1309, 1297])).
% 8.78/5.94 tff(2832,plain,
% 8.78/5.94 (~c2_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1187, 2831])).
% 8.78/5.94 tff(2833,plain,
% 8.78/5.94 (~c1_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1193, 2831])).
% 8.78/5.94 tff(2834,plain,
% 8.78/5.94 (c3_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1204, 2831])).
% 8.78/5.94 tff(2835,plain,
% 8.78/5.94 (~c1_1(a1716)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2709, 2056, 221, 1663, 2834, 1662, 2833, 2832, 428])).
% 8.78/5.94 tff(2836,plain,
% 8.78/5.94 (~hskp29),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2575, 963, 1073])).
% 8.78/5.94 tff(2837,plain,
% 8.78/5.94 (~hskp53),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2626, 963, 1073])).
% 8.78/5.94 tff(2838,plain,
% 8.78/5.94 (hskp52),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[150, 2837, 2836])).
% 8.78/5.94 tff(2839,plain,
% 8.78/5.94 (c0_1(a1654)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[525, 2838])).
% 8.78/5.94 tff(2840,plain,
% 8.78/5.94 (hskp38),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1032, 2838, 2577])).
% 8.78/5.94 tff(2841,plain,
% 8.78/5.94 (~c0_1(a1718)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2583, 2840])).
% 8.78/5.94 tff(2842,plain,
% 8.78/5.94 (~c2_1(a1718)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[970, 2840])).
% 8.78/5.94 tff(2843,plain,
% 8.78/5.94 (c3_1(a1718)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[981, 2840])).
% 8.78/5.94 tff(2844,plain,
% 8.78/5.94 (c3_1(a1654)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[536, 2838])).
% 8.78/5.94 tff(2845,plain,
% 8.78/5.94 (c2_1(a1654)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[547, 2838])).
% 8.78/5.94 tff(2846,plain,
% 8.78/5.94 (~c0_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2795, 2834, 2845, 2844, 2843, 2832, 2842, 2841, 2839, 2833])).
% 8.78/5.94 tff(2847,plain,
% 8.78/5.94 (hskp60),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2719, 2846, 1663, 2834, 1662, 2833, 2835])).
% 8.78/5.94 tff(2848,plain,
% 8.78/5.94 (~c1_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[399, 2847])).
% 8.78/5.94 tff(2849,plain,
% 8.78/5.94 (c3_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[463, 2847])).
% 8.78/5.94 tff(2850,plain,
% 8.78/5.94 (c2_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[452, 2847])).
% 8.78/5.94 tff(2851,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2629, 2850, 2849, 1073, 1662, 963, 2104, 2836, 2835, 2848, 1663])).
% 8.78/5.94 tff(2852,plain,(hskp0 | hskp42 | c3_1(a1716) | hskp73 | (~c2_1(a1716)) | hskp75 | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2853,plain,
% 8.78/5.94 (hskp42),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2852, 2817, 1662, 2104, 1663, 2056, 1309, 1297])).
% 8.78/5.94 tff(2854,plain,
% 8.78/5.94 (~c3_1(a1638)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1087, 2853])).
% 8.78/5.94 tff(2855,plain,
% 8.78/5.94 (hskp61),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2830, 2817, 2632, 1309, 1297])).
% 8.78/5.94 tff(2856,plain,
% 8.78/5.94 (~c2_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1187, 2855])).
% 8.78/5.94 tff(2857,plain,
% 8.78/5.94 (~c1_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1193, 2855])).
% 8.78/5.94 tff(2858,plain,
% 8.78/5.94 (c1_1(a1638)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1109, 2853])).
% 8.78/5.94 tff(2859,plain,
% 8.78/5.94 (c3_1(a1674)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[1204, 2855])).
% 8.78/5.94 tff(2860,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2861,plain,
% 8.78/5.94 ((hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638))) <=> (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2862,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2861])).
% 8.78/5.94 tff(2863,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2862, 2860])).
% 8.78/5.94 tff(2864,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2865,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1674))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2864, 2863])).
% 8.78/5.94 tff(2866,plain,
% 8.78/5.94 (~c2_1(a1638)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2865, 2056, 221, 2859, 2858, 2857, 2856, 2854, 428])).
% 8.78/5.94 tff(2867,plain,
% 8.78/5.94 (~hskp21),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2112, 2632, 2104, 2096, 1297])).
% 8.78/5.94 tff(2868,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2869,plain,
% 8.78/5.94 ((hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2870,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2869])).
% 8.78/5.94 tff(2871,plain,
% 8.78/5.94 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2870, 2868])).
% 8.78/5.94 tff(2872,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2873,plain,
% 8.78/5.94 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 8.78/5.94 tff(2874,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2873, 221, 2867, 2632, 2858, 1309, 2854, 1357, 1297, 2866])).
% 8.78/5.94 tff(2875,plain,(hskp75 | c2_1(a1715) | c0_1(a1715) | c3_1(a1716) | hskp73 | (~c2_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2876,plain,
% 8.78/5.94 (hskp75),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2875, 2098, 1297, 1662, 1309, 2466])).
% 8.78/5.94 tff(2877,plain,
% 8.78/5.94 (~c2_1(a1724)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[441, 2876])).
% 8.78/5.94 tff(2878,plain,
% 8.78/5.94 (c3_1(a1724)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[474, 2876])).
% 8.78/5.94 tff(2879,plain,
% 8.78/5.94 (c0_1(a1724)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[485, 2876])).
% 8.78/5.94 tff(2880,assumption,(hskp60), introduced(assumption)).
% 8.78/5.94 tff(2881,plain,
% 8.78/5.94 (~c1_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[399, 2880])).
% 8.78/5.94 tff(2882,plain,
% 8.78/5.94 (c2_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[452, 2880])).
% 8.78/5.94 tff(2883,plain,
% 8.78/5.94 (c3_1(a1673)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[463, 2880])).
% 8.78/5.94 tff(2884,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2885,plain,
% 8.78/5.94 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2886,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2885])).
% 8.78/5.94 tff(2887,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2886, 2884])).
% 8.78/5.94 tff(2888,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2889,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 8.78/5.94 tff(2890,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2889, 221, 2293, 2298, 2096, 2883, 2882, 2309, 1309, 2881, 376, 1297])).
% 8.78/5.94 tff(2891,plain,((~hskp60) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2892,plain,
% 8.78/5.94 (~hskp60),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2891, 2879, 2878, 2877, 1309, 1297])).
% 8.78/5.94 tff(2893,assumption,(c1_1(a1716)), introduced(assumption)).
% 8.78/5.94 tff(2894,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2895,plain,
% 8.78/5.94 (((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716))) <=> (c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.94 inference(rewrite,[status(thm)],[])).
% 8.78/5.94 tff(2896,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)))),
% 8.78/5.94 inference(monotonicity,[status(thm)],[2895])).
% 8.78/5.94 tff(2897,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.94 inference(transitivity,[status(thm)],[2896, 2894])).
% 8.78/5.94 tff(2898,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.94 inference(quant_inst,[status(thm)],[])).
% 8.78/5.94 tff(2899,plain,
% 8.78/5.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 8.78/5.94 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 8.78/5.94 tff(2900,plain,
% 8.78/5.94 ($false),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2899, 221, 2293, 2298, 1663, 365, 2103, 1662, 102, 1297, 2299, 2893])).
% 8.78/5.94 tff(2901,plain,(c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1724)) | (~c2_1(a1716)) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c0_1(a1715) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.78/5.94 tff(2902,plain,
% 8.78/5.94 (c1_1(a1724)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2901, 2893, 2298, 1663, 365, 2103, 1662, 1297, 2293])).
% 8.78/5.94 tff(2903,plain,
% 8.78/5.94 (hskp13),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[2316, 2902])).
% 8.78/5.94 tff(2904,plain,
% 8.78/5.94 (~c1_1(a1667)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[303, 2903])).
% 8.78/5.94 tff(2905,plain,
% 8.78/5.94 (c3_1(a1667)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[314, 2903])).
% 8.78/5.94 tff(2906,plain,
% 8.78/5.94 (c0_1(a1667)),
% 8.78/5.94 inference(unit_resolution,[status(thm)],[325, 2903])).
% 8.78/5.94 tff(2907,plain,
% 8.78/5.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2908,plain,
% 8.78/5.95 (((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716))) <=> (c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2909,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2908])).
% 8.78/5.95 tff(2910,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2909, 2907])).
% 8.78/5.95 tff(2911,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2912,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 8.78/5.95 tff(2913,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2912, 221, 1663, 365, 2103, 2906, 2905, 1662, 2904, 102, 1297, 2893])).
% 8.78/5.95 tff(2914,plain,((~c1_1(a1716)) | (~c2_1(a1716)) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c0_1(a1715) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2915,plain,
% 8.78/5.95 (~c1_1(a1716)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2914, 365, 1663, 2103, 1662, 1297, 2293, 2298, 2309])).
% 8.78/5.95 tff(2916,plain,
% 8.78/5.95 (hskp60 | c1_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2480, 221, 2103, 1662, 386, 1297])).
% 8.78/5.95 tff(2917,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2916, 2915, 365, 1663, 2711])).
% 8.78/5.95 tff(2918,plain,(c1_1(a1715) | (~c2_1(a1716)) | hskp60 | (~c3_1(a1715)) | c3_1(a1716) | c0_1(a1715) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2919,plain,
% 8.78/5.95 (c1_1(a1715)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2918, 2466, 2892, 2096, 1662, 1297, 2879, 2878, 2877])).
% 8.78/5.95 tff(2920,plain,
% 8.78/5.95 (hskp0),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2830, 834, 1250, 1309, 1297])).
% 8.78/5.95 tff(2921,plain,
% 8.78/5.95 (~c2_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1169, 2920])).
% 8.78/5.95 tff(2922,plain,
% 8.78/5.95 (c1_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1224, 2920])).
% 8.78/5.95 tff(2923,plain,
% 8.78/5.95 (c0_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1180, 2920])).
% 8.78/5.95 tff(2924,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2699, 2923, 2922, 1250, 2921, 834, 2096, 1309])).
% 8.78/5.95 tff(2925,plain,((~c1_1(a1715)) | hskp61 | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2926,plain,
% 8.78/5.95 (hskp61),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2925, 2919, 1309, 1297])).
% 8.78/5.95 tff(2927,plain,
% 8.78/5.95 (~c2_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1187, 2926])).
% 8.78/5.95 tff(2928,plain,
% 8.78/5.95 (~c1_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1193, 2926])).
% 8.78/5.95 tff(2929,plain,
% 8.78/5.95 (c3_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1204, 2926])).
% 8.78/5.95 tff(2930,assumption,(c1_1(a1724)), introduced(assumption)).
% 8.78/5.95 tff(2931,plain,
% 8.78/5.95 ((~c0_1(a1674)) | (~c1_1(a1724))),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2335, 221, 2293, 2298, 2296, 2294, 2338, 647])).
% 8.78/5.95 tff(2932,plain,
% 8.78/5.95 (~c0_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2931, 2930])).
% 8.78/5.95 tff(2933,plain,
% 8.78/5.95 (c1_1(a1716)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2719, 2932, 1663, 2711, 1662, 2294, 2296])).
% 8.78/5.95 tff(2934,plain,
% 8.78/5.95 (hskp13),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2316, 2930])).
% 8.78/5.95 tff(2935,plain,
% 8.78/5.95 (~c1_1(a1667)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[303, 2934])).
% 8.78/5.95 tff(2936,plain,
% 8.78/5.95 (c3_1(a1667)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[314, 2934])).
% 8.78/5.95 tff(2937,plain,
% 8.78/5.95 (c0_1(a1667)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[325, 2934])).
% 8.78/5.95 tff(2938,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2939,plain,
% 8.78/5.95 (((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716))) <=> (c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2940,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2939])).
% 8.78/5.95 tff(2941,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2940, 2938])).
% 8.78/5.95 tff(2942,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1716) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2943,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 8.78/5.95 tff(2944,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2943, 221, 1663, 2296, 2937, 2936, 1662, 2294, 2935, 102, 2932, 2933])).
% 8.78/5.95 tff(2945,plain,((~c1_1(a1724)) | (~c2_1(a1716)) | (~c3_1(a1674)) | c3_1(a1716) | c1_1(a1674) | hskp60 | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1674) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2946,plain,
% 8.78/5.95 (~c1_1(a1724)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2945, 2466, 2929, 1662, 2928, 2892, 2879, 2878, 2927, 2877])).
% 8.78/5.95 tff(2947,plain,
% 8.78/5.95 (~hskp21),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2112, 2919, 2098, 2096, 1297])).
% 8.78/5.95 tff(2948,plain,
% 8.78/5.95 (hskp61),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2925, 834, 1309, 1297])).
% 8.78/5.95 tff(2949,plain,
% 8.78/5.95 (~c2_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1187, 2948])).
% 8.78/5.95 tff(2950,plain,
% 8.78/5.95 (~c1_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1193, 2948])).
% 8.78/5.95 tff(2951,plain,
% 8.78/5.95 (c3_1(a1674)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1204, 2948])).
% 8.78/5.95 tff(2952,plain,
% 8.78/5.95 (~hskp52),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2353, 2299, 2298, 2309, 1309, 1297, 2293, 2950, 2951, 2949])).
% 8.78/5.95 tff(2953,plain,
% 8.78/5.95 (hskp53),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[150, 2952, 138])).
% 8.78/5.95 tff(2954,plain,
% 8.78/5.95 (~c3_1(a1656)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[167, 2953])).
% 8.78/5.95 tff(2955,plain,
% 8.78/5.95 (c0_1(a1656)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[161, 2953])).
% 8.78/5.95 tff(2956,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2957,plain,
% 8.78/5.95 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2958,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2957])).
% 8.78/5.95 tff(2959,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2958, 2956])).
% 8.78/5.95 tff(2960,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2961,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1656) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 8.78/5.95 tff(2962,plain,
% 8.78/5.95 (c1_1(a1656)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2961, 221, 2293, 2298, 2096, 2955, 2309, 1309, 2954, 410, 1297])).
% 8.78/5.95 tff(2963,plain,
% 8.78/5.95 (c2_1(a1656)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[178, 2953])).
% 8.78/5.95 tff(2964,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2965,plain,
% 8.78/5.95 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1656)) | (~c2_1(a1656)) | (~c0_1(a1656))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2966,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1656)) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2965])).
% 8.78/5.95 tff(2967,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1656)) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2966, 2964])).
% 8.78/5.95 tff(2968,plain,
% 8.78/5.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1656)) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2969,plain,
% 8.78/5.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c0_1(a1656))),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 8.78/5.95 tff(2970,plain,
% 8.78/5.95 (hskp0),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2969, 221, 834, 2096, 2963, 2955, 1309, 950, 2962])).
% 8.78/5.95 tff(2971,plain,
% 8.78/5.95 (c0_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1180, 2970])).
% 8.78/5.95 tff(2972,plain,
% 8.78/5.95 (c1_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1224, 2970])).
% 8.78/5.95 tff(2973,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2974,plain,
% 8.78/5.95 (((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2975,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724)))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2974])).
% 8.78/5.95 tff(2976,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2975, 2973])).
% 8.78/5.95 tff(2977,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1724) | c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2978,plain,
% 8.78/5.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724)),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 8.78/5.95 tff(2979,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2978, 221, 2293, 2296, 1229, 1228, 2309, 2294, 2338, 647, 1226, 2299])).
% 8.78/5.95 tff(2980,plain,((~c3_1(a1637)) | (~c0_1(a1724)) | (~c3_1(a1674)) | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | c1_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2981,plain,
% 8.78/5.95 (~c3_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2980, 2972, 2951, 2293, 2971, 2309, 2950, 2949, 2299])).
% 8.78/5.95 tff(2982,plain,
% 8.78/5.95 (~c2_1(a1637)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[1169, 2970])).
% 8.78/5.95 tff(2983,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2984,plain,
% 8.78/5.95 ((hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715))) <=> (hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2985,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2984])).
% 8.78/5.95 tff(2986,plain,
% 8.78/5.95 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715)))),
% 8.78/5.95 inference(transitivity,[status(thm)],[2985, 2983])).
% 8.78/5.95 tff(2987,plain,
% 8.78/5.95 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 8.78/5.95 inference(quant_inst,[status(thm)],[])).
% 8.78/5.95 tff(2988,plain,
% 8.78/5.95 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715))),
% 8.78/5.95 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 8.78/5.95 tff(2989,plain,
% 8.78/5.95 ($false),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2988, 221, 1345, 834, 2972, 1309, 2982, 1357, 2981, 1297])).
% 8.78/5.95 tff(2990,plain,(c1_1(a1724) | hskp21 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715) | (~c0_1(a1724)) | c2_1(a1724) | (~c3_1(a1724)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.78/5.95 tff(2991,plain,
% 8.78/5.95 (hskp29),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2990, 2946, 2919, 1309, 1297, 2879, 2877, 2878, 2947])).
% 8.78/5.95 tff(2992,plain,
% 8.78/5.95 (~c3_1(a1695)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2063, 2991])).
% 8.78/5.95 tff(2993,plain,
% 8.78/5.95 (c0_1(a1695)),
% 8.78/5.95 inference(unit_resolution,[status(thm)],[2074, 2991])).
% 8.78/5.95 tff(2994,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2995,plain,
% 8.78/5.95 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.95 inference(rewrite,[status(thm)],[])).
% 8.78/5.95 tff(2996,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.78/5.95 inference(monotonicity,[status(thm)],[2995])).
% 8.78/5.95 tff(2997,plain,
% 8.78/5.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[2996, 2994])).
% 8.78/5.96 tff(2998,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(2999,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 8.78/5.96 tff(3000,plain,
% 8.78/5.96 (c1_1(a1695)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2999, 221, 2879, 2878, 2096, 2993, 2877, 1309, 2992, 410, 1297])).
% 8.78/5.96 tff(3001,plain,
% 8.78/5.96 (c2_1(a1695)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2085, 2991])).
% 8.78/5.96 tff(3002,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3003,plain,
% 8.78/5.96 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3004,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715))))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3003])).
% 8.78/5.96 tff(3005,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3004, 3002])).
% 8.78/5.96 tff(3006,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3007,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 8.78/5.96 tff(3008,plain,
% 8.78/5.96 (hskp0),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3007, 221, 2919, 2096, 3001, 2993, 1309, 950, 3000])).
% 8.78/5.96 tff(3009,plain,
% 8.78/5.96 (c0_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1180, 3008])).
% 8.78/5.96 tff(3010,plain,
% 8.78/5.96 (c1_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1224, 3008])).
% 8.78/5.96 tff(3011,plain,
% 8.78/5.96 (~c3_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2980, 3010, 2929, 2879, 3009, 2877, 2928, 2927, 2946])).
% 8.78/5.96 tff(3012,plain,
% 8.78/5.96 (~c2_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1169, 3008])).
% 8.78/5.96 tff(3013,plain,
% 8.78/5.96 ($false),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2988, 221, 2947, 2919, 3010, 1309, 3012, 1357, 3011, 1297])).
% 8.78/5.96 tff(3014,plain,(c0_1(a1716) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.96 tff(3015,plain,
% 8.78/5.96 (c0_1(a1716)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3014, 1662, 1297, 1309])).
% 8.78/5.96 tff(3016,plain,
% 8.78/5.96 (~hskp74),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1081, 1073, 963])).
% 8.78/5.96 tff(3017,plain,
% 8.78/5.96 (hskp52),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[150, 2627, 138])).
% 8.78/5.96 tff(3018,plain,
% 8.78/5.96 (hskp38),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1032, 3017, 3016])).
% 8.78/5.96 tff(3019,plain,
% 8.78/5.96 (~c0_1(a1718)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2583, 3018])).
% 8.78/5.96 tff(3020,plain,
% 8.78/5.96 (c3_1(a1718)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[981, 3018])).
% 8.78/5.96 tff(3021,plain,
% 8.78/5.96 (c3_1(a1654)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[536, 3017])).
% 8.78/5.96 tff(3022,plain,
% 8.78/5.96 (c0_1(a1654)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[525, 3017])).
% 8.78/5.96 tff(3023,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3024,plain,
% 8.78/5.96 (((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715))) <=> (c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3025,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3024])).
% 8.78/5.96 tff(3026,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3025, 3023])).
% 8.78/5.96 tff(3027,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3028,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 8.78/5.96 tff(3029,plain,
% 8.78/5.96 (~c1_1(a1654)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3028, 221, 2057, 1677, 365, 2103, 3022, 3021, 1309, 647, 1617])).
% 8.78/5.96 tff(3030,plain,
% 8.78/5.96 (c1_1(a1718)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2603, 3029, 3022, 3021, 3020, 3019, 138])).
% 8.78/5.96 tff(3031,plain,
% 8.78/5.96 (c2_1(a1654)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[547, 3017])).
% 8.78/5.96 tff(3032,plain,
% 8.78/5.96 (~hskp73),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1597, 2057])).
% 8.78/5.96 tff(3033,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3034,plain,
% 8.78/5.96 ((hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718))) <=> (hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3035,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3034])).
% 8.78/5.96 tff(3036,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3035, 3033])).
% 8.78/5.96 tff(3037,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3038,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 8.78/5.96 tff(3039,plain,
% 8.78/5.96 ($false),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3038, 221, 3032, 3031, 3021, 3020, 3019, 1563, 3029, 3030])).
% 8.78/5.96 tff(3040,plain,(hskp42 | hskp29 | c2_1(a1716) | (~c0_1(a1716)) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715) | c1_1(a1716) | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.78/5.96 tff(3041,plain,
% 8.78/5.96 (hskp42),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3040, 138, 2057, 3015, 365, 2096, 1309, 1617, 963])).
% 8.78/5.96 tff(3042,plain,
% 8.78/5.96 (~c3_1(a1638)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1087, 3041])).
% 8.78/5.96 tff(3043,plain,
% 8.78/5.96 (c0_1(a1638)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1098, 3041])).
% 8.78/5.96 tff(3044,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3045,plain,
% 8.78/5.96 (((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3046,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716)))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3045])).
% 8.78/5.96 tff(3047,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3046, 3044])).
% 8.78/5.96 tff(3048,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1715) | c2_1(a1715) | c1_1(a1715) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3049,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c2_1(a1638)) | (~c0_1(a1638)) | c1_1(a1716)),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 8.78/5.96 tff(3050,plain,
% 8.78/5.96 (~c2_1(a1638)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3049, 221, 2057, 365, 3043, 1662, 1309, 3042, 30, 1297, 1617])).
% 8.78/5.96 tff(3051,plain,
% 8.78/5.96 (c1_1(a1638)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1109, 3041])).
% 8.78/5.96 tff(3052,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3053,plain,
% 8.78/5.96 ((hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638))) <=> (hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3054,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638))))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3053])).
% 8.78/5.96 tff(3055,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3054, 3052])).
% 8.78/5.96 tff(3056,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3057,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638))),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 8.78/5.96 tff(3058,plain,
% 8.78/5.96 (hskp69),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3057, 221, 365, 2096, 3051, 3042, 1412, 1297, 3050])).
% 8.78/5.96 tff(3059,plain,
% 8.78/5.96 (~c1_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1431, 3058])).
% 8.78/5.96 tff(3060,plain,
% 8.78/5.96 (c3_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1442, 3058])).
% 8.78/5.96 tff(3061,plain,
% 8.78/5.96 (c0_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1453, 3058])).
% 8.78/5.96 tff(3062,plain,
% 8.78/5.96 ($false),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2446, 221, 138, 365, 2096, 3061, 3060, 3059, 137, 1297])).
% 8.78/5.96 tff(3063,plain,(hskp29 | c1_1(a1715) | c0_1(a1715) | c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | c1_1(a1716) | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.78/5.96 tff(3064,plain,
% 8.78/5.96 (hskp0),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3063, 2095, 1297, 2057, 1662, 1309, 1617, 365])).
% 8.78/5.96 tff(3065,plain,
% 8.78/5.96 (~c2_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1169, 3064])).
% 8.78/5.96 tff(3066,plain,
% 8.78/5.96 (c0_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1180, 3064])).
% 8.78/5.96 tff(3067,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3068,plain,
% 8.78/5.96 (((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716))) <=> (c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3069,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3068])).
% 8.78/5.96 tff(3070,plain,
% 8.78/5.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3069, 3067])).
% 8.78/5.96 tff(3071,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3072,plain,
% 8.78/5.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 8.78/5.96 tff(3073,plain,
% 8.78/5.96 (~c3_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3072, 221, 3015, 2096, 3066, 1662, 1309, 3065, 410, 1297, 1617])).
% 8.78/5.96 tff(3074,plain,
% 8.78/5.96 (c1_1(a1637)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1224, 3064])).
% 8.78/5.96 tff(3075,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3076,plain,
% 8.78/5.96 ((hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637))) <=> (hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3077,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3076])).
% 8.78/5.96 tff(3078,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3077, 3075])).
% 8.78/5.96 tff(3079,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))),
% 8.78/5.96 inference(quant_inst,[status(thm)],[])).
% 8.78/5.96 tff(3080,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)),
% 8.78/5.96 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 8.78/5.96 tff(3081,plain,
% 8.78/5.96 (hskp69),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3080, 221, 365, 2096, 3074, 3065, 1412, 3073, 1297])).
% 8.78/5.96 tff(3082,plain,
% 8.78/5.96 (~c1_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1431, 3081])).
% 8.78/5.96 tff(3083,plain,
% 8.78/5.96 (c3_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1442, 3081])).
% 8.78/5.96 tff(3084,plain,
% 8.78/5.96 (c0_1(a1709)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[1453, 3081])).
% 8.78/5.96 tff(3085,plain,
% 8.78/5.96 ($false),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[2446, 221, 2095, 365, 2096, 3084, 3083, 3082, 137, 1297])).
% 8.78/5.96 tff(3086,plain,(c1_1(a1716) | c1_1(a1715) | c0_1(a1715) | c3_1(a1716) | c2_1(a1715) | c2_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.96 tff(3087,plain,
% 8.78/5.96 (c1_1(a1716)),
% 8.78/5.96 inference(unit_resolution,[status(thm)],[3086, 2057, 1297, 1662, 1309, 365])).
% 8.78/5.96 tff(3088,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3089,plain,
% 8.78/5.96 ((hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1716) | (~c1_1(a1716)) | (~c0_1(a1716))) <=> (hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.96 inference(rewrite,[status(thm)],[])).
% 8.78/5.96 tff(3090,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1716) | (~c1_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716))))),
% 8.78/5.96 inference(monotonicity,[status(thm)],[3089])).
% 8.78/5.96 tff(3091,plain,
% 8.78/5.96 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1716) | (~c1_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.96 inference(transitivity,[status(thm)],[3090, 3088])).
% 8.78/5.96 tff(3092,plain,
% 8.78/5.96 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp30 | (~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1716) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3093,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c2_1(a1716) | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 8.78/5.97 tff(3094,plain,
% 8.78/5.97 (hskp30 | (~c1_1(a1716))),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3093, 221, 2057, 3015, 365, 2096, 2533, 1297])).
% 8.78/5.97 tff(3095,plain,
% 8.78/5.97 (hskp30),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3094, 3087])).
% 8.78/5.97 tff(3096,plain,
% 8.78/5.97 (~c0_1(a1698)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2491, 3095])).
% 8.78/5.97 tff(3097,plain,
% 8.78/5.97 (hskp69 | c2_1(a1716) | c1_1(a1715) | (~c1_1(a1716))),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2387, 221, 2096, 1662, 1412, 1297])).
% 8.78/5.97 tff(3098,plain,
% 8.78/5.97 (hskp69),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3097, 3087, 2057, 365])).
% 8.78/5.97 tff(3099,plain,
% 8.78/5.97 (~c1_1(a1709)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[1431, 3098])).
% 8.78/5.97 tff(3100,plain,
% 8.78/5.97 (c3_1(a1698)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2502, 3095])).
% 8.78/5.97 tff(3101,plain,
% 8.78/5.97 (c1_1(a1698)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2513, 3095])).
% 8.78/5.97 tff(3102,plain,
% 8.78/5.97 (c3_1(a1709)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[1442, 3098])).
% 8.78/5.97 tff(3103,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3104,plain,
% 8.78/5.97 ((hskp73 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c2_1(a1709)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698))) <=> (hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3105,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c2_1(a1709)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3104])).
% 8.78/5.97 tff(3106,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c2_1(a1709)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3105, 3103])).
% 8.78/5.97 tff(3107,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c2_1(a1709)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3108,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1709) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1709)) | (~c2_1(a1709))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3107, 3106])).
% 8.78/5.97 tff(3109,plain,
% 8.78/5.97 (~c2_1(a1709)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3108, 221, 3032, 3102, 3101, 3100, 3099, 3096, 1563])).
% 8.78/5.97 tff(3110,plain,
% 8.78/5.97 (c0_1(a1709)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[1453, 3098])).
% 8.78/5.97 tff(3111,plain,
% 8.78/5.97 (hskp29),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2446, 221, 365, 2096, 3110, 3102, 3099, 137, 1297])).
% 8.78/5.97 tff(3112,plain,
% 8.78/5.97 (~c3_1(a1695)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2063, 3111])).
% 8.78/5.97 tff(3113,plain,
% 8.78/5.97 (c0_1(a1695)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2074, 3111])).
% 8.78/5.97 tff(3114,plain,
% 8.78/5.97 (c1_1(a1695)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2455, 221, 2096, 3110, 3102, 3113, 1309, 3112, 410, 1297, 3109])).
% 8.78/5.97 tff(3115,plain,
% 8.78/5.97 (c2_1(a1695)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2085, 3111])).
% 8.78/5.97 tff(3116,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3117,plain,
% 8.78/5.97 ((hskp75 | (~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c3_1(a1709)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695))) <=> (hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3118,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c3_1(a1709)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709)))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3117])).
% 8.78/5.97 tff(3119,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c3_1(a1709)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3118, 3116])).
% 8.78/5.97 tff(3120,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1709) | c1_1(a1709) | (~c3_1(a1709)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3121,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709)),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3120, 3119])).
% 8.78/5.97 tff(3122,plain,
% 8.78/5.97 ($false),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3121, 2056, 221, 3102, 3115, 3099, 3112, 428, 3109, 3114])).
% 8.78/5.97 tff(3123,plain,(c2_1(a1716) | hskp75 | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.97 tff(3124,plain,
% 8.78/5.97 (c2_1(a1716)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3123, 365, 1309, 1297, 2056, 1662])).
% 8.78/5.97 tff(3125,plain,
% 8.78/5.97 (~c1_1(a1716)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2473, 3124, 2056, 365])).
% 8.78/5.97 tff(3126,plain,
% 8.78/5.97 (hskp60),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2481, 3124, 365, 3125])).
% 8.78/5.97 tff(3127,plain,
% 8.78/5.97 (~c1_1(a1673)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[399, 3126])).
% 8.78/5.97 tff(3128,plain,
% 8.78/5.97 (c2_1(a1673)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[452, 3126])).
% 8.78/5.97 tff(3129,plain,
% 8.78/5.97 (c3_1(a1673)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[463, 3126])).
% 8.78/5.97 tff(3130,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3131,plain,
% 8.78/5.97 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3132,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3131])).
% 8.78/5.97 tff(3133,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3132, 3130])).
% 8.78/5.97 tff(3134,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3135,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 8.78/5.97 tff(3136,plain,
% 8.78/5.97 ($false),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3135, 221, 2096, 1706, 1705, 42, 59, 1309, 1697, 48, 376, 1297])).
% 8.78/5.97 tff(3137,plain,((~hskp7) | (~c3_1(a1673)) | (~c2_1(a1673)) | c2_1(a1715) | c1_1(a1673) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.97 tff(3138,plain,
% 8.78/5.97 (~hskp7),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3137, 3129, 3128, 1309, 3127, 1297])).
% 8.78/5.97 tff(3139,plain,
% 8.78/5.97 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3140,plain,
% 8.78/5.97 ((hskp52 | hskp7 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716))) <=> (hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3141,plain,
% 8.78/5.97 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3140])).
% 8.78/5.97 tff(3142,plain,
% 8.78/5.97 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3141, 3139])).
% 8.78/5.97 tff(3143,plain,
% 8.78/5.97 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3144,plain,
% 8.78/5.97 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 8.78/5.97 tff(3145,plain,
% 8.78/5.97 (hskp52 | hskp7 | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3144, 221, 1662, 189])).
% 8.78/5.97 tff(3146,plain,
% 8.78/5.97 (hskp52),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3145, 3138, 3015, 3124])).
% 8.78/5.97 tff(3147,plain,
% 8.78/5.97 (c3_1(a1654)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[536, 3146])).
% 8.78/5.97 tff(3148,plain,
% 8.78/5.97 (c2_1(a1654)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[547, 3146])).
% 8.78/5.97 tff(3149,plain,
% 8.78/5.97 (c0_1(a1654)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[525, 3146])).
% 8.78/5.97 tff(3150,plain,
% 8.78/5.97 (hskp26),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[663, 221, 3129, 3128, 3149, 3148, 3147, 3127, 20])).
% 8.78/5.97 tff(3151,plain,
% 8.78/5.97 (~c2_1(a1691)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[669, 3150])).
% 8.78/5.97 tff(3152,plain,
% 8.78/5.97 (~c3_1(a1691)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[689, 3150])).
% 8.78/5.97 tff(3153,plain,
% 8.78/5.97 (~c1_1(a1691)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[675, 3150])).
% 8.78/5.97 tff(3154,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3155,plain,
% 8.78/5.97 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3156,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3155])).
% 8.78/5.97 tff(3157,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3156, 3154])).
% 8.78/5.97 tff(3158,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3159,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 8.78/5.97 tff(3160,plain,
% 8.78/5.97 ($false),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3159, 221, 1663, 1677, 1662, 962, 961, 964, 248, 242, 261, 30])).
% 8.78/5.97 tff(3161,plain,((~hskp17) | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.97 tff(3162,plain,
% 8.78/5.97 (~hskp17),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3161, 3153, 3015, 1662, 3124, 3152, 3151])).
% 8.78/5.97 tff(3163,plain,
% 8.78/5.97 (hskp75 | c1_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2472, 221, 2103, 1662, 1309, 428])).
% 8.78/5.97 tff(3164,plain,
% 8.78/5.97 (~c1_1(a1716)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3163, 1663, 2056, 365])).
% 8.78/5.97 tff(3165,plain,
% 8.78/5.97 (~c2_1(a1638)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[2556, 2056, 221, 365, 2103, 2550, 1309, 2549, 428])).
% 8.78/5.97 tff(3166,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3167,plain,
% 8.78/5.97 ((hskp57 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716))) <=> (hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3168,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3167])).
% 8.78/5.97 tff(3169,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3168, 3166])).
% 8.78/5.97 tff(3170,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3171,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 8.78/5.97 tff(3172,plain,
% 8.78/5.97 ($false),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3171, 221, 1628, 1663, 2558, 1662, 2549, 1627, 3165, 3164])).
% 8.78/5.97 tff(3173,plain,((~hskp42) | hskp57 | (~c2_1(a1716)) | c3_1(a1716) | hskp75 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.97 tff(3174,plain,
% 8.78/5.97 (~hskp42),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3173, 1628, 3124, 1662, 2056, 365, 2096, 1309])).
% 8.78/5.97 tff(3175,plain,
% 8.78/5.97 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3176,plain,
% 8.78/5.97 ((hskp42 | hskp0 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716))) <=> (hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3177,plain,
% 8.78/5.97 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3176])).
% 8.78/5.97 tff(3178,plain,
% 8.78/5.97 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3177, 3175])).
% 8.78/5.97 tff(3179,plain,
% 8.78/5.97 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3180,plain,
% 8.78/5.97 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 8.78/5.97 tff(3181,plain,
% 8.78/5.97 (hskp42 | hskp0 | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3180, 221, 1662, 1043])).
% 8.78/5.97 tff(3182,plain,
% 8.78/5.97 (hskp0),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3181, 3174, 3015, 3124])).
% 8.78/5.97 tff(3183,plain,
% 8.78/5.97 (~c2_1(a1637)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[1169, 3182])).
% 8.78/5.97 tff(3184,plain,
% 8.78/5.97 (c0_1(a1637)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[1180, 3182])).
% 8.78/5.97 tff(3185,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3186,plain,
% 8.78/5.97 (((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673))) <=> (c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3187,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673))))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3186])).
% 8.78/5.97 tff(3188,plain,
% 8.78/5.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3187, 3185])).
% 8.78/5.97 tff(3189,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c0_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1673) | (~c3_1(a1673)) | (~c2_1(a1673)))),
% 8.78/5.97 inference(quant_inst,[status(thm)],[])).
% 8.78/5.97 tff(3190,plain,
% 8.78/5.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 8.78/5.97 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 8.78/5.97 tff(3191,plain,
% 8.78/5.97 (~c3_1(a1637)),
% 8.78/5.97 inference(unit_resolution,[status(thm)],[3190, 221, 2096, 3129, 3128, 3184, 1309, 3127, 3183, 376, 1297])).
% 8.78/5.97 tff(3192,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3193,plain,
% 8.78/5.97 ((hskp57 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716))) <=> (hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(rewrite,[status(thm)],[])).
% 8.78/5.97 tff(3194,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.78/5.97 inference(monotonicity,[status(thm)],[3193])).
% 8.78/5.97 tff(3195,plain,
% 8.78/5.97 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.78/5.97 inference(transitivity,[status(thm)],[3194, 3192])).
% 8.78/5.97 tff(3196,plain,
% 8.78/5.97 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c0_1(a1637)) | c3_1(a1716) | c1_1(a1716) | (~c2_1(a1716)))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3197,plain,
% 8.78/5.98 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3196, 3195])).
% 8.78/5.98 tff(3198,plain,
% 8.78/5.98 ($false),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3197, 221, 1628, 3124, 3184, 1662, 3183, 1627, 3191, 3125])).
% 8.78/5.98 tff(3199,plain,(hskp57 | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | hskp75 | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.98 tff(3200,plain,
% 8.78/5.98 (hskp57),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3199, 365, 1309, 1297, 2056, 1662])).
% 8.78/5.98 tff(3201,plain,
% 8.78/5.98 (~c1_1(a1665)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[65, 3200])).
% 8.78/5.98 tff(3202,plain,
% 8.78/5.98 (c3_1(a1665)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[76, 3200])).
% 8.78/5.98 tff(3203,plain,
% 8.78/5.98 (c0_1(a1665)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[90, 3200])).
% 8.78/5.98 tff(3204,plain,
% 8.78/5.98 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3205,plain,
% 8.78/5.98 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665))) <=> (hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3206,plain,
% 8.78/5.98 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.78/5.98 inference(monotonicity,[status(thm)],[3205])).
% 8.78/5.98 tff(3207,plain,
% 8.78/5.98 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.78/5.98 inference(transitivity,[status(thm)],[3206, 3204])).
% 8.78/5.98 tff(3208,plain,
% 8.78/5.98 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3209,plain,
% 8.78/5.98 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 8.78/5.98 tff(3210,plain,
% 8.78/5.98 (hskp17 | hskp16),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3209, 221, 3203, 3202, 3201, 10])).
% 8.78/5.98 tff(3211,plain,
% 8.78/5.98 (hskp16),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3210, 3162])).
% 8.78/5.98 tff(3212,plain,
% 8.78/5.98 (~c1_1(a1677)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[111, 3211])).
% 8.78/5.98 tff(3213,plain,
% 8.78/5.98 (~c2_1(a1677)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[117, 3211])).
% 8.78/5.98 tff(3214,plain,
% 8.78/5.98 (~c0_1(a1677)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[123, 3211])).
% 8.78/5.98 tff(3215,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3216,plain,
% 8.78/5.98 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3217,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.78/5.98 inference(monotonicity,[status(thm)],[3216])).
% 8.78/5.98 tff(3218,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.78/5.98 inference(transitivity,[status(thm)],[3217, 3215])).
% 8.78/5.98 tff(3219,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3220,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 8.78/5.98 tff(3221,plain,
% 8.78/5.98 ($false),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3220, 221, 3124, 3015, 1662, 3152, 3153, 3151, 3214, 3213, 3212, 30])).
% 8.78/5.98 tff(3222,plain,(c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | hskp75), inference(lemma,lemma(discharge,[]))).
% 8.78/5.98 tff(3223,plain,
% 8.78/5.98 (c1_1(a1715)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3222, 2056, 1309, 1297, 1662])).
% 8.78/5.98 tff(3224,plain,
% 8.78/5.98 (~hskp21),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2112, 3032, 834, 2096, 1297])).
% 8.78/5.98 tff(3225,plain,
% 8.78/5.98 (~c1_1(a1716)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2120, 3224, 834, 2057])).
% 8.78/5.98 tff(3226,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3227,plain,
% 8.78/5.98 (((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716))) <=> (c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3228,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716))))),
% 8.78/5.98 inference(monotonicity,[status(thm)],[3227])).
% 8.78/5.98 tff(3229,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.98 inference(transitivity,[status(thm)],[3228, 3226])).
% 8.78/5.98 tff(3230,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1674) | (~c3_1(a1674)) | (~c0_1(a1674)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3231,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716))),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 8.78/5.98 tff(3232,plain,
% 8.78/5.98 ((~c0_1(a1674)) | c1_1(a1716)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3231, 221, 3015, 2096, 2951, 1662, 1309, 2949, 410, 1297])).
% 8.78/5.98 tff(3233,plain,
% 8.78/5.98 (~c0_1(a1674)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3232, 3225])).
% 8.78/5.98 tff(3234,plain,
% 8.78/5.98 (~c3_1(a1637)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3072, 221, 3015, 2096, 2536, 1662, 1309, 2535, 410, 1297, 1617])).
% 8.78/5.98 tff(3235,plain,
% 8.78/5.98 ($false),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2988, 221, 1345, 834, 2537, 1309, 2535, 1357, 3234, 1297])).
% 8.78/5.98 tff(3236,plain,((~hskp0) | hskp21 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.78/5.98 tff(3237,plain,
% 8.78/5.98 (~hskp0),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3236, 3224, 834, 1309, 1297, 1662, 3225])).
% 8.78/5.98 tff(3238,plain,
% 8.78/5.98 (hskp38),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[1032, 3016, 3017])).
% 8.78/5.98 tff(3239,plain,
% 8.78/5.98 (~c0_1(a1718)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2583, 3238])).
% 8.78/5.98 tff(3240,plain,
% 8.78/5.98 (c3_1(a1718)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[981, 3238])).
% 8.78/5.98 tff(3241,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3242,plain,
% 8.78/5.98 (((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3243,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.78/5.98 inference(monotonicity,[status(thm)],[3242])).
% 8.78/5.98 tff(3244,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.78/5.98 inference(transitivity,[status(thm)],[3243, 3241])).
% 8.78/5.98 tff(3245,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3246,plain,
% 8.78/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3245, 3244])).
% 8.78/5.98 tff(3247,plain,
% 8.78/5.98 (~c1_1(a1654)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3246, 221, 2057, 1677, 2296, 3022, 3021, 2294, 2338, 647, 1617])).
% 8.78/5.98 tff(3248,plain,
% 8.78/5.98 (c1_1(a1718)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2603, 3247, 3022, 3021, 3240, 3239, 138])).
% 8.78/5.98 tff(3249,plain,
% 8.78/5.98 ($false),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3038, 221, 3032, 3031, 3021, 3240, 3239, 1563, 3247, 3248])).
% 8.78/5.98 tff(3250,plain,(hskp42 | hskp29 | c2_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | c1_1(a1716) | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.78/5.98 tff(3251,plain,
% 8.78/5.98 (hskp42),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3250, 963, 2057, 1677, 2951, 2950, 2949, 1617, 138])).
% 8.78/5.98 tff(3252,plain,
% 8.78/5.98 (c0_1(a1638)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[1098, 3251])).
% 8.78/5.98 tff(3253,plain,
% 8.78/5.98 (c1_1(a1638)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[1109, 3251])).
% 8.78/5.98 tff(3254,plain,
% 8.78/5.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3255,plain,
% 8.78/5.98 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3256,plain,
% 8.78/5.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.78/5.98 inference(monotonicity,[status(thm)],[3255])).
% 8.78/5.98 tff(3257,plain,
% 8.78/5.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.98 inference(transitivity,[status(thm)],[3256, 3254])).
% 8.78/5.98 tff(3258,plain,
% 8.78/5.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))),
% 8.78/5.98 inference(quant_inst,[status(thm)],[])).
% 8.78/5.98 tff(3259,plain,
% 8.78/5.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.78/5.98 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 8.78/5.98 tff(3260,plain,
% 8.78/5.98 (~c2_1(a1638)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3259, 221, 963, 834, 2096, 3253, 3252, 1309, 950])).
% 8.78/5.98 tff(3261,plain,
% 8.78/5.98 (~c3_1(a1638)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[1087, 3251])).
% 8.78/5.98 tff(3262,plain,
% 8.78/5.98 ($false),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2873, 221, 3224, 834, 3253, 1309, 3261, 1357, 1297, 3260])).
% 8.78/5.98 tff(3263,plain,(hskp0 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715) | c2_1(a1716) | (~c0_1(a1716)) | c1_1(a1716) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.78/5.98 tff(3264,plain,
% 8.78/5.98 (hskp29),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[3263, 3237, 1309, 1297, 2057, 3015, 3225, 834])).
% 8.78/5.98 tff(3265,plain,
% 8.78/5.98 (~c3_1(a1695)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2063, 3264])).
% 8.78/5.98 tff(3266,plain,
% 8.78/5.98 (c0_1(a1695)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2074, 3264])).
% 8.78/5.98 tff(3267,plain,
% 8.78/5.98 (c2_1(a1695)),
% 8.78/5.98 inference(unit_resolution,[status(thm)],[2085, 3264])).
% 8.78/5.98 tff(3268,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3269,plain,
% 8.78/5.98 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716)) <=> (c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716))),
% 8.78/5.98 inference(rewrite,[status(thm)],[])).
% 8.78/5.98 tff(3270,plain,
% 8.78/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716)))),
% 8.86/5.98 inference(monotonicity,[status(thm)],[3269])).
% 8.86/5.98 tff(3271,plain,
% 8.86/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716))),
% 8.86/5.98 inference(transitivity,[status(thm)],[3270, 3268])).
% 8.86/5.98 tff(3272,plain,
% 8.86/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1716) | c1_1(a1716) | c2_1(a1716))),
% 8.86/5.98 inference(quant_inst,[status(thm)],[])).
% 8.86/5.98 tff(3273,plain,
% 8.86/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716)),
% 8.86/5.98 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 8.86/5.98 tff(3274,plain,
% 8.86/5.98 ($false),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3273, 221, 2057, 3267, 3266, 1662, 2950, 2949, 3265, 30, 3233, 3225])).
% 8.86/5.98 tff(3275,plain,(c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | (~c1_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/5.98 tff(3276,plain,
% 8.86/5.98 (c2_1(a1716)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3275, 3223, 1309, 1297, 1662])).
% 8.86/5.98 tff(3277,plain,
% 8.86/5.98 (hskp61),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[2925, 3223, 1309, 1297])).
% 8.86/5.98 tff(3278,plain,
% 8.86/5.98 (~c2_1(a1674)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[1187, 3277])).
% 8.86/5.98 tff(3279,plain,
% 8.86/5.98 (~c1_1(a1674)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[1193, 3277])).
% 8.86/5.98 tff(3280,plain,
% 8.86/5.98 (c3_1(a1674)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[1204, 3277])).
% 8.86/5.98 tff(3281,plain,
% 8.86/5.98 ((~c2_1(a1716)) | (~c1_1(a1716))),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[2709, 2056, 221, 3280, 1662, 3279, 3278, 428])).
% 8.86/5.98 tff(3282,plain,
% 8.86/5.98 (~c1_1(a1716)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3281, 3276])).
% 8.86/5.98 tff(3283,plain,
% 8.86/5.98 ((~c0_1(a1674)) | c1_1(a1716)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3231, 221, 3015, 2096, 3280, 1662, 1309, 3278, 410, 1297])).
% 8.86/5.98 tff(3284,plain,
% 8.86/5.98 (~c0_1(a1674)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3283, 3282])).
% 8.86/5.98 tff(3285,plain,
% 8.86/5.98 (hskp60),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[2719, 3282, 3276, 3284, 1662, 3279, 3280])).
% 8.86/5.98 tff(3286,plain,
% 8.86/5.98 (~c1_1(a1673)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[399, 3285])).
% 8.86/5.98 tff(3287,plain,
% 8.86/5.98 (c2_1(a1673)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[452, 3285])).
% 8.86/5.98 tff(3288,plain,
% 8.86/5.98 (c3_1(a1673)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[463, 3285])).
% 8.86/5.98 tff(3289,plain,
% 8.86/5.98 (~hskp7),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3137, 3288, 3287, 1309, 3286, 1297])).
% 8.86/5.98 tff(3290,plain,
% 8.86/5.98 (hskp52),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3145, 3289, 3015, 3276])).
% 8.86/5.98 tff(3291,plain,
% 8.86/5.98 (c3_1(a1654)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[536, 3290])).
% 8.86/5.98 tff(3292,plain,
% 8.86/5.98 (c2_1(a1654)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[547, 3290])).
% 8.86/5.98 tff(3293,plain,
% 8.86/5.98 (c0_1(a1654)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[525, 3290])).
% 8.86/5.98 tff(3294,plain,
% 8.86/5.98 (hskp26),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[663, 221, 3288, 3287, 3293, 3292, 3291, 3286, 20])).
% 8.86/5.98 tff(3295,plain,
% 8.86/5.98 (~c2_1(a1691)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[669, 3294])).
% 8.86/5.98 tff(3296,plain,
% 8.86/5.98 (~c1_1(a1691)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[675, 3294])).
% 8.86/5.98 tff(3297,plain,
% 8.86/5.98 (~c3_1(a1691)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[689, 3294])).
% 8.86/5.98 tff(3298,plain,
% 8.86/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.98 inference(rewrite,[status(thm)],[])).
% 8.86/5.98 tff(3299,plain,
% 8.86/5.98 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.98 inference(rewrite,[status(thm)],[])).
% 8.86/5.98 tff(3300,plain,
% 8.86/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.86/5.98 inference(monotonicity,[status(thm)],[3299])).
% 8.86/5.98 tff(3301,plain,
% 8.86/5.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.98 inference(transitivity,[status(thm)],[3300, 3298])).
% 8.86/5.98 tff(3302,plain,
% 8.86/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1674) | c2_1(a1674) | c1_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.86/5.98 inference(quant_inst,[status(thm)],[])).
% 8.86/5.98 tff(3303,plain,
% 8.86/5.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.86/5.98 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 8.86/5.98 tff(3304,plain,
% 8.86/5.98 ($false),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3303, 221, 3276, 3015, 1662, 3279, 3278, 3297, 3296, 3295, 30, 3284])).
% 8.86/5.98 tff(3305,plain,(hskp75 | c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/5.98 tff(3306,plain,
% 8.86/5.98 (hskp75),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[3305, 1662, 1309, 1297])).
% 8.86/5.98 tff(3307,plain,
% 8.86/5.98 (~c2_1(a1724)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[441, 3306])).
% 8.86/5.98 tff(3308,plain,
% 8.86/5.98 (c0_1(a1724)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[485, 3306])).
% 8.86/5.98 tff(3309,plain,
% 8.86/5.98 (c3_1(a1724)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[474, 3306])).
% 8.86/5.98 tff(3310,assumption,(hskp13), introduced(assumption)).
% 8.86/5.98 tff(3311,plain,
% 8.86/5.98 (~c1_1(a1667)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[303, 3310])).
% 8.86/5.98 tff(3312,plain,
% 8.86/5.98 (c3_1(a1667)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[314, 3310])).
% 8.86/5.98 tff(3313,plain,
% 8.86/5.98 (c0_1(a1667)),
% 8.86/5.98 inference(unit_resolution,[status(thm)],[325, 3310])).
% 8.86/5.98 tff(3314,plain,
% 8.86/5.98 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3315,plain,
% 8.86/5.99 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3316,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715)))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3315])).
% 8.86/5.99 tff(3317,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3316, 3314])).
% 8.86/5.99 tff(3318,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3319,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715)),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 8.86/5.99 tff(3320,plain,
% 8.86/5.99 ($false),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3319, 221, 138, 365, 2103, 3313, 3312, 3311, 137, 1297])).
% 8.86/5.99 tff(3321,plain,((~hskp13) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/5.99 tff(3322,plain,
% 8.86/5.99 (~hskp13),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3321, 138, 365, 2103, 1297])).
% 8.86/5.99 tff(3323,plain,
% 8.86/5.99 (~c1_1(a1724)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2316, 3322])).
% 8.86/5.99 tff(3324,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3325,plain,
% 8.86/5.99 ((hskp29 | (~ndr1_0) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3326,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3325])).
% 8.86/5.99 tff(3327,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3326, 3324])).
% 8.86/5.99 tff(3328,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3329,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 8.86/5.99 tff(3330,plain,
% 8.86/5.99 ($false),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3329, 221, 138, 2293, 2298, 365, 2103, 137, 1297, 3323])).
% 8.86/5.99 tff(3331,plain,(hskp29 | (~c0_1(a1724)) | (~c3_1(a1724)) | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 8.86/5.99 tff(3332,plain,
% 8.86/5.99 (hskp29),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3331, 365, 3309, 3308, 2096, 1297, 3307])).
% 8.86/5.99 tff(3333,plain,
% 8.86/5.99 (~c3_1(a1695)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2063, 3332])).
% 8.86/5.99 tff(3334,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3335,plain,
% 8.86/5.99 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716))) <=> (c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3336,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3335])).
% 8.86/5.99 tff(3337,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3336, 3334])).
% 8.86/5.99 tff(3338,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1716) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3339,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 8.86/5.99 tff(3340,plain,
% 8.86/5.99 (c1_1(a1716)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3339, 221, 3308, 3309, 3015, 2096, 3307, 1662, 1309, 410, 1297])).
% 8.86/5.99 tff(3341,plain,
% 8.86/5.99 (~c2_1(a1716)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2914, 365, 3340, 2096, 1662, 1297, 3308, 3309, 3307])).
% 8.86/5.99 tff(3342,plain,
% 8.86/5.99 (hskp69),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3097, 3341, 3340, 365])).
% 8.86/5.99 tff(3343,plain,
% 8.86/5.99 (~c1_1(a1709)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1431, 3342])).
% 8.86/5.99 tff(3344,plain,
% 8.86/5.99 (c2_1(a1695)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2085, 3332])).
% 8.86/5.99 tff(3345,plain,
% 8.86/5.99 (c3_1(a1709)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1442, 3342])).
% 8.86/5.99 tff(3346,plain,
% 8.86/5.99 (c0_1(a1709)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1453, 3342])).
% 8.86/5.99 tff(3347,plain,
% 8.86/5.99 (~c1_1(a1695)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2463, 221, 365, 2096, 3346, 3345, 3344, 3343, 3333, 102, 1297])).
% 8.86/5.99 tff(3348,plain,
% 8.86/5.99 (c0_1(a1695)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2074, 3332])).
% 8.86/5.99 tff(3349,plain,
% 8.86/5.99 ($false),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2999, 221, 3308, 3309, 2096, 3348, 3307, 1309, 3333, 410, 1297, 3347])).
% 8.86/5.99 tff(3350,plain,(c1_1(a1715) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.86/5.99 tff(3351,plain,
% 8.86/5.99 (c1_1(a1715)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3350, 1662, 1297, 1309])).
% 8.86/5.99 tff(3352,plain,
% 8.86/5.99 (hskp61),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2925, 3351, 1309, 1297])).
% 8.86/5.99 tff(3353,plain,
% 8.86/5.99 (~c2_1(a1674)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1187, 3352])).
% 8.86/5.99 tff(3354,plain,
% 8.86/5.99 (c2_1(a1716)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3275, 3351, 1309, 1297, 1662])).
% 8.86/5.99 tff(3355,plain,
% 8.86/5.99 (~c1_1(a1674)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1193, 3352])).
% 8.86/5.99 tff(3356,plain,
% 8.86/5.99 (~hskp60),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2891, 3308, 3309, 3307, 1309, 1297])).
% 8.86/5.99 tff(3357,plain,
% 8.86/5.99 (c3_1(a1674)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1204, 3352])).
% 8.86/5.99 tff(3358,plain,
% 8.86/5.99 (~c1_1(a1724)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2945, 3357, 3356, 1662, 3355, 3354, 3308, 3309, 3353, 3307])).
% 8.86/5.99 tff(3359,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3360,plain,
% 8.86/5.99 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3361,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716))))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3360])).
% 8.86/5.99 tff(3362,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3361, 3359])).
% 8.86/5.99 tff(3363,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3364,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716))),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 8.86/5.99 tff(3365,plain,
% 8.86/5.99 (hskp0 | (~c1_1(a1715)) | (~c2_1(a1716))),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3364, 221, 3015, 2096, 1309, 950, 3340])).
% 8.86/5.99 tff(3366,plain,
% 8.86/5.99 (hskp0),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3365, 3354, 3351])).
% 8.86/5.99 tff(3367,plain,
% 8.86/5.99 (c0_1(a1637)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1180, 3366])).
% 8.86/5.99 tff(3368,plain,
% 8.86/5.99 (c1_1(a1637)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1224, 3366])).
% 8.86/5.99 tff(3369,plain,
% 8.86/5.99 (~c3_1(a1637)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2980, 3368, 3308, 3357, 3367, 3307, 3355, 3353, 3358])).
% 8.86/5.99 tff(3370,plain,
% 8.86/5.99 (~c2_1(a1637)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1169, 3366])).
% 8.86/5.99 tff(3371,plain,
% 8.86/5.99 (hskp21),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[2988, 221, 3351, 3368, 1309, 3370, 1357, 3369, 1297])).
% 8.86/5.99 tff(3372,plain,
% 8.86/5.99 (~c1_1(a1683)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1417, 3371])).
% 8.86/5.99 tff(3373,plain,
% 8.86/5.99 (c2_1(a1683)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1383, 3371])).
% 8.86/5.99 tff(3374,plain,
% 8.86/5.99 (c3_1(a1683)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1394, 3371])).
% 8.86/5.99 tff(3375,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3376,plain,
% 8.86/5.99 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683))) <=> (c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3377,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3376])).
% 8.86/5.99 tff(3378,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3377, 3375])).
% 8.86/5.99 tff(3379,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3380,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3379, 3378])).
% 8.86/5.99 tff(3381,plain,
% 8.86/5.99 ($false),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3380, 221, 3308, 3309, 2096, 3374, 3373, 3307, 1309, 3372, 376, 1297])).
% 8.86/5.99 tff(3382,plain,(c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/5.99 tff(3383,plain,
% 8.86/5.99 (c0_1(a1715)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3382, 1309, 1662])).
% 8.86/5.99 tff(3384,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3385,plain,
% 8.86/5.99 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3386,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3385])).
% 8.86/5.99 tff(3387,plain,
% 8.86/5.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3386, 3384])).
% 8.86/5.99 tff(3388,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3389,plain,
% 8.86/5.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.86/5.99 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 8.86/5.99 tff(3390,plain,
% 8.86/5.99 ($false),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3389, 221, 365, 1205, 617, 615, 1309, 1194, 1188, 647, 1835, 882])).
% 8.86/5.99 tff(3391,plain,((~hskp61) | c1_1(a1715) | (~c0_1(a1654)) | (~c3_1(a1654)) | c2_1(a1715) | (~c0_1(a1715)) | (~c1_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.86/5.99 tff(3392,plain,
% 8.86/5.99 (~hskp61),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3391, 882, 929, 894, 1309, 1835, 365])).
% 8.86/5.99 tff(3393,plain,
% 8.86/5.99 (hskp61 | (~c0_1(a1715)) | (~c1_1(a1715))),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[1943, 221, 363, 1309, 1249])).
% 8.86/5.99 tff(3394,plain,
% 8.86/5.99 (~c1_1(a1715)),
% 8.86/5.99 inference(unit_resolution,[status(thm)],[3393, 1250, 1835])).
% 8.86/5.99 tff(3395,assumption,(~c2_1(a1638)), introduced(assumption)).
% 8.86/5.99 tff(3396,assumption,(c0_1(a1638)), introduced(assumption)).
% 8.86/5.99 tff(3397,assumption,(c1_1(a1638)), introduced(assumption)).
% 8.86/5.99 tff(3398,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3399,plain,
% 8.86/5.99 ((hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))) <=> (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/5.99 inference(rewrite,[status(thm)],[])).
% 8.86/5.99 tff(3400,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.86/5.99 inference(monotonicity,[status(thm)],[3399])).
% 8.86/5.99 tff(3401,plain,
% 8.86/5.99 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/5.99 inference(transitivity,[status(thm)],[3400, 3398])).
% 8.86/5.99 tff(3402,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/5.99 inference(quant_inst,[status(thm)],[])).
% 8.86/5.99 tff(3403,plain,
% 8.86/5.99 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 8.86/6.00 tff(3404,plain,
% 8.86/6.00 ($false),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3403, 221, 1250, 363, 3397, 3396, 1309, 1249, 1835, 3395])).
% 8.86/6.00 tff(3405,plain,(c2_1(a1638) | hskp61 | c3_1(a1715) | (~c1_1(a1638)) | (~c0_1(a1638)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.00 tff(3406,plain,
% 8.86/6.00 (c2_1(a1638)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3405, 2550, 363, 1250, 2558, 1309, 1835])).
% 8.86/6.00 tff(3407,assumption,(~hskp2), introduced(assumption)).
% 8.86/6.00 tff(3408,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3409,plain,
% 8.86/6.00 ((hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715))) <=> (hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3410,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3409])).
% 8.86/6.00 tff(3411,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3410, 3408])).
% 8.86/6.00 tff(3412,plain,
% 8.86/6.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3413,plain,
% 8.86/6.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 8.86/6.00 tff(3414,plain,
% 8.86/6.00 ($false),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3413, 221, 3407, 365, 363, 2550, 2558, 2549, 960, 1835])).
% 8.86/6.00 tff(3415,plain,((~hskp42) | hskp2 | c1_1(a1715) | c3_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.00 tff(3416,plain,
% 8.86/6.00 (hskp2),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3415, 2548, 3394, 363, 1835])).
% 8.86/6.00 tff(3417,plain,
% 8.86/6.00 (~c0_1(a1645)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[1122, 3416])).
% 8.86/6.00 tff(3418,plain,
% 8.86/6.00 (~c1_1(a1645)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[1128, 3416])).
% 8.86/6.00 tff(3419,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3420,plain,
% 8.86/6.00 (((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3421,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638))))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3420])).
% 8.86/6.00 tff(3422,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638)))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3421, 3419])).
% 8.86/6.00 tff(3423,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1638)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3424,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1638) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1638)) | (~c0_1(a1638))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3423, 3422])).
% 8.86/6.00 tff(3425,plain,
% 8.86/6.00 (c2_1(a1645) | (~c2_1(a1638))),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3424, 221, 3394, 363, 2558, 1309, 2549, 3418, 3417, 30])).
% 8.86/6.00 tff(3426,plain,
% 8.86/6.00 (c2_1(a1645)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3425, 3406])).
% 8.86/6.00 tff(3427,plain,
% 8.86/6.00 (~c3_1(a1645)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[1144, 3416])).
% 8.86/6.00 tff(3428,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3429,plain,
% 8.86/6.00 ((hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645))) <=> (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3430,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715))))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3429])).
% 8.86/6.00 tff(3431,plain,
% 8.86/6.00 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715)))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3430, 3428])).
% 8.86/6.00 tff(3432,plain,
% 8.86/6.00 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3433,plain,
% 8.86/6.00 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1715))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 8.86/6.00 tff(3434,plain,
% 8.86/6.00 (hskp57 | (~c2_1(a1645))),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3433, 221, 363, 1309, 3418, 3427, 1627, 1835])).
% 8.86/6.00 tff(3435,plain,
% 8.86/6.00 (hskp57),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3434, 3426])).
% 8.86/6.00 tff(3436,plain,
% 8.86/6.00 (c0_1(a1665)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[90, 3435])).
% 8.86/6.00 tff(3437,plain,
% 8.86/6.00 (c3_1(a1665)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[76, 3435])).
% 8.86/6.00 tff(3438,plain,
% 8.86/6.00 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3439,plain,
% 8.86/6.00 ((hskp61 | hskp33 | (~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665))) <=> (hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3440,plain,
% 8.86/6.00 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665)))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3439])).
% 8.86/6.00 tff(3441,plain,
% 8.86/6.00 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3440, 3438])).
% 8.86/6.00 tff(3442,plain,
% 8.86/6.00 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3443,plain,
% 8.86/6.00 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 8.86/6.00 tff(3444,plain,
% 8.86/6.00 (hskp33 | c2_1(a1665)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3443, 221, 1250, 105, 104, 2651])).
% 8.86/6.00 tff(3445,plain,
% 8.86/6.00 (hskp33),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3444, 1813])).
% 8.86/6.00 tff(3446,plain,
% 8.86/6.00 (~c2_1(a1704)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[2664, 3445])).
% 8.86/6.00 tff(3447,plain,
% 8.86/6.00 (~c0_1(a1704)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[2670, 3445])).
% 8.86/6.00 tff(3448,plain,
% 8.86/6.00 (c3_1(a1704)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[2682, 3445])).
% 8.86/6.00 tff(3449,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3450,plain,
% 8.86/6.00 (((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715))) <=> (c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3451,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665)))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3450])).
% 8.86/6.00 tff(3452,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3451, 3449])).
% 8.86/6.00 tff(3453,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3454,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 8.86/6.00 tff(3455,plain,
% 8.86/6.00 ($false),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3454, 221, 365, 363, 105, 104, 3448, 3447, 3446, 410, 1835, 1813])).
% 8.86/6.00 tff(3456,plain,(c2_1(a1665) | c1_1(a1715) | c3_1(a1715) | (~c0_1(a1665)) | (~c3_1(a1665)) | (~c0_1(a1715)) | hskp61), inference(lemma,lemma(discharge,[]))).
% 8.86/6.00 tff(3457,plain,
% 8.86/6.00 (c2_1(a1665)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3456, 3437, 363, 3436, 3394, 1835, 1250])).
% 8.86/6.00 tff(3458,plain,
% 8.86/6.00 (~c1_1(a1665)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[65, 3435])).
% 8.86/6.00 tff(3459,assumption,(c2_1(a1638)), introduced(assumption)).
% 8.86/6.00 tff(3460,assumption,(~c3_1(a1638)), introduced(assumption)).
% 8.86/6.00 tff(3461,assumption,(hskp58), introduced(assumption)).
% 8.86/6.00 tff(3462,plain,
% 8.86/6.00 (((~hskp58) | (~c1_1(a1668))) <=> ((~hskp58) | (~c1_1(a1668)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3463,plain,
% 8.86/6.00 (((~c1_1(a1668)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a1668)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3464,axiom,((~c1_1(a1668)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 8.86/6.00 tff(3465,plain,
% 8.86/6.00 ((~hskp58) | (~c1_1(a1668))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3464, 3463])).
% 8.86/6.00 tff(3466,plain,
% 8.86/6.00 ((~hskp58) | (~c1_1(a1668))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3465, 3462])).
% 8.86/6.00 tff(3467,plain,
% 8.86/6.00 (~c1_1(a1668)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3466, 3461])).
% 8.86/6.00 tff(3468,plain,
% 8.86/6.00 (((~hskp58) | (~c0_1(a1668))) <=> ((~hskp58) | (~c0_1(a1668)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3469,plain,
% 8.86/6.00 (((~c0_1(a1668)) | (~hskp58)) <=> ((~hskp58) | (~c0_1(a1668)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3470,axiom,((~c0_1(a1668)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 8.86/6.00 tff(3471,plain,
% 8.86/6.00 ((~hskp58) | (~c0_1(a1668))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 8.86/6.00 tff(3472,plain,
% 8.86/6.00 ((~hskp58) | (~c0_1(a1668))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3471, 3468])).
% 8.86/6.00 tff(3473,plain,
% 8.86/6.00 (~c0_1(a1668)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3472, 3461])).
% 8.86/6.00 tff(3474,plain,
% 8.86/6.00 (((~hskp58) | c3_1(a1668)) <=> ((~hskp58) | c3_1(a1668))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3475,axiom,((~hskp58) | c3_1(a1668)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 8.86/6.00 tff(3476,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3475, 3474])).
% 8.86/6.00 tff(3477,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3476, 3474])).
% 8.86/6.00 tff(3478,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3477, 3474])).
% 8.86/6.00 tff(3479,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3478, 3474])).
% 8.86/6.00 tff(3480,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3479, 3474])).
% 8.86/6.00 tff(3481,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3480, 3474])).
% 8.86/6.00 tff(3482,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3481, 3474])).
% 8.86/6.00 tff(3483,plain,
% 8.86/6.00 ((~hskp58) | c3_1(a1668)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3482, 3474])).
% 8.86/6.00 tff(3484,plain,
% 8.86/6.00 (c3_1(a1668)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3483, 3461])).
% 8.86/6.00 tff(3485,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3486,plain,
% 8.86/6.00 (((~ndr1_0) | c0_1(a1668) | c1_1(a1668) | (~c3_1(a1668)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638))) <=> (c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3487,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1668) | c1_1(a1668) | (~c3_1(a1668)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3486])).
% 8.86/6.00 tff(3488,plain,
% 8.86/6.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1668) | c1_1(a1668) | (~c3_1(a1668)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3487, 3485])).
% 8.86/6.00 tff(3489,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1668) | c1_1(a1668) | (~c3_1(a1668)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3490,plain,
% 8.86/6.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 8.86/6.00 tff(3491,plain,
% 8.86/6.00 ($false),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3490, 221, 3484, 105, 104, 3397, 3473, 3467, 103, 3460, 102, 3459])).
% 8.86/6.00 tff(3492,plain,((~hskp58) | (~c0_1(a1665)) | (~c3_1(a1665)) | (~c1_1(a1638)) | c1_1(a1665) | c3_1(a1638) | (~c2_1(a1638))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.00 tff(3493,plain,
% 8.86/6.00 (~hskp58),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3492, 3436, 3437, 2550, 3458, 2549, 3406])).
% 8.86/6.00 tff(3494,plain,
% 8.86/6.00 (^[U: $i] : refl((hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 8.86/6.00 inference(bind,[status(th)],[])).
% 8.86/6.00 tff(3495,plain,
% 8.86/6.00 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(quant_intro,[status(thm)],[3494])).
% 8.86/6.00 tff(3496,plain,
% 8.86/6.00 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3497,plain,
% 8.86/6.00 (^[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)) | hskp58) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp58))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) | hskp59) <=> ((hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp59))), rewrite(((hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp59) <=> (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) | hskp59) <=> (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 8.86/6.00 inference(bind,[status(th)],[])).
% 8.86/6.00 tff(3498,plain,
% 8.86/6.00 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) | hskp59) <=> ![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(quant_intro,[status(thm)],[3497])).
% 8.86/6.00 tff(3499,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) | hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause316')).
% 8.86/6.00 tff(3500,plain,
% 8.86/6.00 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3499, 3498])).
% 8.86/6.00 tff(3501,plain,
% 8.86/6.00 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3500, 3496])).
% 8.86/6.00 tff(3502,plain,(
% 8.86/6.00 ![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(skolemize,[status(sab)],[3501])).
% 8.86/6.00 tff(3503,plain,
% 8.86/6.00 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3502, 3495])).
% 8.86/6.00 tff(3504,plain,
% 8.86/6.00 (((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3505,plain,
% 8.86/6.00 ((hskp59 | hskp58 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715))) <=> (hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3506,plain,
% 8.86/6.00 (((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp59 | hskp58 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715))))),
% 8.86/6.00 inference(monotonicity,[status(thm)],[3505])).
% 8.86/6.00 tff(3507,plain,
% 8.86/6.00 (((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp59 | hskp58 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)))),
% 8.86/6.00 inference(transitivity,[status(thm)],[3506, 3504])).
% 8.86/6.00 tff(3508,plain,
% 8.86/6.00 ((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp59 | hskp58 | (~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))),
% 8.86/6.00 inference(quant_inst,[status(thm)],[])).
% 8.86/6.00 tff(3509,plain,
% 8.86/6.00 ((~![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp59 | hskp58 | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3508, 3507])).
% 8.86/6.00 tff(3510,plain,
% 8.86/6.00 (hskp59 | hskp58 | c1_1(a1715) | (~c0_1(a1715))),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3509, 221, 1309, 3503])).
% 8.86/6.00 tff(3511,plain,
% 8.86/6.00 (hskp59),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3510, 3493, 3394, 1835])).
% 8.86/6.00 tff(3512,assumption,(hskp59), introduced(assumption)).
% 8.86/6.00 tff(3513,plain,
% 8.86/6.00 (((~hskp59) | (~c2_1(a1669))) <=> ((~hskp59) | (~c2_1(a1669)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3514,plain,
% 8.86/6.00 (((~c2_1(a1669)) | (~hskp59)) <=> ((~hskp59) | (~c2_1(a1669)))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3515,axiom,((~c2_1(a1669)) | (~hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 8.86/6.00 tff(3516,plain,
% 8.86/6.00 ((~hskp59) | (~c2_1(a1669))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 8.86/6.00 tff(3517,plain,
% 8.86/6.00 ((~hskp59) | (~c2_1(a1669))),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3516, 3513])).
% 8.86/6.00 tff(3518,plain,
% 8.86/6.00 (~c2_1(a1669)),
% 8.86/6.00 inference(unit_resolution,[status(thm)],[3517, 3512])).
% 8.86/6.00 tff(3519,plain,
% 8.86/6.00 (((~hskp59) | c0_1(a1669)) <=> ((~hskp59) | c0_1(a1669))),
% 8.86/6.00 inference(rewrite,[status(thm)],[])).
% 8.86/6.00 tff(3520,axiom,((~hskp59) | c0_1(a1669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 8.86/6.00 tff(3521,plain,
% 8.86/6.00 ((~hskp59) | c0_1(a1669)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3520, 3519])).
% 8.86/6.00 tff(3522,plain,
% 8.86/6.00 ((~hskp59) | c0_1(a1669)),
% 8.86/6.00 inference(modus_ponens,[status(thm)],[3521, 3519])).
% 8.86/6.01 tff(3523,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3522, 3519])).
% 8.86/6.01 tff(3524,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3523, 3519])).
% 8.86/6.01 tff(3525,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3524, 3519])).
% 8.86/6.01 tff(3526,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3525, 3519])).
% 8.86/6.01 tff(3527,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3526, 3519])).
% 8.86/6.01 tff(3528,plain,
% 8.86/6.01 ((~hskp59) | c0_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3527, 3519])).
% 8.86/6.01 tff(3529,plain,
% 8.86/6.01 (c0_1(a1669)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3528, 3512])).
% 8.86/6.01 tff(3530,plain,
% 8.86/6.01 (((~hskp59) | c3_1(a1669)) <=> ((~hskp59) | c3_1(a1669))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3531,axiom,((~hskp59) | c3_1(a1669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 8.86/6.01 tff(3532,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3531, 3530])).
% 8.86/6.01 tff(3533,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3532, 3530])).
% 8.86/6.01 tff(3534,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3533, 3530])).
% 8.86/6.01 tff(3535,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3534, 3530])).
% 8.86/6.01 tff(3536,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3535, 3530])).
% 8.86/6.01 tff(3537,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3536, 3530])).
% 8.86/6.01 tff(3538,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3537, 3530])).
% 8.86/6.01 tff(3539,plain,
% 8.86/6.01 ((~hskp59) | c3_1(a1669)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3538, 3530])).
% 8.86/6.01 tff(3540,plain,
% 8.86/6.01 (c3_1(a1669)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3539, 3512])).
% 8.86/6.01 tff(3541,assumption,(~hskp33), introduced(assumption)).
% 8.86/6.01 tff(3542,plain,
% 8.86/6.01 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3543,plain,
% 8.86/6.01 ((hskp61 | hskp33 | (~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669))) <=> (hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3544,plain,
% 8.86/6.01 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3543])).
% 8.86/6.01 tff(3545,plain,
% 8.86/6.01 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3544, 3542])).
% 8.86/6.01 tff(3546,plain,
% 8.86/6.01 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3547,plain,
% 8.86/6.01 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 8.86/6.01 tff(3548,plain,
% 8.86/6.01 ($false),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3547, 221, 1250, 3541, 3540, 3529, 3518, 2651])).
% 8.86/6.01 tff(3549,plain,((~hskp59) | hskp61 | hskp33), inference(lemma,lemma(discharge,[]))).
% 8.86/6.01 tff(3550,plain,
% 8.86/6.01 (hskp33),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3549, 3511, 1250])).
% 8.86/6.01 tff(3551,plain,
% 8.86/6.01 (~c2_1(a1704)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[2664, 3550])).
% 8.86/6.01 tff(3552,plain,
% 8.86/6.01 (~c0_1(a1704)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[2670, 3550])).
% 8.86/6.01 tff(3553,plain,
% 8.86/6.01 (~c2_1(a1669)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3517, 3511])).
% 8.86/6.01 tff(3554,plain,
% 8.86/6.01 (c3_1(a1704)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[2682, 3550])).
% 8.86/6.01 tff(3555,plain,
% 8.86/6.01 (c0_1(a1669)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3528, 3511])).
% 8.86/6.01 tff(3556,plain,
% 8.86/6.01 (c3_1(a1669)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3539, 3511])).
% 8.86/6.01 tff(3557,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3558,plain,
% 8.86/6.01 (((~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665))) <=> (c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3559,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3558])).
% 8.86/6.01 tff(3560,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3559, 3557])).
% 8.86/6.01 tff(3561,plain,
% 8.86/6.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1669) | (~c3_1(a1669)) | (~c0_1(a1669)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3562,plain,
% 8.86/6.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 8.86/6.01 tff(3563,plain,
% 8.86/6.01 ($false),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3562, 221, 3556, 3555, 3437, 3554, 3553, 3458, 3552, 3551, 376, 3457])).
% 8.86/6.01 tff(3564,plain,((~hskp42) | hskp61 | (~c0_1(a1715)) | c2_1(a1715) | c3_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.01 tff(3565,plain,
% 8.86/6.01 (~hskp42),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3564, 3392, 1835, 1309, 363])).
% 8.86/6.01 tff(3566,plain,
% 8.86/6.01 (~hskp74),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[1081, 3565, 963])).
% 8.86/6.01 tff(3567,plain,
% 8.86/6.01 (hskp38),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[1032, 3566, 881])).
% 8.86/6.01 tff(3568,plain,
% 8.86/6.01 (~c2_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[970, 3567])).
% 8.86/6.01 tff(3569,plain,
% 8.86/6.01 (c3_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[981, 3567])).
% 8.86/6.01 tff(3570,plain,
% 8.86/6.01 (~c1_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[988, 221, 963, 929, 895, 3569, 3568, 950, 882])).
% 8.86/6.01 tff(3571,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3572,plain,
% 8.86/6.01 ((hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))) <=> (hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3573,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3572])).
% 8.86/6.01 tff(3574,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3573, 3571])).
% 8.86/6.01 tff(3575,plain,
% 8.86/6.01 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3576,plain,
% 8.86/6.01 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3575, 3574])).
% 8.86/6.01 tff(3577,plain,
% 8.86/6.01 ($false),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3576, 221, 1250, 363, 2537, 2536, 1309, 2535, 1249, 1835])).
% 8.86/6.01 tff(3578,plain,((~hskp0) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.01 tff(3579,plain,
% 8.86/6.01 (~hskp0),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3578, 1250, 363, 1309, 1835])).
% 8.86/6.01 tff(3580,plain,
% 8.86/6.01 (~hskp42),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3564, 1250, 1835, 1309, 363])).
% 8.86/6.01 tff(3581,plain,
% 8.86/6.01 (~hskp74),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[1081, 3580, 3579])).
% 8.86/6.01 tff(3582,assumption,(~hskp62), introduced(assumption)).
% 8.86/6.01 tff(3583,assumption,(hskp44), introduced(assumption)).
% 8.86/6.01 tff(3584,plain,
% 8.86/6.01 (((~hskp44) | c2_1(a1640)) <=> ((~hskp44) | c2_1(a1640))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3585,axiom,((~hskp44) | c2_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 8.86/6.01 tff(3586,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 8.86/6.01 tff(3587,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3586, 3584])).
% 8.86/6.01 tff(3588,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3587, 3584])).
% 8.86/6.01 tff(3589,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3588, 3584])).
% 8.86/6.01 tff(3590,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3589, 3584])).
% 8.86/6.01 tff(3591,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3590, 3584])).
% 8.86/6.01 tff(3592,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3591, 3584])).
% 8.86/6.01 tff(3593,plain,
% 8.86/6.01 ((~hskp44) | c2_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3592, 3584])).
% 8.86/6.01 tff(3594,plain,
% 8.86/6.01 (c2_1(a1640)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3593, 3583])).
% 8.86/6.01 tff(3595,plain,
% 8.86/6.01 (((~hskp44) | c3_1(a1640)) <=> ((~hskp44) | c3_1(a1640))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3596,axiom,((~hskp44) | c3_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 8.86/6.01 tff(3597,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 8.86/6.01 tff(3598,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3597, 3595])).
% 8.86/6.01 tff(3599,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3598, 3595])).
% 8.86/6.01 tff(3600,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3599, 3595])).
% 8.86/6.01 tff(3601,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3600, 3595])).
% 8.86/6.01 tff(3602,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3601, 3595])).
% 8.86/6.01 tff(3603,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3602, 3595])).
% 8.86/6.01 tff(3604,plain,
% 8.86/6.01 ((~hskp44) | c3_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3603, 3595])).
% 8.86/6.01 tff(3605,plain,
% 8.86/6.01 (c3_1(a1640)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3604, 3583])).
% 8.86/6.01 tff(3606,plain,
% 8.86/6.01 (((~hskp44) | c1_1(a1640)) <=> ((~hskp44) | c1_1(a1640))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3607,axiom,((~hskp44) | c1_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 8.86/6.01 tff(3608,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 8.86/6.01 tff(3609,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3608, 3606])).
% 8.86/6.01 tff(3610,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3609, 3606])).
% 8.86/6.01 tff(3611,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3610, 3606])).
% 8.86/6.01 tff(3612,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3611, 3606])).
% 8.86/6.01 tff(3613,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3612, 3606])).
% 8.86/6.01 tff(3614,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3613, 3606])).
% 8.86/6.01 tff(3615,plain,
% 8.86/6.01 ((~hskp44) | c1_1(a1640)),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3614, 3606])).
% 8.86/6.01 tff(3616,plain,
% 8.86/6.01 (c1_1(a1640)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3615, 3583])).
% 8.86/6.01 tff(3617,assumption,(c1_1(a1640)), introduced(assumption)).
% 8.86/6.01 tff(3618,assumption,(c3_1(a1640)), introduced(assumption)).
% 8.86/6.01 tff(3619,plain,
% 8.86/6.01 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | c0_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3620,plain,
% 8.86/6.01 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3621,plain,
% 8.86/6.01 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | c0_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 8.86/6.01 tff(3622,plain,
% 8.86/6.01 (hskp62 | c0_1(a1640)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3621, 221, 1250, 3618, 3617, 2219])).
% 8.86/6.01 tff(3623,plain,
% 8.86/6.01 (c0_1(a1640)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3622, 3582])).
% 8.86/6.01 tff(3624,assumption,(c2_1(a1640)), introduced(assumption)).
% 8.86/6.01 tff(3625,plain,
% 8.86/6.01 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3626,plain,
% 8.86/6.01 ((hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c2_1(a1640))) <=> (hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3627,plain,
% 8.86/6.01 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c2_1(a1640)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3626])).
% 8.86/6.01 tff(3628,plain,
% 8.86/6.01 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c2_1(a1640)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3627, 3625])).
% 8.86/6.01 tff(3629,plain,
% 8.86/6.01 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c2_1(a1640)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3630,plain,
% 8.86/6.01 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1640))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 8.86/6.01 tff(3631,plain,
% 8.86/6.01 (hskp74 | hskp38 | (~c0_1(a1640))),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3630, 221, 3618, 3624, 1025])).
% 8.86/6.01 tff(3632,plain,
% 8.86/6.01 (hskp38),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3631, 3623, 1027])).
% 8.86/6.01 tff(3633,plain,
% 8.86/6.01 (~c0_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[2583, 3632])).
% 8.86/6.01 tff(3634,plain,
% 8.86/6.01 (c3_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[981, 3632])).
% 8.86/6.01 tff(3635,plain,
% 8.86/6.01 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3636,plain,
% 8.86/6.01 ((hskp62 | hskp61 | (~ndr1_0) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718))) <=> (hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3637,plain,
% 8.86/6.01 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3636])).
% 8.86/6.01 tff(3638,plain,
% 8.86/6.01 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3637, 3635])).
% 8.86/6.01 tff(3639,plain,
% 8.86/6.01 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3640,plain,
% 8.86/6.01 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 8.86/6.01 tff(3641,plain,
% 8.86/6.01 (~c1_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3640, 221, 3582, 1250, 3634, 3633, 2219])).
% 8.86/6.01 tff(3642,plain,
% 8.86/6.01 (~c2_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[970, 3632])).
% 8.86/6.01 tff(3643,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3644,plain,
% 8.86/6.01 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1640)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718))) <=> (c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3645,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1640)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3644])).
% 8.86/6.01 tff(3646,plain,
% 8.86/6.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1640)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3645, 3643])).
% 8.86/6.01 tff(3647,plain,
% 8.86/6.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1640)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3648,plain,
% 8.86/6.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 8.86/6.01 tff(3649,plain,
% 8.86/6.01 ($false),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3648, 221, 365, 3618, 3617, 3634, 1309, 3642, 647, 1835, 3623, 3641])).
% 8.86/6.01 tff(3650,plain,(hskp62 | c1_1(a1715) | (~c3_1(a1640)) | (~c1_1(a1640)) | c2_1(a1715) | (~c0_1(a1715)) | hskp61 | hskp74 | (~c2_1(a1640))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.01 tff(3651,plain,
% 8.86/6.01 ($false),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3650, 3616, 3605, 365, 3582, 1309, 1835, 1250, 1027, 3594])).
% 8.86/6.01 tff(3652,plain,((~hskp44) | c1_1(a1715) | hskp62 | c2_1(a1715) | (~c0_1(a1715)) | hskp61 | hskp74), inference(lemma,lemma(discharge,[]))).
% 8.86/6.01 tff(3653,plain,
% 8.86/6.01 (~hskp44),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3652, 3582, 3394, 1309, 1835, 1250, 3581])).
% 8.86/6.01 tff(3654,plain,
% 8.86/6.01 (c2_1(a1665)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3456, 91, 363, 365, 77, 1835, 1250])).
% 8.86/6.01 tff(3655,plain,
% 8.86/6.01 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3656,plain,
% 8.86/6.01 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.86/6.01 inference(quant_inst,[status(thm)],[])).
% 8.86/6.01 tff(3657,plain,
% 8.86/6.01 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))),
% 8.86/6.01 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 8.86/6.01 tff(3658,plain,
% 8.86/6.01 (hskp38 | (~c2_1(a1665))),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3657, 221, 1027, 91, 77, 1025])).
% 8.86/6.01 tff(3659,plain,
% 8.86/6.01 (hskp38),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3658, 3654])).
% 8.86/6.01 tff(3660,plain,
% 8.86/6.01 (~c0_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[2583, 3659])).
% 8.86/6.01 tff(3661,plain,
% 8.86/6.01 (c3_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[981, 3659])).
% 8.86/6.01 tff(3662,plain,
% 8.86/6.01 (~c1_1(a1718)),
% 8.86/6.01 inference(unit_resolution,[status(thm)],[3640, 221, 3582, 1250, 3661, 3660, 2219])).
% 8.86/6.01 tff(3663,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3664,plain,
% 8.86/6.01 ((hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718))) <=> (hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.01 inference(rewrite,[status(thm)],[])).
% 8.86/6.01 tff(3665,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.86/6.01 inference(monotonicity,[status(thm)],[3664])).
% 8.86/6.01 tff(3666,plain,
% 8.86/6.01 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.01 inference(transitivity,[status(thm)],[3665, 3663])).
% 8.86/6.01 tff(3667,plain,
% 8.86/6.01 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3668,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 8.86/6.02 tff(3669,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3668, 221, 138, 91, 77, 3661, 66, 3660, 137, 3662])).
% 8.86/6.02 tff(3670,plain,((~hskp57) | hskp29 | hskp62 | hskp61 | hskp74 | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3671,plain,
% 8.86/6.02 (~hskp57),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3670, 138, 3581, 1250, 3582, 363, 3394, 1835])).
% 8.86/6.02 tff(3672,assumption,(hskp45), introduced(assumption)).
% 8.86/6.02 tff(3673,plain,
% 8.86/6.02 (((~hskp45) | (~c1_1(a1641))) <=> ((~hskp45) | (~c1_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3674,plain,
% 8.86/6.02 (((~c1_1(a1641)) | (~hskp45)) <=> ((~hskp45) | (~c1_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3675,axiom,((~c1_1(a1641)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause224')).
% 8.86/6.02 tff(3676,plain,
% 8.86/6.02 ((~hskp45) | (~c1_1(a1641))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3675, 3674])).
% 8.86/6.02 tff(3677,plain,
% 8.86/6.02 ((~hskp45) | (~c1_1(a1641))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3676, 3673])).
% 8.86/6.02 tff(3678,plain,
% 8.86/6.02 (~c1_1(a1641)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3677, 3672])).
% 8.86/6.02 tff(3679,plain,
% 8.86/6.02 (((~hskp45) | (~c3_1(a1641))) <=> ((~hskp45) | (~c3_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3680,plain,
% 8.86/6.02 (((~c3_1(a1641)) | (~hskp45)) <=> ((~hskp45) | (~c3_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3681,axiom,((~c3_1(a1641)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause223')).
% 8.86/6.02 tff(3682,plain,
% 8.86/6.02 ((~hskp45) | (~c3_1(a1641))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3681, 3680])).
% 8.86/6.02 tff(3683,plain,
% 8.86/6.02 ((~hskp45) | (~c3_1(a1641))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3682, 3679])).
% 8.86/6.02 tff(3684,plain,
% 8.86/6.02 (~c3_1(a1641)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3683, 3672])).
% 8.86/6.02 tff(3685,plain,
% 8.86/6.02 (((~hskp45) | c2_1(a1641)) <=> ((~hskp45) | c2_1(a1641))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3686,axiom,((~hskp45) | c2_1(a1641)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 8.86/6.02 tff(3687,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 8.86/6.02 tff(3688,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3687, 3685])).
% 8.86/6.02 tff(3689,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3688, 3685])).
% 8.86/6.02 tff(3690,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3689, 3685])).
% 8.86/6.02 tff(3691,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3690, 3685])).
% 8.86/6.02 tff(3692,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3691, 3685])).
% 8.86/6.02 tff(3693,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3692, 3685])).
% 8.86/6.02 tff(3694,plain,
% 8.86/6.02 ((~hskp45) | c2_1(a1641)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3693, 3685])).
% 8.86/6.02 tff(3695,plain,
% 8.86/6.02 (c2_1(a1641)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3694, 3672])).
% 8.86/6.02 tff(3696,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3697,plain,
% 8.86/6.02 ((hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1641) | c1_1(a1641) | (~c2_1(a1641))) <=> (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3698,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1641) | c1_1(a1641) | (~c2_1(a1641)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641))))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3697])).
% 8.86/6.02 tff(3699,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1641) | c1_1(a1641) | (~c2_1(a1641)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641)))),
% 8.86/6.02 inference(transitivity,[status(thm)],[3698, 3696])).
% 8.86/6.02 tff(3700,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1641) | c1_1(a1641) | (~c2_1(a1641)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3701,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3700, 3699])).
% 8.86/6.02 tff(3702,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3701, 221, 1628, 363, 3695, 1309, 3684, 3678, 1627, 1835])).
% 8.86/6.02 tff(3703,plain,((~hskp45) | hskp57 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3704,plain,
% 8.86/6.02 (~hskp45),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3703, 3671, 363, 1309, 1835])).
% 8.86/6.02 tff(3705,plain,
% 8.86/6.02 ((hskp45 | hskp44 | hskp43) <=> (hskp45 | hskp44 | hskp43)),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3706,plain,
% 8.86/6.02 (((hskp43 | hskp44) | hskp45) <=> (hskp45 | hskp44 | hskp43)),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3707,axiom,((hskp43 | hskp44) | hskp45), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 8.86/6.02 tff(3708,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 8.86/6.02 tff(3709,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3708, 3705])).
% 8.86/6.02 tff(3710,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3709, 3705])).
% 8.86/6.02 tff(3711,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3710, 3705])).
% 8.86/6.02 tff(3712,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3711, 3705])).
% 8.86/6.02 tff(3713,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3712, 3705])).
% 8.86/6.02 tff(3714,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3713, 3705])).
% 8.86/6.02 tff(3715,plain,
% 8.86/6.02 (hskp45 | hskp44 | hskp43),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3714, 3705])).
% 8.86/6.02 tff(3716,plain,
% 8.86/6.02 (hskp43),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3715, 3704, 3653])).
% 8.86/6.02 tff(3717,plain,
% 8.86/6.02 (((~hskp43) | c0_1(a1639)) <=> ((~hskp43) | c0_1(a1639))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3718,axiom,((~hskp43) | c0_1(a1639)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 8.86/6.02 tff(3719,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3718, 3717])).
% 8.86/6.02 tff(3720,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3719, 3717])).
% 8.86/6.02 tff(3721,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3720, 3717])).
% 8.86/6.02 tff(3722,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3721, 3717])).
% 8.86/6.02 tff(3723,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3722, 3717])).
% 8.86/6.02 tff(3724,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3723, 3717])).
% 8.86/6.02 tff(3725,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3724, 3717])).
% 8.86/6.02 tff(3726,plain,
% 8.86/6.02 ((~hskp43) | c0_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3725, 3717])).
% 8.86/6.02 tff(3727,plain,
% 8.86/6.02 (c0_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3726, 3716])).
% 8.86/6.02 tff(3728,plain,
% 8.86/6.02 (((~hskp43) | c2_1(a1639)) <=> ((~hskp43) | c2_1(a1639))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3729,axiom,((~hskp43) | c2_1(a1639)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 8.86/6.02 tff(3730,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 8.86/6.02 tff(3731,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3730, 3728])).
% 8.86/6.02 tff(3732,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3731, 3728])).
% 8.86/6.02 tff(3733,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3732, 3728])).
% 8.86/6.02 tff(3734,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3733, 3728])).
% 8.86/6.02 tff(3735,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3734, 3728])).
% 8.86/6.02 tff(3736,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3735, 3728])).
% 8.86/6.02 tff(3737,plain,
% 8.86/6.02 ((~hskp43) | c2_1(a1639)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3736, 3728])).
% 8.86/6.02 tff(3738,plain,
% 8.86/6.02 (c2_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3737, 3716])).
% 8.86/6.02 tff(3739,plain,
% 8.86/6.02 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1639) | (~c0_1(a1639)) | (~c2_1(a1639)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | (~ndr1_0) | c3_1(a1639) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3740,plain,
% 8.86/6.02 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1639) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3741,plain,
% 8.86/6.02 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | (~ndr1_0) | c3_1(a1639) | (~c0_1(a1639)) | (~c2_1(a1639))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 8.86/6.02 tff(3742,plain,
% 8.86/6.02 (c3_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3741, 221, 3580, 3579, 3738, 3727, 1043])).
% 8.86/6.02 tff(3743,assumption,(hskp43), introduced(assumption)).
% 8.86/6.02 tff(3744,plain,
% 8.86/6.02 (c0_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3726, 3743])).
% 8.86/6.02 tff(3745,plain,
% 8.86/6.02 (c2_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3737, 3743])).
% 8.86/6.02 tff(3746,plain,
% 8.86/6.02 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3747,plain,
% 8.86/6.02 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3748,plain,
% 8.86/6.02 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3747, 3746])).
% 8.86/6.02 tff(3749,plain,
% 8.86/6.02 (~c3_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3748, 221, 3016, 1026, 3745, 3744, 1025])).
% 8.86/6.02 tff(3750,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3741, 221, 1073, 963, 3745, 3744, 1043, 3749])).
% 8.86/6.02 tff(3751,plain,((~hskp43) | hskp42 | hskp0 | hskp38), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3752,plain,
% 8.86/6.02 (hskp38),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3751, 3716, 3579, 3580])).
% 8.86/6.02 tff(3753,plain,
% 8.86/6.02 (~c0_1(a1718)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2583, 3752])).
% 8.86/6.02 tff(3754,plain,
% 8.86/6.02 (((~hskp43) | (~c1_1(a1639))) <=> ((~hskp43) | (~c1_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3755,plain,
% 8.86/6.02 (((~c1_1(a1639)) | (~hskp43)) <=> ((~hskp43) | (~c1_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3756,axiom,((~c1_1(a1639)) | (~hskp43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause225')).
% 8.86/6.02 tff(3757,plain,
% 8.86/6.02 ((~hskp43) | (~c1_1(a1639))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 8.86/6.02 tff(3758,plain,
% 8.86/6.02 ((~hskp43) | (~c1_1(a1639))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3757, 3754])).
% 8.86/6.02 tff(3759,plain,
% 8.86/6.02 (~c1_1(a1639)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3758, 3716])).
% 8.86/6.02 tff(3760,plain,
% 8.86/6.02 (c3_1(a1718)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[981, 3752])).
% 8.86/6.02 tff(3761,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3762,plain,
% 8.86/6.02 ((hskp29 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718))) <=> (hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3763,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3762])).
% 8.86/6.02 tff(3764,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.02 inference(transitivity,[status(thm)],[3763, 3761])).
% 8.86/6.02 tff(3765,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3766,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 8.86/6.02 tff(3767,plain,
% 8.86/6.02 (c1_1(a1718)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3766, 221, 138, 3727, 3760, 3759, 3753, 137, 3742])).
% 8.86/6.02 tff(3768,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3640, 221, 3582, 1250, 3760, 3753, 2219, 3767])).
% 8.86/6.02 tff(3769,plain,(hskp29 | hskp62 | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3770,plain,
% 8.86/6.02 (hskp62),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3769, 3392, 363, 138, 1309, 1835])).
% 8.86/6.02 tff(3771,plain,
% 8.86/6.02 (c0_1(a1675)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2237, 3770])).
% 8.86/6.02 tff(3772,plain,
% 8.86/6.02 (~c3_1(a1675)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2254, 3770])).
% 8.86/6.02 tff(3773,plain,
% 8.86/6.02 (c1_1(a1675)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2248, 3770])).
% 8.86/6.02 tff(3774,plain,
% 8.86/6.02 (c2_1(a1675)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2267, 3773, 3772, 3771, 3392])).
% 8.86/6.02 tff(3775,plain,
% 8.86/6.02 (~c0_1(a1718)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2583, 3567])).
% 8.86/6.02 tff(3776,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3777,plain,
% 8.86/6.02 (((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1718) | c2_1(a1718) | c1_1(a1718) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3778,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1718) | c2_1(a1718) | c1_1(a1718) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675))))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3777])).
% 8.86/6.02 tff(3779,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1718) | c2_1(a1718) | c1_1(a1718) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.02 inference(transitivity,[status(thm)],[3778, 3776])).
% 8.86/6.02 tff(3780,plain,
% 8.86/6.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)) | c0_1(a1718) | c2_1(a1718) | c1_1(a1718) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3781,plain,
% 8.86/6.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3780, 3779])).
% 8.86/6.02 tff(3782,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3781, 221, 365, 363, 3771, 1309, 3772, 3568, 3775, 30, 3774, 3570])).
% 8.86/6.02 tff(3783,plain,((~c1_1(a1654)) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | hskp0 | (~hskp52) | hskp29 | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3784,plain,
% 8.86/6.02 (~c1_1(a1654)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3783, 881, 363, 1309, 963, 365, 138, 3383])).
% 8.86/6.02 tff(3785,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3786,plain,
% 8.86/6.02 ((hskp26 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3787,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3786])).
% 8.86/6.02 tff(3788,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.02 inference(transitivity,[status(thm)],[3787, 3785])).
% 8.86/6.02 tff(3789,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3790,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3789, 3788])).
% 8.86/6.02 tff(3791,plain,
% 8.86/6.02 (hskp26),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3790, 221, 929, 895, 894, 20, 3784])).
% 8.86/6.02 tff(3792,plain,
% 8.86/6.02 (~c2_1(a1691)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[669, 3791])).
% 8.86/6.02 tff(3793,plain,
% 8.86/6.02 (~c3_1(a1691)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[689, 3791])).
% 8.86/6.02 tff(3794,plain,
% 8.86/6.02 (~c1_1(a1691)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[675, 3791])).
% 8.86/6.02 tff(3795,plain,
% 8.86/6.02 (hskp37),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2407, 2057, 578, 2097])).
% 8.86/6.02 tff(3796,plain,
% 8.86/6.02 (~c1_1(a1714)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[591, 3795])).
% 8.86/6.02 tff(3797,plain,
% 8.86/6.02 (c0_1(a1714)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[602, 3795])).
% 8.86/6.02 tff(3798,plain,
% 8.86/6.02 (c2_1(a1714)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[613, 3795])).
% 8.86/6.02 tff(3799,plain,
% 8.86/6.02 ($false),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2427, 221, 2057, 2097, 1324, 1323, 1662, 1322, 565, 1321])).
% 8.86/6.02 tff(3800,plain,((~c3_1(a1714)) | c2_1(a1716) | c0_1(a1716) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c1_1(a1714)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.02 tff(3801,plain,
% 8.86/6.02 (~c3_1(a1714)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3800, 2057, 2097, 3798, 3797, 1662, 3796])).
% 8.86/6.02 tff(3802,plain,
% 8.86/6.02 (c1_1(a1716)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[2419, 3801, 2097, 3798, 3797, 1662, 2057])).
% 8.86/6.02 tff(3803,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3804,plain,
% 8.86/6.02 ((hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716))) <=> (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3805,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716))))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3804])).
% 8.86/6.02 tff(3806,plain,
% 8.86/6.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716)))),
% 8.86/6.02 inference(transitivity,[status(thm)],[3805, 3803])).
% 8.86/6.02 tff(3807,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))),
% 8.86/6.02 inference(quant_inst,[status(thm)],[])).
% 8.86/6.02 tff(3808,plain,
% 8.86/6.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716))),
% 8.86/6.02 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 8.86/6.02 tff(3809,plain,
% 8.86/6.02 (hskp21 | c2_1(a1716) | (~c1_1(a1716))),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3808, 221, 2097, 1662, 1357])).
% 8.86/6.02 tff(3810,plain,
% 8.86/6.02 (hskp21),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[3809, 3802, 2057])).
% 8.86/6.02 tff(3811,plain,
% 8.86/6.02 (c2_1(a1683)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[1383, 3810])).
% 8.86/6.02 tff(3812,plain,
% 8.86/6.02 (c3_1(a1683)),
% 8.86/6.02 inference(unit_resolution,[status(thm)],[1394, 3810])).
% 8.86/6.02 tff(3813,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3814,plain,
% 8.86/6.02 (((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716)) <=> (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.02 inference(rewrite,[status(thm)],[])).
% 8.86/6.02 tff(3815,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.86/6.02 inference(monotonicity,[status(thm)],[3814])).
% 8.86/6.02 tff(3816,plain,
% 8.86/6.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3815, 3813])).
% 8.86/6.03 tff(3817,plain,
% 8.86/6.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | (~c2_1(a1683)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1716) | c2_1(a1716) | c0_1(a1716))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3818,plain,
% 8.86/6.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c0_1(a1683)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 8.86/6.03 tff(3819,plain,
% 8.86/6.03 (~c0_1(a1683)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3818, 221, 2057, 2097, 3798, 3797, 3812, 3811, 1662, 3796, 565])).
% 8.86/6.03 tff(3820,plain,
% 8.86/6.03 (~c1_1(a1683)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[1417, 3810])).
% 8.86/6.03 tff(3821,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3822,plain,
% 8.86/6.03 ((hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714))) <=> (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3823,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714))))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3822])).
% 8.86/6.03 tff(3824,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3823, 3821])).
% 8.86/6.03 tff(3825,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1714) | c1_1(a1714) | (~c2_1(a1714)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3826,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3825, 3824])).
% 8.86/6.03 tff(3827,plain,
% 8.86/6.03 ($false),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3826, 221, 1628, 363, 1324, 1309, 1322, 1627, 1835, 2411])).
% 8.86/6.03 tff(3828,plain,(c3_1(a1714) | hskp57 | c3_1(a1715) | (~c2_1(a1714)) | c2_1(a1715) | c1_1(a1714) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.03 tff(3829,plain,
% 8.86/6.03 (hskp57),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3828, 3801, 3383, 363, 1309, 3796, 3798])).
% 8.86/6.03 tff(3830,plain,
% 8.86/6.03 (~c1_1(a1665)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[65, 3829])).
% 8.86/6.03 tff(3831,plain,
% 8.86/6.03 (c3_1(a1665)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[76, 3829])).
% 8.86/6.03 tff(3832,plain,
% 8.86/6.03 (c0_1(a1665)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[90, 3829])).
% 8.86/6.03 tff(3833,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3834,plain,
% 8.86/6.03 ((hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683))) <=> (hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3835,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3834])).
% 8.86/6.03 tff(3836,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3835, 3833])).
% 8.86/6.03 tff(3837,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3838,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3837, 3836])).
% 8.86/6.03 tff(3839,plain,
% 8.86/6.03 ($false),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3838, 221, 138, 3832, 3831, 3812, 3830, 3820, 137, 3819])).
% 8.86/6.03 tff(3840,plain,(c2_1(a1716) | hskp29 | c0_1(a1716) | c3_1(a1716) | c3_1(a1715) | c2_1(a1715) | hskp72), inference(lemma,lemma(discharge,[]))).
% 8.86/6.03 tff(3841,plain,
% 8.86/6.03 (c2_1(a1716)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3840, 363, 2097, 1662, 138, 1309, 2400])).
% 8.86/6.03 tff(3842,plain,
% 8.86/6.03 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 8.86/6.03 inference(bind,[status(th)],[])).
% 8.86/6.03 tff(3843,plain,
% 8.86/6.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(quant_intro,[status(thm)],[3842])).
% 8.86/6.03 tff(3844,plain,
% 8.86/6.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3845,plain,
% 8.86/6.03 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 8.86/6.03 inference(bind,[status(th)],[])).
% 8.86/6.03 tff(3846,plain,
% 8.86/6.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(quant_intro,[status(thm)],[3845])).
% 8.86/6.03 tff(3847,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause339')).
% 8.86/6.03 tff(3848,plain,
% 8.86/6.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 8.86/6.03 tff(3849,plain,
% 8.86/6.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3848, 3844])).
% 8.86/6.03 tff(3850,plain,(
% 8.86/6.03 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(skolemize,[status(sab)],[3849])).
% 8.86/6.03 tff(3851,plain,
% 8.86/6.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3850, 3843])).
% 8.86/6.03 tff(3852,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3853,plain,
% 8.86/6.03 ((hskp22 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1716) | c0_1(a1716) | (~c2_1(a1716))) <=> (hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3854,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1716) | c0_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716))))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3853])).
% 8.86/6.03 tff(3855,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1716) | c0_1(a1716) | (~c2_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3854, 3852])).
% 8.86/6.03 tff(3856,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1716) | c0_1(a1716) | (~c2_1(a1716)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3857,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp22 | c0_1(a1716) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1716))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 8.86/6.03 tff(3858,plain,
% 8.86/6.03 (hskp22 | (~c2_1(a1716))),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3857, 221, 2097, 363, 1662, 1309, 3851, 3383])).
% 8.86/6.03 tff(3859,plain,
% 8.86/6.03 (hskp22),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3858, 3841])).
% 8.86/6.03 tff(3860,plain,
% 8.86/6.03 (((~hskp22) | (~c3_1(a1684))) <=> ((~hskp22) | (~c3_1(a1684)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3861,plain,
% 8.86/6.03 (((~c3_1(a1684)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1684)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3862,axiom,((~c3_1(a1684)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 8.86/6.03 tff(3863,plain,
% 8.86/6.03 ((~hskp22) | (~c3_1(a1684))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 8.86/6.03 tff(3864,plain,
% 8.86/6.03 ((~hskp22) | (~c3_1(a1684))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3863, 3860])).
% 8.86/6.03 tff(3865,plain,
% 8.86/6.03 (~c3_1(a1684)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3864, 3859])).
% 8.86/6.03 tff(3866,plain,
% 8.86/6.03 (((~hskp22) | c2_1(a1684)) <=> ((~hskp22) | c2_1(a1684))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3867,axiom,((~hskp22) | c2_1(a1684)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 8.86/6.03 tff(3868,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 8.86/6.03 tff(3869,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3868, 3866])).
% 8.86/6.03 tff(3870,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3869, 3866])).
% 8.86/6.03 tff(3871,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3870, 3866])).
% 8.86/6.03 tff(3872,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3871, 3866])).
% 8.86/6.03 tff(3873,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3872, 3866])).
% 8.86/6.03 tff(3874,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3873, 3866])).
% 8.86/6.03 tff(3875,plain,
% 8.86/6.03 ((~hskp22) | c2_1(a1684)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3874, 3866])).
% 8.86/6.03 tff(3876,plain,
% 8.86/6.03 (c2_1(a1684)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3875, 3859])).
% 8.86/6.03 tff(3877,plain,
% 8.86/6.03 (c1_1(a1718)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[2603, 627, 617, 615, 2595, 2594, 138])).
% 8.86/6.03 tff(3878,plain,
% 8.86/6.03 ($false),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3038, 221, 2104, 616, 615, 2595, 2594, 1563, 627, 3877])).
% 8.86/6.03 tff(3879,plain,(c1_1(a1654) | hskp73 | (~c2_1(a1654)) | (~c3_1(a1654)) | (~c3_1(a1718)) | c0_1(a1718) | (~c0_1(a1654)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.86/6.03 tff(3880,plain,
% 8.86/6.03 (c1_1(a1654)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3879, 3031, 138, 3021, 3240, 3239, 3022, 2104])).
% 8.86/6.03 tff(3881,assumption,(~c3_1(a1684)), introduced(assumption)).
% 8.86/6.03 tff(3882,assumption,(c2_1(a1684)), introduced(assumption)).
% 8.86/6.03 tff(3883,plain,
% 8.86/6.03 (~hskp74),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[1081, 1073, 3579])).
% 8.86/6.03 tff(3884,plain,
% 8.86/6.03 (~hskp57),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3670, 3582, 138, 1250, 3883, 363, 3394, 1835])).
% 8.86/6.03 tff(3885,assumption,(~hskp44), introduced(assumption)).
% 8.86/6.03 tff(3886,plain,
% 8.86/6.03 (~hskp45),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3703, 1628, 363, 1309, 1835])).
% 8.86/6.03 tff(3887,plain,
% 8.86/6.03 (hskp43),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3715, 3886, 3885])).
% 8.86/6.03 tff(3888,plain,
% 8.86/6.03 (c0_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3726, 3887])).
% 8.86/6.03 tff(3889,plain,
% 8.86/6.03 (c2_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3737, 3887])).
% 8.86/6.03 tff(3890,plain,
% 8.86/6.03 (c3_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3741, 221, 1073, 3579, 3889, 3888, 1043])).
% 8.86/6.03 tff(3891,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3892,plain,
% 8.86/6.03 ((hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1684) | c1_1(a1684) | (~c2_1(a1684))) <=> (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3893,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1684) | c1_1(a1684) | (~c2_1(a1684)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715))))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3892])).
% 8.86/6.03 tff(3894,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1684) | c1_1(a1684) | (~c2_1(a1684)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3893, 3891])).
% 8.86/6.03 tff(3895,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c3_1(a1684) | c1_1(a1684) | (~c2_1(a1684)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3896,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | c1_1(a1684) | (~c0_1(a1715))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 8.86/6.03 tff(3897,plain,
% 8.86/6.03 (hskp57 | c1_1(a1684)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3896, 221, 363, 3882, 1309, 3881, 1627, 1835])).
% 8.86/6.03 tff(3898,plain,
% 8.86/6.03 (c1_1(a1684)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3897, 1628])).
% 8.86/6.03 tff(3899,plain,
% 8.86/6.03 (c3_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3741, 221, 1073, 963, 3745, 3744, 1043])).
% 8.86/6.03 tff(3900,plain,
% 8.86/6.03 (~c1_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3758, 3743])).
% 8.86/6.03 tff(3901,assumption,(~hskp67), introduced(assumption)).
% 8.86/6.03 tff(3902,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3903,plain,
% 8.86/6.03 ((hskp67 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c1_1(a1639) | (~c3_1(a1639)) | (~c2_1(a1639))) <=> (hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3904,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c1_1(a1639) | (~c3_1(a1639)) | (~c2_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639))))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3903])).
% 8.86/6.03 tff(3905,plain,
% 8.86/6.03 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c1_1(a1639) | (~c3_1(a1639)) | (~c2_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3904, 3902])).
% 8.86/6.03 tff(3906,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c1_1(a1639) | (~c3_1(a1639)) | (~c2_1(a1639)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3907,plain,
% 8.86/6.03 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3906, 3905])).
% 8.86/6.03 tff(3908,plain,
% 8.86/6.03 ($false),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3907, 221, 3901, 3745, 3744, 3900, 1517, 3899])).
% 8.86/6.03 tff(3909,plain,((~hskp43) | hskp67 | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.86/6.03 tff(3910,plain,
% 8.86/6.03 (hskp67),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3909, 3887, 1073, 3579])).
% 8.86/6.03 tff(3911,plain,
% 8.86/6.03 (c3_1(a1702)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[1534, 3910])).
% 8.86/6.03 tff(3912,plain,
% 8.86/6.03 (c1_1(a1702)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[1545, 3910])).
% 8.86/6.03 tff(3913,plain,
% 8.86/6.03 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3914,plain,
% 8.86/6.03 ((hskp62 | hskp61 | (~ndr1_0) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702))) <=> (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3915,plain,
% 8.86/6.03 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)))),
% 8.86/6.03 inference(monotonicity,[status(thm)],[3914])).
% 8.86/6.03 tff(3916,plain,
% 8.86/6.03 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.03 inference(transitivity,[status(thm)],[3915, 3913])).
% 8.86/6.03 tff(3917,plain,
% 8.86/6.03 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3918,plain,
% 8.86/6.03 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 8.86/6.03 tff(3919,plain,
% 8.86/6.03 (c0_1(a1702)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3918, 221, 3582, 1250, 3912, 3911, 2219])).
% 8.86/6.03 tff(3920,plain,
% 8.86/6.03 (c2_1(a1702)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[2029, 3910])).
% 8.86/6.03 tff(3921,plain,
% 8.86/6.03 (((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1702)) | (~c0_1(a1702)) | (~c2_1(a1702)))) <=> ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1702)) | (~c0_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3922,plain,
% 8.86/6.03 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1702)) | (~c0_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.03 inference(quant_inst,[status(thm)],[])).
% 8.86/6.03 tff(3923,plain,
% 8.86/6.03 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1702)) | (~c0_1(a1702)) | (~c2_1(a1702))),
% 8.86/6.03 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 8.86/6.03 tff(3924,plain,
% 8.86/6.03 (hskp38),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3923, 221, 3883, 3920, 3911, 1025, 3919])).
% 8.86/6.03 tff(3925,plain,
% 8.86/6.03 (~c0_1(a1718)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[2583, 3924])).
% 8.86/6.03 tff(3926,plain,
% 8.86/6.03 (~c1_1(a1639)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[3758, 3887])).
% 8.86/6.03 tff(3927,plain,
% 8.86/6.03 (c3_1(a1718)),
% 8.86/6.03 inference(unit_resolution,[status(thm)],[981, 3924])).
% 8.86/6.03 tff(3928,plain,
% 8.86/6.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3929,plain,
% 8.86/6.03 (((~ndr1_0) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c3_1(a1684) | (~c2_1(a1684)) | (~c1_1(a1684))) <=> (c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.03 inference(rewrite,[status(thm)],[])).
% 8.86/6.03 tff(3930,plain,
% 8.86/6.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c3_1(a1684) | (~c2_1(a1684)) | (~c1_1(a1684)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[3929])).
% 8.86/6.04 tff(3931,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c3_1(a1684) | (~c2_1(a1684)) | (~c1_1(a1684)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[3930, 3928])).
% 8.86/6.04 tff(3932,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1718) | c1_1(a1718) | (~c3_1(a1718)) | c1_1(a1639) | (~c3_1(a1639)) | (~c0_1(a1639)) | c3_1(a1684) | (~c2_1(a1684)) | (~c1_1(a1684)))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(3933,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[3932, 3931])).
% 8.86/6.04 tff(3934,plain,
% 8.86/6.04 (c1_1(a1718)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3933, 221, 3888, 3927, 3882, 3926, 3925, 3881, 102, 3898, 3890])).
% 8.86/6.04 tff(3935,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3640, 221, 3582, 1250, 3927, 3925, 2219, 3934])).
% 8.86/6.04 tff(3936,plain,(hskp57 | hskp62 | hskp61 | (~c2_1(a1684)) | c3_1(a1684) | hskp42 | hskp44 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3937,plain,
% 8.86/6.04 (hskp44),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3936, 3884, 1250, 3882, 3881, 1073, 3582, 363, 1309, 1835])).
% 8.86/6.04 tff(3938,plain,
% 8.86/6.04 (c2_1(a1640)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3593, 3937])).
% 8.86/6.04 tff(3939,plain,
% 8.86/6.04 (c3_1(a1640)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3604, 3937])).
% 8.86/6.04 tff(3940,plain,
% 8.86/6.04 (c1_1(a1640)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3615, 3937])).
% 8.86/6.04 tff(3941,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3650, 3940, 3939, 3394, 3582, 1309, 1835, 1250, 3883, 3938])).
% 8.86/6.04 tff(3942,plain,(hskp62 | c2_1(a1715) | (~c0_1(a1715)) | hskp61 | (~c2_1(a1684)) | c3_1(a1684) | hskp42 | c3_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3943,plain,
% 8.86/6.04 (hskp62),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3942, 1073, 1835, 1250, 3882, 3881, 1309, 363, 138])).
% 8.86/6.04 tff(3944,plain,
% 8.86/6.04 (~c3_1(a1675)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[2254, 3943])).
% 8.86/6.04 tff(3945,plain,
% 8.86/6.04 (c0_1(a1675)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[2237, 3943])).
% 8.86/6.04 tff(3946,plain,
% 8.86/6.04 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3947,plain,
% 8.86/6.04 ((hskp42 | hskp0 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675))) <=> (hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3948,plain,
% 8.86/6.04 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[3947])).
% 8.86/6.04 tff(3949,plain,
% 8.86/6.04 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[3948, 3946])).
% 8.86/6.04 tff(3950,plain,
% 8.86/6.04 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c2_1(a1675)))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(3951,plain,
% 8.86/6.04 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[3950, 3949])).
% 8.86/6.04 tff(3952,plain,
% 8.86/6.04 (~c2_1(a1675)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3951, 221, 1073, 3579, 3945, 3944, 1043])).
% 8.86/6.04 tff(3953,plain,
% 8.86/6.04 (c1_1(a1675)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[2248, 3943])).
% 8.86/6.04 tff(3954,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3955,plain,
% 8.86/6.04 ((hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))) <=> (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3956,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[3955])).
% 8.86/6.04 tff(3957,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[3956, 3954])).
% 8.86/6.04 tff(3958,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(3959,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 8.86/6.04 tff(3960,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3959, 221, 1250, 363, 3953, 3945, 1309, 1249, 1835, 3952])).
% 8.86/6.04 tff(3961,plain,(hskp42 | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c2_1(a1684)) | c3_1(a1684) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3962,plain,
% 8.86/6.04 (hskp61),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3961, 1073, 1835, 1309, 363, 3882, 138, 3881])).
% 8.86/6.04 tff(3963,plain,
% 8.86/6.04 (~c2_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1187, 3962])).
% 8.86/6.04 tff(3964,plain,
% 8.86/6.04 (~c1_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1193, 3962])).
% 8.86/6.04 tff(3965,plain,
% 8.86/6.04 (c3_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1204, 3962])).
% 8.86/6.04 tff(3966,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3389, 221, 365, 3965, 3022, 3021, 1309, 3964, 3963, 647, 1835, 3880])).
% 8.86/6.04 tff(3967,plain,(hskp42 | c1_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | hskp29 | hskp73 | c3_1(a1715) | (~c2_1(a1684)) | c3_1(a1684) | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3968,plain,
% 8.86/6.04 (hskp42),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3967, 363, 1309, 3383, 138, 2098, 365, 3876, 3865, 963])).
% 8.86/6.04 tff(3969,plain,
% 8.86/6.04 (hskp61),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3564, 3968, 3383, 1309, 363])).
% 8.86/6.04 tff(3970,plain,
% 8.86/6.04 (~c2_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1187, 3969])).
% 8.86/6.04 tff(3971,plain,
% 8.86/6.04 (~c1_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1193, 3969])).
% 8.86/6.04 tff(3972,plain,
% 8.86/6.04 (c3_1(a1674)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1204, 3969])).
% 8.86/6.04 tff(3973,plain,
% 8.86/6.04 (hskp2),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3415, 3968, 365, 363, 3383])).
% 8.86/6.04 tff(3974,plain,
% 8.86/6.04 (~c1_1(a1645)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1128, 3973])).
% 8.86/6.04 tff(3975,plain,
% 8.86/6.04 (~c3_1(a1645)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1144, 3973])).
% 8.86/6.04 tff(3976,plain,
% 8.86/6.04 (~c0_1(a1645)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1122, 3973])).
% 8.86/6.04 tff(3977,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3978,plain,
% 8.86/6.04 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3979,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[3978])).
% 8.86/6.04 tff(3980,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[3979, 3977])).
% 8.86/6.04 tff(3981,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(3982,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[3981, 3980])).
% 8.86/6.04 tff(3983,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3982, 221, 365, 363, 232, 234, 1309, 233, 124, 118, 112, 30])).
% 8.86/6.04 tff(3984,plain,((~hskp16) | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1656)) | (~c0_1(a1656)) | c2_1(a1715) | c3_1(a1656)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3985,plain,
% 8.86/6.04 (~hskp16),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3984, 2358, 363, 365, 2357, 1309, 2356])).
% 8.86/6.04 tff(3986,plain,
% 8.86/6.04 (hskp17 | hskp16),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3209, 221, 105, 104, 103, 10])).
% 8.86/6.04 tff(3987,plain,
% 8.86/6.04 (hskp17),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3986, 3985])).
% 8.86/6.04 tff(3988,plain,
% 8.86/6.04 (~c2_1(a1678)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[260, 3987])).
% 8.86/6.04 tff(3989,plain,
% 8.86/6.04 (~c1_1(a1678)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[241, 3987])).
% 8.86/6.04 tff(3990,plain,
% 8.86/6.04 (~c0_1(a1678)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[247, 3987])).
% 8.86/6.04 tff(3991,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3992,plain,
% 8.86/6.04 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(3993,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[3992])).
% 8.86/6.04 tff(3994,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[3993, 3991])).
% 8.86/6.04 tff(3995,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(3996,plain,
% 8.86/6.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 8.86/6.04 tff(3997,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3996, 221, 365, 363, 2358, 2357, 1309, 2356, 3990, 3989, 3988, 30])).
% 8.86/6.04 tff(3998,plain,((~hskp53) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(3999,plain,
% 8.86/6.04 (~hskp53),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3998, 91, 363, 1309, 365, 77, 66])).
% 8.86/6.04 tff(4000,plain,
% 8.86/6.04 (hskp52),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[150, 3999, 138])).
% 8.86/6.04 tff(4001,plain,
% 8.86/6.04 (c3_1(a1654)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[536, 4000])).
% 8.86/6.04 tff(4002,plain,
% 8.86/6.04 (c0_1(a1654)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[525, 4000])).
% 8.86/6.04 tff(4003,plain,
% 8.86/6.04 (~c1_1(a1654)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3389, 221, 365, 2296, 4002, 4001, 1309, 2294, 2338, 647, 1835])).
% 8.86/6.04 tff(4004,plain,
% 8.86/6.04 (c2_1(a1654)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[547, 4000])).
% 8.86/6.04 tff(4005,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4006,plain,
% 8.86/6.04 ((hskp67 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654))) <=> (hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4007,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[4006])).
% 8.86/6.04 tff(4008,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.04 inference(transitivity,[status(thm)],[4007, 4005])).
% 8.86/6.04 tff(4009,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(4010,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 8.86/6.04 tff(4011,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4010, 221, 3901, 91, 77, 4004, 4001, 66, 1517, 4003])).
% 8.86/6.04 tff(4012,plain,((~hskp57) | hskp67 | c1_1(a1715) | (~c3_1(a1674)) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~c0_1(a1715)) | hskp29 | c3_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(4013,plain,
% 8.86/6.04 (~hskp57),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4012, 3901, 365, 2296, 1309, 2294, 2338, 1835, 138, 363])).
% 8.86/6.04 tff(4014,assumption,(~c3_1(a1645)), introduced(assumption)).
% 8.86/6.04 tff(4015,assumption,(~c1_1(a1645)), introduced(assumption)).
% 8.86/6.04 tff(4016,plain,
% 8.86/6.04 (hskp57 | (~c2_1(a1645))),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3433, 221, 363, 1309, 4015, 4014, 1627, 1835])).
% 8.86/6.04 tff(4017,plain,
% 8.86/6.04 (~c2_1(a1645)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4016, 4013])).
% 8.86/6.04 tff(4018,assumption,(~c0_1(a1645)), introduced(assumption)).
% 8.86/6.04 tff(4019,plain,
% 8.86/6.04 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4020,plain,
% 8.86/6.04 ((hskp72 | hskp37 | (~ndr1_0) | c0_1(a1645) | c3_1(a1645) | c2_1(a1645)) <=> (hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4021,plain,
% 8.86/6.04 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1645) | c3_1(a1645) | c2_1(a1645))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645)))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[4020])).
% 8.86/6.04 tff(4022,plain,
% 8.86/6.04 (((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1645) | c3_1(a1645) | c2_1(a1645))) <=> ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645))),
% 8.86/6.04 inference(transitivity,[status(thm)],[4021, 4019])).
% 8.86/6.04 tff(4023,plain,
% 8.86/6.04 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | (hskp72 | hskp37 | (~ndr1_0) | c0_1(a1645) | c3_1(a1645) | c2_1(a1645))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(4024,plain,
% 8.86/6.04 ((~![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))) | hskp72 | hskp37 | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645)),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 8.86/6.04 tff(4025,plain,
% 8.86/6.04 (hskp37 | c2_1(a1645)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4024, 221, 2400, 4018, 4014, 577])).
% 8.86/6.04 tff(4026,plain,
% 8.86/6.04 (hskp37),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4025, 4017])).
% 8.86/6.04 tff(4027,plain,
% 8.86/6.04 (c2_1(a1714)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[613, 4026])).
% 8.86/6.04 tff(4028,plain,
% 8.86/6.04 (~c1_1(a1714)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[591, 4026])).
% 8.86/6.04 tff(4029,plain,
% 8.86/6.04 (c3_1(a1714)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[3828, 4028, 1835, 363, 1309, 4013, 4027])).
% 8.86/6.04 tff(4030,plain,
% 8.86/6.04 (c0_1(a1714)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[602, 4026])).
% 8.86/6.04 tff(4031,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4032,plain,
% 8.86/6.04 ((hskp67 | (~ndr1_0) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c1_1(a1714) | (~c3_1(a1714)) | (~c2_1(a1714))) <=> (hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4033,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c1_1(a1714) | (~c3_1(a1714)) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[4032])).
% 8.86/6.04 tff(4034,plain,
% 8.86/6.04 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c1_1(a1714) | (~c3_1(a1714)) | (~c2_1(a1714)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.04 inference(transitivity,[status(thm)],[4033, 4031])).
% 8.86/6.04 tff(4035,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c1_1(a1714) | (~c3_1(a1714)) | (~c2_1(a1714)))),
% 8.86/6.04 inference(quant_inst,[status(thm)],[])).
% 8.86/6.04 tff(4036,plain,
% 8.86/6.04 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.86/6.04 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 8.86/6.04 tff(4037,plain,
% 8.86/6.04 ($false),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4036, 221, 3901, 4027, 4030, 4028, 1517, 4029])).
% 8.86/6.04 tff(4038,plain,(hskp67 | (~c0_1(a1715)) | c3_1(a1715) | c2_1(a1715) | c0_1(a1645) | c3_1(a1645) | c1_1(a1645) | c1_1(a1715) | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.86/6.04 tff(4039,plain,
% 8.86/6.04 (hskp67),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[4038, 363, 3383, 1309, 3976, 3975, 3974, 365, 3972, 3971, 3970, 138])).
% 8.86/6.04 tff(4040,assumption,(hskp67), introduced(assumption)).
% 8.86/6.04 tff(4041,plain,
% 8.86/6.04 (c3_1(a1702)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1534, 4040])).
% 8.86/6.04 tff(4042,plain,
% 8.86/6.04 (c1_1(a1702)),
% 8.86/6.04 inference(unit_resolution,[status(thm)],[1545, 4040])).
% 8.86/6.04 tff(4043,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4044,plain,
% 8.86/6.04 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.04 inference(rewrite,[status(thm)],[])).
% 8.86/6.04 tff(4045,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))))),
% 8.86/6.04 inference(monotonicity,[status(thm)],[4044])).
% 8.86/6.04 tff(4046,plain,
% 8.86/6.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4045, 4043])).
% 8.86/6.05 tff(4047,plain,
% 8.86/6.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4048,plain,
% 8.86/6.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 8.86/6.05 tff(4049,plain,
% 8.86/6.05 (~c0_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4048, 221, 365, 4042, 4041, 2296, 1309, 2294, 2338, 647, 1835])).
% 8.86/6.05 tff(4050,plain,
% 8.86/6.05 (c2_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[2029, 4040])).
% 8.86/6.05 tff(4051,plain,
% 8.86/6.05 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4052,plain,
% 8.86/6.05 ((hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702))) <=> (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4053,plain,
% 8.86/6.05 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4052])).
% 8.86/6.05 tff(4054,plain,
% 8.86/6.05 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4053, 4051])).
% 8.86/6.05 tff(4055,plain,
% 8.86/6.05 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4056,plain,
% 8.86/6.05 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 8.86/6.05 tff(4057,plain,
% 8.86/6.05 (hskp12),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4056, 221, 883, 4042, 4050, 4041, 893])).
% 8.86/6.05 tff(4058,plain,
% 8.86/6.05 (~c1_1(a1666)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[905, 4057])).
% 8.86/6.05 tff(4059,plain,
% 8.86/6.05 (c3_1(a1666)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[916, 4057])).
% 8.86/6.05 tff(4060,plain,
% 8.86/6.05 (c2_1(a1666)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[927, 4057])).
% 8.86/6.05 tff(4061,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4062,plain,
% 8.86/6.05 ((hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702))) <=> (hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4063,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4062])).
% 8.86/6.05 tff(4064,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4063, 4061])).
% 8.86/6.05 tff(4065,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4066,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 8.86/6.05 tff(4067,plain,
% 8.86/6.05 ($false),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4066, 221, 2104, 4042, 4041, 4060, 4059, 4058, 1563, 4049])).
% 8.86/6.05 tff(4068,plain,((~hskp67) | hskp73 | c1_1(a1715) | (~c3_1(a1674)) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~c0_1(a1715)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 8.86/6.05 tff(4069,plain,
% 8.86/6.05 (hskp13),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4068, 4039, 365, 3972, 1309, 3971, 3970, 3383, 2098])).
% 8.86/6.05 tff(4070,plain,
% 8.86/6.05 (~c1_1(a1667)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[303, 4069])).
% 8.86/6.05 tff(4071,plain,
% 8.86/6.05 (c3_1(a1667)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[314, 4069])).
% 8.86/6.05 tff(4072,plain,
% 8.86/6.05 (c0_1(a1667)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[325, 4069])).
% 8.86/6.05 tff(4073,plain,
% 8.86/6.05 (c3_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[1534, 4039])).
% 8.86/6.05 tff(4074,plain,
% 8.86/6.05 (c2_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[2029, 4039])).
% 8.86/6.05 tff(4075,plain,
% 8.86/6.05 (c1_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[1545, 4039])).
% 8.86/6.05 tff(4076,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4077,plain,
% 8.86/6.05 ((hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667))) <=> (hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4078,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4077])).
% 8.86/6.05 tff(4079,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4078, 4076])).
% 8.86/6.05 tff(4080,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1702)) | (~c2_1(a1702)) | (~c1_1(a1702)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4081,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c2_1(a1702))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4080, 4079])).
% 8.86/6.05 tff(4082,plain,
% 8.86/6.05 (hskp63),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4081, 221, 4075, 4074, 4073, 4072, 4071, 4070, 2011])).
% 8.86/6.05 tff(4083,plain,
% 8.86/6.05 (~c0_1(a1676)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[2043, 4082])).
% 8.86/6.05 tff(4084,plain,
% 8.86/6.05 (c3_1(a1676)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[2054, 4082])).
% 8.86/6.05 tff(4085,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4086,plain,
% 8.86/6.05 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676))) <=> (hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4087,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676))))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4086])).
% 8.86/6.05 tff(4088,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4087, 4085])).
% 8.86/6.05 tff(4089,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4090,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1676) | (~c3_1(a1676))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 8.86/6.05 tff(4091,plain,
% 8.86/6.05 (c1_1(a1676)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4090, 221, 138, 4084, 4072, 4071, 4083, 4070, 137])).
% 8.86/6.05 tff(4092,plain,
% 8.86/6.05 (~c0_1(a1702)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4048, 221, 365, 4075, 4073, 3972, 1309, 3971, 3970, 647, 3383])).
% 8.86/6.05 tff(4093,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4094,plain,
% 8.86/6.05 ((hskp73 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702))) <=> (hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4095,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4094])).
% 8.86/6.05 tff(4096,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4095, 4093])).
% 8.86/6.05 tff(4097,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4098,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4097, 4096])).
% 8.86/6.05 tff(4099,plain,
% 8.86/6.05 (~c2_1(a1667)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4098, 221, 2098, 4075, 4073, 4071, 4070, 1563, 4092])).
% 8.86/6.05 tff(4100,plain,
% 8.86/6.05 (((~hskp63) | c2_1(a1676)) <=> ((~hskp63) | c2_1(a1676))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4101,axiom,((~hskp63) | c2_1(a1676)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 8.86/6.05 tff(4102,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 8.86/6.05 tff(4103,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4102, 4100])).
% 8.86/6.05 tff(4104,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4103, 4100])).
% 8.86/6.05 tff(4105,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4104, 4100])).
% 8.86/6.05 tff(4106,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4105, 4100])).
% 8.86/6.05 tff(4107,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4106, 4100])).
% 8.86/6.05 tff(4108,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4107, 4100])).
% 8.86/6.05 tff(4109,plain,
% 8.86/6.05 ((~hskp63) | c2_1(a1676)),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4108, 4100])).
% 8.86/6.05 tff(4110,plain,
% 8.86/6.05 (c2_1(a1676)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4109, 4082])).
% 8.86/6.05 tff(4111,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4112,plain,
% 8.86/6.05 ((hskp39 | (~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676))) <=> (hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4113,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676))))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4112])).
% 8.86/6.05 tff(4114,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4113, 4111])).
% 8.86/6.05 tff(4115,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4116,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1676)) | (~c2_1(a1676))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 8.86/6.05 tff(4117,plain,
% 8.86/6.05 (hskp39),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4116, 221, 4110, 4084, 4072, 4071, 4083, 1488, 4099])).
% 8.86/6.05 tff(4118,plain,
% 8.86/6.05 (~c1_1(a1721)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[1506, 4117])).
% 8.86/6.05 tff(4119,plain,
% 8.86/6.05 (c3_1(a1721)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[1586, 4117])).
% 8.86/6.05 tff(4120,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4121,plain,
% 8.86/6.05 ((hskp73 | (~ndr1_0) | c1_1(a1721) | (~c3_1(a1721)) | (~c2_1(a1721)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676))) <=> (hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4122,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1721) | (~c3_1(a1721)) | (~c2_1(a1721)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676))))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4121])).
% 8.86/6.05 tff(4123,plain,
% 8.86/6.05 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1721) | (~c3_1(a1721)) | (~c2_1(a1721)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4122, 4120])).
% 8.86/6.05 tff(4124,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1721) | (~c3_1(a1721)) | (~c2_1(a1721)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4125,plain,
% 8.86/6.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676))),
% 8.86/6.05 inference(modus_ponens,[status(thm)],[4124, 4123])).
% 8.86/6.05 tff(4126,plain,
% 8.86/6.05 (~c2_1(a1721)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[4125, 221, 2098, 4084, 4119, 4083, 4118, 1563, 4091])).
% 8.86/6.05 tff(4127,plain,
% 8.86/6.05 (~c0_1(a1721)),
% 8.86/6.05 inference(unit_resolution,[status(thm)],[1500, 4117])).
% 8.86/6.05 tff(4128,plain,
% 8.86/6.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4129,plain,
% 8.86/6.05 (((~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c2_1(a1721) | (~c3_1(a1721)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715))) <=> (c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721))),
% 8.86/6.05 inference(rewrite,[status(thm)],[])).
% 8.86/6.05 tff(4130,plain,
% 8.86/6.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c2_1(a1721) | (~c3_1(a1721)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721)))),
% 8.86/6.05 inference(monotonicity,[status(thm)],[4129])).
% 8.86/6.05 tff(4131,plain,
% 8.86/6.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c2_1(a1721) | (~c3_1(a1721)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721))),
% 8.86/6.05 inference(transitivity,[status(thm)],[4130, 4128])).
% 8.86/6.05 tff(4132,plain,
% 8.86/6.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c2_1(a1721) | (~c3_1(a1721)) | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715)))),
% 8.86/6.05 inference(quant_inst,[status(thm)],[])).
% 8.86/6.05 tff(4133,plain,
% 8.86/6.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721)),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 8.86/6.06 tff(4134,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4133, 221, 365, 363, 4119, 4072, 4071, 4127, 410, 3383, 4099, 4126])).
% 8.86/6.06 tff(4135,plain,(c3_1(a1715) | c1_1(a1715) | hskp29 | c2_1(a1715) | hskp0 | c0_1(a1716) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4136,plain,
% 8.86/6.06 (c3_1(a1715)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4135, 2097, 138, 1309, 963, 365, 1662])).
% 8.86/6.06 tff(4137,assumption,(~c1_1(a1656)), introduced(assumption)).
% 8.86/6.06 tff(4138,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4139,plain,
% 8.86/6.06 (((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4140,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4139])).
% 8.86/6.06 tff(4141,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4140, 4138])).
% 8.86/6.06 tff(4142,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4143,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 8.86/6.06 tff(4144,plain,
% 8.86/6.06 (~c3_1(a1678)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4143, 221, 2103, 234, 1309, 233, 248, 261, 410, 1835, 4137])).
% 8.86/6.06 tff(4145,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[267, 221, 232, 234, 233, 248, 242, 261, 30, 4144])).
% 8.86/6.06 tff(4146,plain,((~hskp17) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | (~c3_1(a1715)) | c2_1(a1715) | (~c0_1(a1715)) | c1_1(a1656)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4147,plain,
% 8.86/6.06 (~hskp17),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4146, 4137, 234, 233, 2103, 1309, 1835, 232])).
% 8.86/6.06 tff(4148,plain,
% 8.86/6.06 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4149,plain,
% 8.86/6.06 ((hskp17 | hskp16 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715))) <=> (hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4150,plain,
% 8.86/6.06 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4149])).
% 8.86/6.06 tff(4151,plain,
% 8.86/6.06 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4150, 4148])).
% 8.86/6.06 tff(4152,plain,
% 8.86/6.06 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4153,plain,
% 8.86/6.06 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 8.86/6.06 tff(4154,plain,
% 8.86/6.06 (hskp17 | hskp16 | c1_1(a1715) | (~c3_1(a1715))),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4153, 221, 10, 1835])).
% 8.86/6.06 tff(4155,plain,
% 8.86/6.06 (hskp16),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4154, 4147, 365, 2103])).
% 8.86/6.06 tff(4156,plain,
% 8.86/6.06 (~c2_1(a1677)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[117, 4155])).
% 8.86/6.06 tff(4157,plain,
% 8.86/6.06 (~c0_1(a1677)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[123, 4155])).
% 8.86/6.06 tff(4158,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4159,plain,
% 8.86/6.06 (((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4160,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4159])).
% 8.86/6.06 tff(4161,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4160, 4158])).
% 8.86/6.06 tff(4162,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4163,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 8.86/6.06 tff(4164,plain,
% 8.86/6.06 (~c3_1(a1677)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4163, 221, 2103, 234, 1309, 233, 4157, 4156, 410, 1835, 4137])).
% 8.86/6.06 tff(4165,plain,
% 8.86/6.06 (~c1_1(a1677)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[111, 4155])).
% 8.86/6.06 tff(4166,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[346, 221, 232, 234, 233, 4157, 4156, 4165, 30, 4164])).
% 8.86/6.06 tff(4167,plain,(c1_1(a1656) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | (~c3_1(a1715)) | c2_1(a1715) | (~c0_1(a1715)) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4168,plain,
% 8.86/6.06 (c1_1(a1656)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4167, 2358, 2357, 2356, 2103, 1309, 1835, 365])).
% 8.86/6.06 tff(4169,assumption,(c1_1(a1656)), introduced(assumption)).
% 8.86/6.06 tff(4170,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4171,plain,
% 8.86/6.06 (((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656))) <=> (c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4172,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4171])).
% 8.86/6.06 tff(4173,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4172, 4170])).
% 8.86/6.06 tff(4174,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4175,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4174, 4173])).
% 8.86/6.06 tff(4176,plain,
% 8.86/6.06 (~c3_1(a1677)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4175, 221, 365, 2103, 232, 233, 124, 112, 102, 1835, 4169])).
% 8.86/6.06 tff(4177,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[346, 221, 232, 234, 233, 124, 118, 112, 30, 4176])).
% 8.86/6.06 tff(4178,plain,((~hskp16) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1656))), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4179,plain,
% 8.86/6.06 (~hskp16),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4178, 2358, 2357, 2356, 365, 2103, 1835, 4168])).
% 8.86/6.06 tff(4180,plain,
% 8.86/6.06 (hskp17),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4154, 4179, 365, 2103])).
% 8.86/6.06 tff(4181,plain,
% 8.86/6.06 (~c1_1(a1678)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[241, 4180])).
% 8.86/6.06 tff(4182,plain,
% 8.86/6.06 (~c0_1(a1678)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[247, 4180])).
% 8.86/6.06 tff(4183,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4184,plain,
% 8.86/6.06 (((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656))) <=> (c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4185,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4184])).
% 8.86/6.06 tff(4186,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4185, 4183])).
% 8.86/6.06 tff(4187,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4188,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4187, 4186])).
% 8.86/6.06 tff(4189,plain,
% 8.86/6.06 (~c3_1(a1678)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4188, 221, 365, 2103, 2358, 2356, 4182, 4181, 102, 1835, 4168])).
% 8.86/6.06 tff(4190,plain,
% 8.86/6.06 (~c2_1(a1678)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[260, 4180])).
% 8.86/6.06 tff(4191,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[267, 221, 2358, 2357, 2356, 4182, 4181, 4190, 30, 4189])).
% 8.86/6.06 tff(4192,plain,((~hskp53) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4193,plain,
% 8.86/6.06 (~hskp53),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4192, 4136, 365, 3383, 1309])).
% 8.86/6.06 tff(4194,plain,
% 8.86/6.06 (hskp52),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[150, 4193, 138])).
% 8.86/6.06 tff(4195,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4196,plain,
% 8.86/6.06 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715))) <=> (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4197,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4196])).
% 8.86/6.06 tff(4198,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4197, 4195])).
% 8.86/6.06 tff(4199,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4200,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 8.86/6.06 tff(4201,plain,
% 8.86/6.06 (~c1_1(a1654)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4200, 221, 365, 2103, 929, 894, 1309, 647, 1835])).
% 8.86/6.06 tff(4202,plain,
% 8.86/6.06 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4203,plain,
% 8.86/6.06 ((hskp67 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654))) <=> (hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4204,plain,
% 8.86/6.06 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4203])).
% 8.86/6.06 tff(4205,plain,
% 8.86/6.06 (((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4204, 4202])).
% 8.86/6.06 tff(4206,plain,
% 8.86/6.06 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp67 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4207,plain,
% 8.86/6.06 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4206, 4205])).
% 8.86/6.06 tff(4208,plain,
% 8.86/6.06 ($false),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4207, 221, 3901, 365, 2103, 895, 894, 1517, 1835, 4201])).
% 8.86/6.06 tff(4209,plain,((~hskp52) | hskp67 | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.06 tff(4210,plain,
% 8.86/6.06 (hskp67),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4209, 4194, 365, 4136, 3383, 1309])).
% 8.86/6.06 tff(4211,plain,
% 8.86/6.06 (c3_1(a1702)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[1534, 4210])).
% 8.86/6.06 tff(4212,plain,
% 8.86/6.06 (c1_1(a1702)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[1545, 4210])).
% 8.86/6.06 tff(4213,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4214,plain,
% 8.86/6.06 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715))) <=> (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.06 inference(rewrite,[status(thm)],[])).
% 8.86/6.06 tff(4215,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))))),
% 8.86/6.06 inference(monotonicity,[status(thm)],[4214])).
% 8.86/6.06 tff(4216,plain,
% 8.86/6.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)))),
% 8.86/6.06 inference(transitivity,[status(thm)],[4215, 4213])).
% 8.86/6.06 tff(4217,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))),
% 8.86/6.06 inference(quant_inst,[status(thm)],[])).
% 8.86/6.06 tff(4218,plain,
% 8.86/6.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))),
% 8.86/6.06 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 8.86/6.06 tff(4219,plain,
% 8.86/6.06 (~c0_1(a1702)),
% 8.86/6.06 inference(unit_resolution,[status(thm)],[4218, 221, 365, 4136, 4212, 4211, 1309, 647, 3383])).
% 8.86/6.07 tff(4220,plain,
% 8.86/6.07 (c3_1(a1654)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[536, 4194])).
% 8.86/6.07 tff(4221,plain,
% 8.86/6.07 (c0_1(a1654)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[525, 4194])).
% 8.86/6.07 tff(4222,plain,
% 8.86/6.07 (~c1_1(a1654)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4200, 221, 365, 4136, 4221, 4220, 1309, 647, 3383])).
% 8.86/6.07 tff(4223,plain,
% 8.86/6.07 (c2_1(a1654)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[547, 4194])).
% 8.86/6.07 tff(4224,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4225,plain,
% 8.86/6.07 ((hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702))) <=> (hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4226,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4225])).
% 8.86/6.07 tff(4227,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4226, 4224])).
% 8.86/6.07 tff(4228,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4229,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 8.86/6.07 tff(4230,plain,
% 8.86/6.07 ($false),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4229, 221, 2098, 4212, 4211, 4223, 4220, 1563, 4222, 4219])).
% 8.86/6.07 tff(4231,plain,(c0_1(a1716) | c1_1(a1715) | c2_1(a1715) | hskp29 | hskp0 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.07 tff(4232,plain,
% 8.86/6.07 (c0_1(a1716)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4231, 963, 1309, 138, 365, 1662])).
% 8.86/6.07 tff(4233,plain,
% 8.86/6.07 (hskp67),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2017, 221, 929, 895, 894, 1517, 3784])).
% 8.86/6.07 tff(4234,plain,
% 8.86/6.07 (c3_1(a1702)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1534, 4233])).
% 8.86/6.07 tff(4235,plain,
% 8.86/6.07 (c2_1(a1702)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2029, 4233])).
% 8.86/6.07 tff(4236,plain,
% 8.86/6.07 (c1_1(a1702)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1545, 4233])).
% 8.86/6.07 tff(4237,plain,
% 8.86/6.07 (hskp63),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2037, 221, 4236, 4235, 4234, 929, 894, 2011, 3784])).
% 8.86/6.07 tff(4238,plain,
% 8.86/6.07 (~c0_1(a1676)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2043, 4237])).
% 8.86/6.07 tff(4239,plain,
% 8.86/6.07 (c3_1(a1676)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2054, 4237])).
% 8.86/6.07 tff(4240,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4241,plain,
% 8.86/6.07 ((hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676))) <=> (hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4242,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4241])).
% 8.86/6.07 tff(4243,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4242, 4240])).
% 8.86/6.07 tff(4244,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c0_1(a1676) | c1_1(a1676) | (~c3_1(a1676)))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4245,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1676) | (~ndr1_0) | c1_1(a1676) | (~c3_1(a1676)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4244, 4243])).
% 8.86/6.07 tff(4246,plain,
% 8.86/6.07 (c1_1(a1676)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4245, 221, 138, 4239, 929, 894, 4238, 137, 3784])).
% 8.86/6.07 tff(4247,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4248,plain,
% 8.86/6.07 ((hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676))) <=> (hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4249,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4248])).
% 8.86/6.07 tff(4250,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4249, 4247])).
% 8.86/6.07 tff(4251,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4252,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1676)) | (~c1_1(a1676)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4251, 4250])).
% 8.86/6.07 tff(4253,plain,
% 8.86/6.07 (hskp73 | (~c1_1(a1676))),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4252, 221, 4239, 895, 894, 4238, 1563, 3784])).
% 8.86/6.07 tff(4254,plain,
% 8.86/6.07 (hskp73),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4253, 4246])).
% 8.86/6.07 tff(4255,plain,
% 8.86/6.07 (c2_1(a1716)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1597, 4254])).
% 8.86/6.07 tff(4256,plain,
% 8.86/6.07 (~hskp17),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[3161, 4255, 1662, 4232, 3794, 3793, 3792])).
% 8.86/6.07 tff(4257,plain,
% 8.86/6.07 (hskp16),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1276, 4256, 3784])).
% 8.86/6.07 tff(4258,plain,
% 8.86/6.07 (~c1_1(a1677)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[111, 4257])).
% 8.86/6.07 tff(4259,plain,
% 8.86/6.07 (~c2_1(a1677)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[117, 4257])).
% 8.86/6.07 tff(4260,plain,
% 8.86/6.07 (~c0_1(a1677)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[123, 4257])).
% 8.86/6.07 tff(4261,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4262,plain,
% 8.86/6.07 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4263,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4262])).
% 8.86/6.07 tff(4264,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4263, 4261])).
% 8.86/6.07 tff(4265,plain,
% 8.86/6.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4266,plain,
% 8.86/6.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 8.86/6.07 tff(4267,plain,
% 8.86/6.07 ($false),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4266, 221, 4255, 4232, 365, 363, 1662, 1309, 4260, 4259, 4258, 30])).
% 8.86/6.07 tff(4268,plain,((~hskp52) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | hskp29 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.86/6.07 tff(4269,plain,
% 8.86/6.07 (~hskp52),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4268, 363, 365, 1662, 1309, 138, 963])).
% 8.86/6.07 tff(4270,plain,
% 8.86/6.07 (hskp53),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[150, 4269, 138])).
% 8.86/6.07 tff(4271,plain,
% 8.86/6.07 (hskp42),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2626, 4270, 963])).
% 8.86/6.07 tff(4272,plain,
% 8.86/6.07 (hskp2),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[3415, 4271, 365, 363, 3383])).
% 8.86/6.07 tff(4273,plain,
% 8.86/6.07 (~c0_1(a1645)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1122, 4272])).
% 8.86/6.07 tff(4274,plain,
% 8.86/6.07 (~c1_1(a1645)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1128, 4272])).
% 8.86/6.07 tff(4275,plain,
% 8.86/6.07 (~c3_1(a1656)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[167, 4270])).
% 8.86/6.07 tff(4276,plain,
% 8.86/6.07 (c0_1(a1656)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[161, 4270])).
% 8.86/6.07 tff(4277,plain,
% 8.86/6.07 (c2_1(a1656)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[178, 4270])).
% 8.86/6.07 tff(4278,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4279,plain,
% 8.86/6.07 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715)) <=> (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4280,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4279])).
% 8.86/6.07 tff(4281,plain,
% 8.86/6.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4280, 4278])).
% 8.86/6.07 tff(4282,plain,
% 8.86/6.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1715) | c1_1(a1715) | c2_1(a1715))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4283,plain,
% 8.86/6.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4282, 4281])).
% 8.86/6.07 tff(4284,plain,
% 8.86/6.07 (c2_1(a1645)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4283, 221, 365, 363, 4277, 4276, 1309, 4275, 4274, 4273, 30])).
% 8.86/6.07 tff(4285,plain,
% 8.86/6.07 (~c3_1(a1645)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[1144, 4272])).
% 8.86/6.07 tff(4286,plain,
% 8.86/6.07 (hskp57),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[3433, 221, 363, 1309, 4274, 4285, 1627, 3383, 4284])).
% 8.86/6.07 tff(4287,plain,
% 8.86/6.07 (~c1_1(a1665)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[65, 4286])).
% 8.86/6.07 tff(4288,plain,
% 8.86/6.07 (c0_1(a1665)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[90, 4286])).
% 8.86/6.07 tff(4289,plain,
% 8.86/6.07 (c3_1(a1665)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[76, 4286])).
% 8.86/6.07 tff(4290,plain,
% 8.86/6.07 ($false),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[3998, 4289, 4288, 363, 1309, 365, 4270, 4287])).
% 8.86/6.07 tff(4291,plain,(c3_1(a1715) | c2_1(a1715) | c1_1(a1715) | hskp0 | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.07 tff(4292,plain,
% 8.86/6.07 (c3_1(a1715)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4291, 963, 365, 1309, 138, 1662])).
% 8.86/6.07 tff(4293,plain,
% 8.86/6.07 (~hskp53),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4192, 4292, 365, 3383, 1309])).
% 8.86/6.07 tff(4294,plain,
% 8.86/6.07 (hskp52),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[150, 4293, 138])).
% 8.86/6.07 tff(4295,plain,
% 8.86/6.07 (c3_1(a1654)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[536, 4294])).
% 8.86/6.07 tff(4296,plain,
% 8.86/6.07 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4297,plain,
% 8.86/6.07 ((hskp61 | hskp33 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715))) <=> (hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4298,plain,
% 8.86/6.07 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4297])).
% 8.86/6.07 tff(4299,plain,
% 8.86/6.07 (((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4298, 4296])).
% 8.86/6.07 tff(4300,plain,
% 8.86/6.07 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp61 | hskp33 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4301,plain,
% 8.86/6.07 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 8.86/6.07 tff(4302,plain,
% 8.86/6.07 (hskp61 | hskp33 | (~c3_1(a1715))),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4301, 221, 1309, 2651, 1835])).
% 8.86/6.07 tff(4303,plain,
% 8.86/6.07 (hskp33),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4302, 1250, 2103])).
% 8.86/6.07 tff(4304,plain,
% 8.86/6.07 (~c0_1(a1704)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2670, 4303])).
% 8.86/6.07 tff(4305,plain,
% 8.86/6.07 (c3_1(a1704)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[2682, 4303])).
% 8.86/6.07 tff(4306,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4307,plain,
% 8.86/6.07 ((hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c1_1(a1704) | (~c3_1(a1704))) <=> (hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4308,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c1_1(a1704) | (~c3_1(a1704)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715))))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4307])).
% 8.86/6.07 tff(4309,plain,
% 8.86/6.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c1_1(a1704) | (~c3_1(a1704)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.86/6.07 inference(transitivity,[status(thm)],[4308, 4306])).
% 8.86/6.07 tff(4310,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c1_1(a1704) | (~c3_1(a1704)))),
% 8.86/6.07 inference(quant_inst,[status(thm)],[])).
% 8.86/6.07 tff(4311,plain,
% 8.86/6.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 8.86/6.07 inference(modus_ponens,[status(thm)],[4310, 4309])).
% 8.86/6.07 tff(4312,plain,
% 8.86/6.07 (c1_1(a1704)),
% 8.86/6.07 inference(unit_resolution,[status(thm)],[4311, 221, 138, 365, 2103, 4305, 4304, 137, 1835])).
% 8.86/6.07 tff(4313,plain,
% 8.86/6.07 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4314,plain,
% 8.86/6.07 ((hskp62 | hskp61 | (~ndr1_0) | c0_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704))) <=> (hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)))),
% 8.86/6.07 inference(rewrite,[status(thm)],[])).
% 8.86/6.07 tff(4315,plain,
% 8.86/6.07 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704))))),
% 8.86/6.07 inference(monotonicity,[status(thm)],[4314])).
% 8.86/6.07 tff(4316,plain,
% 8.86/6.07 (((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)))) <=> ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)))),
% 8.86/6.08 inference(transitivity,[status(thm)],[4315, 4313])).
% 8.86/6.08 tff(4317,plain,
% 8.86/6.08 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp62 | hskp61 | (~ndr1_0) | c0_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)))),
% 8.86/6.08 inference(quant_inst,[status(thm)],[])).
% 8.86/6.08 tff(4318,plain,
% 8.86/6.08 ((~![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp62 | hskp61 | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704))),
% 8.86/6.08 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 8.86/6.08 tff(4319,plain,
% 8.86/6.08 (hskp62),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4318, 221, 1250, 4305, 4304, 2219, 4312])).
% 8.86/6.08 tff(4320,plain,
% 8.86/6.08 (c0_1(a1675)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[2237, 4319])).
% 8.86/6.08 tff(4321,plain,
% 8.86/6.08 (~c3_1(a1675)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[2254, 4319])).
% 8.86/6.08 tff(4322,plain,
% 8.86/6.08 (c1_1(a1675)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[2248, 4319])).
% 8.86/6.08 tff(4323,plain,
% 8.86/6.08 (c2_1(a1675)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[2267, 4322, 4321, 4320, 1250])).
% 8.86/6.08 tff(4324,plain,
% 8.86/6.08 (~c2_1(a1704)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[2664, 4303])).
% 8.86/6.08 tff(4325,plain,
% 8.86/6.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.08 inference(rewrite,[status(thm)],[])).
% 8.86/6.08 tff(4326,plain,
% 8.86/6.08 ((hskp0 | (~ndr1_0) | c2_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675))) <=> (hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.08 inference(rewrite,[status(thm)],[])).
% 8.86/6.08 tff(4327,plain,
% 8.86/6.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.86/6.08 inference(monotonicity,[status(thm)],[4326])).
% 8.86/6.08 tff(4328,plain,
% 8.86/6.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.08 inference(transitivity,[status(thm)],[4327, 4325])).
% 8.86/6.08 tff(4329,plain,
% 8.86/6.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.86/6.08 inference(quant_inst,[status(thm)],[])).
% 8.86/6.08 tff(4330,plain,
% 8.86/6.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.86/6.08 inference(modus_ponens,[status(thm)],[4329, 4328])).
% 8.86/6.08 tff(4331,plain,
% 8.86/6.08 ($false),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4330, 221, 963, 4322, 4320, 4305, 4324, 950, 4323, 4312])).
% 8.86/6.08 tff(4332,plain,(hskp61 | hskp0 | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.86/6.08 tff(4333,plain,
% 8.86/6.08 (hskp61),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4332, 4292, 138, 365, 963, 3383, 1309])).
% 8.86/6.08 tff(4334,plain,
% 8.86/6.08 (c0_1(a1654)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[525, 4294])).
% 8.86/6.08 tff(4335,plain,
% 8.86/6.08 (~c1_1(a1654)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3391, 4334, 4333, 4295, 1309, 3383, 365])).
% 8.86/6.08 tff(4336,plain,
% 8.86/6.08 (c2_1(a1654)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[547, 4294])).
% 8.86/6.08 tff(4337,plain,
% 8.86/6.08 (hskp26),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3790, 221, 4334, 4336, 4295, 20, 4335])).
% 8.86/6.08 tff(4338,plain,
% 8.86/6.08 (~c2_1(a1691)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[669, 4337])).
% 8.86/6.08 tff(4339,plain,
% 8.86/6.08 (~c3_1(a1691)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[689, 4337])).
% 8.86/6.08 tff(4340,plain,
% 8.86/6.08 (~c1_1(a1691)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[675, 4337])).
% 8.86/6.08 tff(4341,plain,
% 8.86/6.08 (hskp67),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4209, 4294, 365, 4292, 3383, 1309])).
% 8.86/6.08 tff(4342,plain,
% 8.86/6.08 (c3_1(a1702)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[1534, 4341])).
% 8.86/6.08 tff(4343,plain,
% 8.86/6.08 (c1_1(a1702)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[1545, 4341])).
% 8.86/6.08 tff(4344,plain,
% 8.86/6.08 (~c0_1(a1702)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4218, 221, 365, 4292, 4343, 4342, 1309, 647, 3383])).
% 8.86/6.08 tff(4345,plain,
% 8.86/6.08 (hskp73),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4229, 221, 4343, 4342, 4336, 4295, 1563, 4335, 4344])).
% 8.86/6.08 tff(4346,plain,
% 8.86/6.08 (c2_1(a1716)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[1597, 4345])).
% 8.86/6.08 tff(4347,plain,
% 8.86/6.08 (~hskp17),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3161, 4346, 1662, 4232, 4340, 4339, 4338])).
% 8.86/6.08 tff(4348,plain,
% 8.86/6.08 (hskp17 | hskp16 | c1_1(a1715) | (~c3_1(a1715))),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4153, 221, 10, 3383])).
% 8.86/6.08 tff(4349,plain,
% 8.86/6.08 (hskp16),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4348, 4347, 365, 4292])).
% 8.86/6.08 tff(4350,plain,
% 8.86/6.08 (~c1_1(a1677)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[111, 4349])).
% 8.86/6.08 tff(4351,plain,
% 8.86/6.08 (~c2_1(a1677)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[117, 4349])).
% 8.86/6.08 tff(4352,plain,
% 8.86/6.08 (~c0_1(a1677)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[123, 4349])).
% 8.86/6.08 tff(4353,plain,
% 8.86/6.08 ($false),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3220, 221, 4346, 4232, 1662, 4339, 4340, 4338, 4352, 4351, 4350, 30])).
% 8.86/6.08 tff(4354,plain,(hskp0 | c3_1(a1716) | c1_1(a1715) | c2_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.86/6.08 tff(4355,plain,
% 8.86/6.08 (hskp0),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[4354, 365, 1662, 1309, 138])).
% 8.86/6.08 tff(4356,plain,
% 8.86/6.08 (hskp61),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3578, 363, 3383, 1309, 4355])).
% 8.86/6.08 tff(4357,plain,
% 8.86/6.08 (~c1_1(a1654)),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3391, 929, 1182, 894, 1309, 3383, 365])).
% 8.86/6.08 tff(4358,plain,
% 8.86/6.08 (hskp26),
% 8.86/6.08 inference(unit_resolution,[status(thm)],[3790, 221, 929, 895, 894, 20, 4357])).
% 8.86/6.08 tff(4359,plain,
% 8.96/6.08 (~c2_1(a1691)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[669, 4358])).
% 8.96/6.08 tff(4360,plain,
% 8.96/6.08 (~c3_1(a1691)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[689, 4358])).
% 8.96/6.08 tff(4361,plain,
% 8.96/6.08 (~c1_1(a1691)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[675, 4358])).
% 8.96/6.08 tff(4362,plain,
% 8.96/6.08 (hskp67),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[2017, 221, 929, 895, 894, 1517, 4357])).
% 8.96/6.08 tff(4363,plain,
% 8.96/6.08 (c3_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1534, 4362])).
% 8.96/6.08 tff(4364,plain,
% 8.96/6.08 (c1_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1545, 4362])).
% 8.96/6.08 tff(4365,plain,
% 8.96/6.08 (~c0_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4048, 221, 365, 4364, 4363, 1205, 1309, 1194, 1188, 647, 3383])).
% 8.96/6.08 tff(4366,plain,
% 8.96/6.08 (hskp73),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4229, 221, 4364, 4363, 895, 894, 1563, 4357, 4365])).
% 8.96/6.08 tff(4367,plain,
% 8.96/6.08 (c2_1(a1716)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1597, 4366])).
% 8.96/6.08 tff(4368,plain,
% 8.96/6.08 (c0_1(a1716)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1615, 4366])).
% 8.96/6.08 tff(4369,plain,
% 8.96/6.08 (~hskp17),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[3161, 4368, 1662, 4367, 4361, 4360, 4359])).
% 8.96/6.08 tff(4370,plain,
% 8.96/6.08 (hskp17 | hskp16),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[716, 221, 929, 894, 10, 4357])).
% 8.96/6.08 tff(4371,plain,
% 8.96/6.08 (hskp16),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4370, 4369])).
% 8.96/6.08 tff(4372,plain,
% 8.96/6.08 (~c1_1(a1677)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[111, 4371])).
% 8.96/6.08 tff(4373,plain,
% 8.96/6.08 (~c2_1(a1677)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[117, 4371])).
% 8.96/6.08 tff(4374,plain,
% 8.96/6.08 (~c0_1(a1677)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[123, 4371])).
% 8.96/6.08 tff(4375,plain,
% 8.96/6.08 ($false),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4266, 221, 4367, 4368, 365, 363, 1662, 1309, 4374, 4373, 4372, 30])).
% 8.96/6.08 tff(4376,plain,((~hskp52) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~hskp61)), inference(lemma,lemma(discharge,[]))).
% 8.96/6.08 tff(4377,plain,
% 8.96/6.08 (~hskp52),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4376, 363, 365, 1662, 1309, 4356])).
% 8.96/6.08 tff(4378,plain,
% 8.96/6.08 (hskp53),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[150, 4377, 138])).
% 8.96/6.08 tff(4379,plain,
% 8.96/6.08 (~c2_1(a1674)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1187, 4356])).
% 8.96/6.08 tff(4380,plain,
% 8.96/6.08 (~c1_1(a1674)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1193, 4356])).
% 8.96/6.08 tff(4381,plain,
% 8.96/6.08 (c3_1(a1674)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1204, 4356])).
% 8.96/6.08 tff(4382,plain,
% 8.96/6.08 (hskp52 | hskp7 | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[227, 221, 233, 189])).
% 8.96/6.08 tff(4383,plain,
% 8.96/6.08 (hskp7),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4382, 179, 139, 162])).
% 8.96/6.08 tff(4384,plain,
% 8.96/6.08 (c0_1(a1655)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[58, 4383])).
% 8.96/6.08 tff(4385,plain,
% 8.96/6.08 (c3_1(a1655)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[41, 4383])).
% 8.96/6.08 tff(4386,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4387,plain,
% 8.96/6.08 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4388,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4387])).
% 8.96/6.08 tff(4389,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4388, 4386])).
% 8.96/6.08 tff(4390,plain,
% 8.96/6.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4391,plain,
% 8.96/6.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4390, 4389])).
% 8.96/6.08 tff(4392,plain,
% 8.96/6.08 (~c1_1(a1655)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4391, 221, 365, 2296, 4385, 4384, 1309, 2294, 2338, 647, 1835])).
% 8.96/6.08 tff(4393,plain,
% 8.96/6.08 (~hskp16),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[3984, 179, 363, 365, 162, 1309, 233])).
% 8.96/6.08 tff(4394,plain,
% 8.96/6.08 (hskp17 | c1_1(a1655)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[278, 221, 4393, 4385, 4384, 10])).
% 8.96/6.08 tff(4395,plain,
% 8.96/6.08 (hskp17),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4394, 4392])).
% 8.96/6.08 tff(4396,plain,
% 8.96/6.08 (~c2_1(a1678)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[260, 4395])).
% 8.96/6.08 tff(4397,plain,
% 8.96/6.08 (~c1_1(a1678)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[241, 4395])).
% 8.96/6.08 tff(4398,plain,
% 8.96/6.08 (~c0_1(a1678)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[247, 4395])).
% 8.96/6.08 tff(4399,plain,
% 8.96/6.08 ($false),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[3996, 221, 365, 363, 179, 162, 1309, 233, 4398, 4397, 4396, 30])).
% 8.96/6.08 tff(4400,plain,(hskp52 | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674) | (~c0_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.96/6.08 tff(4401,plain,
% 8.96/6.08 (c3_1(a1656)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4400, 4377, 363, 1309, 365, 4381, 4380, 4379, 3383, 138])).
% 8.96/6.08 tff(4402,plain,
% 8.96/6.08 ($false),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[167, 4401, 4378])).
% 8.96/6.08 tff(4403,plain,(c3_1(a1715) | c2_1(a1715) | c1_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.96/6.08 tff(4404,plain,
% 8.96/6.08 (c3_1(a1715)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4403, 365, 1309, 138, 1662])).
% 8.96/6.08 tff(4405,plain,
% 8.96/6.08 (~hskp53),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4192, 4404, 365, 3383, 1309])).
% 8.96/6.08 tff(4406,plain,
% 8.96/6.08 (hskp52),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[150, 4405, 138])).
% 8.96/6.08 tff(4407,plain,
% 8.96/6.08 (hskp67),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4209, 4406, 365, 4404, 3383, 1309])).
% 8.96/6.08 tff(4408,plain,
% 8.96/6.08 (c3_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1534, 4407])).
% 8.96/6.08 tff(4409,plain,
% 8.96/6.08 (c1_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1545, 4407])).
% 8.96/6.08 tff(4410,plain,
% 8.96/6.08 (~c0_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4218, 221, 365, 4404, 4409, 4408, 1309, 647, 3383])).
% 8.96/6.08 tff(4411,plain,
% 8.96/6.08 (c2_1(a1702)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[2029, 4407])).
% 8.96/6.08 tff(4412,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4413,plain,
% 8.96/6.08 ((hskp39 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1702) | (~c3_1(a1702)) | (~c2_1(a1702))) <=> (hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4414,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1702) | (~c3_1(a1702)) | (~c2_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4413])).
% 8.96/6.08 tff(4415,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1702) | (~c3_1(a1702)) | (~c2_1(a1702)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4414, 4412])).
% 8.96/6.08 tff(4416,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1702) | (~c3_1(a1702)) | (~c2_1(a1702)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4417,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1702)) | c0_1(a1702) | (~c2_1(a1702))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 8.96/6.08 tff(4418,plain,
% 8.96/6.08 (hskp39),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4417, 221, 4404, 4411, 4408, 1309, 1488, 3383, 4410])).
% 8.96/6.08 tff(4419,plain,
% 8.96/6.08 (~c0_1(a1721)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1500, 4418])).
% 8.96/6.08 tff(4420,plain,
% 8.96/6.08 (~c1_1(a1721)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1506, 4418])).
% 8.96/6.08 tff(4421,plain,
% 8.96/6.08 (c3_1(a1721)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1586, 4418])).
% 8.96/6.08 tff(4422,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4423,plain,
% 8.96/6.08 ((hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721))) <=> (hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4424,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4423])).
% 8.96/6.08 tff(4425,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4424, 4422])).
% 8.96/6.08 tff(4426,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4427,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 8.96/6.08 tff(4428,plain,
% 8.96/6.08 ($false),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4427, 221, 138, 365, 4404, 4421, 4420, 4419, 137, 3383])).
% 8.96/6.08 tff(4429,plain,(c1_1(a1715) | hskp29 | c2_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.96/6.08 tff(4430,plain,
% 8.96/6.08 (c1_1(a1715)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4429, 1309, 138, 1662])).
% 8.96/6.08 tff(4431,plain,
% 8.96/6.08 (c3_1(a1715)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[1997, 4430, 138, 1309, 3383])).
% 8.96/6.08 tff(4432,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4433,plain,
% 8.96/6.08 ((hskp13 | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4434,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4433])).
% 8.96/6.08 tff(4435,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4434, 4432])).
% 8.96/6.08 tff(4436,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4437,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 8.96/6.08 tff(4438,plain,
% 8.96/6.08 (hskp13),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4437, 221, 4430, 4431, 1309, 290, 3383])).
% 8.96/6.08 tff(4439,plain,
% 8.96/6.08 (~c1_1(a1667)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[303, 4438])).
% 8.96/6.08 tff(4440,plain,
% 8.96/6.08 (c3_1(a1667)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[314, 4438])).
% 8.96/6.08 tff(4441,plain,
% 8.96/6.08 (c0_1(a1667)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[325, 4438])).
% 8.96/6.08 tff(4442,assumption,(~c2_1(a1667)), introduced(assumption)).
% 8.96/6.08 tff(4443,assumption,(~c1_1(a1667)), introduced(assumption)).
% 8.96/6.08 tff(4444,assumption,(c3_1(a1667)), introduced(assumption)).
% 8.96/6.08 tff(4445,assumption,(c0_1(a1667)), introduced(assumption)).
% 8.96/6.08 tff(4446,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4447,plain,
% 8.96/6.08 (((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667))) <=> (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4448,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4447])).
% 8.96/6.08 tff(4449,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4448, 4446])).
% 8.96/6.08 tff(4450,plain,
% 8.96/6.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4451,plain,
% 8.96/6.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4450, 4449])).
% 8.96/6.08 tff(4452,plain,
% 8.96/6.08 ($false),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4451, 221, 834, 2103, 4445, 4444, 4443, 647, 1835, 4442])).
% 8.96/6.08 tff(4453,plain,(c2_1(a1667) | (~c1_1(a1715)) | (~c3_1(a1715)) | (~c0_1(a1667)) | (~c3_1(a1667)) | c1_1(a1667) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.96/6.08 tff(4454,plain,
% 8.96/6.08 (c2_1(a1667)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4453, 4430, 4431, 4441, 4440, 4439, 3383])).
% 8.96/6.08 tff(4455,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4456,plain,
% 8.96/6.08 ((hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667))) <=> (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4457,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4456])).
% 8.96/6.08 tff(4458,plain,
% 8.96/6.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 8.96/6.08 inference(transitivity,[status(thm)],[4457, 4455])).
% 8.96/6.08 tff(4459,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 8.96/6.08 inference(quant_inst,[status(thm)],[])).
% 8.96/6.08 tff(4460,plain,
% 8.96/6.08 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c0_1(a1667))),
% 8.96/6.08 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 8.96/6.08 tff(4461,plain,
% 8.96/6.08 (hskp26 | (~c2_1(a1667))),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4460, 221, 4441, 4440, 4439, 20])).
% 8.96/6.08 tff(4462,plain,
% 8.96/6.08 (hskp26),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4461, 4454])).
% 8.96/6.08 tff(4463,plain,
% 8.96/6.08 (~c2_1(a1691)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[669, 4462])).
% 8.96/6.08 tff(4464,plain,
% 8.96/6.08 (~c3_1(a1691)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[689, 4462])).
% 8.96/6.08 tff(4465,plain,
% 8.96/6.08 (c1_1(a1656)),
% 8.96/6.08 inference(unit_resolution,[status(thm)],[4146, 236, 2103, 233, 234, 1309, 1835, 232])).
% 8.96/6.08 tff(4466,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4467,plain,
% 8.96/6.08 (((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656))) <=> (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.96/6.08 inference(rewrite,[status(thm)],[])).
% 8.96/6.08 tff(4468,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656))))),
% 8.96/6.08 inference(monotonicity,[status(thm)],[4467])).
% 8.96/6.08 tff(4469,plain,
% 8.96/6.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.96/6.09 inference(transitivity,[status(thm)],[4468, 4466])).
% 8.96/6.09 tff(4470,plain,
% 8.96/6.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.96/6.09 inference(quant_inst,[status(thm)],[])).
% 8.96/6.09 tff(4471,plain,
% 8.96/6.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 8.96/6.09 inference(modus_ponens,[status(thm)],[4470, 4469])).
% 8.96/6.09 tff(4472,plain,
% 8.96/6.09 (~c3_1(a1678)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[4471, 221, 232, 4445, 4444, 233, 248, 242, 4443, 102, 4465])).
% 8.96/6.09 tff(4473,plain,
% 8.96/6.09 ($false),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[267, 221, 232, 234, 233, 248, 242, 261, 30, 4472])).
% 8.96/6.09 tff(4474,plain,((~hskp17) | (~c2_1(a1656)) | (~c0_1(a1656)) | c3_1(a1656) | (~c0_1(a1667)) | (~c3_1(a1667)) | c1_1(a1667) | (~c3_1(a1715)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.96/6.09 tff(4475,plain,
% 8.96/6.09 (~hskp17),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[4474, 2358, 2357, 2356, 4445, 4444, 4443, 2103, 1309, 1835])).
% 8.96/6.09 tff(4476,plain,
% 8.96/6.09 (hskp17 | hskp16),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[332, 221, 4445, 4444, 4443, 10])).
% 8.96/6.09 tff(4477,plain,
% 8.96/6.09 (hskp16),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[4476, 4475])).
% 8.96/6.09 tff(4478,plain,
% 8.96/6.09 (~c1_1(a1677)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[111, 4477])).
% 8.96/6.09 tff(4479,plain,
% 8.96/6.09 (~c0_1(a1677)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[123, 4477])).
% 8.96/6.09 tff(4480,plain,
% 8.96/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)))),
% 8.96/6.09 inference(rewrite,[status(thm)],[])).
% 8.96/6.09 tff(4481,plain,
% 8.96/6.09 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))) <=> (hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)))),
% 8.96/6.09 inference(rewrite,[status(thm)],[])).
% 8.96/6.09 tff(4482,plain,
% 8.96/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677))))),
% 8.96/6.09 inference(monotonicity,[status(thm)],[4481])).
% 8.96/6.09 tff(4483,plain,
% 8.96/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)))),
% 8.96/6.09 inference(transitivity,[status(thm)],[4482, 4480])).
% 8.96/6.09 tff(4484,plain,
% 8.96/6.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 8.96/6.09 inference(quant_inst,[status(thm)],[])).
% 8.96/6.09 tff(4485,plain,
% 8.96/6.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677))),
% 8.96/6.09 inference(modus_ponens,[status(thm)],[4484, 4483])).
% 8.96/6.09 tff(4486,plain,
% 8.96/6.09 (~c3_1(a1677)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[4485, 221, 138, 4445, 4444, 4479, 4478, 4443, 137])).
% 8.96/6.09 tff(4487,plain,
% 8.96/6.09 (~c2_1(a1677)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[117, 4477])).
% 8.96/6.09 tff(4488,plain,
% 8.96/6.09 ($false),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[346, 221, 2358, 2357, 2356, 4479, 4487, 4478, 30, 4486])).
% 8.96/6.09 tff(4489,plain,((~hskp53) | hskp29 | (~c0_1(a1667)) | (~c3_1(a1667)) | c1_1(a1667) | (~c3_1(a1715)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.96/6.09 tff(4490,plain,
% 8.96/6.09 (~hskp53),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[4489, 4441, 138, 4440, 4439, 4431, 1309, 3383])).
% 8.96/6.09 tff(4491,plain,
% 8.96/6.09 (hskp52),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[150, 4490, 138])).
% 8.96/6.09 tff(4492,plain,
% 8.96/6.09 (c3_1(a1654)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[536, 4491])).
% 8.96/6.09 tff(4493,plain,
% 8.96/6.09 (c2_1(a1654)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[547, 4491])).
% 8.96/6.09 tff(4494,plain,
% 8.96/6.09 (c0_1(a1654)),
% 8.96/6.09 inference(unit_resolution,[status(thm)],[525, 4491])).
% 8.96/6.09 tff(4495,plain,
% 8.96/6.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.96/6.09 inference(rewrite,[status(thm)],[])).
% 8.96/6.09 tff(4496,plain,
% 8.96/6.09 (((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691)) <=> (c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.96/6.09 inference(rewrite,[status(thm)],[])).
% 8.96/6.09 tff(4497,plain,
% 8.96/6.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.96/6.09 inference(monotonicity,[status(thm)],[4496])).
% 8.96/6.09 tff(4498,plain,
% 8.96/6.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.96/6.09 inference(transitivity,[status(thm)],[4497, 4495])).
% 8.96/6.09 tff(4499,plain,
% 8.97/6.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))),
% 8.97/6.09 inference(quant_inst,[status(thm)],[])).
% 8.97/6.09 tff(4500,plain,
% 8.97/6.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1691) | c2_1(a1691) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1691) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4499, 4498])).
% 8.97/6.09 tff(4501,plain,
% 8.97/6.09 (c0_1(a1691)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4500, 221, 4494, 4493, 4492, 4441, 4464, 4463, 4439, 565, 4454])).
% 8.97/6.09 tff(4502,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4503,plain,
% 8.97/6.09 ((hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715))) <=> (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4504,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))))),
% 8.97/6.09 inference(monotonicity,[status(thm)],[4503])).
% 8.97/6.09 tff(4505,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(transitivity,[status(thm)],[4504, 4502])).
% 8.97/6.09 tff(4506,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)))),
% 8.97/6.09 inference(quant_inst,[status(thm)],[])).
% 8.97/6.09 tff(4507,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 8.97/6.09 tff(4508,plain,
% 8.97/6.09 (hskp47),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4507, 221, 4430, 4431, 4464, 4463, 1848, 3383, 4501])).
% 8.97/6.09 tff(4509,plain,
% 8.97/6.09 (~c0_1(a1644)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[1861, 4508])).
% 8.97/6.09 tff(4510,plain,
% 8.97/6.09 (~c1_1(a1644)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[1867, 4508])).
% 8.97/6.09 tff(4511,plain,
% 8.97/6.09 (^[V: $i, U: $i] : refl((hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 8.97/6.09 inference(bind,[status(th)],[])).
% 8.97/6.09 tff(4512,plain,
% 8.97/6.09 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(quant_intro,[status(thm)],[4511])).
% 8.97/6.09 tff(4513,plain,
% 8.97/6.09 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4514,plain,
% 8.97/6.09 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp34) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp34))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp34) <=> (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 8.97/6.09 inference(bind,[status(th)],[])).
% 8.97/6.09 tff(4515,plain,
% 8.97/6.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp34) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(quant_intro,[status(thm)],[4514])).
% 8.97/6.09 tff(4516,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause350')).
% 8.97/6.09 tff(4517,plain,
% 8.97/6.09 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 8.97/6.09 tff(4518,plain,
% 8.97/6.09 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4517, 4513])).
% 8.97/6.09 tff(4519,plain,(
% 8.97/6.09 ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(skolemize,[status(sab)],[4518])).
% 8.97/6.09 tff(4520,plain,
% 8.97/6.09 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4519, 4512])).
% 8.97/6.09 tff(4521,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4522,plain,
% 8.97/6.09 ((hskp34 | (~ndr1_0) | c1_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4523,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c1_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715))))),
% 8.97/6.09 inference(monotonicity,[status(thm)],[4522])).
% 8.97/6.09 tff(4524,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c1_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(transitivity,[status(thm)],[4523, 4521])).
% 8.97/6.09 tff(4525,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c1_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.97/6.09 inference(quant_inst,[status(thm)],[])).
% 8.97/6.09 tff(4526,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp34 | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c2_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4525, 4524])).
% 8.97/6.09 tff(4527,plain,
% 8.97/6.09 (hskp34 | (~c2_1(a1667))),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4526, 221, 4430, 4431, 4441, 1309, 4439, 4520])).
% 8.97/6.09 tff(4528,plain,
% 8.97/6.09 (hskp34),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4527, 4454])).
% 8.97/6.09 tff(4529,plain,
% 8.97/6.09 (((~hskp34) | (~c1_1(a1705))) <=> ((~hskp34) | (~c1_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4530,plain,
% 8.97/6.09 (((~c1_1(a1705)) | (~hskp34)) <=> ((~hskp34) | (~c1_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4531,axiom,((~c1_1(a1705)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 8.97/6.09 tff(4532,plain,
% 8.97/6.09 ((~hskp34) | (~c1_1(a1705))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4531, 4530])).
% 8.97/6.09 tff(4533,plain,
% 8.97/6.09 ((~hskp34) | (~c1_1(a1705))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4532, 4529])).
% 8.97/6.09 tff(4534,plain,
% 8.97/6.09 (~c1_1(a1705)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4533, 4528])).
% 8.97/6.09 tff(4535,plain,
% 8.97/6.09 (((~hskp34) | (~c3_1(a1705))) <=> ((~hskp34) | (~c3_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4536,plain,
% 8.97/6.09 (((~c3_1(a1705)) | (~hskp34)) <=> ((~hskp34) | (~c3_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4537,axiom,((~c3_1(a1705)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause240')).
% 8.97/6.09 tff(4538,plain,
% 8.97/6.09 ((~hskp34) | (~c3_1(a1705))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 8.97/6.09 tff(4539,plain,
% 8.97/6.09 ((~hskp34) | (~c3_1(a1705))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4538, 4535])).
% 8.97/6.09 tff(4540,plain,
% 8.97/6.09 (~c3_1(a1705)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4539, 4528])).
% 8.97/6.09 tff(4541,plain,
% 8.97/6.09 (((~hskp34) | c2_1(a1705)) <=> ((~hskp34) | c2_1(a1705))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4542,axiom,((~hskp34) | c2_1(a1705)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 8.97/6.09 tff(4543,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 8.97/6.09 tff(4544,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4543, 4541])).
% 8.97/6.09 tff(4545,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4544, 4541])).
% 8.97/6.09 tff(4546,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4545, 4541])).
% 8.97/6.09 tff(4547,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4546, 4541])).
% 8.97/6.09 tff(4548,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4547, 4541])).
% 8.97/6.09 tff(4549,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4548, 4541])).
% 8.97/6.09 tff(4550,plain,
% 8.97/6.09 ((~hskp34) | c2_1(a1705)),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4549, 4541])).
% 8.97/6.09 tff(4551,plain,
% 8.97/6.09 (c2_1(a1705)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4550, 4528])).
% 8.97/6.09 tff(4552,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4553,plain,
% 8.97/6.09 ((hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1705) | c1_1(a1705) | (~c2_1(a1705))) <=> (hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4554,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1705) | c1_1(a1705) | (~c2_1(a1705)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705))))),
% 8.97/6.09 inference(monotonicity,[status(thm)],[4553])).
% 8.97/6.09 tff(4555,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1705) | c1_1(a1705) | (~c2_1(a1705)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705)))),
% 8.97/6.09 inference(transitivity,[status(thm)],[4554, 4552])).
% 8.97/6.09 tff(4556,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1705) | c1_1(a1705) | (~c2_1(a1705)))),
% 8.97/6.09 inference(quant_inst,[status(thm)],[])).
% 8.97/6.09 tff(4557,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 8.97/6.09 tff(4558,plain,
% 8.97/6.09 (hskp57),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4557, 221, 4551, 4540, 4534, 4464, 4463, 1627, 4501])).
% 8.97/6.09 tff(4559,plain,
% 8.97/6.09 (~c1_1(a1665)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[65, 4558])).
% 8.97/6.09 tff(4560,plain,
% 8.97/6.09 (c3_1(a1644)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[1880, 4508])).
% 8.97/6.09 tff(4561,plain,
% 8.97/6.09 (c3_1(a1665)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[76, 4558])).
% 8.97/6.09 tff(4562,plain,
% 8.97/6.09 (c0_1(a1665)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[90, 4558])).
% 8.97/6.09 tff(4563,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4564,plain,
% 8.97/6.09 ((hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644))) <=> (hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.09 inference(rewrite,[status(thm)],[])).
% 8.97/6.09 tff(4565,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.97/6.09 inference(monotonicity,[status(thm)],[4564])).
% 8.97/6.09 tff(4566,plain,
% 8.97/6.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.09 inference(transitivity,[status(thm)],[4565, 4563])).
% 8.97/6.09 tff(4567,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 8.97/6.09 inference(quant_inst,[status(thm)],[])).
% 8.97/6.09 tff(4568,plain,
% 8.97/6.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.97/6.09 inference(modus_ponens,[status(thm)],[4567, 4566])).
% 8.97/6.09 tff(4569,plain,
% 8.97/6.09 ($false),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4568, 221, 138, 4562, 4561, 4560, 4559, 4510, 4509, 137])).
% 8.97/6.09 tff(4570,plain,(c2_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.97/6.09 tff(4571,plain,
% 8.97/6.09 (c2_1(a1715)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[4570, 1662, 138])).
% 8.97/6.09 tff(4572,plain,
% 8.97/6.09 (~hskp72),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[553, 4571])).
% 8.97/6.09 tff(4573,plain,
% 8.97/6.09 (c3_1(a1715)),
% 8.97/6.09 inference(unit_resolution,[status(thm)],[1295, 364, 138])).
% 8.97/6.09 tff(4574,plain,
% 8.97/6.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4575,plain,
% 8.97/6.10 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715))) <=> (c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4576,plain,
% 8.97/6.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4575])).
% 8.97/6.10 tff(4577,plain,
% 8.97/6.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4576, 4574])).
% 8.97/6.10 tff(4578,plain,
% 8.97/6.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4579,plain,
% 8.97/6.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4578, 4577])).
% 8.97/6.10 tff(4580,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4579, 221, 365, 2103, 78, 80, 364, 124, 118, 79, 376, 366])).
% 8.97/6.10 tff(4581,plain,((~hskp16) | c1_1(a1715) | (~c3_1(a1715)) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c2_1(a1715)) | c2_1(a1655) | (~c0_1(a1656)) | c3_1(a1656) | (~c2_1(a1656))), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4582,plain,
% 8.97/6.10 (~hskp16),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4581, 230, 4573, 365, 229, 364, 231, 162, 168, 179])).
% 8.97/6.10 tff(4583,plain,
% 8.97/6.10 (hskp17),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[334, 4582, 230, 229, 231])).
% 8.97/6.10 tff(4584,plain,
% 8.97/6.10 (~c2_1(a1678)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[260, 4583])).
% 8.97/6.10 tff(4585,plain,
% 8.97/6.10 (~c1_1(a1678)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[241, 4583])).
% 8.97/6.10 tff(4586,plain,
% 8.97/6.10 (~c0_1(a1678)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[247, 4583])).
% 8.97/6.10 tff(4587,plain,
% 8.97/6.10 (c1_1(a1655)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[269, 4583, 162, 168, 138, 230, 229, 179])).
% 8.97/6.10 tff(4588,plain,
% 8.97/6.10 (hskp13),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[498, 4587])).
% 8.97/6.10 tff(4589,plain,
% 8.97/6.10 (c0_1(a1715)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[3321, 4588, 138, 4573, 365])).
% 8.97/6.10 tff(4590,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4591,plain,
% 8.97/6.10 ((hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715))) <=> (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4592,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4591])).
% 8.97/6.10 tff(4593,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4592, 4590])).
% 8.97/6.10 tff(4594,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4595,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4594, 4593])).
% 8.97/6.10 tff(4596,plain,
% 8.97/6.10 (hskp26 | (~c0_1(a1715))),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4595, 221, 365, 4573, 364, 20])).
% 8.97/6.10 tff(4597,plain,
% 8.97/6.10 (hskp26),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4596, 4589])).
% 8.97/6.10 tff(4598,plain,
% 8.97/6.10 (~c2_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[669, 4597])).
% 8.97/6.10 tff(4599,plain,
% 8.97/6.10 (~c1_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[675, 4597])).
% 8.97/6.10 tff(4600,plain,
% 8.97/6.10 (~c3_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[689, 4597])).
% 8.97/6.10 tff(4601,plain,
% 8.97/6.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4602,plain,
% 8.97/6.10 (((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4603,plain,
% 8.97/6.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4602])).
% 8.97/6.10 tff(4604,plain,
% 8.97/6.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4603, 4601])).
% 8.97/6.10 tff(4605,plain,
% 8.97/6.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1656) | (~c0_1(a1656)) | (~c2_1(a1656)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4606,plain,
% 8.97/6.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 8.97/6.10 tff(4607,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4606, 221, 179, 162, 168, 4600, 4599, 4598, 4586, 4585, 4584, 30])).
% 8.97/6.10 tff(4608,plain,(hskp52 | c1_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4609,plain,
% 8.97/6.10 (hskp52),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4608, 365, 4571, 138])).
% 8.97/6.10 tff(4610,plain,
% 8.97/6.10 (c3_1(a1654)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[536, 4609])).
% 8.97/6.10 tff(4611,plain,
% 8.97/6.10 (c2_1(a1654)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[547, 4609])).
% 8.97/6.10 tff(4612,plain,
% 8.97/6.10 (c0_1(a1654)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[525, 4609])).
% 8.97/6.10 tff(4613,plain,
% 8.97/6.10 (c3_1(a1715)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1295, 4571, 138])).
% 8.97/6.10 tff(4614,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4615,plain,
% 8.97/6.10 ((hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4616,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4615])).
% 8.97/6.10 tff(4617,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4616, 4614])).
% 8.97/6.10 tff(4618,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4619,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 8.97/6.10 tff(4620,plain,
% 8.97/6.10 (hskp26),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4619, 221, 365, 4613, 4612, 4611, 4610, 4571, 20])).
% 8.97/6.10 tff(4621,plain,
% 8.97/6.10 (~c2_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[669, 4620])).
% 8.97/6.10 tff(4622,plain,
% 8.97/6.10 (~c3_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[689, 4620])).
% 8.97/6.10 tff(4623,assumption,(~c0_1(a1691)), introduced(assumption)).
% 8.97/6.10 tff(4624,plain,
% 8.97/6.10 (hskp37 | c0_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[696, 221, 578, 962, 964, 577])).
% 8.97/6.10 tff(4625,plain,
% 8.97/6.10 (hskp37),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4624, 4623])).
% 8.97/6.10 tff(4626,plain,
% 8.97/6.10 (~c1_1(a1714)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[591, 4625])).
% 8.97/6.10 tff(4627,plain,
% 8.97/6.10 (c0_1(a1714)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[602, 4625])).
% 8.97/6.10 tff(4628,plain,
% 8.97/6.10 (c2_1(a1714)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[613, 4625])).
% 8.97/6.10 tff(4629,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[707, 221, 617, 616, 615, 4628, 4627, 4626, 962, 964, 565, 4623])).
% 8.97/6.10 tff(4630,plain,(c0_1(a1691) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4631,plain,
% 8.97/6.10 (c0_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4630, 4612, 4611, 4610, 4622, 4621, 4572])).
% 8.97/6.10 tff(4632,plain,
% 8.97/6.10 (~c1_1(a1691)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[675, 4620])).
% 8.97/6.10 tff(4633,plain,
% 8.97/6.10 (hskp67),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[2017, 221, 4612, 4611, 4610, 1517, 627])).
% 8.97/6.10 tff(4634,plain,
% 8.97/6.10 (c3_1(a1702)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1534, 4633])).
% 8.97/6.10 tff(4635,plain,
% 8.97/6.10 (c2_1(a1702)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[2029, 4633])).
% 8.97/6.10 tff(4636,plain,
% 8.97/6.10 (c1_1(a1702)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1545, 4633])).
% 8.97/6.10 tff(4637,plain,
% 8.97/6.10 (hskp63),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[2037, 221, 4636, 4635, 4634, 4612, 4610, 2011, 627])).
% 8.97/6.10 tff(4638,plain,
% 8.97/6.10 (~c0_1(a1676)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[2043, 4637])).
% 8.97/6.10 tff(4639,plain,
% 8.97/6.10 (c3_1(a1676)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[2054, 4637])).
% 8.97/6.10 tff(4640,plain,
% 8.97/6.10 (c1_1(a1676)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4245, 221, 138, 4639, 4612, 4610, 4638, 137, 627])).
% 8.97/6.10 tff(4641,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4642,plain,
% 8.97/6.10 ((hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676))) <=> (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4643,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4642])).
% 8.97/6.10 tff(4644,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4643, 4641])).
% 8.97/6.10 tff(4645,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4646,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4645, 4644])).
% 8.97/6.10 tff(4647,plain,
% 8.97/6.10 (hskp73 | (~c1_1(a1676))),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4646, 221, 365, 4613, 4639, 4571, 4638, 1563])).
% 8.97/6.10 tff(4648,plain,
% 8.97/6.10 (hskp73),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4647, 4640])).
% 8.97/6.10 tff(4649,plain,
% 8.97/6.10 (c2_1(a1716)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1597, 4648])).
% 8.97/6.10 tff(4650,plain,
% 8.97/6.10 (c0_1(a1716)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1615, 4648])).
% 8.97/6.10 tff(4651,plain,
% 8.97/6.10 (~hskp17),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[3161, 4650, 1662, 4649, 4632, 4622, 4621])).
% 8.97/6.10 tff(4652,plain,
% 8.97/6.10 (hskp17 | hskp16 | c1_1(a1654)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[716, 221, 4612, 4610, 10])).
% 8.97/6.10 tff(4653,plain,
% 8.97/6.10 (hskp16),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4652, 4651, 627])).
% 8.97/6.10 tff(4654,plain,
% 8.97/6.10 (~c0_1(a1677)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[123, 4653])).
% 8.97/6.10 tff(4655,plain,
% 8.97/6.10 (~c1_1(a1677)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[111, 4653])).
% 8.97/6.10 tff(4656,plain,
% 8.97/6.10 (~c2_1(a1677)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[117, 4653])).
% 8.97/6.10 tff(4657,plain,
% 8.97/6.10 (c3_1(a1677)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[798, 4656, 4572, 4610, 4611, 4654, 4612])).
% 8.97/6.10 tff(4658,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[808, 4657, 4655, 138, 4610, 4612, 627, 4654])).
% 8.97/6.10 tff(4659,plain,(c1_1(a1654) | hskp29 | c3_1(a1716) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4660,plain,
% 8.97/6.10 (c1_1(a1654)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4659, 365, 1662, 138])).
% 8.97/6.10 tff(4661,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4662,plain,
% 8.97/6.10 ((hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654))) <=> (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4663,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4662])).
% 8.97/6.10 tff(4664,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4663, 4661])).
% 8.97/6.10 tff(4665,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4666,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp47 | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 8.97/6.10 tff(4667,plain,
% 8.97/6.10 (hskp47 | (~c0_1(a1691)) | (~c1_1(a1654))),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4666, 221, 4612, 4610, 4622, 4621, 1848])).
% 8.97/6.10 tff(4668,plain,
% 8.97/6.10 (hskp47),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4667, 4631, 4660])).
% 8.97/6.10 tff(4669,plain,
% 8.97/6.10 (~c0_1(a1644)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1861, 4668])).
% 8.97/6.10 tff(4670,plain,
% 8.97/6.10 (~c1_1(a1644)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1867, 4668])).
% 8.97/6.10 tff(4671,plain,
% 8.97/6.10 (c3_1(a1644)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1880, 4668])).
% 8.97/6.10 tff(4672,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4673,plain,
% 8.97/6.10 ((hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644))) <=> (hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4674,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4673])).
% 8.97/6.10 tff(4675,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4674, 4672])).
% 8.97/6.10 tff(4676,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4677,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4676, 4675])).
% 8.97/6.10 tff(4678,plain,
% 8.97/6.10 (~c0_1(a1715)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4677, 221, 138, 365, 4613, 4671, 4670, 4669, 137])).
% 8.97/6.10 tff(4679,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4680,plain,
% 8.97/6.10 ((hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.10 inference(rewrite,[status(thm)],[])).
% 8.97/6.10 tff(4681,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.97/6.10 inference(monotonicity,[status(thm)],[4680])).
% 8.97/6.10 tff(4682,plain,
% 8.97/6.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.97/6.10 inference(transitivity,[status(thm)],[4681, 4679])).
% 8.97/6.10 tff(4683,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.97/6.10 inference(quant_inst,[status(thm)],[])).
% 8.97/6.10 tff(4684,plain,
% 8.97/6.10 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.97/6.10 inference(modus_ponens,[status(thm)],[4683, 4682])).
% 8.97/6.10 tff(4685,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4684, 221, 138, 365, 2103, 91, 77, 66, 137, 1297])).
% 8.97/6.10 tff(4686,plain,((~hskp57) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4687,plain,
% 8.97/6.10 (~hskp57),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4686, 4678, 138, 4613, 365])).
% 8.97/6.10 tff(4688,plain,
% 8.97/6.10 (~hskp13),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[3321, 4678, 138, 4613, 365])).
% 8.97/6.10 tff(4689,plain,
% 8.97/6.10 (~hskp61),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1213, 4631, 4610, 4632, 4621, 4660, 4612])).
% 8.97/6.10 tff(4690,plain,
% 8.97/6.10 (~c3_1(a1637)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1237, 2537, 883, 2536, 2535])).
% 8.97/6.10 tff(4691,plain,
% 8.97/6.10 ($false),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1258, 4690, 2537, 1250, 2536, 2535])).
% 8.97/6.10 tff(4692,plain,((~hskp0) | hskp61 | hskp13), inference(lemma,lemma(discharge,[]))).
% 8.97/6.10 tff(4693,plain,
% 8.97/6.10 (~hskp0),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[4692, 4689, 4688])).
% 8.97/6.10 tff(4694,plain,
% 8.97/6.10 (hskp42),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1081, 1044, 963])).
% 8.97/6.10 tff(4695,plain,
% 8.97/6.10 (~c3_1(a1638)),
% 8.97/6.10 inference(unit_resolution,[status(thm)],[1087, 4694])).
% 8.97/6.11 tff(4696,plain,
% 8.97/6.11 (c0_1(a1638)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1098, 4694])).
% 8.97/6.11 tff(4697,plain,
% 8.97/6.11 (c1_1(a1638)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1109, 4694])).
% 8.97/6.11 tff(4698,plain,
% 8.97/6.11 (hskp2),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1116, 221, 4697, 4696, 4695, 962, 961, 960, 940])).
% 8.97/6.11 tff(4699,plain,
% 8.97/6.11 (~c0_1(a1645)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1122, 4698])).
% 8.97/6.11 tff(4700,plain,
% 8.97/6.11 (~c1_1(a1645)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1128, 4698])).
% 8.97/6.11 tff(4701,plain,
% 8.97/6.11 (c2_1(a1645)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1138, 221, 1072, 1061, 1050, 962, 961, 964, 4700, 4699, 30])).
% 8.97/6.11 tff(4702,plain,
% 8.97/6.11 (~c3_1(a1645)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1144, 4698])).
% 8.97/6.11 tff(4703,plain,
% 8.97/6.11 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691)))),
% 8.97/6.11 inference(rewrite,[status(thm)],[])).
% 8.97/6.11 tff(4704,plain,
% 8.97/6.11 ((hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645))) <=> (hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691)))),
% 8.97/6.11 inference(rewrite,[status(thm)],[])).
% 8.97/6.11 tff(4705,plain,
% 8.97/6.11 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691))))),
% 8.97/6.11 inference(monotonicity,[status(thm)],[4704])).
% 8.97/6.11 tff(4706,plain,
% 8.97/6.11 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691)))),
% 8.97/6.11 inference(transitivity,[status(thm)],[4705, 4703])).
% 8.97/6.11 tff(4707,plain,
% 8.97/6.11 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1645) | c1_1(a1645) | (~c2_1(a1645)))),
% 8.97/6.11 inference(quant_inst,[status(thm)],[])).
% 8.97/6.11 tff(4708,plain,
% 8.97/6.11 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691))),
% 8.97/6.11 inference(modus_ponens,[status(thm)],[4707, 4706])).
% 8.97/6.11 tff(4709,plain,
% 8.97/6.11 ($false),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[4708, 221, 1628, 962, 964, 4700, 4702, 1627, 940, 4701])).
% 8.97/6.11 tff(4710,plain,((~hskp74) | hskp57 | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c1_1(a1691) | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.97/6.11 tff(4711,plain,
% 8.97/6.11 (~hskp74),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[4710, 4693, 4622, 4621, 4631, 4632, 4687])).
% 8.97/6.11 tff(4712,plain,
% 8.97/6.11 (hskp38),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[1032, 4711, 4609])).
% 8.97/6.11 tff(4713,plain,
% 8.97/6.11 (~c2_1(a1718)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[970, 4712])).
% 8.97/6.11 tff(4714,plain,
% 8.97/6.11 (c3_1(a1718)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[981, 4712])).
% 8.97/6.11 tff(4715,plain,
% 8.97/6.11 (~c1_1(a1718)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[988, 221, 4693, 4612, 4611, 4714, 4713, 950, 4660])).
% 8.97/6.11 tff(4716,plain,
% 8.97/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.11 inference(rewrite,[status(thm)],[])).
% 8.97/6.11 tff(4717,plain,
% 8.97/6.11 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718))) <=> (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.11 inference(rewrite,[status(thm)],[])).
% 8.97/6.11 tff(4718,plain,
% 8.97/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.97/6.11 inference(monotonicity,[status(thm)],[4717])).
% 8.97/6.11 tff(4719,plain,
% 8.97/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.97/6.11 inference(transitivity,[status(thm)],[4718, 4716])).
% 8.97/6.11 tff(4720,plain,
% 8.97/6.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))),
% 8.97/6.11 inference(quant_inst,[status(thm)],[])).
% 8.97/6.11 tff(4721,plain,
% 8.97/6.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.97/6.11 inference(modus_ponens,[status(thm)],[4720, 4719])).
% 8.97/6.11 tff(4722,plain,
% 8.97/6.11 ($false),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[4721, 221, 4612, 4610, 4714, 4713, 4632, 4621, 647, 4660, 4715, 4631])).
% 8.97/6.11 tff(4723,plain,(c1_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.97/6.11 tff(4724,plain,
% 8.97/6.11 (c1_1(a1715)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[4723, 1662, 138])).
% 8.97/6.11 tff(4725,plain,
% 8.97/6.11 (c1_1(a1655)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[357, 230, 138, 229, 179, 168, 162, 231])).
% 8.97/6.11 tff(4726,plain,
% 8.97/6.11 (hskp13),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[498, 4725])).
% 8.97/6.11 tff(4727,plain,
% 8.97/6.11 (~c1_1(a1667)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[303, 4726])).
% 8.97/6.11 tff(4728,plain,
% 8.97/6.11 (c3_1(a1667)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[314, 4726])).
% 8.97/6.11 tff(4729,plain,
% 8.97/6.11 (c0_1(a1667)),
% 8.97/6.11 inference(unit_resolution,[status(thm)],[325, 4726])).
% 8.97/6.11 tff(4730,plain,
% 8.97/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4731,plain,
% 8.99/6.11 ((hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667))) <=> (hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4732,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715))))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4731])).
% 8.99/6.11 tff(4733,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4732, 4730])).
% 8.99/6.11 tff(4734,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4735,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 8.99/6.11 tff(4736,plain,
% 8.99/6.11 (hskp63),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4735, 221, 834, 4573, 4729, 4728, 364, 4727, 2011])).
% 8.99/6.11 tff(4737,plain,
% 8.99/6.11 (~c0_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[2043, 4736])).
% 8.99/6.11 tff(4738,plain,
% 8.99/6.11 (c3_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[2054, 4736])).
% 8.99/6.11 tff(4739,plain,
% 8.99/6.11 (c2_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4109, 4736])).
% 8.99/6.11 tff(4740,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4741,plain,
% 8.99/6.11 ((hskp39 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676))) <=> (hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4742,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676))))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4741])).
% 8.99/6.11 tff(4743,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4742, 4740])).
% 8.99/6.11 tff(4744,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1676) | (~c3_1(a1676)) | (~c2_1(a1676)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4745,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp39 | c0_1(a1676) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1676)) | (~c2_1(a1676))),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 8.99/6.11 tff(4746,plain,
% 8.99/6.11 (hskp39),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4745, 221, 4739, 4738, 230, 229, 4737, 231, 1488])).
% 8.99/6.11 tff(4747,plain,
% 8.99/6.11 (~c0_1(a1721)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[1500, 4746])).
% 8.99/6.11 tff(4748,plain,
% 8.99/6.11 (~c1_1(a1721)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[1506, 4746])).
% 8.99/6.11 tff(4749,plain,
% 8.99/6.11 (c3_1(a1721)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[1586, 4746])).
% 8.99/6.11 tff(4750,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4751,plain,
% 8.99/6.11 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721))) <=> (hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4752,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721))))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4751])).
% 8.99/6.11 tff(4753,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721)))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4752, 4750])).
% 8.99/6.11 tff(4754,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4755,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721))),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4754, 4753])).
% 8.99/6.11 tff(4756,plain,
% 8.99/6.11 ($false),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4755, 221, 138, 4749, 4729, 4728, 4748, 4747, 4727, 137])).
% 8.99/6.11 tff(4757,plain,(hskp52 | hskp29 | (~c1_1(a1715)) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.11 tff(4758,plain,
% 8.99/6.11 (hskp52),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4757, 4724, 138, 4571])).
% 8.99/6.11 tff(4759,plain,
% 8.99/6.11 (c2_1(a1654)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[547, 4758])).
% 8.99/6.11 tff(4760,plain,
% 8.99/6.11 (c3_1(a1654)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[536, 4758])).
% 8.99/6.11 tff(4761,plain,
% 8.99/6.11 (c0_1(a1654)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[525, 4758])).
% 8.99/6.11 tff(4762,plain,
% 8.99/6.11 (hskp26),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[3790, 221, 4761, 4759, 4760, 20, 627])).
% 8.99/6.11 tff(4763,plain,
% 8.99/6.11 (~c2_1(a1691)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[669, 4762])).
% 8.99/6.11 tff(4764,plain,
% 8.99/6.11 (~c3_1(a1691)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[689, 4762])).
% 8.99/6.11 tff(4765,plain,
% 8.99/6.11 (~c1_1(a1691)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[675, 4762])).
% 8.99/6.11 tff(4766,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4767,plain,
% 8.99/6.11 ((hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654))) <=> (hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4768,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4767])).
% 8.99/6.11 tff(4769,plain,
% 8.99/6.11 (((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4768, 4766])).
% 8.99/6.11 tff(4770,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp63 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4771,plain,
% 8.99/6.11 ((~![V: $i, U: $i] : (hskp63 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp63 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4770, 4769])).
% 8.99/6.11 tff(4772,plain,
% 8.99/6.11 (hskp63),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4771, 221, 4724, 4613, 4761, 4760, 4571, 2011, 627])).
% 8.99/6.11 tff(4773,plain,
% 8.99/6.11 (~c0_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[2043, 4772])).
% 8.99/6.11 tff(4774,plain,
% 8.99/6.11 (c3_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[2054, 4772])).
% 8.99/6.11 tff(4775,plain,
% 8.99/6.11 (c1_1(a1676)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4245, 221, 138, 4774, 4761, 4760, 4773, 137, 627])).
% 8.99/6.11 tff(4776,plain,
% 8.99/6.11 (hskp73 | (~c1_1(a1676))),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4252, 221, 4774, 4759, 4760, 4773, 1563, 627])).
% 8.99/6.11 tff(4777,plain,
% 8.99/6.11 (hskp73),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4776, 4775])).
% 8.99/6.11 tff(4778,plain,
% 8.99/6.11 (c2_1(a1716)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[1597, 4777])).
% 8.99/6.11 tff(4779,plain,
% 8.99/6.11 (c0_1(a1716)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[1615, 4777])).
% 8.99/6.11 tff(4780,plain,
% 8.99/6.11 (~hskp17),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[3161, 4779, 1662, 4778, 4765, 4764, 4763])).
% 8.99/6.11 tff(4781,plain,
% 8.99/6.11 (hskp17 | hskp16 | c1_1(a1654)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[716, 221, 4761, 4760, 10])).
% 8.99/6.11 tff(4782,plain,
% 8.99/6.11 (hskp16),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4781, 4780, 627])).
% 8.99/6.11 tff(4783,plain,
% 8.99/6.11 (~c0_1(a1677)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[123, 4782])).
% 8.99/6.11 tff(4784,plain,
% 8.99/6.11 (~c1_1(a1677)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[111, 4782])).
% 8.99/6.11 tff(4785,plain,
% 8.99/6.11 (~c2_1(a1677)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[117, 4782])).
% 8.99/6.11 tff(4786,plain,
% 8.99/6.11 (c3_1(a1677)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[798, 4785, 4572, 4760, 4759, 4783, 4761])).
% 8.99/6.11 tff(4787,plain,
% 8.99/6.11 ($false),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[808, 4786, 4784, 138, 4760, 4761, 627, 4783])).
% 8.99/6.11 tff(4788,plain,(c1_1(a1654) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.11 tff(4789,plain,
% 8.99/6.11 (c1_1(a1654)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4788, 1662, 138])).
% 8.99/6.11 tff(4790,assumption,(~hskp26), introduced(assumption)).
% 8.99/6.11 tff(4791,assumption,(hskp12), introduced(assumption)).
% 8.99/6.11 tff(4792,plain,
% 8.99/6.11 (~c1_1(a1666)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[905, 4791])).
% 8.99/6.11 tff(4793,plain,
% 8.99/6.11 (c3_1(a1666)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[916, 4791])).
% 8.99/6.11 tff(4794,plain,
% 8.99/6.11 (c2_1(a1666)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[927, 4791])).
% 8.99/6.11 tff(4795,plain,
% 8.99/6.11 ($false),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[935, 221, 4790, 617, 616, 615, 4794, 4793, 4792, 20])).
% 8.99/6.11 tff(4796,plain,((~hskp12) | hskp26 | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.11 tff(4797,plain,
% 8.99/6.11 (~hskp12),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4796, 4790, 617, 616, 615])).
% 8.99/6.11 tff(4798,plain,
% 8.99/6.11 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4799,plain,
% 8.99/6.11 ((hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715))) <=> (hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4800,plain,
% 8.99/6.11 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715))))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4799])).
% 8.99/6.11 tff(4801,plain,
% 8.99/6.11 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4800, 4798])).
% 8.99/6.11 tff(4802,plain,
% 8.99/6.11 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1715)) | (~c2_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4803,plain,
% 8.99/6.11 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 8.99/6.11 tff(4804,plain,
% 8.99/6.11 (hskp13 | hskp12 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4803, 221, 364, 893])).
% 8.99/6.11 tff(4805,plain,
% 8.99/6.11 (hskp13),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4804, 4797, 2103, 834])).
% 8.99/6.11 tff(4806,plain,
% 8.99/6.11 (~c1_1(a1667)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[303, 4805])).
% 8.99/6.11 tff(4807,plain,
% 8.99/6.11 (c3_1(a1667)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[314, 4805])).
% 8.99/6.11 tff(4808,plain,
% 8.99/6.11 (c0_1(a1667)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[325, 4805])).
% 8.99/6.11 tff(4809,plain,
% 8.99/6.11 (~c2_1(a1667)),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4460, 221, 4790, 4808, 4807, 4806, 20])).
% 8.99/6.11 tff(4810,plain,
% 8.99/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4811,plain,
% 8.99/6.11 (((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667))) <=> (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.11 inference(rewrite,[status(thm)],[])).
% 8.99/6.11 tff(4812,plain,
% 8.99/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.11 inference(monotonicity,[status(thm)],[4811])).
% 8.99/6.11 tff(4813,plain,
% 8.99/6.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.11 inference(transitivity,[status(thm)],[4812, 4810])).
% 8.99/6.11 tff(4814,plain,
% 8.99/6.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1667) | c1_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))),
% 8.99/6.11 inference(quant_inst,[status(thm)],[])).
% 8.99/6.11 tff(4815,plain,
% 8.99/6.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.11 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 8.99/6.11 tff(4816,plain,
% 8.99/6.11 ($false),
% 8.99/6.11 inference(unit_resolution,[status(thm)],[4815, 221, 617, 615, 4808, 4807, 4806, 647, 882, 4809])).
% 8.99/6.11 tff(4817,plain,(hskp26 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1715)) | (~c2_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.12 tff(4818,plain,
% 8.99/6.12 (hskp26),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4817, 4761, 4760, 4789, 4613, 4724, 4571, 4759])).
% 8.99/6.12 tff(4819,plain,
% 8.99/6.12 (~c3_1(a1691)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[689, 4818])).
% 8.99/6.12 tff(4820,plain,
% 8.99/6.12 (~c2_1(a1691)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[669, 4818])).
% 8.99/6.12 tff(4821,plain,
% 8.99/6.12 (c0_1(a1691)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4630, 962, 4759, 4760, 4761, 964, 4572])).
% 8.99/6.12 tff(4822,plain,
% 8.99/6.12 (hskp47),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4666, 221, 4761, 4760, 962, 964, 1848, 4789, 4821])).
% 8.99/6.12 tff(4823,plain,
% 8.99/6.12 (~c0_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1861, 4822])).
% 8.99/6.12 tff(4824,plain,
% 8.99/6.12 (~c1_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1867, 4822])).
% 8.99/6.12 tff(4825,plain,
% 8.99/6.12 (c3_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1880, 4822])).
% 8.99/6.12 tff(4826,assumption,(~c0_1(a1644)), introduced(assumption)).
% 8.99/6.12 tff(4827,assumption,(~c1_1(a1644)), introduced(assumption)).
% 8.99/6.12 tff(4828,assumption,(c3_1(a1644)), introduced(assumption)).
% 8.99/6.12 tff(4829,plain,
% 8.99/6.12 ($false),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1887, 221, 138, 4828, 3313, 3312, 4827, 4826, 3311, 137])).
% 8.99/6.12 tff(4830,plain,((~hskp13) | hskp29 | (~c3_1(a1644)) | c1_1(a1644) | c0_1(a1644)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.12 tff(4831,plain,
% 8.99/6.12 (~hskp13),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4830, 4825, 138, 4824, 4823])).
% 8.99/6.12 tff(4832,plain,
% 8.99/6.12 (hskp13 | hskp12 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4803, 221, 4571, 893])).
% 8.99/6.12 tff(4833,plain,
% 8.99/6.12 (hskp12),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4832, 4831, 4613, 4724])).
% 8.99/6.12 tff(4834,plain,
% 8.99/6.12 (~c1_1(a1666)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[905, 4833])).
% 8.99/6.12 tff(4835,plain,
% 8.99/6.12 (c3_1(a1666)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[916, 4833])).
% 8.99/6.12 tff(4836,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4837,plain,
% 8.99/6.12 ((hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644))) <=> (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4838,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4837])).
% 8.99/6.12 tff(4839,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4838, 4836])).
% 8.99/6.12 tff(4840,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4841,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4840, 4839])).
% 8.99/6.12 tff(4842,plain,
% 8.99/6.12 (~c0_1(a1666)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4841, 221, 138, 4825, 4835, 4824, 4823, 4834, 137])).
% 8.99/6.12 tff(4843,plain,
% 8.99/6.12 (c2_1(a1666)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[927, 4833])).
% 8.99/6.12 tff(4844,plain,
% 8.99/6.12 (hskp26),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[935, 221, 4761, 4759, 4760, 4843, 4835, 4834, 20])).
% 8.99/6.12 tff(4845,plain,
% 8.99/6.12 (~c1_1(a1691)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[675, 4844])).
% 8.99/6.12 tff(4846,plain,
% 8.99/6.12 (~hskp61),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1213, 4845, 4760, 4789, 964, 4821, 4761])).
% 8.99/6.12 tff(4847,plain,
% 8.99/6.12 (~hskp0),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4692, 4846, 4831])).
% 8.99/6.12 tff(4848,plain,
% 8.99/6.12 (c0_1(a1691)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4630, 962, 895, 894, 929, 964, 554])).
% 8.99/6.12 tff(4849,plain,
% 8.99/6.12 (~hskp74),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4710, 963, 962, 964, 4848, 961, 1628])).
% 8.99/6.12 tff(4850,plain,
% 8.99/6.12 (~hskp61),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1213, 961, 615, 882, 964, 940, 617])).
% 8.99/6.12 tff(4851,plain,
% 8.99/6.12 (hskp62 | hskp61 | c0_1(a1715) | (~c1_1(a1715))),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[2225, 221, 2103, 2219])).
% 8.99/6.12 tff(4852,plain,
% 8.99/6.12 (hskp62),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4851, 1297, 834, 4850])).
% 8.99/6.12 tff(4853,plain,
% 8.99/6.12 (c0_1(a1675)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[2237, 4852])).
% 8.99/6.12 tff(4854,plain,
% 8.99/6.12 (~c3_1(a1675)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[2254, 4852])).
% 8.99/6.12 tff(4855,plain,
% 8.99/6.12 (c1_1(a1675)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[2248, 4852])).
% 8.99/6.12 tff(4856,plain,
% 8.99/6.12 (c2_1(a1675)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[2267, 4855, 4854, 4853, 4850])).
% 8.99/6.12 tff(4857,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4858,plain,
% 8.99/6.12 ((hskp2 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c1_1(a1675)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691))) <=> (hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4859,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c1_1(a1675)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4858])).
% 8.99/6.12 tff(4860,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c1_1(a1675)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4859, 4857])).
% 8.99/6.12 tff(4861,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1675) | (~c0_1(a1675)) | (~c1_1(a1675)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4862,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1675) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4861, 4860])).
% 8.99/6.12 tff(4863,plain,
% 8.99/6.12 (hskp2),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4862, 221, 4855, 4853, 4854, 962, 961, 960, 940])).
% 8.99/6.12 tff(4864,plain,
% 8.99/6.12 (~c0_1(a1645)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1122, 4863])).
% 8.99/6.12 tff(4865,plain,
% 8.99/6.12 (~c1_1(a1645)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1128, 4863])).
% 8.99/6.12 tff(4866,plain,
% 8.99/6.12 (hskp47),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4666, 221, 617, 615, 962, 964, 1848, 882, 940])).
% 8.99/6.12 tff(4867,plain,
% 8.99/6.12 (~c1_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1867, 4866])).
% 8.99/6.12 tff(4868,plain,
% 8.99/6.12 (c3_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1880, 4866])).
% 8.99/6.12 tff(4869,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4870,plain,
% 8.99/6.12 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1644) | c2_1(a1644) | (~c3_1(a1644))) <=> (c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4871,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1644) | c2_1(a1644) | (~c3_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4870])).
% 8.99/6.12 tff(4872,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1644) | c2_1(a1644) | (~c3_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4871, 4869])).
% 8.99/6.12 tff(4873,plain,
% 8.99/6.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1644) | c2_1(a1644) | (~c3_1(a1644)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4874,plain,
% 8.99/6.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1644) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1644)) | c2_1(a1644) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4873, 4872])).
% 8.99/6.12 tff(4875,plain,
% 8.99/6.12 (c1_1(a1691) | c2_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4874, 221, 617, 615, 4868, 4867, 964, 647, 882, 940])).
% 8.99/6.12 tff(4876,plain,
% 8.99/6.12 (c2_1(a1644)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4875, 961])).
% 8.99/6.12 tff(4877,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4878,plain,
% 8.99/6.12 ((hskp73 | (~ndr1_0) | c1_1(a1644) | (~c3_1(a1644)) | (~c2_1(a1644)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4879,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1644) | (~c3_1(a1644)) | (~c2_1(a1644)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4878])).
% 8.99/6.12 tff(4880,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1644) | (~c3_1(a1644)) | (~c2_1(a1644)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4879, 4877])).
% 8.99/6.12 tff(4881,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1644) | (~c3_1(a1644)) | (~c2_1(a1644)) | c0_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4882,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715)) | (~c3_1(a1644)) | (~c2_1(a1644))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 8.99/6.12 tff(4883,plain,
% 8.99/6.12 (hskp73),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4882, 221, 834, 2103, 4868, 4867, 1563, 1297, 4876])).
% 8.99/6.12 tff(4884,plain,
% 8.99/6.12 (c0_1(a1716)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1615, 4883])).
% 8.99/6.12 tff(4885,plain,
% 8.99/6.12 (c2_1(a1716)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1597, 4883])).
% 8.99/6.12 tff(4886,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4887,plain,
% 8.99/6.12 (((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4888,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4887])).
% 8.99/6.12 tff(4889,plain,
% 8.99/6.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4888, 4886])).
% 8.99/6.12 tff(4890,plain,
% 8.99/6.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1716) | (~c0_1(a1716)) | (~c2_1(a1716)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4891,plain,
% 8.99/6.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 8.99/6.12 tff(4892,plain,
% 8.99/6.12 (c2_1(a1645)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4891, 221, 4885, 4884, 1662, 962, 961, 964, 4865, 4864, 30])).
% 8.99/6.12 tff(4893,plain,
% 8.99/6.12 (~c3_1(a1645)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1144, 4863])).
% 8.99/6.12 tff(4894,plain,
% 8.99/6.12 (hskp40),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[1151, 221, 617, 615, 4865, 4893, 728, 882, 4892])).
% 8.99/6.12 tff(4895,plain,
% 8.99/6.12 (~c2_1(a1725)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[741, 4894])).
% 8.99/6.12 tff(4896,plain,
% 8.99/6.12 (c3_1(a1725)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[752, 4894])).
% 8.99/6.12 tff(4897,plain,
% 8.99/6.12 (c1_1(a1725)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[763, 4894])).
% 8.99/6.12 tff(4898,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4899,plain,
% 8.99/6.12 ((hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675))) <=> (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4900,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4899])).
% 8.99/6.12 tff(4901,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4900, 4898])).
% 8.99/6.12 tff(4902,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1725) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4903,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 8.99/6.12 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 8.99/6.12 tff(4904,plain,
% 8.99/6.12 ($false),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4903, 221, 963, 4855, 4853, 4897, 4896, 4895, 950, 4856])).
% 8.99/6.12 tff(4905,plain,(c0_1(a1715) | hskp0 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c1_1(a1654)) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | (~c1_1(a1715)) | (~c3_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.12 tff(4906,plain,
% 8.99/6.12 (c0_1(a1715)),
% 8.99/6.12 inference(unit_resolution,[status(thm)],[4905, 963, 929, 894, 882, 1662, 962, 961, 964, 4848, 834, 2103])).
% 8.99/6.12 tff(4907,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4908,plain,
% 8.99/6.12 ((hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715))) <=> (hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.12 inference(rewrite,[status(thm)],[])).
% 8.99/6.12 tff(4909,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718))))),
% 8.99/6.12 inference(monotonicity,[status(thm)],[4908])).
% 8.99/6.12 tff(4910,plain,
% 8.99/6.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.12 inference(transitivity,[status(thm)],[4909, 4907])).
% 8.99/6.12 tff(4911,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c1_1(a1715)) | (~c2_1(a1715)) | (~c0_1(a1715)))),
% 8.99/6.12 inference(quant_inst,[status(thm)],[])).
% 8.99/6.12 tff(4912,plain,
% 8.99/6.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | (~c2_1(a1715)) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 8.99/6.13 tff(4913,plain,
% 8.99/6.13 (~c1_1(a1718)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4912, 221, 963, 834, 982, 364, 971, 950, 1835])).
% 8.99/6.13 tff(4914,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4915,plain,
% 8.99/6.13 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718))) <=> (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4916,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[4915])).
% 8.99/6.13 tff(4917,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718)))),
% 8.99/6.13 inference(transitivity,[status(thm)],[4916, 4914])).
% 8.99/6.13 tff(4918,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1715)) | c1_1(a1718) | c2_1(a1718) | (~c3_1(a1718)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(4919,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4918, 4917])).
% 8.99/6.13 tff(4920,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4919, 221, 834, 2103, 982, 971, 961, 964, 647, 1835, 4913, 940])).
% 8.99/6.13 tff(4921,plain,((~hskp38) | (~c1_1(a1715)) | (~c3_1(a1715)) | c1_1(a1691) | c2_1(a1691) | (~c0_1(a1715)) | (~c0_1(a1691)) | hskp0 | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4922,plain,
% 8.99/6.13 (~hskp38),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4921, 4906, 2103, 961, 964, 834, 4848, 963, 364])).
% 8.99/6.13 tff(4923,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1032, 4922, 4849, 881])).
% 8.99/6.13 tff(4924,plain,(hskp0 | (~hskp52) | (~c3_1(a1715)) | c1_1(a1691) | c2_1(a1691) | (~c1_1(a1715)) | (~c2_1(a1715)) | c3_1(a1691) | hskp57 | (~c1_1(a1654)) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4925,plain,
% 8.99/6.13 (hskp57),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4924, 4847, 4613, 4845, 964, 4724, 4571, 962, 4758, 4789, 1662])).
% 8.99/6.13 tff(4926,plain,
% 8.99/6.13 (~c1_1(a1665)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[65, 4925])).
% 8.99/6.13 tff(4927,plain,
% 8.99/6.13 (c3_1(a1665)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[76, 4925])).
% 8.99/6.13 tff(4928,plain,
% 8.99/6.13 (c0_1(a1665)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[90, 4925])).
% 8.99/6.13 tff(4929,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4930,plain,
% 8.99/6.13 ((hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1666) | c1_1(a1666) | (~c3_1(a1666))) <=> (hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4931,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1666) | c1_1(a1666) | (~c3_1(a1666)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[4930])).
% 8.99/6.13 tff(4932,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1666) | c1_1(a1666) | (~c3_1(a1666)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.13 inference(transitivity,[status(thm)],[4931, 4929])).
% 8.99/6.13 tff(4933,plain,
% 8.99/6.13 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1666) | c1_1(a1666) | (~c3_1(a1666)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(4934,plain,
% 8.99/6.13 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4933, 4932])).
% 8.99/6.13 tff(4935,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4934, 221, 138, 4928, 4927, 4835, 4926, 4834, 137, 4842])).
% 8.99/6.13 tff(4936,plain,(c3_1(a1691) | hskp29 | c2_1(a1691) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4937,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4936, 4820, 4819, 138, 1662])).
% 8.99/6.13 tff(4938,plain,(c3_1(a1716) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4939,plain,
% 8.99/6.13 (c3_1(a1716)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4938, 138])).
% 8.99/6.13 tff(4940,plain,
% 8.99/6.13 (~hskp73),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1575, 4939])).
% 8.99/6.13 tff(4941,plain,
% 8.99/6.13 (~c1_1(a1676)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4252, 221, 4940, 2055, 616, 615, 2044, 1563, 627])).
% 8.99/6.13 tff(4942,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4245, 221, 138, 2055, 617, 615, 2044, 137, 4941, 627])).
% 8.99/6.13 tff(4943,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4944,plain,
% 8.99/6.13 (c1_1(a1654)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4943, 2001, 138, 2000, 1999])).
% 8.99/6.13 tff(4945,plain,
% 8.99/6.13 (hskp0),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3783, 4944, 363, 1998, 1900, 1296, 138, 1834])).
% 8.99/6.13 tff(4946,plain,
% 8.99/6.13 (~hskp61),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3391, 4944, 1998, 1296, 2000, 1834, 2001])).
% 8.99/6.13 tff(4947,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3578, 4946, 4945, 363, 1296, 1834])).
% 8.99/6.13 tff(4948,plain,(c3_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4949,plain,
% 8.99/6.13 (c3_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4948, 138])).
% 8.99/6.13 tff(4950,plain,
% 8.99/6.13 (~c2_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4608, 365, 139, 138])).
% 8.99/6.13 tff(4951,plain,
% 8.99/6.13 (c0_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3321, 365, 138, 4949, 359])).
% 8.99/6.13 tff(4952,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4192, 4951, 4950, 4949, 365, 151])).
% 8.99/6.13 tff(4953,plain,(c1_1(a1715) | hskp29 | hskp52), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4954,plain,
% 8.99/6.13 (c1_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4953, 139, 138])).
% 8.99/6.13 tff(4955,plain,
% 8.99/6.13 (~c2_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4757, 4954, 138, 139])).
% 8.99/6.13 tff(4956,plain,
% 8.99/6.13 (~c0_1(a1715)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4489, 4955, 138, 4949, 151, 362, 361, 360])).
% 8.99/6.13 tff(4957,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4958,plain,
% 8.99/6.13 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656))) <=> (c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4959,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656))))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[4958])).
% 8.99/6.13 tff(4960,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.99/6.13 inference(transitivity,[status(thm)],[4959, 4957])).
% 8.99/6.13 tff(4961,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1656) | c1_1(a1656) | (~c0_1(a1656)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(4962,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1656) | (~c0_1(a1656))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4961, 4960])).
% 8.99/6.13 tff(4963,plain,
% 8.99/6.13 (c1_1(a1656)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4962, 221, 4949, 162, 230, 229, 4955, 168, 231, 410, 4956])).
% 8.99/6.13 tff(4964,plain,
% 8.99/6.13 (hskp61),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[2925, 4956, 4955, 4954])).
% 8.99/6.13 tff(4965,plain,
% 8.99/6.13 (~c2_1(a1674)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1187, 4964])).
% 8.99/6.13 tff(4966,plain,
% 8.99/6.13 (~c1_1(a1674)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1193, 4964])).
% 8.99/6.13 tff(4967,plain,
% 8.99/6.13 (c3_1(a1674)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1204, 4964])).
% 8.99/6.13 tff(4968,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4969,plain,
% 8.99/6.13 (((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4970,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674))))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[4969])).
% 8.99/6.13 tff(4971,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674)))),
% 8.99/6.13 inference(transitivity,[status(thm)],[4970, 4968])).
% 8.99/6.13 tff(4972,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1674) | c1_1(a1674) | (~c0_1(a1674)) | (~c3_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1655)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(4973,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c3_1(a1674)) | (~c0_1(a1674))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4972, 4971])).
% 8.99/6.13 tff(4974,plain,
% 8.99/6.13 (~c0_1(a1674)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4973, 221, 4967, 230, 229, 4966, 4965, 647, 358])).
% 8.99/6.13 tff(4975,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4976,plain,
% 8.99/6.13 (((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656))) <=> (c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(4977,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674)))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[4976])).
% 8.99/6.13 tff(4978,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.13 inference(transitivity,[status(thm)],[4977, 4975])).
% 8.99/6.13 tff(4979,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1656) | (~c2_1(a1656)) | (~c1_1(a1656)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(4980,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674)),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[4979, 4978])).
% 8.99/6.13 tff(4981,plain,
% 8.99/6.13 ($false),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4980, 221, 4967, 179, 362, 361, 4966, 168, 360, 102, 4974, 4963])).
% 8.99/6.13 tff(4982,plain,(hskp52 | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.13 tff(4983,plain,
% 8.99/6.13 (hskp52),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4982, 138])).
% 8.99/6.13 tff(4984,plain,
% 8.99/6.13 (c0_1(a1654)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[525, 4983])).
% 8.99/6.13 tff(4985,plain,
% 8.99/6.13 (c2_1(a1654)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[547, 4983])).
% 8.99/6.13 tff(4986,plain,
% 8.99/6.13 (c3_1(a1716)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3382, 1309, 1297])).
% 8.99/6.13 tff(4987,plain,
% 8.99/6.13 (~hskp13),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3321, 138, 365, 2096, 1297])).
% 8.99/6.13 tff(4988,assumption,(c3_1(a1716)), introduced(assumption)).
% 8.99/6.13 tff(4989,plain,
% 8.99/6.13 (~hskp73),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[1575, 4988])).
% 8.99/6.13 tff(4990,plain,
% 8.99/6.13 (c1_1(a1654)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[3879, 3031, 4989, 3021, 3240, 3239, 3022, 138])).
% 8.99/6.13 tff(4991,plain,
% 8.99/6.13 (hskp12 | (~c1_1(a1654))),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[898, 221, 883, 3031, 3021, 893])).
% 8.99/6.13 tff(4992,plain,
% 8.99/6.13 (hskp12),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[4991, 882])).
% 8.99/6.13 tff(4993,plain,
% 8.99/6.13 (~c1_1(a1666)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[905, 4992])).
% 8.99/6.13 tff(4994,plain,
% 8.99/6.13 (c3_1(a1666)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[916, 4992])).
% 8.99/6.13 tff(4995,plain,
% 8.99/6.13 (c2_1(a1666)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[927, 4992])).
% 8.99/6.13 tff(4996,plain,
% 8.99/6.13 (hskp26),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[935, 221, 3022, 3031, 3021, 4995, 4994, 4993, 20])).
% 8.99/6.13 tff(4997,plain,
% 8.99/6.13 (~c2_1(a1691)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[669, 4996])).
% 8.99/6.13 tff(4998,plain,
% 8.99/6.13 (~c1_1(a1691)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[675, 4996])).
% 8.99/6.13 tff(4999,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5000,plain,
% 8.99/6.13 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715))) <=> (c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5001,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[5000])).
% 8.99/6.13 tff(5002,plain,
% 8.99/6.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.13 inference(transitivity,[status(thm)],[5001, 4999])).
% 8.99/6.13 tff(5003,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(5004,plain,
% 8.99/6.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[5003, 5002])).
% 8.99/6.13 tff(5005,plain,
% 8.99/6.13 (~c0_1(a1691)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[5004, 221, 365, 2103, 3022, 3021, 1309, 4998, 4997, 647, 882])).
% 8.99/6.13 tff(5006,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5007,plain,
% 8.99/6.13 ((hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716))) <=> (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5008,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716)))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[5007])).
% 8.99/6.13 tff(5009,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716))),
% 8.99/6.13 inference(transitivity,[status(thm)],[5008, 5006])).
% 8.99/6.13 tff(5010,plain,
% 8.99/6.13 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))),
% 8.99/6.13 inference(quant_inst,[status(thm)],[])).
% 8.99/6.13 tff(5011,plain,
% 8.99/6.13 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716)),
% 8.99/6.13 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 8.99/6.13 tff(5012,plain,
% 8.99/6.13 (~c0_1(a1666)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[5011, 221, 138, 2097, 4994, 4988, 4993, 137, 1617])).
% 8.99/6.13 tff(5013,plain,
% 8.99/6.13 (~c3_1(a1691)),
% 8.99/6.13 inference(unit_resolution,[status(thm)],[689, 4996])).
% 8.99/6.13 tff(5014,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5015,plain,
% 8.99/6.13 ((hskp70 | (~ndr1_0) | c0_1(a1666) | c1_1(a1666) | (~c2_1(a1666)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691)) <=> (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691))),
% 8.99/6.13 inference(rewrite,[status(thm)],[])).
% 8.99/6.13 tff(5016,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1666) | c1_1(a1666) | (~c2_1(a1666)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691)))),
% 8.99/6.13 inference(monotonicity,[status(thm)],[5015])).
% 8.99/6.13 tff(5017,plain,
% 8.99/6.13 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1666) | c1_1(a1666) | (~c2_1(a1666)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5016, 5014])).
% 8.99/6.14 tff(5018,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1666) | c1_1(a1666) | (~c2_1(a1666)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5019,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1666) | (~ndr1_0) | (~c2_1(a1666)) | c0_1(a1666) | c0_1(a1691)),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5018, 5017])).
% 8.99/6.14 tff(5020,plain,
% 8.99/6.14 (hskp70 | c0_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5019, 221, 4995, 5013, 4997, 4993, 2131, 5012])).
% 8.99/6.14 tff(5021,plain,
% 8.99/6.14 (hskp70),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5020, 5005])).
% 8.99/6.14 tff(5022,plain,
% 8.99/6.14 (~c3_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2184, 5021])).
% 8.99/6.14 tff(5023,plain,
% 8.99/6.14 (~c0_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2190, 5021])).
% 8.99/6.14 tff(5024,plain,
% 8.99/6.14 (c1_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2201, 5021])).
% 8.99/6.14 tff(5025,plain,
% 8.99/6.14 (c2_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2208, 221, 1345, 5024, 5023, 5022, 1357])).
% 8.99/6.14 tff(5026,plain,
% 8.99/6.14 (hskp37 | c0_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[696, 221, 2400, 5013, 4997, 577])).
% 8.99/6.14 tff(5027,plain,
% 8.99/6.14 (hskp37),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5026, 5005])).
% 8.99/6.14 tff(5028,plain,
% 8.99/6.14 (c0_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[602, 5027])).
% 8.99/6.14 tff(5029,plain,
% 8.99/6.14 (c2_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[613, 5027])).
% 8.99/6.14 tff(5030,plain,
% 8.99/6.14 (((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))) <=> ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5031,plain,
% 8.99/6.14 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp42 | hskp0 | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5032,plain,
% 8.99/6.14 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5031, 5030])).
% 8.99/6.14 tff(5033,plain,
% 8.99/6.14 (c3_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5032, 221, 1073, 963, 5029, 5028, 1043])).
% 8.99/6.14 tff(5034,plain,
% 8.99/6.14 (~c1_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[591, 5027])).
% 8.99/6.14 tff(5035,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5036,plain,
% 8.99/6.14 (((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710))) <=> (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5037,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716)))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5036])).
% 8.99/6.14 tff(5038,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5037, 5035])).
% 8.99/6.14 tff(5039,plain,
% 8.99/6.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1714) | (~c3_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | (~c2_1(a1710)) | (~c1_1(a1710)))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5040,plain,
% 8.99/6.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716)),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5039, 5038])).
% 8.99/6.14 tff(5041,plain,
% 8.99/6.14 ($false),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5040, 221, 2097, 5024, 5028, 4988, 5022, 5034, 102, 5033, 5025, 1617])).
% 8.99/6.14 tff(5042,plain,((~c1_1(a1654)) | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1716) | hskp21 | hskp42 | hskp0 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715) | hskp29 | hskp13), inference(lemma,lemma(discharge,[]))).
% 8.99/6.14 tff(5043,plain,
% 8.99/6.14 (hskp21),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5042, 4990, 4988, 1617, 2097, 1073, 963, 365, 2103, 1309, 138, 883])).
% 8.99/6.14 tff(5044,plain,
% 8.99/6.14 (~c1_1(a1683)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[1417, 5043])).
% 8.99/6.14 tff(5045,plain,
% 8.99/6.14 (c2_1(a1683)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[1383, 5043])).
% 8.99/6.14 tff(5046,plain,
% 8.99/6.14 (c3_1(a1683)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[1394, 5043])).
% 8.99/6.14 tff(5047,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5048,plain,
% 8.99/6.14 ((hskp26 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5049,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5048])).
% 8.99/6.14 tff(5050,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5049, 5047])).
% 8.99/6.14 tff(5051,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5052,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 8.99/6.14 tff(5053,plain,
% 8.99/6.14 (hskp26),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5052, 221, 3022, 3031, 3021, 5046, 5045, 5044, 20])).
% 8.99/6.14 tff(5054,plain,
% 8.99/6.14 (~c2_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[669, 5053])).
% 8.99/6.14 tff(5055,plain,
% 8.99/6.14 (~c1_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[675, 5053])).
% 8.99/6.14 tff(5056,plain,
% 8.99/6.14 (~c0_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5004, 221, 365, 2103, 3022, 3021, 1309, 5055, 5054, 647, 4990])).
% 8.99/6.14 tff(5057,plain,
% 8.99/6.14 (~c3_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[689, 5053])).
% 8.99/6.14 tff(5058,plain,
% 8.99/6.14 (hskp37 | c0_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[696, 221, 2400, 5057, 5054, 577])).
% 8.99/6.14 tff(5059,plain,
% 8.99/6.14 (hskp37),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5058, 5056])).
% 8.99/6.14 tff(5060,plain,
% 8.99/6.14 (c0_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[602, 5059])).
% 8.99/6.14 tff(5061,plain,
% 8.99/6.14 (c2_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[613, 5059])).
% 8.99/6.14 tff(5062,plain,
% 8.99/6.14 (c3_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5032, 221, 1073, 963, 5061, 5060, 1043])).
% 8.99/6.14 tff(5063,plain,
% 8.99/6.14 (~c1_1(a1714)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[591, 5059])).
% 8.99/6.14 tff(5064,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5065,plain,
% 8.99/6.14 ((hskp29 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c0_1(a1683)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716))) <=> (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5066,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c0_1(a1683)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716)))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5065])).
% 8.99/6.14 tff(5067,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c0_1(a1683)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5066, 5064])).
% 8.99/6.14 tff(5068,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c0_1(a1683)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5069,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c0_1(a1683)) | c1_1(a1716)),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5068, 5067])).
% 8.99/6.14 tff(5070,plain,
% 8.99/6.14 (~c0_1(a1683)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5069, 221, 138, 2097, 5046, 4988, 5044, 137, 1617])).
% 8.99/6.14 tff(5071,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5072,plain,
% 8.99/6.14 ((hskp70 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c2_1(a1683)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691)) <=> (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5073,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c2_1(a1683)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691)))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5072])).
% 8.99/6.14 tff(5074,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c2_1(a1683)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))) <=> ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5073, 5071])).
% 8.99/6.14 tff(5075,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp70 | (~ndr1_0) | c0_1(a1683) | c1_1(a1683) | (~c2_1(a1683)) | c3_1(a1691) | c0_1(a1691) | c2_1(a1691))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5076,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp70 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp70 | c3_1(a1691) | c2_1(a1691) | c1_1(a1683) | (~ndr1_0) | (~c2_1(a1683)) | c0_1(a1683) | c0_1(a1691)),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 8.99/6.14 tff(5077,plain,
% 8.99/6.14 (hskp70 | c0_1(a1691)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5076, 221, 5045, 5057, 5054, 5044, 2131, 5070])).
% 8.99/6.14 tff(5078,plain,
% 8.99/6.14 (hskp70),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5077, 5056])).
% 8.99/6.14 tff(5079,plain,
% 8.99/6.14 (~c3_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2184, 5078])).
% 8.99/6.14 tff(5080,plain,
% 8.99/6.14 (c1_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2201, 5078])).
% 8.99/6.14 tff(5081,plain,
% 8.99/6.14 (~c2_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5040, 221, 2097, 5080, 5060, 4988, 5079, 5063, 102, 5062, 1617])).
% 8.99/6.14 tff(5082,plain,
% 8.99/6.14 (~c0_1(a1710)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[2190, 5078])).
% 8.99/6.14 tff(5083,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5084,plain,
% 8.99/6.14 (((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | c2_1(a1710) | c0_1(a1710)) <=> (c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5085,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | c2_1(a1710) | c0_1(a1710))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5084])).
% 8.99/6.14 tff(5086,plain,
% 8.99/6.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | c2_1(a1710) | c0_1(a1710))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5085, 5083])).
% 8.99/6.14 tff(5087,plain,
% 8.99/6.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1710) | c2_1(a1710) | c0_1(a1710))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5088,plain,
% 8.99/6.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 8.99/6.14 tff(5089,plain,
% 8.99/6.14 ($false),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5088, 221, 3022, 3031, 3021, 5061, 5060, 5082, 5079, 5063, 565, 5081])).
% 8.99/6.14 tff(5090,plain,(hskp42 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1716) | hskp0 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715) | hskp29 | hskp13), inference(lemma,lemma(discharge,[]))).
% 8.99/6.14 tff(5091,plain,
% 8.99/6.14 (hskp42),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5090, 138, 4986, 1617, 963, 365, 2096, 1309, 2097, 4987])).
% 8.99/6.14 tff(5092,plain,
% 8.99/6.14 (~c3_1(a1638)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[1087, 5091])).
% 8.99/6.14 tff(5093,plain,
% 8.99/6.14 (c1_1(a1638)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[1109, 5091])).
% 8.99/6.14 tff(5094,assumption,(hskp75), introduced(assumption)).
% 8.99/6.14 tff(5095,plain,
% 8.99/6.14 (~c2_1(a1724)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[441, 5094])).
% 8.99/6.14 tff(5096,plain,
% 8.99/6.14 (c0_1(a1724)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[485, 5094])).
% 8.99/6.14 tff(5097,plain,
% 8.99/6.14 (c3_1(a1724)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[474, 5094])).
% 8.99/6.14 tff(5098,plain,
% 8.99/6.14 ($false),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[3331, 5097, 5096, 365, 138, 2103, 1297, 5095])).
% 8.99/6.14 tff(5099,plain,((~hskp75) | c1_1(a1715) | hskp29 | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.14 tff(5100,plain,
% 8.99/6.14 (~hskp75),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5099, 138, 365, 2096, 1297])).
% 8.99/6.14 tff(5101,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5102,plain,
% 8.99/6.14 ((hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638))) <=> (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5103,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716)))),
% 8.99/6.14 inference(monotonicity,[status(thm)],[5102])).
% 8.99/6.14 tff(5104,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.14 inference(transitivity,[status(thm)],[5103, 5101])).
% 8.99/6.14 tff(5105,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1638)))),
% 8.99/6.14 inference(quant_inst,[status(thm)],[])).
% 8.99/6.14 tff(5106,plain,
% 8.99/6.14 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1716)),
% 8.99/6.14 inference(modus_ponens,[status(thm)],[5105, 5104])).
% 8.99/6.14 tff(5107,plain,
% 8.99/6.14 (~c2_1(a1638)),
% 8.99/6.14 inference(unit_resolution,[status(thm)],[5106, 5100, 221, 2057, 5093, 4986, 5092, 428, 1617])).
% 8.99/6.14 tff(5108,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5109,plain,
% 8.99/6.14 ((hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638))) <=> (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.14 inference(rewrite,[status(thm)],[])).
% 8.99/6.14 tff(5110,plain,
% 8.99/6.14 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5109])).
% 8.99/6.15 tff(5111,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5110, 5108])).
% 8.99/6.15 tff(5112,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5113,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | c1_1(a1716)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5112, 5111])).
% 8.99/6.15 tff(5114,plain,
% 8.99/6.15 (hskp69),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5113, 221, 2097, 5093, 4986, 5092, 1412, 5107, 1617])).
% 8.99/6.15 tff(5115,plain,
% 8.99/6.15 (~c1_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1431, 5114])).
% 8.99/6.15 tff(5116,plain,
% 8.99/6.15 (c3_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1442, 5114])).
% 8.99/6.15 tff(5117,plain,
% 8.99/6.15 (c0_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1453, 5114])).
% 8.99/6.15 tff(5118,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5119,plain,
% 8.99/6.15 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716))) <=> (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5120,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5119])).
% 8.99/6.15 tff(5121,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5120, 5118])).
% 8.99/6.15 tff(5122,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5123,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5122, 5121])).
% 8.99/6.15 tff(5124,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5123, 221, 138, 2097, 5117, 5116, 4986, 5115, 137, 1617])).
% 8.99/6.15 tff(5125,plain,(hskp29 | c0_1(a1716) | c1_1(a1716) | c2_1(a1716) | hskp0 | c1_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5126,plain,
% 8.99/6.15 (hskp29),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5125, 963, 1617, 2057, 2097, 365, 1309, 1297])).
% 8.99/6.15 tff(5127,plain,
% 8.99/6.15 (hskp42),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2575, 5126, 963])).
% 8.99/6.15 tff(5128,plain,
% 8.99/6.15 (c0_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2074, 5126])).
% 8.99/6.15 tff(5129,plain,
% 8.99/6.15 (~c3_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2063, 5126])).
% 8.99/6.15 tff(5130,plain,
% 8.99/6.15 (c2_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2085, 5126])).
% 8.99/6.15 tff(5131,assumption,(c1_1(a1695)), introduced(assumption)).
% 8.99/6.15 tff(5132,assumption,(~c3_1(a1695)), introduced(assumption)).
% 8.99/6.15 tff(5133,assumption,(c2_1(a1695)), introduced(assumption)).
% 8.99/6.15 tff(5134,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5135,plain,
% 8.99/6.15 ((hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695))) <=> (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5136,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5135])).
% 8.99/6.15 tff(5137,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5136, 5134])).
% 8.99/6.15 tff(5138,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp75 | (~ndr1_0) | c2_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~c1_1(a1695)) | (~c2_1(a1695)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5139,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c2_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5138, 5137])).
% 8.99/6.15 tff(5140,plain,
% 8.99/6.15 (hskp75 | (~c1_1(a1695))),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5139, 221, 2057, 5133, 4988, 5132, 428, 1617])).
% 8.99/6.15 tff(5141,plain,
% 8.99/6.15 (hskp75),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5140, 5131])).
% 8.99/6.15 tff(5142,plain,
% 8.99/6.15 (~c2_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[441, 5141])).
% 8.99/6.15 tff(5143,assumption,(c0_1(a1695)), introduced(assumption)).
% 8.99/6.15 tff(5144,plain,
% 8.99/6.15 (c3_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[474, 5141])).
% 8.99/6.15 tff(5145,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724)))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5146,plain,
% 8.99/6.15 ((hskp0 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695))) <=> (hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724)))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5147,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724))))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5146])).
% 8.99/6.15 tff(5148,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724)))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5147, 5145])).
% 8.99/6.15 tff(5149,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c1_1(a1724)) | (~c1_1(a1695)) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5150,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1724) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1724)) | (~c1_1(a1724))),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 8.99/6.15 tff(5151,plain,
% 8.99/6.15 (~c1_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5150, 221, 963, 5144, 5133, 5143, 5142, 950, 5131])).
% 8.99/6.15 tff(5152,plain,
% 8.99/6.15 (c0_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[485, 5141])).
% 8.99/6.15 tff(5153,plain,
% 8.99/6.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5154,plain,
% 8.99/6.15 (((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5155,plain,
% 8.99/6.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5154])).
% 8.99/6.15 tff(5156,plain,
% 8.99/6.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5155, 5153])).
% 8.99/6.15 tff(5157,plain,
% 8.99/6.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5158,plain,
% 8.99/6.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5157, 5156])).
% 8.99/6.15 tff(5159,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5158, 221, 5152, 5144, 2097, 5133, 4988, 5132, 102, 5151, 1617, 5131])).
% 8.99/6.15 tff(5160,plain,((~c1_1(a1695)) | c0_1(a1716) | (~c2_1(a1695)) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1716) | hskp0 | (~c0_1(a1695)) | c2_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5161,plain,
% 8.99/6.15 (~c1_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5160, 5130, 2097, 4986, 5129, 1617, 963, 5128, 2057])).
% 8.99/6.15 tff(5162,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5163,plain,
% 8.99/6.15 ((hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716))) <=> (hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5164,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5163])).
% 8.99/6.15 tff(5165,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5164, 5162])).
% 8.99/6.15 tff(5166,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5167,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 8.99/6.15 tff(5168,plain,
% 8.99/6.15 (hskp60 | c1_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5167, 221, 2097, 5130, 4986, 5129, 386, 1617])).
% 8.99/6.15 tff(5169,plain,
% 8.99/6.15 (hskp60),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5168, 5161])).
% 8.99/6.15 tff(5170,plain,
% 8.99/6.15 (~c1_1(a1673)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[399, 5169])).
% 8.99/6.15 tff(5171,plain,
% 8.99/6.15 (c3_1(a1673)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[463, 5169])).
% 8.99/6.15 tff(5172,plain,
% 8.99/6.15 (~hskp73),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1575, 4986])).
% 8.99/6.15 tff(5173,plain,
% 8.99/6.15 (c2_1(a1673)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[452, 5169])).
% 8.99/6.15 tff(5174,plain,
% 8.99/6.15 (~hskp30),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2522, 5173, 5172, 5171, 5170])).
% 8.99/6.15 tff(5175,plain,
% 8.99/6.15 (hskp75),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2566, 5174, 365, 1297, 5127, 1309])).
% 8.99/6.15 tff(5176,plain,
% 8.99/6.15 (~c2_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[441, 5175])).
% 8.99/6.15 tff(5177,plain,
% 8.99/6.15 (c0_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[485, 5175])).
% 8.99/6.15 tff(5178,plain,
% 8.99/6.15 (c3_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[474, 5175])).
% 8.99/6.15 tff(5179,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2891, 5178, 5177, 5169, 5176, 1309, 1297])).
% 8.99/6.15 tff(5180,plain,(hskp0 | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c0_1(a1716) | c1_1(a1716) | c2_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5181,plain,
% 8.99/6.15 (hskp0),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5180, 2097, 1297, 365, 1309, 1617, 2057])).
% 8.99/6.15 tff(5182,plain,
% 8.99/6.15 (c0_1(a1637)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1180, 5181])).
% 8.99/6.15 tff(5183,plain,
% 8.99/6.15 (~c2_1(a1637)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1169, 5181])).
% 8.99/6.15 tff(5184,plain,
% 8.99/6.15 (c1_1(a1637)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1224, 5181])).
% 8.99/6.15 tff(5185,plain,
% 8.99/6.15 (~c3_1(a1637)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1237, 4987, 1229, 1228, 1227])).
% 8.99/6.15 tff(5186,plain,
% 8.99/6.15 (hskp61),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1258, 5185, 1229, 1228, 1227])).
% 8.99/6.15 tff(5187,plain,
% 8.99/6.15 (~c1_1(a1674)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1193, 5186])).
% 8.99/6.15 tff(5188,plain,
% 8.99/6.15 (~c2_1(a1674)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1187, 5186])).
% 8.99/6.15 tff(5189,plain,
% 8.99/6.15 (c3_1(a1674)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1204, 5186])).
% 8.99/6.15 tff(5190,plain,
% 8.99/6.15 (~c0_1(a1674)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2797, 5189, 138, 5188, 5187, 1309, 1297, 5100])).
% 8.99/6.15 tff(5191,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5192,plain,
% 8.99/6.15 ((hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637))) <=> (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5193,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716)))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5192])).
% 8.99/6.15 tff(5194,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5193, 5191])).
% 8.99/6.15 tff(5195,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5196,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c0_1(a1716) | (~c3_1(a1716)) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c1_1(a1716)),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 8.99/6.15 tff(5197,plain,
% 8.99/6.15 (hskp69),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5196, 221, 2097, 1229, 4986, 1227, 1412, 5185, 1617])).
% 8.99/6.15 tff(5198,plain,
% 8.99/6.15 (~c1_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1431, 5197])).
% 8.99/6.15 tff(5199,plain,
% 8.99/6.15 (c3_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1442, 5197])).
% 8.99/6.15 tff(5200,plain,
% 8.99/6.15 (c0_1(a1709)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[1453, 5197])).
% 8.99/6.15 tff(5201,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5202,plain,
% 8.99/6.15 ((hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674))) <=> (hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5203,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709))))),
% 8.99/6.15 inference(monotonicity,[status(thm)],[5202])).
% 8.99/6.15 tff(5204,plain,
% 8.99/6.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709)))),
% 8.99/6.15 inference(transitivity,[status(thm)],[5203, 5201])).
% 8.99/6.15 tff(5205,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))),
% 8.99/6.15 inference(quant_inst,[status(thm)],[])).
% 8.99/6.15 tff(5206,plain,
% 8.99/6.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 8.99/6.15 inference(modus_ponens,[status(thm)],[5205, 5204])).
% 8.99/6.15 tff(5207,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5206, 221, 138, 5200, 5199, 5189, 5198, 5187, 137, 5190])).
% 8.99/6.15 tff(5208,plain,(hskp29 | c0_1(a1716) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1716) | c2_1(a1715) | c0_1(a1715) | (~c0_1(a1637)) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5209,plain,
% 8.99/6.15 (hskp29),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5208, 2097, 5184, 5183, 1617, 1309, 1297, 5182, 365])).
% 8.99/6.15 tff(5210,plain,
% 8.99/6.15 (~c3_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2063, 5209])).
% 8.99/6.15 tff(5211,plain,
% 8.99/6.15 (c2_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2085, 5209])).
% 8.99/6.15 tff(5212,plain,
% 8.99/6.15 (hskp30),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2546, 5181, 365, 2096, 1297])).
% 8.99/6.15 tff(5213,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2522, 2882, 2883, 2104, 2486, 2881])).
% 8.99/6.15 tff(5214,plain,((~hskp60) | hskp73 | (~hskp30)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5215,plain,
% 8.99/6.15 (~hskp60),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5214, 5212, 5172])).
% 8.99/6.15 tff(5216,plain,
% 8.99/6.15 (c1_1(a1695)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5167, 221, 5215, 2097, 5211, 4986, 5210, 386, 1617])).
% 8.99/6.15 tff(5217,plain,
% 8.99/6.15 (hskp75 | (~c1_1(a1695))),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5139, 221, 2057, 5211, 4986, 5210, 428, 1617])).
% 8.99/6.15 tff(5218,plain,
% 8.99/6.15 (hskp75),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5217, 5216])).
% 8.99/6.15 tff(5219,plain,
% 8.99/6.15 (c3_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[474, 5218])).
% 8.99/6.15 tff(5220,plain,
% 8.99/6.15 (c0_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[485, 5218])).
% 8.99/6.15 tff(5221,plain,
% 8.99/6.15 ($false),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5158, 221, 2293, 2298, 2097, 5133, 4988, 5132, 102, 2299, 1617, 5131])).
% 8.99/6.15 tff(5222,plain,(c1_1(a1724) | (~c0_1(a1724)) | (~c3_1(a1724)) | c0_1(a1716) | (~c2_1(a1695)) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1716) | (~c1_1(a1695))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.15 tff(5223,plain,
% 8.99/6.15 (c1_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5222, 5220, 5219, 2097, 5211, 4986, 5210, 1617, 5216])).
% 8.99/6.15 tff(5224,plain,
% 8.99/6.15 (~c2_1(a1724)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[441, 5218])).
% 8.99/6.15 tff(5225,plain,
% 8.99/6.15 (hskp13 | (~c1_1(a1724))),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[2315, 221, 5220, 5219, 5224, 290])).
% 8.99/6.15 tff(5226,plain,
% 8.99/6.15 (hskp13),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[5225, 5223])).
% 8.99/6.15 tff(5227,plain,
% 8.99/6.15 (~c1_1(a1667)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[303, 5226])).
% 8.99/6.15 tff(5228,plain,
% 8.99/6.15 (c3_1(a1667)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[314, 5226])).
% 8.99/6.15 tff(5229,plain,
% 8.99/6.15 (c0_1(a1667)),
% 8.99/6.15 inference(unit_resolution,[status(thm)],[325, 5226])).
% 8.99/6.15 tff(5230,plain,
% 8.99/6.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.15 inference(rewrite,[status(thm)],[])).
% 8.99/6.15 tff(5231,plain,
% 8.99/6.15 (((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5232,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716)))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5231])).
% 8.99/6.16 tff(5233,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5232, 5230])).
% 8.99/6.16 tff(5234,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5235,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716)),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5234, 5233])).
% 8.99/6.16 tff(5236,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5235, 221, 2097, 5211, 5229, 5228, 4986, 5210, 5227, 102, 1617, 5216])).
% 8.99/6.16 tff(5237,plain,(c0_1(a1716) | c1_1(a1716) | c2_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5238,plain,
% 8.99/6.16 (c0_1(a1716)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5237, 2057, 1617, 1309, 1297, 365])).
% 8.99/6.16 tff(5239,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5240,plain,
% 8.99/6.16 ((hskp29 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5241,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5240])).
% 8.99/6.16 tff(5242,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5241, 5239])).
% 8.99/6.16 tff(5243,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5244,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 8.99/6.16 tff(5245,plain,
% 8.99/6.16 (hskp29 | (~c0_1(a1716))),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5244, 221, 365, 2096, 4986, 137, 1297, 1617])).
% 8.99/6.16 tff(5246,plain,
% 8.99/6.16 (hskp29),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5245, 5238])).
% 8.99/6.16 tff(5247,plain,
% 8.99/6.16 (~c3_1(a1695)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2063, 5246])).
% 8.99/6.16 tff(5248,plain,
% 8.99/6.16 (c2_1(a1695)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2085, 5246])).
% 8.99/6.16 tff(5249,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5250,plain,
% 8.99/6.16 (((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5251,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5250])).
% 8.99/6.16 tff(5252,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5251, 5249])).
% 8.99/6.16 tff(5253,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5254,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5253, 5252])).
% 8.99/6.16 tff(5255,plain,
% 8.99/6.16 (~c1_1(a1695)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5254, 221, 5238, 365, 2096, 5248, 4986, 5247, 102, 1297, 1617])).
% 8.99/6.16 tff(5256,plain,
% 8.99/6.16 (c0_1(a1695)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2074, 5246])).
% 8.99/6.16 tff(5257,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5258,plain,
% 8.99/6.16 (((~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5259,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5258])).
% 8.99/6.16 tff(5260,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5259, 5257])).
% 8.99/6.16 tff(5261,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5262,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716))),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 8.99/6.16 tff(5263,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5262, 221, 2057, 5238, 2096, 5256, 4986, 1309, 5247, 410, 1297, 5255])).
% 8.99/6.16 tff(5264,plain,(c2_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5265,plain,
% 8.99/6.16 (c2_1(a1716)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5264, 1617, 1297, 365, 1309])).
% 8.99/6.16 tff(5266,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5267,plain,
% 8.99/6.16 ((hskp73 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698))) <=> (hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5268,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716)))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5267])).
% 8.99/6.16 tff(5269,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5268, 5266])).
% 8.99/6.16 tff(5270,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5271,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716)),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5270, 5269])).
% 8.99/6.16 tff(5272,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5271, 221, 4989, 1663, 2514, 2503, 4988, 2492, 1563, 1617])).
% 8.99/6.16 tff(5273,plain,((~hskp30) | (~c2_1(a1716)) | (~c3_1(a1716)) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5274,plain,
% 8.99/6.16 (~hskp30),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5273, 5265, 4986, 1617])).
% 8.99/6.16 tff(5275,plain,
% 8.99/6.16 (~hskp0),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2546, 5274, 365, 2096, 1297])).
% 8.99/6.16 tff(5276,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5277,plain,
% 8.99/6.16 (((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716))) <=> (c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5278,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5277])).
% 8.99/6.16 tff(5279,plain,
% 8.99/6.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5278, 5276])).
% 8.99/6.16 tff(5280,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c2_1(a1715) | (~c3_1(a1715)) | c1_1(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5281,plain,
% 8.99/6.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5280, 5279])).
% 8.99/6.16 tff(5282,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5281, 221, 5096, 5097, 1663, 2096, 5095, 4986, 1309, 376, 1297, 1617])).
% 8.99/6.16 tff(5283,plain,((~hskp75) | (~c2_1(a1716)) | c2_1(a1715) | c0_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5284,plain,
% 8.99/6.16 (~hskp75),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5283, 5265, 1309, 1297, 1617])).
% 8.99/6.16 tff(5285,plain,
% 8.99/6.16 (~hskp42),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2566, 5284, 365, 1297, 5274, 1309])).
% 8.99/6.16 tff(5286,plain,
% 8.99/6.16 (~hskp29),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2575, 5285, 5275])).
% 8.99/6.16 tff(5287,plain,
% 8.99/6.16 (~hskp13),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[3321, 5286, 365, 2096, 1297])).
% 8.99/6.16 tff(5288,plain,
% 8.99/6.16 (~c0_1(a1716)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5245, 5286])).
% 8.99/6.16 tff(5289,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5090, 5288, 5286, 4986, 1617, 5275, 365, 2096, 1309, 5285, 5287])).
% 8.99/6.16 tff(5290,plain,(c1_1(a1716) | c1_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5291,plain,
% 8.99/6.16 (c1_1(a1716)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5290, 365, 1309, 1297])).
% 8.99/6.16 tff(5292,assumption,(~hskp12), introduced(assumption)).
% 8.99/6.16 tff(5293,plain,
% 8.99/6.16 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5294,plain,
% 8.99/6.16 ((hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c1_1(a1716))) <=> (hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5295,plain,
% 8.99/6.16 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5294])).
% 8.99/6.16 tff(5296,plain,
% 8.99/6.16 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c1_1(a1716)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5295, 5293])).
% 8.99/6.16 tff(5297,plain,
% 8.99/6.16 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5298,plain,
% 8.99/6.16 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5297, 5296])).
% 8.99/6.16 tff(5299,plain,
% 8.99/6.16 (hskp13 | hskp12 | (~c2_1(a1716)) | (~c1_1(a1716))),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5298, 221, 4986, 893])).
% 8.99/6.16 tff(5300,plain,
% 8.99/6.16 (~c2_1(a1716)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5299, 4987, 5291, 5292])).
% 8.99/6.16 tff(5301,assumption,(hskp69), introduced(assumption)).
% 8.99/6.16 tff(5302,plain,
% 8.99/6.16 (~c1_1(a1709)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1431, 5301])).
% 8.99/6.16 tff(5303,plain,
% 8.99/6.16 (c3_1(a1709)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1442, 5301])).
% 8.99/6.16 tff(5304,plain,
% 8.99/6.16 (c0_1(a1709)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1453, 5301])).
% 8.99/6.16 tff(5305,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2446, 221, 138, 365, 2103, 5304, 5303, 5302, 137, 1297])).
% 8.99/6.16 tff(5306,plain,((~hskp69) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5307,plain,
% 8.99/6.16 (~hskp69),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5306, 138, 365, 2096, 1297])).
% 8.99/6.16 tff(5308,plain,
% 8.99/6.16 (hskp61),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1258, 4690, 2537, 2536, 2535])).
% 8.99/6.16 tff(5309,plain,
% 8.99/6.16 (~c1_1(a1674)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1193, 5308])).
% 8.99/6.16 tff(5310,plain,
% 8.99/6.16 (~c2_1(a1674)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1187, 5308])).
% 8.99/6.16 tff(5311,plain,
% 8.99/6.16 (c3_1(a1674)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[1204, 5308])).
% 8.99/6.16 tff(5312,plain,
% 8.99/6.16 (~c0_1(a1674)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[2797, 5311, 138, 5310, 5309, 1309, 1297, 2056])).
% 8.99/6.16 tff(5313,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5314,plain,
% 8.99/6.16 ((hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637))) <=> (hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5315,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5314])).
% 8.99/6.16 tff(5316,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5315, 5313])).
% 8.99/6.16 tff(5317,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp69 | (~ndr1_0) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5318,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)),
% 8.99/6.16 inference(modus_ponens,[status(thm)],[5317, 5316])).
% 8.99/6.16 tff(5319,plain,
% 8.99/6.16 ($false),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5318, 221, 2381, 5311, 2537, 5309, 2535, 1412, 4690, 5312])).
% 8.99/6.16 tff(5320,plain,((~hskp0) | hskp69 | hskp29 | c2_1(a1715) | c0_1(a1715) | hskp75 | hskp13), inference(lemma,lemma(discharge,[]))).
% 8.99/6.16 tff(5321,plain,
% 8.99/6.16 (~hskp0),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[5320, 5307, 138, 1309, 1297, 5100, 4987])).
% 8.99/6.16 tff(5322,plain,
% 8.99/6.16 (c1_1(a1654)),
% 8.99/6.16 inference(unit_resolution,[status(thm)],[3879, 3239, 4989, 3021, 3031, 3240, 3022, 138])).
% 8.99/6.16 tff(5323,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5324,plain,
% 8.99/6.16 ((hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))) <=> (hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.16 inference(rewrite,[status(thm)],[])).
% 8.99/6.16 tff(5325,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.16 inference(monotonicity,[status(thm)],[5324])).
% 8.99/6.16 tff(5326,plain,
% 8.99/6.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.16 inference(transitivity,[status(thm)],[5325, 5323])).
% 8.99/6.16 tff(5327,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.16 inference(quant_inst,[status(thm)],[])).
% 8.99/6.16 tff(5328,plain,
% 8.99/6.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5327, 5326])).
% 8.99/6.17 tff(5329,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5328, 221, 883, 2057, 3022, 3021, 4988, 290, 2893, 5322])).
% 8.99/6.17 tff(5330,plain,(hskp42 | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | hskp29 | hskp0), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5331,plain,
% 8.99/6.17 (hskp42),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5330, 963, 2057, 4986, 5291, 138, 4987])).
% 8.99/6.17 tff(5332,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5333,plain,
% 8.99/6.17 ((hskp61 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))) <=> (hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5334,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5333])).
% 8.99/6.17 tff(5335,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5334, 5332])).
% 8.99/6.17 tff(5336,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c0_1(a1638)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5337,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5336, 5335])).
% 8.99/6.17 tff(5338,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5337, 221, 1250, 2550, 2558, 2549, 1249, 3165])).
% 8.99/6.17 tff(5339,plain,((~hskp42) | hskp61 | hskp75 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5340,plain,
% 8.99/6.17 (hskp61),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5339, 5331, 5100, 365, 2096, 1309])).
% 8.99/6.17 tff(5341,plain,
% 8.99/6.17 (~c1_1(a1674)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1193, 5340])).
% 8.99/6.17 tff(5342,plain,
% 8.99/6.17 (~c2_1(a1674)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1187, 5340])).
% 8.99/6.17 tff(5343,plain,
% 8.99/6.17 (c3_1(a1674)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1204, 5340])).
% 8.99/6.17 tff(5344,plain,
% 8.99/6.17 (~c0_1(a1674)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2797, 5343, 138, 5342, 5341, 1309, 1297, 5100])).
% 8.99/6.17 tff(5345,plain,
% 8.99/6.17 (c0_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1098, 5331])).
% 8.99/6.17 tff(5346,plain,
% 8.99/6.17 (c1_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1109, 5331])).
% 8.99/6.17 tff(5347,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5348,plain,
% 8.99/6.17 ((hskp0 | (~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638))) <=> (hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5349,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5348])).
% 8.99/6.17 tff(5350,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5349, 5347])).
% 8.99/6.17 tff(5351,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c1_1(a1638)) | (~c2_1(a1638)) | (~c0_1(a1638)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5352,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5351, 5350])).
% 8.99/6.17 tff(5353,plain,
% 8.99/6.17 (~c2_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5352, 221, 963, 2057, 5346, 5345, 4986, 950, 5291])).
% 8.99/6.17 tff(5354,plain,
% 8.99/6.17 (~c3_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1087, 5331])).
% 8.99/6.17 tff(5355,plain,
% 8.99/6.17 (hskp69),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[3057, 221, 365, 2096, 5346, 5354, 1412, 1297, 5353])).
% 8.99/6.17 tff(5356,plain,
% 8.99/6.17 (~c1_1(a1709)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1431, 5355])).
% 8.99/6.17 tff(5357,plain,
% 8.99/6.17 (c3_1(a1709)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1442, 5355])).
% 8.99/6.17 tff(5358,plain,
% 8.99/6.17 (c0_1(a1709)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1453, 5355])).
% 8.99/6.17 tff(5359,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5206, 221, 138, 5358, 5357, 5343, 5356, 5341, 137, 5344])).
% 8.99/6.17 tff(5360,plain,(hskp0 | hskp29 | c1_1(a1715) | c0_1(a1715) | c2_1(a1716) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5361,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5360, 5321, 5300, 365, 1297, 138, 1309])).
% 8.99/6.17 tff(5362,plain,(hskp29 | c1_1(a1715) | c0_1(a1715) | c2_1(a1715) | hskp12), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5363,plain,
% 8.99/6.17 (hskp12),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5362, 138, 1297, 1309, 365])).
% 8.99/6.17 tff(5364,plain,
% 8.99/6.17 (~c1_1(a1666)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[905, 5363])).
% 8.99/6.17 tff(5365,plain,
% 8.99/6.17 (c3_1(a1666)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[916, 5363])).
% 8.99/6.17 tff(5366,plain,
% 8.99/6.17 (c2_1(a1666)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[927, 5363])).
% 8.99/6.17 tff(5367,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5368,plain,
% 8.99/6.17 ((hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))) <=> (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5369,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5368])).
% 8.99/6.17 tff(5370,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5369, 5367])).
% 8.99/6.17 tff(5371,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5372,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5371, 5370])).
% 8.99/6.17 tff(5373,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5372, 221, 4989, 2097, 4794, 4793, 4988, 4792, 1563, 2893])).
% 8.99/6.17 tff(5374,plain,((~hskp12) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5375,plain,
% 8.99/6.17 (~hskp12),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5374, 2097, 4986, 5291])).
% 8.99/6.17 tff(5376,plain,
% 8.99/6.17 (hskp29),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5362, 5375, 1297, 1309, 365])).
% 8.99/6.17 tff(5377,plain,
% 8.99/6.17 (hskp42),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2575, 963, 2058])).
% 8.99/6.17 tff(5378,plain,
% 8.99/6.17 (c0_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1098, 5377])).
% 8.99/6.17 tff(5379,plain,
% 8.99/6.17 (c1_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1109, 5377])).
% 8.99/6.17 tff(5380,plain,
% 8.99/6.17 (~c2_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5352, 221, 963, 2057, 5379, 5378, 4988, 950, 2893])).
% 8.99/6.17 tff(5381,plain,
% 8.99/6.17 (~c3_1(a1638)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1087, 5377])).
% 8.99/6.17 tff(5382,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5383,plain,
% 8.99/6.17 ((hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))) <=> (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5384,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5383])).
% 8.99/6.17 tff(5385,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5384, 5382])).
% 8.99/6.17 tff(5386,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1683) | (~c3_1(a1683)) | (~c2_1(a1683)) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5387,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5386, 5385])).
% 8.99/6.17 tff(5388,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5387, 221, 4989, 2097, 2102, 2101, 4988, 2100, 1563, 2893])).
% 8.99/6.17 tff(5389,plain,((~hskp21) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5390,plain,
% 8.99/6.17 (~hskp21),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5389, 2097, 4988, 2893])).
% 8.99/6.17 tff(5391,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5392,plain,
% 8.99/6.17 ((hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716))) <=> (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5393,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5392])).
% 8.99/6.17 tff(5394,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5393, 5391])).
% 8.99/6.17 tff(5395,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1638) | c2_1(a1638) | (~c1_1(a1638)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5396,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5395, 5394])).
% 8.99/6.17 tff(5397,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5396, 221, 5390, 2057, 2097, 5379, 5381, 1357, 5380, 2893])).
% 8.99/6.17 tff(5398,plain,(hskp0 | c2_1(a1716) | c0_1(a1716) | (~c1_1(a1716)) | (~c3_1(a1716)) | (~hskp29)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5399,plain,
% 8.99/6.17 (hskp0),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5398, 2057, 2097, 2893, 4988, 2058])).
% 8.99/6.17 tff(5400,plain,
% 8.99/6.17 (hskp30),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2546, 5399, 365, 2103, 1297])).
% 8.99/6.17 tff(5401,plain,
% 8.99/6.17 (~hskp60),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5214, 5400, 4989])).
% 8.99/6.17 tff(5402,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5403,plain,
% 8.99/6.17 ((hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715))) <=> (hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5404,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715)))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5403])).
% 8.99/6.17 tff(5405,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5404, 5402])).
% 8.99/6.17 tff(5406,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp60 | (~ndr1_0) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5407,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c1_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | (~c3_1(a1715)) | c0_1(a1715)),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 8.99/6.17 tff(5408,plain,
% 8.99/6.17 (hskp60 | c1_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5407, 221, 365, 2103, 2086, 2064, 386, 1297])).
% 8.99/6.17 tff(5409,plain,
% 8.99/6.17 (c1_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5408, 5401])).
% 8.99/6.17 tff(5410,plain,
% 8.99/6.17 (~c2_1(a1637)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1169, 5399])).
% 8.99/6.17 tff(5411,plain,
% 8.99/6.17 (c0_1(a1637)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1180, 5399])).
% 8.99/6.17 tff(5412,plain,
% 8.99/6.17 (c1_1(a1637)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1224, 5399])).
% 8.99/6.17 tff(5413,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5414,plain,
% 8.99/6.17 ((hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716))) <=> (hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5415,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716))))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5414])).
% 8.99/6.17 tff(5416,plain,
% 8.99/6.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716)))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5415, 5413])).
% 8.99/6.17 tff(5417,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5418,plain,
% 8.99/6.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716))),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5417, 5416])).
% 8.99/6.17 tff(5419,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5418, 221, 1345, 2057, 2097, 1229, 1227, 1357, 1239, 2893])).
% 8.99/6.17 tff(5420,plain,(c3_1(a1637) | hskp21 | c2_1(a1716) | c0_1(a1716) | (~c1_1(a1637)) | c2_1(a1637) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5421,plain,
% 8.99/6.17 (c3_1(a1637)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5420, 2057, 5390, 2097, 5412, 5410, 2893])).
% 8.99/6.17 tff(5422,plain,
% 8.99/6.17 (hskp13),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[1237, 5421, 5412, 5411, 5410])).
% 8.99/6.17 tff(5423,plain,
% 8.99/6.17 (~c1_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[303, 5422])).
% 8.99/6.17 tff(5424,plain,
% 8.99/6.17 (c3_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[314, 5422])).
% 8.99/6.17 tff(5425,plain,
% 8.99/6.17 (c0_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[325, 5422])).
% 8.99/6.17 tff(5426,plain,
% 8.99/6.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5427,plain,
% 8.99/6.17 (((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(rewrite,[status(thm)],[])).
% 8.99/6.17 tff(5428,plain,
% 8.99/6.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715)))),
% 8.99/6.17 inference(monotonicity,[status(thm)],[5427])).
% 8.99/6.17 tff(5429,plain,
% 8.99/6.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715))),
% 8.99/6.17 inference(transitivity,[status(thm)],[5428, 5426])).
% 8.99/6.17 tff(5430,plain,
% 8.99/6.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.17 inference(quant_inst,[status(thm)],[])).
% 8.99/6.17 tff(5431,plain,
% 8.99/6.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715)),
% 8.99/6.17 inference(modus_ponens,[status(thm)],[5430, 5429])).
% 8.99/6.17 tff(5432,plain,
% 8.99/6.17 ($false),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5431, 221, 365, 2103, 2086, 5425, 5424, 2064, 5423, 102, 1297, 5409])).
% 8.99/6.17 tff(5433,plain,(c2_1(a1716) | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715) | c0_1(a1716) | (~c1_1(a1716)) | (~c3_1(a1716)) | (~hskp29)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.17 tff(5434,plain,
% 8.99/6.17 (c2_1(a1716)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5433, 2097, 2096, 1297, 365, 5291, 4986, 5376])).
% 8.99/6.17 tff(5435,plain,
% 8.99/6.17 (hskp13),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5299, 5434, 5291, 5375])).
% 8.99/6.17 tff(5436,plain,
% 8.99/6.17 (~c1_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[303, 5435])).
% 8.99/6.17 tff(5437,plain,
% 8.99/6.17 (~c3_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2063, 5376])).
% 8.99/6.17 tff(5438,plain,
% 8.99/6.17 (c3_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[314, 5435])).
% 8.99/6.17 tff(5439,plain,
% 8.99/6.17 (c0_1(a1667)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[325, 5435])).
% 8.99/6.17 tff(5440,plain,
% 8.99/6.17 (c2_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2085, 5376])).
% 8.99/6.17 tff(5441,plain,
% 8.99/6.17 (~c1_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5431, 221, 365, 2096, 5440, 5439, 5438, 5437, 5436, 102, 1297])).
% 8.99/6.17 tff(5442,plain,
% 8.99/6.17 (hskp60 | c1_1(a1695)),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5407, 221, 365, 2096, 5440, 5437, 386, 1297])).
% 8.99/6.17 tff(5443,plain,
% 8.99/6.17 (hskp60),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5442, 5441])).
% 8.99/6.17 tff(5444,plain,
% 8.99/6.17 (~hskp30),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[5214, 5443, 5172])).
% 8.99/6.17 tff(5445,plain,
% 8.99/6.17 (~hskp0),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2546, 5444, 365, 2096, 1297])).
% 8.99/6.17 tff(5446,plain,
% 8.99/6.17 (hskp42),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2575, 5445, 5376])).
% 8.99/6.17 tff(5447,plain,
% 8.99/6.17 (hskp75),
% 8.99/6.17 inference(unit_resolution,[status(thm)],[2566, 5446, 365, 1297, 5444, 1309])).
% 8.99/6.18 tff(5448,plain,
% 8.99/6.18 (~c2_1(a1724)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[441, 5447])).
% 8.99/6.18 tff(5449,plain,
% 8.99/6.18 (c0_1(a1724)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[485, 5447])).
% 8.99/6.18 tff(5450,plain,
% 8.99/6.18 (c3_1(a1724)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[474, 5447])).
% 8.99/6.18 tff(5451,plain,
% 8.99/6.18 ($false),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2891, 5450, 5449, 5443, 5448, 1309, 1297])).
% 8.99/6.18 tff(5452,plain,(c0_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.18 tff(5453,plain,
% 8.99/6.18 (c0_1(a1716)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5452, 365, 1297, 1309])).
% 8.99/6.18 tff(5454,plain,
% 8.99/6.18 (c2_1(a1716)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5360, 5321, 365, 1297, 138, 1309])).
% 8.99/6.18 tff(5455,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5456,plain,
% 8.99/6.18 ((hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716))) <=> (hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5457,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5456])).
% 8.99/6.18 tff(5458,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5457, 5455])).
% 8.99/6.18 tff(5459,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1716)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5460,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5459, 5458])).
% 8.99/6.18 tff(5461,plain,
% 8.99/6.18 (hskp26),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5460, 221, 5454, 5453, 5366, 5365, 4986, 5364, 20])).
% 8.99/6.18 tff(5462,plain,
% 8.99/6.18 (~c2_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[669, 5461])).
% 8.99/6.18 tff(5463,plain,
% 8.99/6.18 (~c1_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[675, 5461])).
% 8.99/6.18 tff(5464,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5465,plain,
% 8.99/6.18 (((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715))) <=> (c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5466,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5465])).
% 8.99/6.18 tff(5467,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5466, 5464])).
% 8.99/6.18 tff(5468,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1691) | c1_1(a1691) | (~c0_1(a1691)) | (~c3_1(a1716)) | (~c1_1(a1716)) | (~c0_1(a1716)) | c1_1(a1715) | c2_1(a1715) | (~c3_1(a1715)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5469,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | (~c3_1(a1716)) | c2_1(a1715) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c1_1(a1716)) | (~c0_1(a1716))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5468, 5467])).
% 8.99/6.18 tff(5470,plain,
% 8.99/6.18 (~c0_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5469, 221, 5453, 365, 2096, 4986, 1309, 5463, 5462, 647, 5291])).
% 8.99/6.18 tff(5471,plain,
% 8.99/6.18 (~c3_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[689, 5461])).
% 8.99/6.18 tff(5472,plain,
% 8.99/6.18 (hskp37 | c0_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[696, 221, 2400, 5471, 5462, 577])).
% 8.99/6.18 tff(5473,plain,
% 8.99/6.18 (hskp37),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5472, 5470])).
% 8.99/6.18 tff(5474,plain,
% 8.99/6.18 (~c1_1(a1714)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[591, 5473])).
% 8.99/6.18 tff(5475,plain,
% 8.99/6.18 (c0_1(a1714)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[602, 5473])).
% 8.99/6.18 tff(5476,plain,
% 8.99/6.18 (c2_1(a1714)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[613, 5473])).
% 8.99/6.18 tff(5477,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5478,plain,
% 8.99/6.18 (((~ndr1_0) | (~c3_1(a1716)) | (~c0_1(a1716)) | (~c2_1(a1716)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691)) <=> ((~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5479,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1716)) | (~c0_1(a1716)) | (~c2_1(a1716)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5478])).
% 8.99/6.18 tff(5480,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1716)) | (~c0_1(a1716)) | (~c2_1(a1716)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5479, 5477])).
% 8.99/6.18 tff(5481,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a1716)) | (~c0_1(a1716)) | (~c2_1(a1716)) | c1_1(a1714) | (~c2_1(a1714)) | (~c0_1(a1714)) | c3_1(a1691) | c2_1(a1691) | c0_1(a1691))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5482,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5481, 5480])).
% 8.99/6.18 tff(5483,plain,
% 8.99/6.18 ($false),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5482, 221, 5454, 5453, 5476, 5475, 4986, 5474, 5471, 5462, 565, 5470])).
% 8.99/6.18 tff(5484,plain,(hskp29 | c1_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.18 tff(5485,plain,
% 8.99/6.18 (c0_1(a1715)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5484, 1309, 138, 365])).
% 8.99/6.18 tff(5486,plain,
% 8.99/6.18 (c3_1(a1654)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[536, 4983])).
% 8.99/6.18 tff(5487,plain,
% 8.99/6.18 (c1_1(a1654)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4943, 4984, 138, 5486, 4985])).
% 8.99/6.18 tff(5488,plain,
% 8.99/6.18 (~hskp61),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[3391, 1309, 5487, 365, 5486, 5485, 4984])).
% 8.99/6.18 tff(5489,plain,
% 8.99/6.18 (hskp0),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4332, 5485, 138, 4949, 365, 5488, 1309])).
% 8.99/6.18 tff(5490,plain,
% 8.99/6.18 (hskp13),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4692, 5488, 5489])).
% 8.99/6.18 tff(5491,plain,
% 8.99/6.18 (~c1_1(a1667)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[303, 5490])).
% 8.99/6.18 tff(5492,plain,
% 8.99/6.18 (hskp61 | hskp33 | c2_1(a1715) | (~c0_1(a1715))),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4301, 221, 4949, 2651])).
% 8.99/6.18 tff(5493,plain,
% 8.99/6.18 (hskp33),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5492, 5488, 1309, 5485])).
% 8.99/6.18 tff(5494,plain,
% 8.99/6.18 (~c2_1(a1704)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2664, 5493])).
% 8.99/6.18 tff(5495,plain,
% 8.99/6.18 (~c0_1(a1704)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2670, 5493])).
% 8.99/6.18 tff(5496,plain,
% 8.99/6.18 (c3_1(a1667)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[314, 5490])).
% 8.99/6.18 tff(5497,plain,
% 8.99/6.18 (c3_1(a1704)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2682, 5493])).
% 8.99/6.18 tff(5498,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5499,plain,
% 8.99/6.18 (((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667))) <=> (c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5500,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5499])).
% 8.99/6.18 tff(5501,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5500, 5498])).
% 8.99/6.18 tff(5502,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c2_1(a1704) | (~c3_1(a1704)) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5503,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c0_1(a1704) | c2_1(a1704) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1704)) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 8.99/6.18 tff(5504,plain,
% 8.99/6.18 (~c2_1(a1667)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5503, 221, 4949, 5497, 5496, 1309, 5495, 5494, 5491, 376, 5485])).
% 8.99/6.18 tff(5505,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5506,plain,
% 8.99/6.18 (((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667))) <=> (c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5507,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5506])).
% 8.99/6.18 tff(5508,plain,
% 8.99/6.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5507, 5505])).
% 8.99/6.18 tff(5509,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1715) | c1_1(a1715) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1667) | c2_1(a1667) | (~c3_1(a1667)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5510,plain,
% 8.99/6.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 8.99/6.18 tff(5511,plain,
% 8.99/6.18 ($false),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5510, 221, 365, 4984, 5486, 5496, 1309, 5491, 647, 5485, 5487, 5504])).
% 8.99/6.18 tff(5512,plain,(c2_1(a1715) | c1_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.18 tff(5513,plain,
% 8.99/6.18 (c2_1(a1715)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5512, 365, 138])).
% 8.99/6.18 tff(5514,plain,
% 8.99/6.18 (hskp26 | (~c2_1(a1715))),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4619, 221, 365, 4949, 4984, 4985, 5486, 20])).
% 8.99/6.18 tff(5515,plain,
% 8.99/6.18 (hskp26),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5514, 5513])).
% 8.99/6.18 tff(5516,plain,
% 8.99/6.18 (~c2_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[669, 5515])).
% 8.99/6.18 tff(5517,plain,
% 8.99/6.18 (~c3_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[689, 5515])).
% 8.99/6.18 tff(5518,plain,
% 8.99/6.18 (c0_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4630, 5517, 2400, 5486, 4985, 5516, 4984])).
% 8.99/6.18 tff(5519,plain,
% 8.99/6.18 (~c1_1(a1691)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[675, 5515])).
% 8.99/6.18 tff(5520,plain,
% 8.99/6.18 (~hskp61),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1213, 5519, 5486, 5487, 5516, 5518, 4984])).
% 8.99/6.18 tff(5521,plain,
% 8.99/6.18 (hskp47),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4666, 221, 4984, 5486, 5517, 5516, 1848, 5487, 5518])).
% 8.99/6.18 tff(5522,plain,
% 8.99/6.18 (~c0_1(a1644)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1861, 5521])).
% 8.99/6.18 tff(5523,plain,
% 8.99/6.18 (c3_1(a1644)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1880, 5521])).
% 8.99/6.18 tff(5524,plain,
% 8.99/6.18 (~c1_1(a1644)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1867, 5521])).
% 8.99/6.18 tff(5525,plain,
% 8.99/6.18 (~hskp13),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4830, 5524, 138, 5523, 5522])).
% 8.99/6.18 tff(5526,plain,
% 8.99/6.18 (~hskp0),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4692, 5525, 5520])).
% 8.99/6.18 tff(5527,plain,
% 8.99/6.18 (~c0_1(a1715)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4677, 221, 138, 365, 4949, 5523, 5524, 5522, 137])).
% 8.99/6.18 tff(5528,plain,
% 8.99/6.18 (~hskp57),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4686, 5527, 138, 4949, 365])).
% 8.99/6.18 tff(5529,plain,
% 8.99/6.18 (~hskp74),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4710, 5528, 5517, 5516, 5518, 5519, 5526])).
% 8.99/6.18 tff(5530,plain,
% 8.99/6.18 (hskp38),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1032, 5529, 4983])).
% 8.99/6.18 tff(5531,plain,
% 8.99/6.18 (~c0_1(a1718)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2583, 5530])).
% 8.99/6.18 tff(5532,plain,
% 8.99/6.18 (c3_1(a1718)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[981, 5530])).
% 8.99/6.18 tff(5533,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5534,plain,
% 8.99/6.18 ((hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718))) <=> (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5535,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5534])).
% 8.99/6.18 tff(5536,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))) <=> ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5535, 5533])).
% 8.99/6.18 tff(5537,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp73 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5538,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5537, 5536])).
% 8.99/6.18 tff(5539,plain,
% 8.99/6.18 (~c1_1(a1718)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5538, 221, 4940, 365, 4949, 5532, 5513, 5531, 1563])).
% 8.99/6.18 tff(5540,plain,
% 8.99/6.18 (~c2_1(a1718)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[970, 5530])).
% 8.99/6.18 tff(5541,plain,
% 8.99/6.18 ($false),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[4721, 221, 4984, 5486, 5532, 5540, 5519, 5516, 647, 5487, 5539, 5518])).
% 8.99/6.18 tff(5542,plain,(c1_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.18 tff(5543,plain,
% 8.99/6.18 (c1_1(a1715)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5542, 138])).
% 8.99/6.18 tff(5544,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5545,plain,
% 8.99/6.18 ((hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5546,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.18 inference(monotonicity,[status(thm)],[5545])).
% 8.99/6.18 tff(5547,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(transitivity,[status(thm)],[5546, 5544])).
% 8.99/6.18 tff(5548,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.99/6.18 inference(quant_inst,[status(thm)],[])).
% 8.99/6.18 tff(5549,plain,
% 8.99/6.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.18 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 8.99/6.18 tff(5550,plain,
% 8.99/6.18 (hskp0),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[5549, 221, 5543, 4949, 4984, 4985, 1309, 950, 5487])).
% 8.99/6.18 tff(5551,plain,
% 8.99/6.18 (c1_1(a1637)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1224, 5550])).
% 8.99/6.18 tff(5552,plain,
% 8.99/6.18 (c0_1(a1637)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1180, 5550])).
% 8.99/6.18 tff(5553,plain,
% 8.99/6.18 (~c2_1(a1637)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1169, 5550])).
% 8.99/6.18 tff(5554,plain,
% 8.99/6.18 (hskp61),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2699, 5553, 4949, 5543, 1309, 5552, 5551])).
% 8.99/6.18 tff(5555,plain,
% 8.99/6.18 (~c2_1(a1674)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1187, 5554])).
% 8.99/6.18 tff(5556,plain,
% 8.99/6.18 (~c1_1(a1674)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1193, 5554])).
% 8.99/6.18 tff(5557,plain,
% 8.99/6.18 (c3_1(a1674)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[1204, 5554])).
% 8.99/6.18 tff(5558,plain,
% 8.99/6.18 (~c0_1(a1674)),
% 8.99/6.18 inference(unit_resolution,[status(thm)],[2784, 221, 5557, 4984, 5486, 5556, 5555, 647, 5487])).
% 8.99/6.18 tff(5559,plain,
% 8.99/6.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.18 tff(5560,plain,
% 8.99/6.18 ((hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715))) <=> (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.18 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5561,plain,
% 8.99/6.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5560])).
% 8.99/6.19 tff(5562,plain,
% 8.99/6.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5561, 5559])).
% 8.99/6.19 tff(5563,plain,
% 8.99/6.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5564,plain,
% 8.99/6.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5563, 5562])).
% 8.99/6.19 tff(5565,plain,
% 8.99/6.19 (hskp13),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5564, 221, 5543, 4949, 4984, 5486, 1309, 290, 5487])).
% 8.99/6.19 tff(5566,plain,
% 8.99/6.19 (~c1_1(a1667)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[303, 5565])).
% 8.99/6.19 tff(5567,plain,
% 8.99/6.19 (c3_1(a1667)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[314, 5565])).
% 8.99/6.19 tff(5568,plain,
% 8.99/6.19 (c0_1(a1667)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[325, 5565])).
% 8.99/6.19 tff(5569,plain,
% 8.99/6.19 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5570,plain,
% 8.99/6.19 ((hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674))) <=> (hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5571,plain,
% 8.99/6.19 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674)))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5570])).
% 8.99/6.19 tff(5572,plain,
% 8.99/6.19 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5571, 5569])).
% 8.99/6.19 tff(5573,plain,
% 8.99/6.19 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5574,plain,
% 8.99/6.19 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674)),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 8.99/6.19 tff(5575,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5574, 221, 138, 5557, 5568, 5567, 5556, 5566, 137, 5558])).
% 8.99/6.19 tff(5576,plain,(c2_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5577,plain,
% 8.99/6.19 (c2_1(a1715)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5576, 138])).
% 8.99/6.19 tff(5578,plain,
% 8.99/6.19 (hskp26),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4817, 5577, 4949, 4984, 5487, 5486, 5543, 4985])).
% 8.99/6.19 tff(5579,plain,
% 8.99/6.19 (~c2_1(a1691)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[669, 5578])).
% 8.99/6.19 tff(5580,plain,
% 8.99/6.19 (~hskp72),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[553, 5577])).
% 8.99/6.19 tff(5581,plain,
% 8.99/6.19 (~c3_1(a1691)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[689, 5578])).
% 8.99/6.19 tff(5582,plain,
% 8.99/6.19 (c0_1(a1691)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4630, 5581, 5580, 5486, 4985, 5579, 4984])).
% 8.99/6.19 tff(5583,plain,
% 8.99/6.19 (hskp47),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4666, 221, 4984, 5486, 5581, 5579, 1848, 5487, 5582])).
% 8.99/6.19 tff(5584,plain,
% 8.99/6.19 (~c0_1(a1644)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[1861, 5583])).
% 8.99/6.19 tff(5585,plain,
% 8.99/6.19 (~c1_1(a1644)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[1867, 5583])).
% 8.99/6.19 tff(5586,plain,
% 8.99/6.19 (~c1_1(a1691)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[675, 5578])).
% 8.99/6.19 tff(5587,plain,
% 8.99/6.19 (~hskp61),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[1213, 5579, 5486, 5487, 5586, 5582, 4984])).
% 8.99/6.19 tff(5588,plain,
% 8.99/6.19 (c3_1(a1644)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[1880, 5583])).
% 8.99/6.19 tff(5589,plain,
% 8.99/6.19 (~hskp13),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4830, 5585, 138, 5588, 5584])).
% 8.99/6.19 tff(5590,plain,
% 8.99/6.19 (~hskp0),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4692, 5589, 5587])).
% 8.99/6.19 tff(5591,plain,
% 8.99/6.19 (c2_1(a1644)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4874, 221, 4984, 5486, 5588, 5585, 5586, 5579, 647, 5487, 5582])).
% 8.99/6.19 tff(5592,assumption,(c2_1(a1644)), introduced(assumption)).
% 8.99/6.19 tff(5593,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4882, 221, 2104, 834, 2103, 4828, 4827, 1563, 1297, 5592])).
% 8.99/6.19 tff(5594,plain,(c0_1(a1715) | hskp73 | (~c1_1(a1715)) | (~c3_1(a1715)) | (~c3_1(a1644)) | c1_1(a1644) | (~c2_1(a1644))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5595,plain,
% 8.99/6.19 (c0_1(a1715)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5594, 4940, 5543, 4949, 5588, 5585, 5591])).
% 8.99/6.19 tff(5596,plain,
% 8.99/6.19 (~hskp38),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4921, 5595, 4949, 5577, 5579, 5586, 5582, 5590, 5543])).
% 8.99/6.19 tff(5597,plain,
% 8.99/6.19 (hskp74),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[1032, 5596, 4983])).
% 8.99/6.19 tff(5598,plain,
% 8.99/6.19 (hskp57),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4710, 5597, 5581, 5579, 5582, 5586, 5590])).
% 8.99/6.19 tff(5599,plain,
% 8.99/6.19 (~c1_1(a1665)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[65, 5598])).
% 8.99/6.19 tff(5600,plain,
% 8.99/6.19 (c3_1(a1665)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[76, 5598])).
% 8.99/6.19 tff(5601,plain,
% 8.99/6.19 (c0_1(a1665)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[90, 5598])).
% 8.99/6.19 tff(5602,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[4568, 221, 138, 5601, 5600, 5588, 5599, 5585, 5584, 137])).
% 8.99/6.19 tff(5603,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5604,plain,
% 8.99/6.19 (~c3_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[2063, 5603])).
% 8.99/6.19 tff(5605,plain,
% 8.99/6.19 (c2_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[2085, 5603])).
% 8.99/6.19 tff(5606,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5607,plain,
% 8.99/6.19 (((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5608,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5607])).
% 8.99/6.19 tff(5609,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5608, 5606])).
% 8.99/6.19 tff(5610,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5611,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5610, 5609])).
% 8.99/6.19 tff(5612,plain,
% 8.99/6.19 ((~c3_1(a1677)) | (~c1_1(a1695))),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5611, 221, 105, 104, 5605, 103, 5604, 127, 126, 102])).
% 8.99/6.19 tff(5613,plain,
% 8.99/6.19 (~c1_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5612, 125])).
% 8.99/6.19 tff(5614,plain,
% 8.99/6.19 (c0_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[2074, 5603])).
% 8.99/6.19 tff(5615,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5616,plain,
% 8.99/6.19 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5617,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5616])).
% 8.99/6.19 tff(5618,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5617, 5615])).
% 8.99/6.19 tff(5619,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | (~c3_1(a1677)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5620,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5619, 5618])).
% 8.99/6.19 tff(5621,plain,
% 8.99/6.19 ((~c3_1(a1677)) | c1_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5620, 221, 5614, 78, 80, 5604, 127, 340, 79, 410])).
% 8.99/6.19 tff(5622,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5621, 5613, 125])).
% 8.99/6.19 tff(5623,plain,((~c3_1(a1677)) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665) | c1_1(a1677)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5624,plain,
% 8.99/6.19 (~c3_1(a1677)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5623, 124, 80, 78, 118, 79, 105, 104, 103, 112])).
% 8.99/6.19 tff(5625,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5626,plain,
% 8.99/6.19 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677)) <=> (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5627,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5626])).
% 8.99/6.19 tff(5628,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5627, 5625])).
% 8.99/6.19 tff(5629,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1677) | c1_1(a1677) | c2_1(a1677))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5630,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5629, 5628])).
% 8.99/6.19 tff(5631,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5630, 221, 5605, 5614, 5604, 124, 118, 112, 30, 5624])).
% 8.99/6.19 tff(5632,plain,((~hskp16) | (~c0_1(a1655)) | (~c3_1(a1655)) | c2_1(a1655) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5633,plain,
% 8.99/6.19 (~hskp16),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5632, 105, 78, 79, 80, 104, 103])).
% 8.99/6.19 tff(5634,plain,
% 8.99/6.19 (hskp17),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[334, 5633, 78, 80, 79])).
% 8.99/6.19 tff(5635,plain,
% 8.99/6.19 (~c1_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[241, 5634])).
% 8.99/6.19 tff(5636,plain,
% 8.99/6.19 (~c0_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[247, 5634])).
% 8.99/6.19 tff(5637,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5638,plain,
% 8.99/6.19 (((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5639,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5638])).
% 8.99/6.19 tff(5640,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5639, 5637])).
% 8.99/6.19 tff(5641,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678)) | c1_1(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5642,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1665) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 8.99/6.19 tff(5643,plain,
% 8.99/6.19 ((~c3_1(a1678)) | (~c1_1(a1695))),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5642, 221, 105, 104, 5605, 103, 5604, 5636, 5635, 102])).
% 8.99/6.19 tff(5644,plain,
% 8.99/6.19 (~c1_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5643, 92])).
% 8.99/6.19 tff(5645,plain,
% 8.99/6.19 (~c2_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[260, 5634])).
% 8.99/6.19 tff(5646,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5647,plain,
% 8.99/6.19 (((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695))) <=> (c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5648,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5647])).
% 8.99/6.19 tff(5649,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5648, 5646])).
% 8.99/6.19 tff(5650,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)) | c0_1(a1678) | c2_1(a1678) | (~c3_1(a1678)) | c3_1(a1695) | c1_1(a1695) | (~c0_1(a1695)))),
% 8.99/6.19 inference(quant_inst,[status(thm)],[])).
% 8.99/6.19 tff(5651,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695))),
% 8.99/6.19 inference(modus_ponens,[status(thm)],[5650, 5649])).
% 8.99/6.19 tff(5652,plain,
% 8.99/6.19 ((~c3_1(a1678)) | c1_1(a1695)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5651, 221, 5614, 78, 80, 5604, 5636, 5645, 79, 410])).
% 8.99/6.19 tff(5653,plain,
% 8.99/6.19 ($false),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5652, 5644, 92])).
% 8.99/6.19 tff(5654,plain,((~c3_1(a1678)) | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1655) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.19 tff(5655,plain,
% 8.99/6.19 (~c3_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5654, 91, 80, 79, 78, 77, 66])).
% 8.99/6.19 tff(5656,plain,
% 8.99/6.19 (~hskp16),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[5632, 91, 78, 79, 80, 77, 66])).
% 8.99/6.19 tff(5657,plain,
% 8.99/6.19 (hskp17),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[334, 5656, 78, 80, 79])).
% 8.99/6.19 tff(5658,plain,
% 8.99/6.19 (~c2_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[260, 5657])).
% 8.99/6.19 tff(5659,plain,
% 8.99/6.19 (~c1_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[241, 5657])).
% 8.99/6.19 tff(5660,plain,
% 8.99/6.19 (~c0_1(a1678)),
% 8.99/6.19 inference(unit_resolution,[status(thm)],[247, 5657])).
% 8.99/6.19 tff(5661,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5662,plain,
% 8.99/6.19 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678)) <=> (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(rewrite,[status(thm)],[])).
% 8.99/6.19 tff(5663,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.19 inference(monotonicity,[status(thm)],[5662])).
% 8.99/6.19 tff(5664,plain,
% 8.99/6.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.19 inference(transitivity,[status(thm)],[5663, 5661])).
% 8.99/6.19 tff(5665,plain,
% 8.99/6.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1678) | c1_1(a1678) | c2_1(a1678))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5666,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5665, 5664])).
% 8.99/6.20 tff(5667,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5666, 221, 5605, 5614, 5604, 5660, 5659, 5658, 30, 5655])).
% 8.99/6.20 tff(5668,plain,((~hskp57) | (~c0_1(a1655)) | c2_1(a1655) | (~c3_1(a1655))), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5669,plain,
% 8.99/6.20 (~hskp57),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5668, 59, 48, 42])).
% 8.99/6.20 tff(5670,plain,
% 8.99/6.20 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5671,plain,
% 8.99/6.20 ((hskp57 | hskp11 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655))) <=> (hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5672,plain,
% 8.99/6.20 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5671])).
% 8.99/6.20 tff(5673,plain,
% 8.99/6.20 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5672, 5670])).
% 8.99/6.20 tff(5674,plain,
% 8.99/6.20 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1655) | (~c3_1(a1655)) | (~c0_1(a1655)))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5675,plain,
% 8.99/6.20 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5674, 5673])).
% 8.99/6.20 tff(5676,plain,
% 8.99/6.20 (hskp57 | hskp11),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5675, 221, 42, 59, 48, 1639])).
% 8.99/6.20 tff(5677,plain,
% 8.99/6.20 (hskp11),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5676, 5669])).
% 8.99/6.20 tff(5678,plain,
% 8.99/6.20 (~c1_1(a1664)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1675, 5677])).
% 8.99/6.20 tff(5679,plain,
% 8.99/6.20 (~c2_1(a1664)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1654, 5677])).
% 8.99/6.20 tff(5680,plain,
% 8.99/6.20 (~c3_1(a1664)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1660, 5677])).
% 8.99/6.20 tff(5681,assumption,(~c1_1(a1664)), introduced(assumption)).
% 8.99/6.20 tff(5682,assumption,(~c2_1(a1664)), introduced(assumption)).
% 8.99/6.20 tff(5683,assumption,(~c3_1(a1664)), introduced(assumption)).
% 8.99/6.20 tff(5684,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5685,plain,
% 8.99/6.20 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664)) <=> (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5686,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5685])).
% 8.99/6.20 tff(5687,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5686, 5684])).
% 8.99/6.20 tff(5688,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5689,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 8.99/6.20 tff(5690,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5689, 221, 5605, 5614, 5604, 248, 242, 261, 5683, 5682, 5681, 30])).
% 8.99/6.20 tff(5691,plain,((~hskp17) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5692,plain,
% 8.99/6.20 (~hskp17),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5691, 5680, 5679, 5678])).
% 8.99/6.20 tff(5693,plain,
% 8.99/6.20 (hskp16),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[334, 5692, 42, 59, 48])).
% 8.99/6.20 tff(5694,plain,
% 8.99/6.20 (~c1_1(a1677)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[111, 5693])).
% 8.99/6.20 tff(5695,plain,
% 8.99/6.20 (~c2_1(a1677)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[117, 5693])).
% 8.99/6.20 tff(5696,plain,
% 8.99/6.20 (~c0_1(a1677)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[123, 5693])).
% 8.99/6.20 tff(5697,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5698,plain,
% 8.99/6.20 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664)) <=> (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5699,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5698])).
% 8.99/6.20 tff(5700,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5699, 5697])).
% 8.99/6.20 tff(5701,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c1_1(a1664) | c2_1(a1664))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5702,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 8.99/6.20 tff(5703,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5702, 221, 5605, 5614, 5604, 5696, 5695, 5694, 5680, 5679, 5678, 30])).
% 8.99/6.20 tff(5704,plain,(~hskp7), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5705,plain,
% 8.99/6.20 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5706,plain,
% 8.99/6.20 ((hskp52 | hskp7 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695))) <=> (hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5707,plain,
% 8.99/6.20 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5706])).
% 8.99/6.20 tff(5708,plain,
% 8.99/6.20 (((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))) <=> ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5707, 5705])).
% 8.99/6.20 tff(5709,plain,
% 8.99/6.20 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp52 | hskp7 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5710,plain,
% 8.99/6.20 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5709, 5708])).
% 8.99/6.20 tff(5711,plain,
% 8.99/6.20 (hskp52 | hskp7),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5710, 221, 5605, 5614, 5604, 189])).
% 8.99/6.20 tff(5712,plain,
% 8.99/6.20 (hskp52),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5711, 5704])).
% 8.99/6.20 tff(5713,plain,
% 8.99/6.20 (c3_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[536, 5712])).
% 8.99/6.20 tff(5714,plain,
% 8.99/6.20 (c2_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[547, 5712])).
% 8.99/6.20 tff(5715,plain,
% 8.99/6.20 (c0_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[525, 5712])).
% 8.99/6.20 tff(5716,plain,
% 8.99/6.20 (~hskp12),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[4796, 4790, 5715, 5714, 5713])).
% 8.99/6.20 tff(5717,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[3790, 221, 4790, 5715, 5714, 5713, 20, 627])).
% 8.99/6.20 tff(5718,plain,(c1_1(a1654) | hskp26), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5719,plain,
% 8.99/6.20 (c1_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5718, 4790])).
% 8.99/6.20 tff(5720,plain,
% 8.99/6.20 (hskp13 | hskp12 | (~c1_1(a1654))),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[898, 221, 5714, 5713, 893])).
% 8.99/6.20 tff(5721,plain,
% 8.99/6.20 (hskp13),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5720, 5719, 5716])).
% 8.99/6.20 tff(5722,plain,
% 8.99/6.20 (~c1_1(a1667)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[303, 5721])).
% 8.99/6.20 tff(5723,plain,
% 8.99/6.20 (c3_1(a1667)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[314, 5721])).
% 8.99/6.20 tff(5724,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5725,plain,
% 8.99/6.20 ((hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654))) <=> (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5726,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5725])).
% 8.99/6.20 tff(5727,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5726, 5724])).
% 8.99/6.20 tff(5728,plain,
% 8.99/6.20 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5729,plain,
% 8.99/6.20 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5728, 5727])).
% 8.99/6.20 tff(5730,plain,
% 8.99/6.20 (~c2_1(a1667)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5729, 221, 4790, 5715, 5714, 5713, 5723, 5722, 20])).
% 8.99/6.20 tff(5731,plain,
% 8.99/6.20 (c0_1(a1667)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[325, 5721])).
% 8.99/6.20 tff(5732,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[4815, 221, 5715, 5713, 5731, 5723, 5722, 647, 5719, 5730])).
% 8.99/6.20 tff(5733,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5734,plain,
% 8.99/6.20 (~c2_1(a1691)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[669, 5733])).
% 8.99/6.20 tff(5735,plain,
% 8.99/6.20 (~c1_1(a1691)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[675, 5733])).
% 8.99/6.20 tff(5736,plain,
% 8.99/6.20 (~c3_1(a1691)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[689, 5733])).
% 8.99/6.20 tff(5737,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5738,plain,
% 8.99/6.20 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5739,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5738])).
% 8.99/6.20 tff(5740,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5739, 5737])).
% 8.99/6.20 tff(5741,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1678) | c2_1(a1678) | c1_1(a1678) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5742,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5741, 5740])).
% 8.99/6.20 tff(5743,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5742, 221, 5605, 5614, 5604, 962, 961, 964, 248, 242, 261, 30])).
% 8.99/6.20 tff(5744,plain,((~hskp17) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5745,plain,
% 8.99/6.20 (~hskp17),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5744, 5736, 5735, 5734])).
% 8.99/6.20 tff(5746,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5747,plain,
% 8.99/6.20 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)) <=> (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5748,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5747])).
% 8.99/6.20 tff(5749,plain,
% 8.99/6.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5748, 5746])).
% 8.99/6.20 tff(5750,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5751,plain,
% 8.99/6.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 8.99/6.20 tff(5752,plain,
% 8.99/6.20 ($false),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5751, 221, 5605, 5614, 5604, 5736, 5735, 5734, 124, 118, 112, 30])).
% 8.99/6.20 tff(5753,plain,(~hskp16), inference(lemma,lemma(discharge,[]))).
% 8.99/6.20 tff(5754,plain,
% 8.99/6.20 (hskp17 | hskp16 | c1_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[716, 221, 5715, 5713, 10])).
% 8.99/6.20 tff(5755,plain,
% 8.99/6.20 (c1_1(a1654)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5754, 5753, 5745])).
% 8.99/6.20 tff(5756,assumption,(c1_1(a1691)), introduced(assumption)).
% 8.99/6.20 tff(5757,plain,
% 8.99/6.20 (c0_1(a1691)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[4630, 962, 5714, 5713, 578, 964, 5715])).
% 8.99/6.20 tff(5758,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5759,plain,
% 8.99/6.20 ((hskp61 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c2_1(a1691) | (~c1_1(a1691)) | (~c0_1(a1691))) <=> (hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5760,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c2_1(a1691) | (~c1_1(a1691)) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691))))),
% 8.99/6.20 inference(monotonicity,[status(thm)],[5759])).
% 8.99/6.20 tff(5761,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c2_1(a1691) | (~c1_1(a1691)) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)))),
% 8.99/6.20 inference(transitivity,[status(thm)],[5760, 5758])).
% 8.99/6.20 tff(5762,plain,
% 8.99/6.20 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp61 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c2_1(a1691) | (~c1_1(a1691)) | (~c0_1(a1691)))),
% 8.99/6.20 inference(quant_inst,[status(thm)],[])).
% 8.99/6.20 tff(5763,plain,
% 8.99/6.20 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1691) | (~c1_1(a1691)) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691))),
% 8.99/6.20 inference(modus_ponens,[status(thm)],[5762, 5761])).
% 8.99/6.20 tff(5764,plain,
% 8.99/6.20 (hskp61 | (~c1_1(a1691))),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5763, 221, 962, 964, 1249, 5757])).
% 8.99/6.20 tff(5765,plain,
% 8.99/6.20 (hskp61),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[5764, 5756])).
% 8.99/6.20 tff(5766,plain,
% 8.99/6.20 (~c2_1(a1674)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1187, 5765])).
% 8.99/6.20 tff(5767,plain,
% 8.99/6.20 (~c1_1(a1674)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1193, 5765])).
% 8.99/6.20 tff(5768,plain,
% 8.99/6.20 (c3_1(a1674)),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[1204, 5765])).
% 8.99/6.20 tff(5769,plain,
% 8.99/6.20 (~hskp26),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[675, 5756])).
% 8.99/6.20 tff(5770,plain,
% 8.99/6.20 (~hskp12),
% 8.99/6.20 inference(unit_resolution,[status(thm)],[4796, 5769, 5715, 5714, 5713])).
% 8.99/6.20 tff(5771,plain,
% 8.99/6.20 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.20 tff(5772,plain,
% 8.99/6.20 ((hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695))) <=> (hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695))),
% 8.99/6.20 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5773,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695)))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5772])).
% 8.99/6.21 tff(5774,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5773, 5771])).
% 8.99/6.21 tff(5775,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp57 | (~ndr1_0) | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1695) | c1_1(a1695) | (~c2_1(a1695)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5776,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695)),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5775, 5774])).
% 8.99/6.21 tff(5777,plain,
% 8.99/6.21 (hskp57 | c1_1(a1695)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5776, 221, 5605, 5604, 962, 964, 1627, 5757])).
% 8.99/6.21 tff(5778,plain,
% 8.99/6.21 (c1_1(a1695)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5777, 1628])).
% 8.99/6.21 tff(5779,plain,
% 8.99/6.21 (hskp75 | (~c1_1(a1695))),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[2814, 221, 2296, 5605, 2294, 2338, 5604, 428])).
% 8.99/6.21 tff(5780,plain,
% 8.99/6.21 (hskp75),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5779, 5778])).
% 8.99/6.21 tff(5781,plain,
% 8.99/6.21 (~c2_1(a1724)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[441, 5780])).
% 8.99/6.21 tff(5782,plain,
% 8.99/6.21 (c3_1(a1724)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[474, 5780])).
% 8.99/6.21 tff(5783,plain,
% 8.99/6.21 (c0_1(a1724)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[485, 5780])).
% 8.99/6.21 tff(5784,plain,
% 8.99/6.21 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5785,plain,
% 8.99/6.21 ((hskp57 | hskp11 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724))) <=> (hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5786,plain,
% 8.99/6.21 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5785])).
% 8.99/6.21 tff(5787,plain,
% 8.99/6.21 (((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)))) <=> ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5786, 5784])).
% 8.99/6.21 tff(5788,plain,
% 8.99/6.21 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp57 | hskp11 | (~ndr1_0) | c2_1(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5789,plain,
% 8.99/6.21 ((~![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp57 | hskp11 | c2_1(a1724) | (~ndr1_0) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 8.99/6.21 tff(5790,plain,
% 8.99/6.21 (hskp11),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5789, 221, 1628, 5783, 5782, 5781, 1639])).
% 8.99/6.21 tff(5791,plain,
% 8.99/6.21 (~c1_1(a1664)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1675, 5790])).
% 8.99/6.21 tff(5792,plain,
% 8.99/6.21 (~c2_1(a1664)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1654, 5790])).
% 8.99/6.21 tff(5793,plain,
% 8.99/6.21 (~c3_1(a1664)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1660, 5790])).
% 8.99/6.21 tff(5794,plain,
% 8.99/6.21 (~hskp17),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5691, 5793, 5792, 5791])).
% 8.99/6.21 tff(5795,plain,
% 8.99/6.21 (hskp16),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5754, 627, 271])).
% 8.99/6.21 tff(5796,plain,
% 8.99/6.21 (~c2_1(a1677)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[117, 5795])).
% 8.99/6.21 tff(5797,plain,
% 8.99/6.21 (~c0_1(a1677)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[123, 5795])).
% 8.99/6.21 tff(5798,plain,
% 8.99/6.21 (c3_1(a1677)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[798, 5797, 5714, 5713, 578, 5796, 5715])).
% 8.99/6.21 tff(5799,plain,
% 8.99/6.21 (~c1_1(a1677)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[111, 5795])).
% 8.99/6.21 tff(5800,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5801,plain,
% 8.99/6.21 (((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5802,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5801])).
% 8.99/6.21 tff(5803,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5802, 5800])).
% 8.99/6.21 tff(5804,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677)) | c1_1(a1654) | (~c3_1(a1654)) | (~c0_1(a1654)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5805,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5804, 5803])).
% 8.99/6.21 tff(5806,plain,
% 8.99/6.21 ($false),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5805, 221, 5715, 5713, 5605, 5604, 5797, 5799, 102, 627, 5131, 5798])).
% 8.99/6.21 tff(5807,plain,(c1_1(a1654) | (~c1_1(a1695)) | hskp72 | hskp17), inference(lemma,lemma(discharge,[]))).
% 8.99/6.21 tff(5808,plain,
% 8.99/6.21 (c1_1(a1654)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5807, 5778, 578, 5794])).
% 8.99/6.21 tff(5809,plain,
% 8.99/6.21 (hskp13),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5720, 5808, 5292])).
% 8.99/6.21 tff(5810,plain,
% 8.99/6.21 (~c1_1(a1667)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[303, 5809])).
% 8.99/6.21 tff(5811,plain,
% 8.99/6.21 (hskp47 | (~c1_1(a1654))),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[4666, 221, 5715, 5713, 962, 964, 1848, 5757])).
% 8.99/6.21 tff(5812,plain,
% 8.99/6.21 (hskp47),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5811, 5808])).
% 8.99/6.21 tff(5813,plain,
% 8.99/6.21 (~c0_1(a1644)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1861, 5812])).
% 8.99/6.21 tff(5814,plain,
% 8.99/6.21 (~c1_1(a1644)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1867, 5812])).
% 8.99/6.21 tff(5815,plain,
% 8.99/6.21 (c3_1(a1667)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[314, 5809])).
% 8.99/6.21 tff(5816,plain,
% 8.99/6.21 (c0_1(a1667)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[325, 5809])).
% 8.99/6.21 tff(5817,plain,
% 8.99/6.21 (c3_1(a1644)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1880, 5812])).
% 8.99/6.21 tff(5818,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5819,plain,
% 8.99/6.21 (((~ndr1_0) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695))) <=> (c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5820,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5819])).
% 8.99/6.21 tff(5821,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5820, 5818])).
% 8.99/6.21 tff(5822,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5823,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644))),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5822, 5821])).
% 8.99/6.21 tff(5824,plain,
% 8.99/6.21 ($false),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5823, 221, 5817, 5605, 5816, 5815, 5814, 5813, 5604, 5810, 102, 5778])).
% 8.99/6.21 tff(5825,plain,(hskp57 | hskp12 | c3_1(a1691) | c2_1(a1691) | hskp72 | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674)), inference(lemma,lemma(discharge,[]))).
% 8.99/6.21 tff(5826,plain,
% 8.99/6.21 (hskp57),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5825, 5770, 962, 964, 578, 5768, 5767, 5766])).
% 8.99/6.21 tff(5827,plain,
% 8.99/6.21 (~c1_1(a1665)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[65, 5826])).
% 8.99/6.21 tff(5828,plain,
% 8.99/6.21 (c3_1(a1665)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[76, 5826])).
% 8.99/6.21 tff(5829,plain,
% 8.99/6.21 (c0_1(a1665)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[90, 5826])).
% 8.99/6.21 tff(5830,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5831,plain,
% 8.99/6.21 ((hskp26 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c0_1(a1665))) <=> (hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5832,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5831])).
% 8.99/6.21 tff(5833,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c0_1(a1665)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5832, 5830])).
% 8.99/6.21 tff(5834,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | c1_1(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c0_1(a1665)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5835,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 8.99/6.21 tff(5836,plain,
% 8.99/6.21 (~c2_1(a1665)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5835, 221, 5769, 5829, 5828, 5827, 20])).
% 8.99/6.21 tff(5837,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5838,plain,
% 8.99/6.21 (((~ndr1_0) | c2_1(a1665) | c1_1(a1665) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674))) <=> (c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5839,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1665) | c1_1(a1665) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5838])).
% 8.99/6.21 tff(5840,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1665) | c1_1(a1665) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5839, 5837])).
% 8.99/6.21 tff(5841,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1665) | c1_1(a1665) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c1_1(a1654)) | (~c0_1(a1654)) | c1_1(a1674) | c2_1(a1674) | (~c3_1(a1674)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5842,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5841, 5840])).
% 8.99/6.21 tff(5843,plain,
% 8.99/6.21 (~c1_1(a1654)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5842, 221, 5768, 5829, 5715, 5713, 5767, 5766, 5827, 647, 5836])).
% 8.99/6.21 tff(5844,plain,
% 8.99/6.21 ($false),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[3790, 221, 5769, 5715, 5714, 5713, 20, 5843])).
% 8.99/6.21 tff(5845,plain,((~c1_1(a1691)) | c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 8.99/6.21 tff(5846,plain,
% 8.99/6.21 (~c1_1(a1691)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5845, 962, 964, 578])).
% 8.99/6.21 tff(5847,plain,
% 8.99/6.21 (~hskp17),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5744, 5846, 962, 964])).
% 8.99/6.21 tff(5848,plain,
% 8.99/6.21 (hskp57 | c1_1(a1695)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5776, 221, 5605, 5604, 962, 964, 1627, 940])).
% 8.99/6.21 tff(5849,plain,
% 8.99/6.21 (c1_1(a1695)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5848, 1628])).
% 8.99/6.21 tff(5850,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5851,plain,
% 8.99/6.21 ((hskp2 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c1_1(a1695)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691))) <=> (hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5852,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c1_1(a1695)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5851])).
% 8.99/6.21 tff(5853,plain,
% 8.99/6.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c1_1(a1695)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5852, 5850])).
% 8.99/6.21 tff(5854,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c1_1(a1695)) | c3_1(a1691) | c1_1(a1691) | (~c0_1(a1691)))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 8.99/6.21 tff(5855,plain,
% 8.99/6.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c1_1(a1695)) | (~c0_1(a1695))),
% 8.99/6.21 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 8.99/6.21 tff(5856,plain,
% 8.99/6.21 (hskp2 | c1_1(a1691) | (~c1_1(a1695))),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5855, 221, 5614, 5604, 962, 960, 940])).
% 8.99/6.21 tff(5857,plain,
% 8.99/6.21 (hskp2),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[5856, 5849, 961])).
% 8.99/6.21 tff(5858,plain,
% 8.99/6.21 (~c3_1(a1645)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1144, 5857])).
% 8.99/6.21 tff(5859,plain,
% 8.99/6.21 (~c0_1(a1645)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1122, 5857])).
% 8.99/6.21 tff(5860,plain,
% 8.99/6.21 (~c1_1(a1645)),
% 8.99/6.21 inference(unit_resolution,[status(thm)],[1128, 5857])).
% 8.99/6.21 tff(5861,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5862,plain,
% 8.99/6.21 (((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1645) | c1_1(a1645) | c2_1(a1645)) <=> (c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(rewrite,[status(thm)],[])).
% 8.99/6.21 tff(5863,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1645) | c1_1(a1645) | c2_1(a1645))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695))))),
% 8.99/6.21 inference(monotonicity,[status(thm)],[5862])).
% 8.99/6.21 tff(5864,plain,
% 8.99/6.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1645) | c1_1(a1645) | c2_1(a1645))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695)))),
% 8.99/6.21 inference(transitivity,[status(thm)],[5863, 5861])).
% 8.99/6.21 tff(5865,plain,
% 8.99/6.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1695) | (~c0_1(a1695)) | (~c2_1(a1695)) | c0_1(a1645) | c2_1(a1645) | c1_1(a1645) | c3_1(a1645) | c1_1(a1645) | c2_1(a1645))),
% 8.99/6.21 inference(quant_inst,[status(thm)],[])).
% 9.09/6.23 tff(5866,plain,
% 9.09/6.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 9.09/6.23 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 9.09/6.23 tff(5867,plain,
% 9.09/6.23 (c2_1(a1645)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5866, 221, 5605, 5614, 5604, 5860, 5859, 5858, 30])).
% 9.09/6.23 tff(5868,plain,
% 9.09/6.23 ($false),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[4708, 221, 1628, 962, 964, 5860, 5858, 1627, 940, 5867])).
% 9.09/6.23 tff(5869,plain,(hskp57 | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c1_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 9.09/6.23 tff(5870,plain,
% 9.09/6.23 (hskp57),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5869, 962, 964, 5757, 5846])).
% 9.09/6.23 tff(5871,plain,
% 9.09/6.23 ($false),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[3209, 221, 271, 272, 91, 77, 66, 10])).
% 9.09/6.23 tff(5872,plain,((~hskp57) | hskp17 | hskp16), inference(lemma,lemma(discharge,[]))).
% 9.09/6.23 tff(5873,plain,
% 9.09/6.23 (hskp16),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5872, 5870, 5847])).
% 9.09/6.23 tff(5874,plain,
% 9.09/6.23 (~c1_1(a1677)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[111, 5873])).
% 9.09/6.23 tff(5875,plain,
% 9.09/6.23 (~c2_1(a1677)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[117, 5873])).
% 9.09/6.23 tff(5876,plain,
% 9.09/6.23 (~c0_1(a1677)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[123, 5873])).
% 9.09/6.23 tff(5877,plain,
% 9.09/6.23 ($false),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5751, 221, 5605, 5614, 5604, 962, 5846, 964, 5876, 5875, 5874, 30])).
% 9.09/6.23 tff(5878,plain,(c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 9.09/6.23 tff(5879,plain,
% 9.09/6.23 (hskp72),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5878, 5734, 5736])).
% 9.09/6.23 tff(5880,plain,
% 9.09/6.23 (~c2_1(a1715)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[553, 5879])).
% 9.09/6.23 tff(5881,plain,
% 9.09/6.23 (c3_1(a1715)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[1307, 5879])).
% 9.09/6.23 tff(5882,plain,
% 9.09/6.23 (c1_1(a1715)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[2399, 5879])).
% 9.09/6.23 tff(5883,plain,
% 9.09/6.23 (hskp13 | (~c1_1(a1654))),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5564, 221, 5882, 5881, 5715, 5713, 5880, 290])).
% 9.09/6.23 tff(5884,plain,
% 9.09/6.23 (hskp13),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[5883, 5755])).
% 9.09/6.23 tff(5885,plain,
% 9.09/6.23 (~c1_1(a1667)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[303, 5884])).
% 9.09/6.23 tff(5886,plain,
% 9.09/6.23 (c3_1(a1667)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[314, 5884])).
% 9.09/6.23 tff(5887,plain,
% 9.09/6.23 (c0_1(a1667)),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[325, 5884])).
% 9.09/6.23 tff(5888,plain,
% 9.09/6.23 ($false),
% 9.09/6.23 inference(unit_resolution,[status(thm)],[332, 221, 5745, 5753, 5887, 5886, 5885, 10])).
% 9.09/6.23 % SZS output end Proof
%------------------------------------------------------------------------------