%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN457-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:11 AM UTC 2025
% Result : Unsatisfiable 4.49s 4.66s
% Output : Proof 4.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN457-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.49/4.66 % SZS status Unsatisfiable
% 4.49/4.66 % SZS output start Proof
% 4.49/4.66 tff(c0_1_type, type, (
% 4.49/4.66 c0_1: $i > $o)).
% 4.49/4.66 tff(c3_1_type, type, (
% 4.49/4.66 c3_1: $i > $o)).
% 4.49/4.66 tff(c1_1_type, type, (
% 4.49/4.66 c1_1: $i > $o)).
% 4.49/4.66 tff(ndr1_0_type, type, (
% 4.49/4.66 ndr1_0: $o)).
% 4.49/4.66 tff(hskp16_type, type, (
% 4.49/4.66 hskp16: $o)).
% 4.49/4.66 tff(hskp17_type, type, (
% 4.49/4.66 hskp17: $o)).
% 4.49/4.66 tff(a1667_type, type, (
% 4.49/4.66 a1667: $i)).
% 4.49/4.66 tff(hskp13_type, type, (
% 4.49/4.66 hskp13: $o)).
% 4.49/4.66 tff(a1654_type, type, (
% 4.49/4.66 a1654: $i)).
% 4.49/4.66 tff(c2_1_type, type, (
% 4.49/4.66 c2_1: $i > $o)).
% 4.49/4.66 tff(a1691_type, type, (
% 4.49/4.66 a1691: $i)).
% 4.49/4.66 tff(hskp26_type, type, (
% 4.49/4.66 hskp26: $o)).
% 4.49/4.66 tff(hskp12_type, type, (
% 4.49/4.66 hskp12: $o)).
% 4.49/4.66 tff(hskp52_type, type, (
% 4.49/4.66 hskp52: $o)).
% 4.49/4.66 tff(hskp7_type, type, (
% 4.49/4.66 hskp7: $o)).
% 4.49/4.66 tff(a1664_type, type, (
% 4.49/4.66 a1664: $i)).
% 4.49/4.66 tff(hskp11_type, type, (
% 4.49/4.66 hskp11: $o)).
% 4.49/4.66 tff(hskp57_type, type, (
% 4.49/4.66 hskp57: $o)).
% 4.49/4.66 tff(a1655_type, type, (
% 4.49/4.66 a1655: $i)).
% 4.49/4.66 tff(a1678_type, type, (
% 4.49/4.66 a1678: $i)).
% 4.49/4.66 tff(a1665_type, type, (
% 4.49/4.66 a1665: $i)).
% 4.49/4.66 tff(a1695_type, type, (
% 4.49/4.66 a1695: $i)).
% 4.49/4.66 tff(a1677_type, type, (
% 4.49/4.66 a1677: $i)).
% 4.49/4.66 tff(hskp29_type, type, (
% 4.49/4.66 hskp29: $o)).
% 4.49/4.66 tff(a1644_type, type, (
% 4.49/4.66 a1644: $i)).
% 4.49/4.66 tff(hskp47_type, type, (
% 4.49/4.66 hskp47: $o)).
% 4.49/4.66 tff(a1656_type, type, (
% 4.49/4.66 a1656: $i)).
% 4.49/4.66 tff(a1715_type, type, (
% 4.49/4.66 a1715: $i)).
% 4.49/4.66 tff(hskp53_type, type, (
% 4.49/4.66 hskp53: $o)).
% 4.49/4.66 tff(hskp23_type, type, (
% 4.49/4.66 hskp23: $o)).
% 4.49/4.66 tff(hskp65_type, type, (
% 4.49/4.66 hskp65: $o)).
% 4.49/4.66 tff(hskp64_type, type, (
% 4.49/4.66 hskp64: $o)).
% 4.49/4.66 tff(a1673_type, type, (
% 4.49/4.66 a1673: $i)).
% 4.49/4.66 tff(hskp60_type, type, (
% 4.49/4.66 hskp60: $o)).
% 4.49/4.66 tff(a1724_type, type, (
% 4.49/4.66 a1724: $i)).
% 4.49/4.66 tff(hskp75_type, type, (
% 4.49/4.66 hskp75: $o)).
% 4.49/4.66 tff(hskp72_type, type, (
% 4.49/4.66 hskp72: $o)).
% 4.49/4.66 tff(a1714_type, type, (
% 4.49/4.66 a1714: $i)).
% 4.49/4.66 tff(hskp37_type, type, (
% 4.49/4.66 hskp37: $o)).
% 4.49/4.66 tff(a1725_type, type, (
% 4.49/4.66 a1725: $i)).
% 4.49/4.66 tff(hskp40_type, type, (
% 4.49/4.66 hskp40: $o)).
% 4.49/4.66 tff(a1637_type, type, (
% 4.49/4.66 a1637: $i)).
% 4.49/4.66 tff(hskp0_type, type, (
% 4.49/4.66 hskp0: $o)).
% 4.49/4.66 tff(a1666_type, type, (
% 4.49/4.66 a1666: $i)).
% 4.49/4.66 tff(a1645_type, type, (
% 4.49/4.66 a1645: $i)).
% 4.49/4.66 tff(hskp2_type, type, (
% 4.49/4.66 hskp2: $o)).
% 4.49/4.66 tff(a1638_type, type, (
% 4.49/4.66 a1638: $i)).
% 4.49/4.66 tff(hskp42_type, type, (
% 4.49/4.66 hskp42: $o)).
% 4.49/4.66 tff(hskp74_type, type, (
% 4.49/4.66 hskp74: $o)).
% 4.49/4.66 tff(hskp38_type, type, (
% 4.49/4.66 hskp38: $o)).
% 4.49/4.66 tff(a1718_type, type, (
% 4.49/4.66 a1718: $i)).
% 4.49/4.66 tff(a1717_type, type, (
% 4.49/4.66 a1717: $i)).
% 4.49/4.66 tff(hskp61_type, type, (
% 4.49/4.66 hskp61: $o)).
% 4.49/4.66 tff(a1674_type, type, (
% 4.49/4.66 a1674: $i)).
% 4.49/4.66 tff(a1709_type, type, (
% 4.49/4.66 a1709: $i)).
% 4.49/4.66 tff(hskp69_type, type, (
% 4.49/4.66 hskp69: $o)).
% 4.49/4.66 tff(a1683_type, type, (
% 4.49/4.66 a1683: $i)).
% 4.49/4.66 tff(hskp21_type, type, (
% 4.49/4.66 hskp21: $o)).
% 4.49/4.66 tff(a1716_type, type, (
% 4.49/4.66 a1716: $i)).
% 4.49/4.66 tff(a1721_type, type, (
% 4.49/4.66 a1721: $i)).
% 4.49/4.66 tff(hskp39_type, type, (
% 4.49/4.66 hskp39: $o)).
% 4.49/4.66 tff(hskp73_type, type, (
% 4.49/4.66 hskp73: $o)).
% 4.49/4.66 tff(a1702_type, type, (
% 4.49/4.66 a1702: $i)).
% 4.49/4.66 tff(hskp67_type, type, (
% 4.49/4.66 hskp67: $o)).
% 4.49/4.66 tff(a1712_type, type, (
% 4.49/4.66 a1712: $i)).
% 4.49/4.66 tff(hskp36_type, type, (
% 4.49/4.66 hskp36: $o)).
% 4.49/4.66 tff(hskp71_type, type, (
% 4.49/4.66 hskp71: $o)).
% 4.49/4.66 tff(a1713_type, type, (
% 4.49/4.66 a1713: $i)).
% 4.49/4.66 tff(a1676_type, type, (
% 4.49/4.66 a1676: $i)).
% 4.49/4.66 tff(hskp63_type, type, (
% 4.49/4.66 hskp63: $o)).
% 4.49/4.66 tff(a1698_type, type, (
% 4.49/4.66 a1698: $i)).
% 4.49/4.66 tff(hskp30_type, type, (
% 4.49/4.66 hskp30: $o)).
% 4.49/4.66 tff(a1710_type, type, (
% 4.49/4.66 a1710: $i)).
% 4.49/4.66 tff(hskp70_type, type, (
% 4.49/4.66 hskp70: $o)).
% 4.49/4.66 tff(a1690_type, type, (
% 4.49/4.66 a1690: $i)).
% 4.49/4.66 tff(hskp25_type, type, (
% 4.49/4.66 hskp25: $o)).
% 4.49/4.66 tff(a1675_type, type, (
% 4.49/4.66 a1675: $i)).
% 4.49/4.66 tff(hskp62_type, type, (
% 4.49/4.66 hskp62: $o)).
% 4.49/4.66 tff(a1704_type, type, (
% 4.49/4.66 a1704: $i)).
% 4.49/4.66 tff(hskp33_type, type, (
% 4.49/4.66 hskp33: $o)).
% 4.49/4.66 tff(hskp59_type, type, (
% 4.49/4.66 hskp59: $o)).
% 4.49/4.66 tff(hskp58_type, type, (
% 4.49/4.66 hskp58: $o)).
% 4.49/4.66 tff(a1668_type, type, (
% 4.49/4.66 a1668: $i)).
% 4.49/4.66 tff(a1669_type, type, (
% 4.49/4.66 a1669: $i)).
% 4.49/4.66 tff(a1639_type, type, (
% 4.49/4.66 a1639: $i)).
% 4.49/4.66 tff(hskp43_type, type, (
% 4.49/4.66 hskp43: $o)).
% 4.49/4.66 tff(hskp44_type, type, (
% 4.49/4.66 hskp44: $o)).
% 4.49/4.66 tff(a1640_type, type, (
% 4.49/4.66 a1640: $i)).
% 4.49/4.66 tff(hskp45_type, type, (
% 4.49/4.66 hskp45: $o)).
% 4.49/4.66 tff(a1641_type, type, (
% 4.49/4.66 a1641: $i)).
% 4.49/4.66 tff(a1684_type, type, (
% 4.49/4.66 a1684: $i)).
% 4.49/4.66 tff(hskp22_type, type, (
% 4.49/4.66 hskp22: $o)).
% 4.49/4.66 tff(a1705_type, type, (
% 4.49/4.66 a1705: $i)).
% 4.49/4.66 tff(hskp34_type, type, (
% 4.49/4.66 hskp34: $o)).
% 4.49/4.66 tff(1,plain,
% 4.49/4.66 (^[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))))),
% 4.49/4.66 inference(bind,[status(th)],[])).
% 4.49/4.66 tff(2,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(quant_intro,[status(thm)],[1])).
% 4.49/4.66 tff(3,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(rewrite,[status(thm)],[])).
% 4.49/4.66 tff(4,plain,
% 4.49/4.66 (^[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)))))),
% 4.49/4.66 inference(bind,[status(th)],[])).
% 4.49/4.66 tff(5,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(quant_intro,[status(thm)],[4])).
% 4.49/4.66 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')).
% 4.49/4.66 tff(7,plain,
% 4.49/4.66 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[6, 5])).
% 4.49/4.66 tff(8,plain,
% 4.49/4.66 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.49/4.66 tff(9,plain,(
% 4.49/4.66 ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.49/4.66 inference(skolemize,[status(sab)],[8])).
% 4.49/4.66 tff(10,plain,
% 4.49/4.66 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[9, 2])).
% 4.49/4.66 tff(11,plain,
% 4.49/4.66 (^[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))))),
% 4.49/4.66 inference(bind,[status(th)],[])).
% 4.49/4.66 tff(12,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(quant_intro,[status(thm)],[11])).
% 4.49/4.66 tff(13,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(rewrite,[status(thm)],[])).
% 4.49/4.66 tff(14,plain,
% 4.49/4.66 (^[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)))))),
% 4.49/4.66 inference(bind,[status(th)],[])).
% 4.49/4.66 tff(15,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(quant_intro,[status(thm)],[14])).
% 4.49/4.66 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')).
% 4.49/4.66 tff(17,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[16, 15])).
% 4.49/4.66 tff(18,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[17, 13])).
% 4.49/4.66 tff(19,plain,(
% 4.49/4.66 ![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)))),
% 4.49/4.66 inference(skolemize,[status(sab)],[18])).
% 4.49/4.66 tff(20,plain,
% 4.49/4.66 (![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)))),
% 4.49/4.66 inference(modus_ponens,[status(thm)],[19, 12])).
% 4.49/4.66 tff(21,plain,
% 4.49/4.66 (^[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)))),
% 4.49/4.66 inference(bind,[status(th)],[])).
% 4.49/4.66 tff(22,plain,
% 4.49/4.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.49/4.66 inference(quant_intro,[status(thm)],[21])).
% 4.49/4.66 tff(23,plain,
% 4.49/4.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.49/4.66 inference(rewrite,[status(thm)],[])).
% 4.49/4.66 tff(24,plain,
% 4.49/4.66 (^[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))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(25,plain,
% 4.49/4.67 (![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))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[24])).
% 4.49/4.67 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')).
% 4.49/4.67 tff(27,plain,
% 4.49/4.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[26, 25])).
% 4.49/4.67 tff(28,plain,
% 4.49/4.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[27, 23])).
% 4.49/4.67 tff(29,plain,(
% 4.49/4.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 4.49/4.67 inference(skolemize,[status(sab)],[28])).
% 4.49/4.67 tff(30,plain,
% 4.49/4.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[29, 22])).
% 4.49/4.67 tff(31,assumption,(hskp7), introduced(assumption)).
% 4.49/4.67 tff(32,plain,
% 4.49/4.67 (((~hskp7) | c3_1(a1655)) <=> ((~hskp7) | c3_1(a1655))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(33,axiom,((~hskp7) | c3_1(a1655)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 4.49/4.67 tff(34,plain,
% 4.49/4.67 ((~hskp7) | c3_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[33, 32])).
% 4.49/4.67 tff(35,plain,
% 4.49/4.67 ((~hskp7) | c3_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[34, 32])).
% 4.49/4.67 tff(36,plain,
% 4.49/4.67 ((~hskp7) | c3_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[35, 32])).
% 4.49/4.67 tff(37,plain,
% 4.49/4.67 ((~hskp7) | c3_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[36, 32])).
% 4.49/4.67 tff(38,plain,
% 4.49/4.67 ((~hskp7) | c3_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[37, 32])).
% 4.49/4.67 tff(39,plain,
% 4.49/4.67 (c3_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[38, 31])).
% 4.49/4.67 tff(40,plain,
% 4.49/4.67 (((~hskp7) | (~c2_1(a1655))) <=> ((~hskp7) | (~c2_1(a1655)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(41,plain,
% 4.49/4.67 (((~c2_1(a1655)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1655)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(42,axiom,((~c2_1(a1655)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause297')).
% 4.49/4.67 tff(43,plain,
% 4.49/4.67 ((~hskp7) | (~c2_1(a1655))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[42, 41])).
% 4.49/4.67 tff(44,plain,
% 4.49/4.67 ((~hskp7) | (~c2_1(a1655))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[43, 40])).
% 4.49/4.67 tff(45,plain,
% 4.49/4.67 (~c2_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[44, 31])).
% 4.49/4.67 tff(46,plain,
% 4.49/4.67 (((~hskp7) | c0_1(a1655)) <=> ((~hskp7) | c0_1(a1655))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(47,axiom,((~hskp7) | c0_1(a1655)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 4.49/4.67 tff(48,plain,
% 4.49/4.67 ((~hskp7) | c0_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.49/4.67 tff(49,plain,
% 4.49/4.67 ((~hskp7) | c0_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[48, 46])).
% 4.49/4.67 tff(50,plain,
% 4.49/4.67 ((~hskp7) | c0_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[49, 46])).
% 4.49/4.67 tff(51,plain,
% 4.49/4.67 ((~hskp7) | c0_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[50, 46])).
% 4.49/4.67 tff(52,plain,
% 4.49/4.67 ((~hskp7) | c0_1(a1655)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[51, 46])).
% 4.49/4.67 tff(53,plain,
% 4.49/4.67 (c0_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[52, 31])).
% 4.49/4.67 tff(54,assumption,(hskp57), introduced(assumption)).
% 4.49/4.67 tff(55,plain,
% 4.49/4.67 (((~hskp57) | (~c1_1(a1665))) <=> ((~hskp57) | (~c1_1(a1665)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(56,plain,
% 4.49/4.67 (((~c1_1(a1665)) | (~hskp57)) <=> ((~hskp57) | (~c1_1(a1665)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(57,axiom,((~c1_1(a1665)) | (~hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause209')).
% 4.49/4.67 tff(58,plain,
% 4.49/4.67 ((~hskp57) | (~c1_1(a1665))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 4.49/4.67 tff(59,plain,
% 4.49/4.67 ((~hskp57) | (~c1_1(a1665))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[58, 55])).
% 4.49/4.67 tff(60,plain,
% 4.49/4.67 (~c1_1(a1665)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[59, 54])).
% 4.49/4.67 tff(61,plain,
% 4.49/4.67 (((~hskp57) | c3_1(a1665)) <=> ((~hskp57) | c3_1(a1665))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(62,axiom,((~hskp57) | c3_1(a1665)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 4.49/4.67 tff(63,plain,
% 4.49/4.67 ((~hskp57) | c3_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[62, 61])).
% 4.49/4.67 tff(64,plain,
% 4.49/4.67 ((~hskp57) | c3_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[63, 61])).
% 4.49/4.67 tff(65,plain,
% 4.49/4.67 ((~hskp57) | c3_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[64, 61])).
% 4.49/4.67 tff(66,plain,
% 4.49/4.67 ((~hskp57) | c3_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[65, 61])).
% 4.49/4.67 tff(67,plain,
% 4.49/4.67 ((~hskp57) | c3_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[66, 61])).
% 4.49/4.67 tff(68,plain,
% 4.49/4.67 (c3_1(a1665)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[67, 54])).
% 4.49/4.67 tff(69,assumption,(c3_1(a1655)), introduced(assumption)).
% 4.49/4.67 tff(70,assumption,(~c2_1(a1655)), introduced(assumption)).
% 4.49/4.67 tff(71,assumption,(c0_1(a1655)), introduced(assumption)).
% 4.49/4.67 tff(72,plain,
% 4.49/4.67 (((~hskp57) | c0_1(a1665)) <=> ((~hskp57) | c0_1(a1665))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(73,axiom,((~hskp57) | c0_1(a1665)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 4.49/4.67 tff(74,plain,
% 4.49/4.67 ((~hskp57) | c0_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[73, 72])).
% 4.49/4.67 tff(75,plain,
% 4.49/4.67 ((~hskp57) | c0_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[74, 72])).
% 4.49/4.67 tff(76,plain,
% 4.49/4.67 ((~hskp57) | c0_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[75, 72])).
% 4.49/4.67 tff(77,plain,
% 4.49/4.67 ((~hskp57) | c0_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[76, 72])).
% 4.49/4.67 tff(78,plain,
% 4.49/4.67 ((~hskp57) | c0_1(a1665)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[77, 72])).
% 4.49/4.67 tff(79,plain,
% 4.49/4.67 (c0_1(a1665)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[78, 54])).
% 4.49/4.67 tff(80,assumption,(c3_1(a1678)), introduced(assumption)).
% 4.49/4.67 tff(81,plain,
% 4.49/4.67 (^[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))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(82,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[81])).
% 4.49/4.67 tff(83,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(84,plain,
% 4.49/4.67 (^[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)))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(85,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[84])).
% 4.49/4.67 tff(86,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')).
% 4.49/4.67 tff(87,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[86, 85])).
% 4.49/4.67 tff(88,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[87, 83])).
% 4.49/4.67 tff(89,plain,(
% 4.49/4.67 ![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)))),
% 4.49/4.67 inference(skolemize,[status(sab)],[88])).
% 4.49/4.67 tff(90,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[89, 82])).
% 4.49/4.67 tff(91,assumption,(~c1_1(a1665)), introduced(assumption)).
% 4.49/4.67 tff(92,assumption,(c3_1(a1665)), introduced(assumption)).
% 4.49/4.67 tff(93,assumption,(c0_1(a1665)), introduced(assumption)).
% 4.49/4.67 tff(94,assumption,(hskp16), introduced(assumption)).
% 4.49/4.67 tff(95,plain,
% 4.49/4.67 (((~hskp16) | (~c1_1(a1677))) <=> ((~hskp16) | (~c1_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(96,plain,
% 4.49/4.67 (((~c1_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(97,axiom,((~c1_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause280')).
% 4.49/4.67 tff(98,plain,
% 4.49/4.67 ((~hskp16) | (~c1_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[97, 96])).
% 4.49/4.67 tff(99,plain,
% 4.49/4.67 ((~hskp16) | (~c1_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[98, 95])).
% 4.49/4.67 tff(100,plain,
% 4.49/4.67 (~c1_1(a1677)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[99, 94])).
% 4.49/4.67 tff(101,plain,
% 4.49/4.67 (((~hskp16) | (~c2_1(a1677))) <=> ((~hskp16) | (~c2_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(102,plain,
% 4.49/4.67 (((~c2_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(103,axiom,((~c2_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 4.49/4.67 tff(104,plain,
% 4.49/4.67 ((~hskp16) | (~c2_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[103, 102])).
% 4.49/4.67 tff(105,plain,
% 4.49/4.67 ((~hskp16) | (~c2_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[104, 101])).
% 4.49/4.67 tff(106,plain,
% 4.49/4.67 (~c2_1(a1677)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[105, 94])).
% 4.49/4.67 tff(107,plain,
% 4.49/4.67 (((~hskp16) | (~c0_1(a1677))) <=> ((~hskp16) | (~c0_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(108,plain,
% 4.49/4.67 (((~c0_1(a1677)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1677)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(109,axiom,((~c0_1(a1677)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause278')).
% 4.49/4.67 tff(110,plain,
% 4.49/4.67 ((~hskp16) | (~c0_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[109, 108])).
% 4.49/4.67 tff(111,plain,
% 4.49/4.67 ((~hskp16) | (~c0_1(a1677))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[110, 107])).
% 4.49/4.67 tff(112,plain,
% 4.49/4.67 (~c0_1(a1677)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[111, 94])).
% 4.49/4.67 tff(113,assumption,(c3_1(a1677)), introduced(assumption)).
% 4.49/4.67 tff(114,assumption,(~c1_1(a1677)), introduced(assumption)).
% 4.49/4.67 tff(115,assumption,(~c0_1(a1677)), introduced(assumption)).
% 4.49/4.67 tff(116,plain,
% 4.49/4.67 (^[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))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(117,plain,
% 4.49/4.67 (![V: $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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[116])).
% 4.49/4.67 tff(118,plain,
% 4.49/4.67 (![V: $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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(119,plain,
% 4.49/4.67 (^[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)))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(120,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[119])).
% 4.49/4.67 tff(121,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')).
% 4.49/4.67 tff(122,plain,
% 4.49/4.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.49/4.67 tff(123,plain,
% 4.49/4.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[122, 118])).
% 4.49/4.67 tff(124,plain,(
% 4.49/4.67 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 4.49/4.67 inference(skolemize,[status(sab)],[123])).
% 4.49/4.67 tff(125,plain,
% 4.49/4.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[124, 117])).
% 4.49/4.67 tff(126,assumption,(~hskp29), introduced(assumption)).
% 4.49/4.67 tff(127,assumption,(~hskp52), introduced(assumption)).
% 4.49/4.67 tff(128,plain,
% 4.49/4.67 ((hskp53 | hskp52 | hskp29) <=> (hskp53 | hskp52 | hskp29)),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(129,plain,
% 4.49/4.67 (((hskp29 | hskp52) | hskp53) <=> (hskp53 | hskp52 | hskp29)),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(130,axiom,((hskp29 | hskp52) | hskp53), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 4.49/4.67 tff(131,plain,
% 4.49/4.67 (hskp53 | hskp52 | hskp29),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[130, 129])).
% 4.49/4.67 tff(132,plain,
% 4.49/4.67 (hskp53 | hskp52 | hskp29),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[131, 128])).
% 4.49/4.67 tff(133,plain,
% 4.49/4.67 (hskp53 | hskp52 | hskp29),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[132, 128])).
% 4.49/4.67 tff(134,plain,
% 4.49/4.67 (hskp53 | hskp52 | hskp29),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[133, 128])).
% 4.49/4.67 tff(135,plain,
% 4.49/4.67 (hskp53 | hskp52 | hskp29),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[134, 128])).
% 4.49/4.67 tff(136,plain,
% 4.49/4.67 (hskp53),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[135, 127, 126])).
% 4.49/4.67 tff(137,plain,
% 4.49/4.67 (((~hskp53) | c0_1(a1656)) <=> ((~hskp53) | c0_1(a1656))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(138,axiom,((~hskp53) | c0_1(a1656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 4.49/4.67 tff(139,plain,
% 4.49/4.67 ((~hskp53) | c0_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[138, 137])).
% 4.49/4.67 tff(140,plain,
% 4.49/4.67 ((~hskp53) | c0_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[139, 137])).
% 4.49/4.67 tff(141,plain,
% 4.49/4.67 ((~hskp53) | c0_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[140, 137])).
% 4.49/4.67 tff(142,plain,
% 4.49/4.67 ((~hskp53) | c0_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[141, 137])).
% 4.49/4.67 tff(143,plain,
% 4.49/4.67 ((~hskp53) | c0_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[142, 137])).
% 4.49/4.67 tff(144,plain,
% 4.49/4.67 (c0_1(a1656)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[143, 136])).
% 4.49/4.67 tff(145,plain,
% 4.49/4.67 (((~hskp53) | (~c3_1(a1656))) <=> ((~hskp53) | (~c3_1(a1656)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(146,plain,
% 4.49/4.67 (((~c3_1(a1656)) | (~hskp53)) <=> ((~hskp53) | (~c3_1(a1656)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(147,axiom,((~c3_1(a1656)) | (~hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause214')).
% 4.49/4.67 tff(148,plain,
% 4.49/4.67 ((~hskp53) | (~c3_1(a1656))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.49/4.67 tff(149,plain,
% 4.49/4.67 ((~hskp53) | (~c3_1(a1656))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[148, 145])).
% 4.49/4.67 tff(150,plain,
% 4.49/4.67 (~c3_1(a1656)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[149, 136])).
% 4.49/4.67 tff(151,plain,
% 4.49/4.67 (((~hskp53) | c2_1(a1656)) <=> ((~hskp53) | c2_1(a1656))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(152,axiom,((~hskp53) | c2_1(a1656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 4.49/4.67 tff(153,plain,
% 4.49/4.67 ((~hskp53) | c2_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[152, 151])).
% 4.49/4.67 tff(154,plain,
% 4.49/4.67 ((~hskp53) | c2_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[153, 151])).
% 4.49/4.67 tff(155,plain,
% 4.49/4.67 ((~hskp53) | c2_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[154, 151])).
% 4.49/4.67 tff(156,plain,
% 4.49/4.67 ((~hskp53) | c2_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[155, 151])).
% 4.49/4.67 tff(157,plain,
% 4.49/4.67 ((~hskp53) | c2_1(a1656)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[156, 151])).
% 4.49/4.67 tff(158,plain,
% 4.49/4.67 (c2_1(a1656)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[157, 136])).
% 4.49/4.67 tff(159,plain,
% 4.49/4.67 (^[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))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(160,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[159])).
% 4.49/4.67 tff(161,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(162,plain,
% 4.49/4.67 (^[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)))))),
% 4.49/4.67 inference(bind,[status(th)],[])).
% 4.49/4.67 tff(163,plain,
% 4.49/4.67 (![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)))),
% 4.49/4.67 inference(quant_intro,[status(thm)],[162])).
% 4.49/4.67 tff(164,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp52) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause324')).
% 4.49/4.67 tff(165,plain,
% 4.49/4.67 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[164, 163])).
% 4.49/4.67 tff(166,plain,
% 4.49/4.67 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[165, 161])).
% 4.49/4.67 tff(167,plain,(
% 4.49/4.67 ![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.49/4.67 inference(skolemize,[status(sab)],[166])).
% 4.49/4.67 tff(168,plain,
% 4.49/4.67 (![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[167, 160])).
% 4.49/4.67 tff(169,assumption,(~ndr1_0), introduced(assumption)).
% 4.49/4.67 tff(170,plain,
% 4.49/4.67 ((ndr1_0 | (~hskp23)) <=> (ndr1_0 | (~hskp23))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(171,plain,
% 4.49/4.67 (((~hskp23) | ndr1_0) <=> (ndr1_0 | (~hskp23))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(172,axiom,((~hskp23) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 4.49/4.67 tff(173,plain,
% 4.49/4.67 (ndr1_0 | (~hskp23)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[172, 171])).
% 4.49/4.67 tff(174,plain,
% 4.49/4.67 (ndr1_0 | (~hskp23)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[173, 170])).
% 4.49/4.67 tff(175,plain,
% 4.49/4.67 (~hskp23),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[174, 169])).
% 4.49/4.67 tff(176,plain,
% 4.49/4.67 ((ndr1_0 | (~hskp65)) <=> (ndr1_0 | (~hskp65))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(177,plain,
% 4.49/4.67 (((~hskp65) | ndr1_0) <=> (ndr1_0 | (~hskp65))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(178,axiom,((~hskp65) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 4.49/4.67 tff(179,plain,
% 4.49/4.67 (ndr1_0 | (~hskp65)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[178, 177])).
% 4.49/4.67 tff(180,plain,
% 4.49/4.67 (ndr1_0 | (~hskp65)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[179, 176])).
% 4.49/4.67 tff(181,plain,
% 4.49/4.67 (~hskp65),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[180, 169])).
% 4.49/4.67 tff(182,plain,
% 4.49/4.67 ((ndr1_0 | (~hskp64)) <=> (ndr1_0 | (~hskp64))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(183,plain,
% 4.49/4.67 (((~hskp64) | ndr1_0) <=> (ndr1_0 | (~hskp64))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(184,axiom,((~hskp64) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 4.49/4.67 tff(185,plain,
% 4.49/4.67 (ndr1_0 | (~hskp64)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[184, 183])).
% 4.49/4.67 tff(186,plain,
% 4.49/4.67 (ndr1_0 | (~hskp64)),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[185, 182])).
% 4.49/4.67 tff(187,plain,
% 4.49/4.67 (~hskp64),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[186, 169])).
% 4.49/4.67 tff(188,plain,
% 4.49/4.67 ((hskp65 | hskp64 | hskp23) <=> (hskp65 | hskp64 | hskp23)),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(189,plain,
% 4.49/4.67 (((hskp23 | hskp64) | hskp65) <=> (hskp65 | hskp64 | hskp23)),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(190,axiom,((hskp23 | hskp64) | hskp65), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 4.49/4.67 tff(191,plain,
% 4.49/4.67 (hskp65 | hskp64 | hskp23),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[190, 189])).
% 4.49/4.67 tff(192,plain,
% 4.49/4.67 (hskp65 | hskp64 | hskp23),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[191, 188])).
% 4.49/4.67 tff(193,plain,
% 4.49/4.67 (hskp65 | hskp64 | hskp23),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[192, 188])).
% 4.49/4.67 tff(194,plain,
% 4.49/4.67 (hskp65 | hskp64 | hskp23),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[193, 188])).
% 4.49/4.67 tff(195,plain,
% 4.49/4.67 (hskp65 | hskp64 | hskp23),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[194, 188])).
% 4.49/4.67 tff(196,plain,
% 4.49/4.67 ($false),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[195, 187, 181, 175])).
% 4.49/4.67 tff(197,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 4.49/4.67 tff(198,plain,
% 4.49/4.67 (((~![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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(199,plain,
% 4.49/4.67 ((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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(200,plain,
% 4.49/4.67 (((~![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))))),
% 4.49/4.67 inference(monotonicity,[status(thm)],[199])).
% 4.49/4.67 tff(201,plain,
% 4.49/4.67 (((~![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)))),
% 4.49/4.67 inference(transitivity,[status(thm)],[200, 198])).
% 4.49/4.67 tff(202,plain,
% 4.49/4.67 ((~![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)))),
% 4.49/4.67 inference(quant_inst,[status(thm)],[])).
% 4.49/4.67 tff(203,plain,
% 4.49/4.67 ((~![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))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[202, 201])).
% 4.49/4.67 tff(204,plain,
% 4.49/4.67 (hskp7),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[203, 197, 127, 158, 144, 150, 168])).
% 4.49/4.67 tff(205,plain,
% 4.49/4.67 (c0_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[52, 204])).
% 4.49/4.67 tff(206,plain,
% 4.49/4.67 (c3_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[38, 204])).
% 4.49/4.67 tff(207,plain,
% 4.49/4.67 (~c2_1(a1655)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[44, 204])).
% 4.49/4.67 tff(208,assumption,(c2_1(a1656)), introduced(assumption)).
% 4.49/4.67 tff(209,assumption,(~c3_1(a1656)), introduced(assumption)).
% 4.49/4.67 tff(210,assumption,(c0_1(a1656)), introduced(assumption)).
% 4.49/4.67 tff(211,assumption,(~c1_1(a1655)), introduced(assumption)).
% 4.49/4.67 tff(212,assumption,(hskp17), introduced(assumption)).
% 4.49/4.67 tff(213,plain,
% 4.49/4.67 (((~hskp17) | (~c1_1(a1678))) <=> ((~hskp17) | (~c1_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(214,plain,
% 4.49/4.67 (((~c1_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(215,axiom,((~c1_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause276')).
% 4.49/4.67 tff(216,plain,
% 4.49/4.67 ((~hskp17) | (~c1_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[215, 214])).
% 4.49/4.67 tff(217,plain,
% 4.49/4.67 ((~hskp17) | (~c1_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[216, 213])).
% 4.49/4.67 tff(218,plain,
% 4.49/4.67 (~c1_1(a1678)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[217, 212])).
% 4.49/4.67 tff(219,plain,
% 4.49/4.67 (((~hskp17) | (~c0_1(a1678))) <=> ((~hskp17) | (~c0_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(220,plain,
% 4.49/4.67 (((~c0_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(221,axiom,((~c0_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause275')).
% 4.49/4.67 tff(222,plain,
% 4.49/4.67 ((~hskp17) | (~c0_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[221, 220])).
% 4.49/4.67 tff(223,plain,
% 4.49/4.67 ((~hskp17) | (~c0_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[222, 219])).
% 4.49/4.67 tff(224,plain,
% 4.49/4.67 (~c0_1(a1678)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[223, 212])).
% 4.49/4.67 tff(225,plain,
% 4.49/4.67 (((~![V: $i, 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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(226,plain,
% 4.49/4.67 ((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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(227,plain,
% 4.49/4.67 (((~![V: $i, 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))))),
% 4.49/4.67 inference(monotonicity,[status(thm)],[226])).
% 4.49/4.67 tff(228,plain,
% 4.49/4.67 (((~![V: $i, 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)))),
% 4.49/4.67 inference(transitivity,[status(thm)],[227, 225])).
% 4.49/4.67 tff(229,plain,
% 4.49/4.67 ((~![V: $i, 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)))),
% 4.49/4.67 inference(quant_inst,[status(thm)],[])).
% 4.49/4.67 tff(230,plain,
% 4.49/4.67 ((~![V: $i, 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))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[229, 228])).
% 4.49/4.67 tff(231,plain,
% 4.49/4.67 (~c3_1(a1678)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[230, 197, 126, 69, 71, 224, 218, 125, 211])).
% 4.49/4.67 tff(232,plain,
% 4.49/4.67 (((~hskp17) | (~c2_1(a1678))) <=> ((~hskp17) | (~c2_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(233,plain,
% 4.49/4.67 (((~c2_1(a1678)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1678)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(234,axiom,((~c2_1(a1678)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause277')).
% 4.49/4.67 tff(235,plain,
% 4.49/4.67 ((~hskp17) | (~c2_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[234, 233])).
% 4.49/4.67 tff(236,plain,
% 4.49/4.67 ((~hskp17) | (~c2_1(a1678))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[235, 232])).
% 4.49/4.67 tff(237,plain,
% 4.49/4.67 (~c2_1(a1678)),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[236, 212])).
% 4.49/4.67 tff(238,plain,
% 4.49/4.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(239,plain,
% 4.49/4.67 (((~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)))),
% 4.49/4.67 inference(rewrite,[status(thm)],[])).
% 4.49/4.67 tff(240,plain,
% 4.49/4.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.49/4.67 inference(monotonicity,[status(thm)],[239])).
% 4.49/4.67 tff(241,plain,
% 4.49/4.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.49/4.67 inference(transitivity,[status(thm)],[240, 238])).
% 4.49/4.67 tff(242,plain,
% 4.49/4.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.49/4.67 inference(quant_inst,[status(thm)],[])).
% 4.49/4.67 tff(243,plain,
% 4.49/4.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.49/4.67 inference(modus_ponens,[status(thm)],[242, 241])).
% 4.49/4.67 tff(244,plain,
% 4.49/4.67 ($false),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[243, 197, 208, 210, 209, 224, 218, 237, 30, 231])).
% 4.49/4.67 tff(245,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,[]))).
% 4.49/4.67 tff(246,plain,
% 4.49/4.67 (~hskp17),
% 4.49/4.67 inference(unit_resolution,[status(thm)],[245, 211, 210, 209, 126, 69, 71, 208])).
% 4.49/4.67 tff(247,assumption,(~hskp17), introduced(assumption)).
% 4.49/4.67 tff(248,assumption,(~hskp16), introduced(assumption)).
% 4.49/4.68 tff(249,plain,
% 4.49/4.68 (((~![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))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(250,plain,
% 4.49/4.68 ((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))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(251,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[250])).
% 4.49/4.68 tff(252,plain,
% 4.49/4.68 (((~![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))),
% 4.49/4.68 inference(transitivity,[status(thm)],[251, 249])).
% 4.49/4.68 tff(253,plain,
% 4.49/4.68 ((~![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)))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(254,plain,
% 4.49/4.68 ((~![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)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[253, 252])).
% 4.49/4.68 tff(255,plain,
% 4.49/4.68 (hskp17 | hskp16 | c1_1(a1655)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[254, 197, 69, 71, 10])).
% 4.49/4.68 tff(256,plain,
% 4.49/4.68 (c1_1(a1655)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[255, 248, 247])).
% 4.49/4.68 tff(257,plain,
% 4.49/4.68 (^[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))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(258,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[257])).
% 4.49/4.68 tff(259,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(260,plain,
% 4.49/4.68 (^[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)))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(261,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[260])).
% 4.49/4.68 tff(262,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')).
% 4.49/4.68 tff(263,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[262, 261])).
% 4.49/4.68 tff(264,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[263, 259])).
% 4.49/4.68 tff(265,plain,(
% 4.49/4.68 ![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)))),
% 4.49/4.68 inference(skolemize,[status(sab)],[264])).
% 4.49/4.68 tff(266,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[265, 258])).
% 4.49/4.68 tff(267,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(268,plain,
% 4.49/4.68 ((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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(269,plain,
% 4.49/4.68 (((~![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))))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[268])).
% 4.49/4.68 tff(270,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(transitivity,[status(thm)],[269, 267])).
% 4.49/4.68 tff(271,plain,
% 4.49/4.68 ((~![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)))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(272,plain,
% 4.49/4.68 ((~![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))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[271, 270])).
% 4.49/4.68 tff(273,plain,
% 4.49/4.68 (hskp13 | (~c1_1(a1655))),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[272, 197, 69, 71, 70, 266])).
% 4.49/4.68 tff(274,plain,
% 4.49/4.68 (hskp13),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[273, 256])).
% 4.49/4.68 tff(275,plain,
% 4.49/4.68 (((~hskp13) | (~c1_1(a1667))) <=> ((~hskp13) | (~c1_1(a1667)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(276,plain,
% 4.49/4.68 (((~c1_1(a1667)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1667)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(277,axiom,((~c1_1(a1667)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 4.49/4.68 tff(278,plain,
% 4.49/4.68 ((~hskp13) | (~c1_1(a1667))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[277, 276])).
% 4.49/4.68 tff(279,plain,
% 4.49/4.68 ((~hskp13) | (~c1_1(a1667))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[278, 275])).
% 4.49/4.68 tff(280,plain,
% 4.49/4.68 (~c1_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[279, 274])).
% 4.49/4.68 tff(281,plain,
% 4.49/4.68 (((~hskp13) | c3_1(a1667)) <=> ((~hskp13) | c3_1(a1667))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(282,axiom,((~hskp13) | c3_1(a1667)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 4.49/4.68 tff(283,plain,
% 4.49/4.68 ((~hskp13) | c3_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[282, 281])).
% 4.49/4.68 tff(284,plain,
% 4.49/4.68 ((~hskp13) | c3_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[283, 281])).
% 4.49/4.68 tff(285,plain,
% 4.49/4.68 ((~hskp13) | c3_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[284, 281])).
% 4.49/4.68 tff(286,plain,
% 4.49/4.68 ((~hskp13) | c3_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[285, 281])).
% 4.49/4.68 tff(287,plain,
% 4.49/4.68 ((~hskp13) | c3_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[286, 281])).
% 4.49/4.68 tff(288,plain,
% 4.49/4.68 (c3_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[287, 274])).
% 4.49/4.68 tff(289,plain,
% 4.49/4.68 (((~hskp13) | c0_1(a1667)) <=> ((~hskp13) | c0_1(a1667))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(290,axiom,((~hskp13) | c0_1(a1667)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 4.49/4.68 tff(291,plain,
% 4.49/4.68 ((~hskp13) | c0_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[290, 289])).
% 4.49/4.68 tff(292,plain,
% 4.49/4.68 ((~hskp13) | c0_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[291, 289])).
% 4.49/4.68 tff(293,plain,
% 4.49/4.68 ((~hskp13) | c0_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[292, 289])).
% 4.49/4.68 tff(294,plain,
% 4.49/4.68 ((~hskp13) | c0_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[293, 289])).
% 4.49/4.68 tff(295,plain,
% 4.49/4.68 ((~hskp13) | c0_1(a1667)),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[294, 289])).
% 4.49/4.68 tff(296,plain,
% 4.49/4.68 (c0_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[295, 274])).
% 4.49/4.68 tff(297,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(298,plain,
% 4.49/4.68 ((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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(299,plain,
% 4.49/4.68 (((~![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))))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[298])).
% 4.49/4.68 tff(300,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(transitivity,[status(thm)],[299, 297])).
% 4.49/4.68 tff(301,plain,
% 4.49/4.68 ((~![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)))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(302,plain,
% 4.49/4.68 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp16 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[301, 300])).
% 4.49/4.68 tff(303,plain,
% 4.49/4.68 ($false),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[302, 197, 247, 248, 296, 288, 280, 10])).
% 4.49/4.68 tff(304,plain,(hskp16 | hskp17 | (~c3_1(a1655)) | (~c0_1(a1655)) | c2_1(a1655)), inference(lemma,lemma(discharge,[]))).
% 4.49/4.68 tff(305,plain,
% 4.49/4.68 (hskp16),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[304, 246, 69, 71, 70])).
% 4.49/4.68 tff(306,plain,
% 4.49/4.68 (~c1_1(a1677)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[99, 305])).
% 4.49/4.68 tff(307,plain,
% 4.49/4.68 (~c2_1(a1677)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[105, 305])).
% 4.49/4.68 tff(308,plain,
% 4.49/4.68 (~c0_1(a1677)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[111, 305])).
% 4.49/4.68 tff(309,assumption,(~c3_1(a1677)), introduced(assumption)).
% 4.49/4.68 tff(310,assumption,(~c2_1(a1677)), introduced(assumption)).
% 4.49/4.68 tff(311,plain,
% 4.49/4.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(312,plain,
% 4.49/4.68 (((~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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(313,plain,
% 4.49/4.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[312])).
% 4.49/4.68 tff(314,plain,
% 4.49/4.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.49/4.68 inference(transitivity,[status(thm)],[313, 311])).
% 4.49/4.68 tff(315,plain,
% 4.49/4.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(316,plain,
% 4.49/4.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[315, 314])).
% 4.49/4.68 tff(317,plain,
% 4.49/4.68 ($false),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[316, 197, 208, 210, 209, 115, 310, 114, 30, 309])).
% 4.49/4.68 tff(318,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,[]))).
% 4.49/4.68 tff(319,plain,
% 4.49/4.68 (c3_1(a1677)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[318, 308, 208, 209, 210, 307, 306])).
% 4.49/4.68 tff(320,plain,
% 4.49/4.68 (((~![V: $i, 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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(321,plain,
% 4.49/4.68 ((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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(322,plain,
% 4.49/4.68 (((~![V: $i, 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))))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[321])).
% 4.49/4.68 tff(323,plain,
% 4.49/4.68 (((~![V: $i, 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)))),
% 4.49/4.68 inference(transitivity,[status(thm)],[322, 320])).
% 4.49/4.68 tff(324,plain,
% 4.49/4.68 ((~![V: $i, 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)))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(325,plain,
% 4.49/4.68 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[324, 323])).
% 4.49/4.68 tff(326,plain,
% 4.49/4.68 ($false),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[325, 197, 126, 69, 71, 308, 306, 125, 211, 319])).
% 4.49/4.68 tff(327,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,[]))).
% 4.49/4.68 tff(328,plain,
% 4.49/4.68 (c1_1(a1655)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[327, 207, 206, 205, 158, 150, 144, 126])).
% 4.49/4.68 tff(329,plain,
% 4.49/4.68 (hskp13),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[272, 197, 206, 205, 207, 266, 328])).
% 4.49/4.68 tff(330,plain,
% 4.49/4.68 (~c1_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[279, 329])).
% 4.49/4.68 tff(331,plain,
% 4.49/4.68 (c3_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[287, 329])).
% 4.49/4.68 tff(332,plain,
% 4.49/4.68 (c0_1(a1667)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[295, 329])).
% 4.49/4.68 tff(333,assumption,(~c3_1(a1715)), introduced(assumption)).
% 4.49/4.68 tff(334,assumption,(c2_1(a1715)), introduced(assumption)).
% 4.49/4.68 tff(335,assumption,(~c1_1(a1715)), introduced(assumption)).
% 4.49/4.68 tff(336,plain,
% 4.49/4.68 (c3_1(a1677)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[318, 112, 210, 209, 208, 106, 100])).
% 4.49/4.68 tff(337,plain,
% 4.49/4.68 (^[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))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(338,plain,
% 4.49/4.68 (![W: $i, 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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[337])).
% 4.49/4.68 tff(339,plain,
% 4.49/4.68 (![W: $i, 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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(340,plain,
% 4.49/4.68 (^[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)))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(341,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[340])).
% 4.49/4.68 tff(342,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')).
% 4.49/4.68 tff(343,plain,
% 4.49/4.68 (![W: $i, 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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[342, 341])).
% 4.49/4.68 tff(344,plain,
% 4.49/4.68 (![W: $i, 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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[343, 339])).
% 4.49/4.68 tff(345,plain,(
% 4.49/4.68 ![W: $i, 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)))),
% 4.49/4.68 inference(skolemize,[status(sab)],[344])).
% 4.49/4.68 tff(346,plain,
% 4.49/4.68 (![W: $i, 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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[345, 338])).
% 4.49/4.68 tff(347,plain,
% 4.49/4.68 (^[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))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(348,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[347])).
% 4.49/4.68 tff(349,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(350,plain,
% 4.49/4.68 (^[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)))))),
% 4.49/4.68 inference(bind,[status(th)],[])).
% 4.49/4.68 tff(351,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(quant_intro,[status(thm)],[350])).
% 4.49/4.68 tff(352,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')).
% 4.49/4.68 tff(353,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[352, 351])).
% 4.49/4.68 tff(354,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[353, 349])).
% 4.49/4.68 tff(355,plain,(
% 4.49/4.68 ![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)))),
% 4.49/4.68 inference(skolemize,[status(sab)],[354])).
% 4.49/4.68 tff(356,plain,
% 4.49/4.68 (![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)))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[355, 348])).
% 4.49/4.68 tff(357,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(358,plain,
% 4.49/4.68 ((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)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(359,plain,
% 4.49/4.68 (((~![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))))),
% 4.49/4.68 inference(monotonicity,[status(thm)],[358])).
% 4.49/4.68 tff(360,plain,
% 4.49/4.68 (((~![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)))),
% 4.49/4.68 inference(transitivity,[status(thm)],[359, 357])).
% 4.49/4.68 tff(361,plain,
% 4.49/4.68 ((~![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)))),
% 4.49/4.68 inference(quant_inst,[status(thm)],[])).
% 4.49/4.68 tff(362,plain,
% 4.49/4.68 ((~![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))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[361, 360])).
% 4.49/4.68 tff(363,plain,
% 4.49/4.68 (hskp60 | (~c3_1(a1677))),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[362, 197, 335, 333, 334, 112, 100, 356])).
% 4.49/4.68 tff(364,plain,
% 4.49/4.68 (hskp60),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[363, 336])).
% 4.49/4.68 tff(365,plain,
% 4.49/4.68 (((~hskp60) | (~c1_1(a1673))) <=> ((~hskp60) | (~c1_1(a1673)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(366,plain,
% 4.49/4.68 (((~c1_1(a1673)) | (~hskp60)) <=> ((~hskp60) | (~c1_1(a1673)))),
% 4.49/4.68 inference(rewrite,[status(thm)],[])).
% 4.49/4.68 tff(367,axiom,((~c1_1(a1673)) | (~hskp60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 4.49/4.68 tff(368,plain,
% 4.49/4.68 ((~hskp60) | (~c1_1(a1673))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[367, 366])).
% 4.49/4.68 tff(369,plain,
% 4.49/4.68 ((~hskp60) | (~c1_1(a1673))),
% 4.49/4.68 inference(modus_ponens,[status(thm)],[368, 365])).
% 4.49/4.68 tff(370,plain,
% 4.49/4.68 (~c1_1(a1673)),
% 4.49/4.68 inference(unit_resolution,[status(thm)],[369, 364])).
% 4.49/4.68 tff(371,plain,
% 4.49/4.68 (^[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))))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(372,plain,
% 4.49/4.69 (![W: $i, 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)))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[371])).
% 4.49/4.69 tff(373,plain,
% 4.49/4.69 (![W: $i, 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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(374,plain,
% 4.49/4.69 (^[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)))))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(375,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[374])).
% 4.49/4.69 tff(376,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')).
% 4.49/4.69 tff(377,plain,
% 4.49/4.69 (![W: $i, 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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[376, 375])).
% 4.49/4.69 tff(378,plain,
% 4.49/4.69 (![W: $i, 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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[377, 373])).
% 4.49/4.69 tff(379,plain,(
% 4.49/4.69 ![W: $i, 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)))),
% 4.49/4.69 inference(skolemize,[status(sab)],[378])).
% 4.49/4.69 tff(380,plain,
% 4.49/4.69 (![W: $i, 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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[379, 372])).
% 4.49/4.69 tff(381,plain,
% 4.49/4.69 (((~![W: $i, 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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(382,plain,
% 4.49/4.69 (((~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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(383,plain,
% 4.49/4.69 (((~![W: $i, 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))))),
% 4.49/4.69 inference(monotonicity,[status(thm)],[382])).
% 4.49/4.69 tff(384,plain,
% 4.49/4.69 (((~![W: $i, 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)))),
% 4.49/4.69 inference(transitivity,[status(thm)],[383, 381])).
% 4.49/4.69 tff(385,plain,
% 4.49/4.69 ((~![W: $i, 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)))),
% 4.49/4.69 inference(quant_inst,[status(thm)],[])).
% 4.49/4.69 tff(386,plain,
% 4.49/4.69 ((~![W: $i, 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))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[385, 384])).
% 4.49/4.69 tff(387,plain,
% 4.49/4.69 ((~c3_1(a1677)) | c1_1(a1656)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[386, 197, 210, 69, 71, 209, 112, 106, 70, 380])).
% 4.49/4.69 tff(388,plain,
% 4.49/4.69 (c1_1(a1656)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[387, 336])).
% 4.49/4.69 tff(389,plain,
% 4.49/4.69 (^[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))))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(390,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[389])).
% 4.49/4.69 tff(391,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(392,plain,
% 4.49/4.69 (^[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)))))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(393,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[392])).
% 4.49/4.69 tff(394,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')).
% 4.49/4.69 tff(395,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[394, 393])).
% 4.49/4.69 tff(396,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[395, 391])).
% 4.49/4.69 tff(397,plain,(
% 4.49/4.69 ![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)))),
% 4.49/4.69 inference(skolemize,[status(sab)],[396])).
% 4.49/4.69 tff(398,plain,
% 4.49/4.69 (![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)))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[397, 390])).
% 4.49/4.69 tff(399,plain,
% 4.49/4.69 (((~![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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(400,plain,
% 4.49/4.69 ((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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(401,plain,
% 4.49/4.69 (((~![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))))),
% 4.49/4.69 inference(monotonicity,[status(thm)],[400])).
% 4.49/4.69 tff(402,plain,
% 4.49/4.69 (((~![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)))),
% 4.49/4.69 inference(transitivity,[status(thm)],[401, 399])).
% 4.49/4.69 tff(403,plain,
% 4.49/4.69 ((~![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)))),
% 4.49/4.69 inference(quant_inst,[status(thm)],[])).
% 4.49/4.69 tff(404,plain,
% 4.49/4.69 ((~![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))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[403, 402])).
% 4.49/4.69 tff(405,plain,
% 4.49/4.69 (hskp75 | (~c3_1(a1677)) | (~c1_1(a1656))),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[404, 197, 208, 209, 106, 100, 398])).
% 4.49/4.69 tff(406,plain,
% 4.49/4.69 (hskp75),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[405, 388, 336])).
% 4.49/4.69 tff(407,plain,
% 4.49/4.69 (((~hskp75) | (~c2_1(a1724))) <=> ((~hskp75) | (~c2_1(a1724)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(408,plain,
% 4.49/4.69 (((~c2_1(a1724)) | (~hskp75)) <=> ((~hskp75) | (~c2_1(a1724)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(409,axiom,((~c2_1(a1724)) | (~hskp75)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 4.49/4.69 tff(410,plain,
% 4.49/4.69 ((~hskp75) | (~c2_1(a1724))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[409, 408])).
% 4.49/4.69 tff(411,plain,
% 4.49/4.69 ((~hskp75) | (~c2_1(a1724))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[410, 407])).
% 4.49/4.69 tff(412,plain,
% 4.49/4.69 (~c2_1(a1724)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[411, 406])).
% 4.49/4.69 tff(413,plain,
% 4.49/4.69 (((~hskp60) | c2_1(a1673)) <=> ((~hskp60) | c2_1(a1673))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(414,axiom,((~hskp60) | c2_1(a1673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 4.49/4.69 tff(415,plain,
% 4.49/4.69 ((~hskp60) | c2_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[414, 413])).
% 4.49/4.69 tff(416,plain,
% 4.49/4.69 ((~hskp60) | c2_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[415, 413])).
% 4.49/4.69 tff(417,plain,
% 4.49/4.69 ((~hskp60) | c2_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[416, 413])).
% 4.49/4.69 tff(418,plain,
% 4.49/4.69 ((~hskp60) | c2_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[417, 413])).
% 4.49/4.69 tff(419,plain,
% 4.49/4.69 ((~hskp60) | c2_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[418, 413])).
% 4.49/4.69 tff(420,plain,
% 4.49/4.69 (c2_1(a1673)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[419, 364])).
% 4.49/4.69 tff(421,plain,
% 4.49/4.69 (((~hskp60) | c3_1(a1673)) <=> ((~hskp60) | c3_1(a1673))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(422,axiom,((~hskp60) | c3_1(a1673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 4.49/4.69 tff(423,plain,
% 4.49/4.69 ((~hskp60) | c3_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[422, 421])).
% 4.49/4.69 tff(424,plain,
% 4.49/4.69 ((~hskp60) | c3_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[423, 421])).
% 4.49/4.69 tff(425,plain,
% 4.49/4.69 ((~hskp60) | c3_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[424, 421])).
% 4.49/4.69 tff(426,plain,
% 4.49/4.69 ((~hskp60) | c3_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[425, 421])).
% 4.49/4.69 tff(427,plain,
% 4.49/4.69 ((~hskp60) | c3_1(a1673)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[426, 421])).
% 4.49/4.69 tff(428,plain,
% 4.49/4.69 (c3_1(a1673)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[427, 364])).
% 4.49/4.69 tff(429,plain,
% 4.49/4.69 (((~hskp75) | c3_1(a1724)) <=> ((~hskp75) | c3_1(a1724))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(430,axiom,((~hskp75) | c3_1(a1724)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 4.49/4.69 tff(431,plain,
% 4.49/4.69 ((~hskp75) | c3_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[430, 429])).
% 4.49/4.69 tff(432,plain,
% 4.49/4.69 ((~hskp75) | c3_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[431, 429])).
% 4.49/4.69 tff(433,plain,
% 4.49/4.69 ((~hskp75) | c3_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[432, 429])).
% 4.49/4.69 tff(434,plain,
% 4.49/4.69 ((~hskp75) | c3_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[433, 429])).
% 4.49/4.69 tff(435,plain,
% 4.49/4.69 ((~hskp75) | c3_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[434, 429])).
% 4.49/4.69 tff(436,plain,
% 4.49/4.69 (c3_1(a1724)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[435, 406])).
% 4.49/4.69 tff(437,plain,
% 4.49/4.69 (((~hskp75) | c0_1(a1724)) <=> ((~hskp75) | c0_1(a1724))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(438,axiom,((~hskp75) | c0_1(a1724)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 4.49/4.69 tff(439,plain,
% 4.49/4.69 ((~hskp75) | c0_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[438, 437])).
% 4.49/4.69 tff(440,plain,
% 4.49/4.69 ((~hskp75) | c0_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[439, 437])).
% 4.49/4.69 tff(441,plain,
% 4.49/4.69 ((~hskp75) | c0_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[440, 437])).
% 4.49/4.69 tff(442,plain,
% 4.49/4.69 ((~hskp75) | c0_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[441, 437])).
% 4.49/4.69 tff(443,plain,
% 4.49/4.69 ((~hskp75) | c0_1(a1724)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[442, 437])).
% 4.49/4.69 tff(444,plain,
% 4.49/4.69 (c0_1(a1724)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[443, 406])).
% 4.49/4.69 tff(445,plain,
% 4.49/4.69 (((~![W: $i, 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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(446,plain,
% 4.49/4.69 (((~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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(447,plain,
% 4.49/4.69 (((~![W: $i, 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))))),
% 4.49/4.69 inference(monotonicity,[status(thm)],[446])).
% 4.49/4.69 tff(448,plain,
% 4.49/4.69 (((~![W: $i, 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)))),
% 4.49/4.69 inference(transitivity,[status(thm)],[447, 445])).
% 4.49/4.69 tff(449,plain,
% 4.49/4.69 ((~![W: $i, 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)))),
% 4.49/4.69 inference(quant_inst,[status(thm)],[])).
% 4.49/4.69 tff(450,plain,
% 4.49/4.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c1_1(a1673) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[449, 448])).
% 4.49/4.69 tff(451,plain,
% 4.49/4.69 ($false),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[450, 197, 444, 436, 428, 420, 412, 370, 112, 106, 346, 336])).
% 4.49/4.69 tff(452,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,[]))).
% 4.49/4.69 tff(453,plain,
% 4.49/4.69 (~hskp16),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[452, 158, 150, 335, 333, 334, 144, 206, 205, 207])).
% 4.49/4.69 tff(454,plain,
% 4.49/4.69 (hskp17),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[304, 453, 206, 205, 207])).
% 4.49/4.69 tff(455,plain,
% 4.49/4.69 (c1_1(a1655)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[245, 454, 144, 150, 126, 206, 205, 158])).
% 4.49/4.69 tff(456,plain,
% 4.49/4.69 (hskp13 | (~c1_1(a1655))),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[272, 197, 206, 205, 207, 266])).
% 4.49/4.69 tff(457,plain,
% 4.49/4.69 (hskp13),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[456, 455])).
% 4.49/4.69 tff(458,plain,
% 4.49/4.69 (~c1_1(a1667)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[279, 457])).
% 4.49/4.69 tff(459,plain,
% 4.49/4.69 (~c1_1(a1678)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[217, 454])).
% 4.49/4.69 tff(460,plain,
% 4.49/4.69 (~c0_1(a1678)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[223, 454])).
% 4.49/4.69 tff(461,plain,
% 4.49/4.69 (c3_1(a1667)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[287, 457])).
% 4.49/4.69 tff(462,plain,
% 4.49/4.69 (c0_1(a1667)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[295, 457])).
% 4.49/4.69 tff(463,plain,
% 4.49/4.69 (((~![V: $i, 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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(464,plain,
% 4.49/4.69 ((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)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(465,plain,
% 4.49/4.69 (((~![V: $i, 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))))),
% 4.49/4.69 inference(monotonicity,[status(thm)],[464])).
% 4.49/4.69 tff(466,plain,
% 4.49/4.69 (((~![V: $i, 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)))),
% 4.49/4.69 inference(transitivity,[status(thm)],[465, 463])).
% 4.49/4.69 tff(467,plain,
% 4.49/4.69 ((~![V: $i, 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)))),
% 4.49/4.69 inference(quant_inst,[status(thm)],[])).
% 4.49/4.69 tff(468,plain,
% 4.49/4.69 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[467, 466])).
% 4.49/4.69 tff(469,plain,
% 4.49/4.69 (~c3_1(a1678)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[468, 197, 126, 462, 461, 460, 459, 458, 125])).
% 4.49/4.69 tff(470,plain,
% 4.49/4.69 (~c2_1(a1678)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[236, 454])).
% 4.49/4.69 tff(471,plain,
% 4.49/4.69 ($false),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[243, 197, 158, 144, 150, 460, 459, 470, 30, 469])).
% 4.49/4.69 tff(472,plain,(hskp52 | hskp29 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.69 tff(473,plain,
% 4.49/4.69 (hskp52),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[472, 335, 126, 333, 334])).
% 4.49/4.69 tff(474,plain,
% 4.49/4.69 (((~hskp52) | c0_1(a1654)) <=> ((~hskp52) | c0_1(a1654))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(475,axiom,((~hskp52) | c0_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 4.49/4.69 tff(476,plain,
% 4.49/4.69 ((~hskp52) | c0_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[475, 474])).
% 4.49/4.69 tff(477,plain,
% 4.49/4.69 ((~hskp52) | c0_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[476, 474])).
% 4.49/4.69 tff(478,plain,
% 4.49/4.69 ((~hskp52) | c0_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[477, 474])).
% 4.49/4.69 tff(479,plain,
% 4.49/4.69 ((~hskp52) | c0_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[478, 474])).
% 4.49/4.69 tff(480,plain,
% 4.49/4.69 ((~hskp52) | c0_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[479, 474])).
% 4.49/4.69 tff(481,plain,
% 4.49/4.69 (c0_1(a1654)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[480, 473])).
% 4.49/4.69 tff(482,plain,
% 4.49/4.69 (((~hskp52) | c3_1(a1654)) <=> ((~hskp52) | c3_1(a1654))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(483,axiom,((~hskp52) | c3_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 4.49/4.69 tff(484,plain,
% 4.49/4.69 ((~hskp52) | c3_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[483, 482])).
% 4.49/4.69 tff(485,plain,
% 4.49/4.69 ((~hskp52) | c3_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[484, 482])).
% 4.49/4.69 tff(486,plain,
% 4.49/4.69 ((~hskp52) | c3_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[485, 482])).
% 4.49/4.69 tff(487,plain,
% 4.49/4.69 ((~hskp52) | c3_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[486, 482])).
% 4.49/4.69 tff(488,plain,
% 4.49/4.69 ((~hskp52) | c3_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[487, 482])).
% 4.49/4.69 tff(489,plain,
% 4.49/4.69 (c3_1(a1654)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[488, 473])).
% 4.49/4.69 tff(490,plain,
% 4.49/4.69 (((~hskp52) | c2_1(a1654)) <=> ((~hskp52) | c2_1(a1654))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(491,axiom,((~hskp52) | c2_1(a1654)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 4.49/4.69 tff(492,plain,
% 4.49/4.69 ((~hskp52) | c2_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[491, 490])).
% 4.49/4.69 tff(493,plain,
% 4.49/4.69 ((~hskp52) | c2_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[492, 490])).
% 4.49/4.69 tff(494,plain,
% 4.49/4.69 ((~hskp52) | c2_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[493, 490])).
% 4.49/4.69 tff(495,plain,
% 4.49/4.69 ((~hskp52) | c2_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[494, 490])).
% 4.49/4.69 tff(496,plain,
% 4.49/4.69 ((~hskp52) | c2_1(a1654)),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[495, 490])).
% 4.49/4.69 tff(497,plain,
% 4.49/4.69 (c2_1(a1654)),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[496, 473])).
% 4.49/4.69 tff(498,plain,
% 4.49/4.69 (((~hskp72) | (~c2_1(a1715))) <=> ((~hskp72) | (~c2_1(a1715)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(499,plain,
% 4.49/4.69 (((~c2_1(a1715)) | (~hskp72)) <=> ((~hskp72) | (~c2_1(a1715)))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(500,axiom,((~c2_1(a1715)) | (~hskp72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 4.49/4.69 tff(501,plain,
% 4.49/4.69 ((~hskp72) | (~c2_1(a1715))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[500, 499])).
% 4.49/4.69 tff(502,plain,
% 4.49/4.69 ((~hskp72) | (~c2_1(a1715))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[501, 498])).
% 4.49/4.69 tff(503,plain,
% 4.49/4.69 (~hskp72),
% 4.49/4.69 inference(unit_resolution,[status(thm)],[502, 334])).
% 4.49/4.69 tff(504,assumption,(~c3_1(a1678)), introduced(assumption)).
% 4.49/4.69 tff(505,plain,
% 4.49/4.69 (^[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)))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(506,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[505])).
% 4.49/4.69 tff(507,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(508,plain,
% 4.49/4.69 (^[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))))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(509,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[508])).
% 4.49/4.69 tff(510,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')).
% 4.49/4.69 tff(511,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[510, 509])).
% 4.49/4.69 tff(512,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[511, 507])).
% 4.49/4.69 tff(513,plain,(
% 4.49/4.69 ![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))),
% 4.49/4.69 inference(skolemize,[status(sab)],[512])).
% 4.49/4.69 tff(514,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(modus_ponens,[status(thm)],[513, 506])).
% 4.49/4.69 tff(515,assumption,(~c2_1(a1678)), introduced(assumption)).
% 4.49/4.69 tff(516,assumption,(~c0_1(a1678)), introduced(assumption)).
% 4.49/4.69 tff(517,plain,
% 4.49/4.69 (^[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)))),
% 4.49/4.69 inference(bind,[status(th)],[])).
% 4.49/4.69 tff(518,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(quant_intro,[status(thm)],[517])).
% 4.49/4.69 tff(519,plain,
% 4.49/4.69 (![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))),
% 4.49/4.69 inference(rewrite,[status(thm)],[])).
% 4.49/4.69 tff(520,plain,
% 4.49/4.69 (^[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))))),
% 4.49/4.70 inference(bind,[status(th)],[])).
% 4.49/4.70 tff(521,plain,
% 4.49/4.70 (![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))),
% 4.49/4.70 inference(quant_intro,[status(thm)],[520])).
% 4.49/4.70 tff(522,axiom,(![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c0_1(U)) | c2_1(U)) | hskp37) | hskp72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause314')).
% 4.49/4.70 tff(523,plain,
% 4.49/4.70 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[522, 521])).
% 4.49/4.70 tff(524,plain,
% 4.49/4.70 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[523, 519])).
% 4.49/4.70 tff(525,plain,(
% 4.49/4.70 ![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 4.49/4.70 inference(skolemize,[status(sab)],[524])).
% 4.49/4.70 tff(526,plain,
% 4.49/4.70 (![U: $i] : (hskp72 | hskp37 | (~ndr1_0) | c0_1(U) | c3_1(U) | c2_1(U))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[525, 518])).
% 4.49/4.70 tff(527,assumption,(~hskp72), introduced(assumption)).
% 4.49/4.70 tff(528,plain,
% 4.49/4.70 (((~![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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(529,plain,
% 4.49/4.70 ((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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(530,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[529])).
% 4.49/4.70 tff(531,plain,
% 4.49/4.70 (((~![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))),
% 4.49/4.70 inference(transitivity,[status(thm)],[530, 528])).
% 4.49/4.70 tff(532,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(533,plain,
% 4.49/4.70 ((~![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)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[532, 531])).
% 4.49/4.70 tff(534,plain,
% 4.49/4.70 (hskp37 | c3_1(a1678)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[533, 197, 527, 516, 515, 526])).
% 4.49/4.70 tff(535,plain,
% 4.49/4.70 (hskp37),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[534, 504])).
% 4.49/4.70 tff(536,plain,
% 4.49/4.70 (((~hskp37) | (~c1_1(a1714))) <=> ((~hskp37) | (~c1_1(a1714)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(537,plain,
% 4.49/4.70 (((~c1_1(a1714)) | (~hskp37)) <=> ((~hskp37) | (~c1_1(a1714)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(538,axiom,((~c1_1(a1714)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 4.49/4.70 tff(539,plain,
% 4.49/4.70 ((~hskp37) | (~c1_1(a1714))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[538, 537])).
% 4.49/4.70 tff(540,plain,
% 4.49/4.70 ((~hskp37) | (~c1_1(a1714))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[539, 536])).
% 4.49/4.70 tff(541,plain,
% 4.49/4.70 (~c1_1(a1714)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[540, 535])).
% 4.49/4.70 tff(542,plain,
% 4.49/4.70 (((~hskp37) | c0_1(a1714)) <=> ((~hskp37) | c0_1(a1714))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(543,axiom,((~hskp37) | c0_1(a1714)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 4.49/4.70 tff(544,plain,
% 4.49/4.70 ((~hskp37) | c0_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[543, 542])).
% 4.49/4.70 tff(545,plain,
% 4.49/4.70 ((~hskp37) | c0_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[544, 542])).
% 4.49/4.70 tff(546,plain,
% 4.49/4.70 ((~hskp37) | c0_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[545, 542])).
% 4.49/4.70 tff(547,plain,
% 4.49/4.70 ((~hskp37) | c0_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[546, 542])).
% 4.49/4.70 tff(548,plain,
% 4.49/4.70 ((~hskp37) | c0_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[547, 542])).
% 4.49/4.70 tff(549,plain,
% 4.49/4.70 (c0_1(a1714)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[548, 535])).
% 4.49/4.70 tff(550,plain,
% 4.49/4.70 (((~hskp37) | c2_1(a1714)) <=> ((~hskp37) | c2_1(a1714))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(551,axiom,((~hskp37) | c2_1(a1714)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 4.49/4.70 tff(552,plain,
% 4.49/4.70 ((~hskp37) | c2_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[551, 550])).
% 4.49/4.70 tff(553,plain,
% 4.49/4.70 ((~hskp37) | c2_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[552, 550])).
% 4.49/4.70 tff(554,plain,
% 4.49/4.70 ((~hskp37) | c2_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[553, 550])).
% 4.49/4.70 tff(555,plain,
% 4.49/4.70 ((~hskp37) | c2_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[554, 550])).
% 4.49/4.70 tff(556,plain,
% 4.49/4.70 ((~hskp37) | c2_1(a1714)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[555, 550])).
% 4.49/4.70 tff(557,plain,
% 4.49/4.70 (c2_1(a1714)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[556, 535])).
% 4.49/4.70 tff(558,assumption,(c3_1(a1654)), introduced(assumption)).
% 4.49/4.70 tff(559,assumption,(c2_1(a1654)), introduced(assumption)).
% 4.49/4.70 tff(560,assumption,(c0_1(a1654)), introduced(assumption)).
% 4.49/4.70 tff(561,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(562,plain,
% 4.49/4.70 (((~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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(563,plain,
% 4.49/4.70 (((~![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))))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[562])).
% 4.49/4.70 tff(564,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(transitivity,[status(thm)],[563, 561])).
% 4.49/4.70 tff(565,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(566,plain,
% 4.49/4.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[565, 564])).
% 4.49/4.70 tff(567,plain,
% 4.49/4.70 ($false),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[566, 197, 560, 559, 558, 557, 549, 541, 516, 515, 514, 504])).
% 4.49/4.70 tff(568,plain,(c3_1(a1678) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c0_1(a1678) | c2_1(a1678) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.49/4.70 tff(569,plain,
% 4.49/4.70 (c3_1(a1678)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[568, 224, 503, 497, 489, 237, 481])).
% 4.49/4.70 tff(570,assumption,(~c1_1(a1654)), introduced(assumption)).
% 4.49/4.70 tff(571,assumption,(~c1_1(a1678)), introduced(assumption)).
% 4.49/4.70 tff(572,plain,
% 4.49/4.70 (((~![V: $i, 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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(573,plain,
% 4.49/4.70 ((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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(574,plain,
% 4.49/4.70 (((~![V: $i, 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)))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[573])).
% 4.49/4.70 tff(575,plain,
% 4.49/4.70 (((~![V: $i, 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))),
% 4.49/4.70 inference(transitivity,[status(thm)],[574, 572])).
% 4.49/4.70 tff(576,plain,
% 4.49/4.70 ((~![V: $i, 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)))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(577,plain,
% 4.49/4.70 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[576, 575])).
% 4.49/4.70 tff(578,plain,
% 4.49/4.70 ($false),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[577, 197, 126, 560, 558, 516, 571, 125, 570, 80])).
% 4.49/4.70 tff(579,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | c0_1(a1678) | c1_1(a1678) | (~c3_1(a1678))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.70 tff(580,plain,
% 4.49/4.70 (c1_1(a1654)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[579, 224, 481, 489, 126, 218, 569])).
% 4.49/4.70 tff(581,plain,
% 4.49/4.70 (^[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))))),
% 4.49/4.70 inference(bind,[status(th)],[])).
% 4.49/4.70 tff(582,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(quant_intro,[status(thm)],[581])).
% 4.49/4.70 tff(583,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(584,plain,
% 4.49/4.70 (^[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)))))),
% 4.49/4.70 inference(bind,[status(th)],[])).
% 4.49/4.70 tff(585,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(quant_intro,[status(thm)],[584])).
% 4.49/4.70 tff(586,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')).
% 4.49/4.70 tff(587,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[586, 585])).
% 4.49/4.70 tff(588,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[587, 583])).
% 4.49/4.70 tff(589,plain,(
% 4.49/4.70 ![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)))),
% 4.49/4.70 inference(skolemize,[status(sab)],[588])).
% 4.49/4.70 tff(590,plain,
% 4.49/4.70 (![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)))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[589, 582])).
% 4.49/4.70 tff(591,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(592,plain,
% 4.49/4.70 ((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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(593,plain,
% 4.49/4.70 (((~![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))))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[592])).
% 4.49/4.70 tff(594,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(transitivity,[status(thm)],[593, 591])).
% 4.49/4.70 tff(595,plain,
% 4.49/4.70 ((~![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)))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(596,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[595, 594])).
% 4.49/4.70 tff(597,plain,
% 4.49/4.70 (hskp60),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[596, 197, 335, 333, 334, 224, 218, 356, 569])).
% 4.49/4.70 tff(598,plain,
% 4.49/4.70 (~c1_1(a1673)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[369, 597])).
% 4.49/4.70 tff(599,plain,
% 4.49/4.70 (c2_1(a1673)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[419, 597])).
% 4.49/4.70 tff(600,plain,
% 4.49/4.70 (c3_1(a1673)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[427, 597])).
% 4.49/4.70 tff(601,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(602,plain,
% 4.49/4.70 ((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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(603,plain,
% 4.49/4.70 (((~![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))))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[602])).
% 4.49/4.70 tff(604,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(transitivity,[status(thm)],[603, 601])).
% 4.49/4.70 tff(605,plain,
% 4.49/4.70 ((~![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)))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(606,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[605, 604])).
% 4.49/4.70 tff(607,plain,
% 4.49/4.70 (hskp26),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[606, 197, 600, 599, 481, 497, 489, 598, 20])).
% 4.49/4.70 tff(608,plain,
% 4.49/4.70 (((~hskp26) | (~c2_1(a1691))) <=> ((~hskp26) | (~c2_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(609,plain,
% 4.49/4.70 (((~c2_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(610,axiom,((~c2_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause256')).
% 4.49/4.70 tff(611,plain,
% 4.49/4.70 ((~hskp26) | (~c2_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[610, 609])).
% 4.49/4.70 tff(612,plain,
% 4.49/4.70 ((~hskp26) | (~c2_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[611, 608])).
% 4.49/4.70 tff(613,plain,
% 4.49/4.70 (~c2_1(a1691)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[612, 607])).
% 4.49/4.70 tff(614,plain,
% 4.49/4.70 (((~hskp26) | (~c1_1(a1691))) <=> ((~hskp26) | (~c1_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(615,plain,
% 4.49/4.70 (((~c1_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(616,axiom,((~c1_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause255')).
% 4.49/4.70 tff(617,plain,
% 4.49/4.70 ((~hskp26) | (~c1_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[616, 615])).
% 4.49/4.70 tff(618,plain,
% 4.49/4.70 ((~hskp26) | (~c1_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[617, 614])).
% 4.49/4.70 tff(619,plain,
% 4.49/4.70 (~c1_1(a1691)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[618, 607])).
% 4.49/4.70 tff(620,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(621,plain,
% 4.49/4.70 (((~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)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(622,plain,
% 4.49/4.70 (((~![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))))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[621])).
% 4.49/4.70 tff(623,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(transitivity,[status(thm)],[622, 620])).
% 4.49/4.70 tff(624,plain,
% 4.49/4.70 ((~![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)))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(625,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[624, 623])).
% 4.49/4.70 tff(626,plain,
% 4.49/4.70 ((~c0_1(a1691)) | (~c1_1(a1654))),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[625, 197, 481, 489, 619, 613, 218, 237, 590, 569])).
% 4.49/4.70 tff(627,plain,
% 4.49/4.70 (~c0_1(a1691)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[626, 580])).
% 4.49/4.70 tff(628,plain,
% 4.49/4.70 (((~hskp26) | (~c3_1(a1691))) <=> ((~hskp26) | (~c3_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(629,plain,
% 4.49/4.70 (((~c3_1(a1691)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a1691)))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(630,axiom,((~c3_1(a1691)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause254')).
% 4.49/4.70 tff(631,plain,
% 4.49/4.70 ((~hskp26) | (~c3_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[630, 629])).
% 4.49/4.70 tff(632,plain,
% 4.49/4.70 ((~hskp26) | (~c3_1(a1691))),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[631, 628])).
% 4.49/4.70 tff(633,plain,
% 4.49/4.70 (~c3_1(a1691)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[632, 607])).
% 4.49/4.70 tff(634,plain,
% 4.49/4.70 (((~![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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(635,plain,
% 4.49/4.70 ((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))),
% 4.49/4.70 inference(rewrite,[status(thm)],[])).
% 4.49/4.70 tff(636,plain,
% 4.49/4.70 (((~![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)))),
% 4.49/4.70 inference(monotonicity,[status(thm)],[635])).
% 4.49/4.70 tff(637,plain,
% 4.49/4.70 (((~![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))),
% 4.49/4.70 inference(transitivity,[status(thm)],[636, 634])).
% 4.49/4.70 tff(638,plain,
% 4.49/4.70 ((~![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))),
% 4.49/4.70 inference(quant_inst,[status(thm)],[])).
% 4.49/4.70 tff(639,plain,
% 4.49/4.70 ((~![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)),
% 4.49/4.70 inference(modus_ponens,[status(thm)],[638, 637])).
% 4.49/4.70 tff(640,plain,
% 4.49/4.70 (hskp37 | c0_1(a1691)),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[639, 197, 503, 633, 613, 526])).
% 4.49/4.70 tff(641,plain,
% 4.49/4.70 (hskp37),
% 4.49/4.70 inference(unit_resolution,[status(thm)],[640, 627])).
% 4.49/4.70 tff(642,plain,
% 4.49/4.70 (~c1_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[540, 641])).
% 4.49/4.71 tff(643,plain,
% 4.49/4.71 (c0_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[548, 641])).
% 4.49/4.71 tff(644,plain,
% 4.49/4.71 (c2_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[556, 641])).
% 4.49/4.71 tff(645,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(646,plain,
% 4.49/4.71 (((~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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(647,plain,
% 4.49/4.71 (((~![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))))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[646])).
% 4.49/4.71 tff(648,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(transitivity,[status(thm)],[647, 645])).
% 4.49/4.71 tff(649,plain,
% 4.49/4.71 ((~![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))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(650,plain,
% 4.49/4.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[649, 648])).
% 4.49/4.71 tff(651,plain,
% 4.49/4.71 ($false),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[650, 197, 481, 497, 489, 644, 643, 642, 633, 613, 514, 627])).
% 4.49/4.71 tff(652,plain,((~hskp17) | hskp29 | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.71 tff(653,plain,
% 4.49/4.71 (~hskp17),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[652, 335, 126, 333, 334])).
% 4.49/4.71 tff(654,plain,
% 4.49/4.71 (((~![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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(655,plain,
% 4.49/4.71 ((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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(656,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[655])).
% 4.49/4.71 tff(657,plain,
% 4.49/4.71 (((~![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))),
% 4.49/4.71 inference(transitivity,[status(thm)],[656, 654])).
% 4.49/4.71 tff(658,plain,
% 4.49/4.71 ((~![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)))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(659,plain,
% 4.49/4.71 ((~![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)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[658, 657])).
% 4.49/4.71 tff(660,plain,
% 4.49/4.71 (hskp17 | hskp16 | c1_1(a1654)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[659, 197, 560, 558, 10])).
% 4.49/4.71 tff(661,plain,
% 4.49/4.71 (c1_1(a1654)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[660, 247, 248])).
% 4.49/4.71 tff(662,plain,
% 4.49/4.71 (^[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))))),
% 4.49/4.71 inference(bind,[status(th)],[])).
% 4.49/4.71 tff(663,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(quant_intro,[status(thm)],[662])).
% 4.49/4.71 tff(664,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(665,plain,
% 4.49/4.71 (^[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)))))),
% 4.49/4.71 inference(bind,[status(th)],[])).
% 4.49/4.71 tff(666,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(quant_intro,[status(thm)],[665])).
% 4.49/4.71 tff(667,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')).
% 4.49/4.71 tff(668,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[667, 666])).
% 4.49/4.71 tff(669,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[668, 664])).
% 4.49/4.71 tff(670,plain,(
% 4.49/4.71 ![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)))),
% 4.49/4.71 inference(skolemize,[status(sab)],[669])).
% 4.49/4.71 tff(671,plain,
% 4.49/4.71 (![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)))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[670, 663])).
% 4.49/4.71 tff(672,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(673,plain,
% 4.49/4.71 ((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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(674,plain,
% 4.49/4.71 (((~![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))))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[673])).
% 4.49/4.71 tff(675,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(transitivity,[status(thm)],[674, 672])).
% 4.49/4.71 tff(676,plain,
% 4.49/4.71 ((~![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)))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(677,plain,
% 4.49/4.71 ((~![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))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[676, 675])).
% 4.49/4.71 tff(678,plain,
% 4.49/4.71 (hskp40 | (~c1_1(a1654))),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[677, 197, 335, 333, 560, 558, 334, 671])).
% 4.49/4.71 tff(679,plain,
% 4.49/4.71 (hskp40),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[678, 661])).
% 4.49/4.71 tff(680,plain,
% 4.49/4.71 (((~hskp40) | (~c2_1(a1725))) <=> ((~hskp40) | (~c2_1(a1725)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(681,plain,
% 4.49/4.71 (((~c2_1(a1725)) | (~hskp40)) <=> ((~hskp40) | (~c2_1(a1725)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(682,axiom,((~c2_1(a1725)) | (~hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 4.49/4.71 tff(683,plain,
% 4.49/4.71 ((~hskp40) | (~c2_1(a1725))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[682, 681])).
% 4.49/4.71 tff(684,plain,
% 4.49/4.71 ((~hskp40) | (~c2_1(a1725))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[683, 680])).
% 4.49/4.71 tff(685,plain,
% 4.49/4.71 (~c2_1(a1725)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[684, 679])).
% 4.49/4.71 tff(686,plain,
% 4.49/4.71 (((~hskp40) | c3_1(a1725)) <=> ((~hskp40) | c3_1(a1725))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(687,axiom,((~hskp40) | c3_1(a1725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 4.49/4.71 tff(688,plain,
% 4.49/4.71 ((~hskp40) | c3_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[687, 686])).
% 4.49/4.71 tff(689,plain,
% 4.49/4.71 ((~hskp40) | c3_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[688, 686])).
% 4.49/4.71 tff(690,plain,
% 4.49/4.71 ((~hskp40) | c3_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[689, 686])).
% 4.49/4.71 tff(691,plain,
% 4.49/4.71 ((~hskp40) | c3_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[690, 686])).
% 4.49/4.71 tff(692,plain,
% 4.49/4.71 ((~hskp40) | c3_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[691, 686])).
% 4.49/4.71 tff(693,plain,
% 4.49/4.71 (c3_1(a1725)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[692, 679])).
% 4.49/4.71 tff(694,plain,
% 4.49/4.71 (((~hskp40) | c1_1(a1725)) <=> ((~hskp40) | c1_1(a1725))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(695,axiom,((~hskp40) | c1_1(a1725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 4.49/4.71 tff(696,plain,
% 4.49/4.71 ((~hskp40) | c1_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[695, 694])).
% 4.49/4.71 tff(697,plain,
% 4.49/4.71 ((~hskp40) | c1_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[696, 694])).
% 4.49/4.71 tff(698,plain,
% 4.49/4.71 ((~hskp40) | c1_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[697, 694])).
% 4.49/4.71 tff(699,plain,
% 4.49/4.71 ((~hskp40) | c1_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[698, 694])).
% 4.49/4.71 tff(700,plain,
% 4.49/4.71 ((~hskp40) | c1_1(a1725)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[699, 694])).
% 4.49/4.71 tff(701,plain,
% 4.49/4.71 (c1_1(a1725)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[700, 679])).
% 4.49/4.71 tff(702,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(703,plain,
% 4.49/4.71 ((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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(704,plain,
% 4.49/4.71 (((~![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))))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[703])).
% 4.49/4.71 tff(705,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(transitivity,[status(thm)],[704, 702])).
% 4.49/4.71 tff(706,plain,
% 4.49/4.71 ((~![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)))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(707,plain,
% 4.49/4.71 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[706, 705])).
% 4.49/4.71 tff(708,plain,
% 4.49/4.71 (hskp13),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[707, 197, 560, 558, 701, 693, 685, 266, 661])).
% 4.49/4.71 tff(709,plain,
% 4.49/4.71 (~c1_1(a1667)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[279, 708])).
% 4.49/4.71 tff(710,plain,
% 4.49/4.71 (c3_1(a1667)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[287, 708])).
% 4.49/4.71 tff(711,plain,
% 4.49/4.71 (c0_1(a1667)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[295, 708])).
% 4.49/4.71 tff(712,plain,
% 4.49/4.71 ($false),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[302, 197, 247, 248, 711, 710, 709, 10])).
% 4.49/4.71 tff(713,plain,(hskp17 | hskp16 | (~c0_1(a1654)) | (~c3_1(a1654)) | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.71 tff(714,plain,
% 4.49/4.71 (hskp16),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[713, 653, 481, 489, 335, 333, 334])).
% 4.49/4.71 tff(715,plain,
% 4.49/4.71 (~c2_1(a1677)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[105, 714])).
% 4.49/4.71 tff(716,plain,
% 4.49/4.71 (~c0_1(a1677)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[111, 714])).
% 4.49/4.71 tff(717,plain,
% 4.49/4.71 (((~![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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(718,plain,
% 4.49/4.71 ((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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(719,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[718])).
% 4.49/4.71 tff(720,plain,
% 4.49/4.71 (((~![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))),
% 4.49/4.71 inference(transitivity,[status(thm)],[719, 717])).
% 4.49/4.71 tff(721,plain,
% 4.49/4.71 ((~![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))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(722,plain,
% 4.49/4.71 ((~![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)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[721, 720])).
% 4.49/4.71 tff(723,plain,
% 4.49/4.71 (hskp37 | c3_1(a1677)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[722, 197, 527, 115, 310, 526])).
% 4.49/4.71 tff(724,plain,
% 4.49/4.71 (hskp37),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[723, 309])).
% 4.49/4.71 tff(725,plain,
% 4.49/4.71 (~c1_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[540, 724])).
% 4.49/4.71 tff(726,plain,
% 4.49/4.71 (c0_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[548, 724])).
% 4.49/4.71 tff(727,plain,
% 4.49/4.71 (c2_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[556, 724])).
% 4.49/4.71 tff(728,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(729,plain,
% 4.49/4.71 (((~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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(730,plain,
% 4.49/4.71 (((~![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))))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[729])).
% 4.49/4.71 tff(731,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(transitivity,[status(thm)],[730, 728])).
% 4.49/4.71 tff(732,plain,
% 4.49/4.71 ((~![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))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(733,plain,
% 4.49/4.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1714) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[732, 731])).
% 4.49/4.71 tff(734,plain,
% 4.49/4.71 ($false),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[733, 197, 560, 559, 558, 727, 726, 725, 115, 310, 514, 309])).
% 4.49/4.71 tff(735,plain,(c3_1(a1677) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c0_1(a1677) | c2_1(a1677) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.49/4.71 tff(736,plain,
% 4.49/4.71 (c3_1(a1677)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[735, 716, 503, 489, 497, 715, 481])).
% 4.49/4.71 tff(737,plain,
% 4.49/4.71 (~c1_1(a1677)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[99, 714])).
% 4.49/4.71 tff(738,plain,
% 4.49/4.71 (((~![V: $i, 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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(739,plain,
% 4.49/4.71 ((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))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(740,plain,
% 4.49/4.71 (((~![V: $i, 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)))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[739])).
% 4.49/4.71 tff(741,plain,
% 4.49/4.71 (((~![V: $i, 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))),
% 4.49/4.71 inference(transitivity,[status(thm)],[740, 738])).
% 4.49/4.71 tff(742,plain,
% 4.49/4.71 ((~![V: $i, 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)))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(743,plain,
% 4.49/4.71 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[742, 741])).
% 4.49/4.71 tff(744,plain,
% 4.49/4.71 ($false),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[743, 197, 126, 560, 558, 115, 114, 125, 570, 113])).
% 4.49/4.71 tff(745,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | c0_1(a1677) | c1_1(a1677) | (~c3_1(a1677))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.71 tff(746,plain,
% 4.49/4.71 (c1_1(a1654)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[745, 481, 126, 489, 716, 737, 736])).
% 4.49/4.71 tff(747,plain,
% 4.49/4.71 (hskp60),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[362, 197, 335, 333, 334, 716, 737, 356, 736])).
% 4.49/4.71 tff(748,plain,
% 4.49/4.71 (~c1_1(a1673)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[369, 747])).
% 4.49/4.71 tff(749,plain,
% 4.49/4.71 (c2_1(a1673)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[419, 747])).
% 4.49/4.71 tff(750,plain,
% 4.49/4.71 (c3_1(a1673)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[427, 747])).
% 4.49/4.71 tff(751,plain,
% 4.49/4.71 (hskp26),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[606, 197, 750, 749, 481, 497, 489, 748, 20])).
% 4.49/4.71 tff(752,plain,
% 4.49/4.71 (~c2_1(a1691)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[612, 751])).
% 4.49/4.71 tff(753,plain,
% 4.49/4.71 (~c1_1(a1691)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[618, 751])).
% 4.49/4.71 tff(754,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(755,plain,
% 4.49/4.71 (((~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)))),
% 4.49/4.71 inference(rewrite,[status(thm)],[])).
% 4.49/4.71 tff(756,plain,
% 4.49/4.71 (((~![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))))),
% 4.49/4.71 inference(monotonicity,[status(thm)],[755])).
% 4.49/4.71 tff(757,plain,
% 4.49/4.71 (((~![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)))),
% 4.49/4.71 inference(transitivity,[status(thm)],[756, 754])).
% 4.49/4.71 tff(758,plain,
% 4.49/4.71 ((~![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)))),
% 4.49/4.71 inference(quant_inst,[status(thm)],[])).
% 4.49/4.71 tff(759,plain,
% 4.49/4.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1691) | c2_1(a1691) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c0_1(a1691)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.49/4.71 inference(modus_ponens,[status(thm)],[758, 757])).
% 4.49/4.71 tff(760,plain,
% 4.49/4.71 ((~c0_1(a1691)) | (~c1_1(a1654))),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[759, 197, 481, 489, 753, 752, 715, 737, 590, 736])).
% 4.49/4.71 tff(761,plain,
% 4.49/4.71 (~c0_1(a1691)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[760, 746])).
% 4.49/4.71 tff(762,plain,
% 4.49/4.71 (~c3_1(a1691)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[632, 751])).
% 4.49/4.71 tff(763,plain,
% 4.49/4.71 (hskp37 | c0_1(a1691)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[639, 197, 503, 762, 752, 526])).
% 4.49/4.71 tff(764,plain,
% 4.49/4.71 (hskp37),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[763, 761])).
% 4.49/4.71 tff(765,plain,
% 4.49/4.71 (~c1_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[540, 764])).
% 4.49/4.71 tff(766,plain,
% 4.49/4.71 (c0_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[548, 764])).
% 4.49/4.71 tff(767,plain,
% 4.49/4.71 (c2_1(a1714)),
% 4.49/4.71 inference(unit_resolution,[status(thm)],[556, 764])).
% 4.49/4.72 tff(768,plain,
% 4.49/4.72 ($false),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[650, 197, 481, 497, 489, 767, 766, 765, 762, 752, 514, 761])).
% 4.49/4.72 tff(769,plain,(c1_1(a1715) | hskp29 | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.49/4.72 tff(770,plain,
% 4.49/4.72 (c1_1(a1715)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[769, 333, 126, 334])).
% 4.49/4.72 tff(771,assumption,(c1_1(a1715)), introduced(assumption)).
% 4.49/4.72 tff(772,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(773,plain,
% 4.49/4.72 (((~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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(774,plain,
% 4.49/4.72 (((~![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))))),
% 4.49/4.72 inference(monotonicity,[status(thm)],[773])).
% 4.49/4.72 tff(775,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(transitivity,[status(thm)],[774, 772])).
% 4.49/4.72 tff(776,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.72 inference(quant_inst,[status(thm)],[])).
% 4.49/4.72 tff(777,plain,
% 4.49/4.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | c1_1(a1655) | (~c3_1(a1677)) | (~c1_1(a1715))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[776, 775])).
% 4.49/4.72 tff(778,plain,
% 4.49/4.72 ($false),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[777, 197, 771, 333, 69, 71, 334, 115, 114, 90, 211, 113])).
% 4.49/4.72 tff(779,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,[]))).
% 4.49/4.72 tff(780,plain,
% 4.49/4.72 (c1_1(a1655)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[779, 112, 333, 69, 71, 334, 771, 100, 336])).
% 4.49/4.72 tff(781,plain,
% 4.49/4.72 (hskp13),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[273, 780])).
% 4.49/4.72 tff(782,plain,
% 4.49/4.72 (~c1_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[279, 781])).
% 4.49/4.72 tff(783,plain,
% 4.49/4.72 (c3_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[287, 781])).
% 4.49/4.72 tff(784,plain,
% 4.49/4.72 (c0_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[295, 781])).
% 4.49/4.72 tff(785,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(786,plain,
% 4.49/4.72 (((~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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(787,plain,
% 4.49/4.72 (((~![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))))),
% 4.49/4.72 inference(monotonicity,[status(thm)],[786])).
% 4.49/4.72 tff(788,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(transitivity,[status(thm)],[787, 785])).
% 4.49/4.72 tff(789,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.72 inference(quant_inst,[status(thm)],[])).
% 4.49/4.72 tff(790,plain,
% 4.49/4.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677)) | (~c1_1(a1715))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[789, 788])).
% 4.49/4.72 tff(791,plain,
% 4.49/4.72 ($false),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[790, 197, 771, 333, 784, 783, 334, 112, 100, 782, 90, 336])).
% 4.49/4.72 tff(792,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,[]))).
% 4.49/4.72 tff(793,plain,
% 4.49/4.72 (~hskp16),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[792, 206, 333, 334, 770, 205, 207, 144, 150, 158])).
% 4.49/4.72 tff(794,plain,
% 4.49/4.72 (hskp17),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[304, 793, 206, 205, 207])).
% 4.49/4.72 tff(795,plain,
% 4.49/4.72 (c1_1(a1655)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[245, 794, 144, 150, 126, 206, 205, 158])).
% 4.49/4.72 tff(796,plain,
% 4.49/4.72 (hskp13),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[456, 795])).
% 4.49/4.72 tff(797,plain,
% 4.49/4.72 (~c1_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[279, 796])).
% 4.49/4.72 tff(798,plain,
% 4.49/4.72 (~c1_1(a1678)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[217, 794])).
% 4.49/4.72 tff(799,plain,
% 4.49/4.72 (~c0_1(a1678)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[223, 794])).
% 4.49/4.72 tff(800,plain,
% 4.49/4.72 (c3_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[287, 796])).
% 4.49/4.72 tff(801,plain,
% 4.49/4.72 (c0_1(a1667)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[295, 796])).
% 4.49/4.72 tff(802,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(803,plain,
% 4.49/4.72 (((~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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(804,plain,
% 4.49/4.72 (((~![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))))),
% 4.49/4.72 inference(monotonicity,[status(thm)],[803])).
% 4.49/4.72 tff(805,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(transitivity,[status(thm)],[804, 802])).
% 4.49/4.72 tff(806,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.72 inference(quant_inst,[status(thm)],[])).
% 4.49/4.72 tff(807,plain,
% 4.49/4.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1715) | (~c2_1(a1715)) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c1_1(a1715))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[806, 805])).
% 4.49/4.72 tff(808,plain,
% 4.49/4.72 (~c3_1(a1678)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[807, 197, 770, 333, 801, 800, 334, 799, 798, 797, 90])).
% 4.49/4.72 tff(809,plain,
% 4.49/4.72 (~c2_1(a1678)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[236, 794])).
% 4.49/4.72 tff(810,plain,
% 4.49/4.72 ($false),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[243, 197, 158, 144, 150, 799, 798, 809, 30, 808])).
% 4.49/4.72 tff(811,plain,(hskp52 | c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.49/4.72 tff(812,plain,
% 4.49/4.72 (hskp52),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[811, 333, 334, 126])).
% 4.49/4.72 tff(813,plain,
% 4.49/4.72 (c0_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[480, 812])).
% 4.49/4.72 tff(814,plain,
% 4.49/4.72 (c3_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[488, 812])).
% 4.49/4.72 tff(815,plain,
% 4.49/4.72 (c2_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[496, 812])).
% 4.49/4.72 tff(816,plain,
% 4.49/4.72 (c3_1(a1678)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[568, 237, 503, 815, 814, 224, 813])).
% 4.49/4.72 tff(817,plain,
% 4.49/4.72 (c1_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[579, 816, 813, 814, 126, 224, 218])).
% 4.49/4.72 tff(818,assumption,(hskp52), introduced(assumption)).
% 4.49/4.72 tff(819,assumption,(c1_1(a1654)), introduced(assumption)).
% 4.49/4.72 tff(820,assumption,(~hskp13), introduced(assumption)).
% 4.49/4.72 tff(821,plain,
% 4.49/4.72 (^[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))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(822,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[821])).
% 4.49/4.72 tff(823,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(824,plain,
% 4.49/4.72 (^[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)))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(825,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[824])).
% 4.49/4.72 tff(826,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause332')).
% 4.49/4.72 tff(827,plain,
% 4.49/4.72 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[826, 825])).
% 4.49/4.72 tff(828,plain,
% 4.49/4.72 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[827, 823])).
% 4.49/4.72 tff(829,plain,(
% 4.49/4.72 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 4.49/4.72 inference(skolemize,[status(sab)],[828])).
% 4.49/4.72 tff(830,plain,
% 4.49/4.72 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[829, 822])).
% 4.49/4.72 tff(831,plain,
% 4.49/4.72 (c3_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[488, 818])).
% 4.49/4.72 tff(832,plain,
% 4.49/4.72 (c2_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[496, 818])).
% 4.49/4.72 tff(833,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(834,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.72 inference(quant_inst,[status(thm)],[])).
% 4.49/4.72 tff(835,plain,
% 4.49/4.72 ((~![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))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[834, 833])).
% 4.49/4.72 tff(836,plain,
% 4.49/4.72 (hskp13 | hskp12 | (~c1_1(a1654))),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[835, 197, 832, 831, 830])).
% 4.49/4.72 tff(837,plain,
% 4.49/4.72 (hskp12),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[836, 820, 819])).
% 4.49/4.72 tff(838,plain,
% 4.49/4.72 (((~hskp12) | (~c1_1(a1666))) <=> ((~hskp12) | (~c1_1(a1666)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(839,plain,
% 4.49/4.72 (((~c1_1(a1666)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a1666)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(840,axiom,((~c1_1(a1666)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 4.49/4.72 tff(841,plain,
% 4.49/4.72 ((~hskp12) | (~c1_1(a1666))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[840, 839])).
% 4.49/4.72 tff(842,plain,
% 4.49/4.72 ((~hskp12) | (~c1_1(a1666))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[841, 838])).
% 4.49/4.72 tff(843,plain,
% 4.49/4.72 (~c1_1(a1666)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[842, 837])).
% 4.49/4.72 tff(844,plain,
% 4.49/4.72 (((~hskp12) | c3_1(a1666)) <=> ((~hskp12) | c3_1(a1666))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(845,axiom,((~hskp12) | c3_1(a1666)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 4.49/4.72 tff(846,plain,
% 4.49/4.72 ((~hskp12) | c3_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[845, 844])).
% 4.49/4.72 tff(847,plain,
% 4.49/4.72 ((~hskp12) | c3_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[846, 844])).
% 4.49/4.72 tff(848,plain,
% 4.49/4.72 ((~hskp12) | c3_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[847, 844])).
% 4.49/4.72 tff(849,plain,
% 4.49/4.72 ((~hskp12) | c3_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[848, 844])).
% 4.49/4.72 tff(850,plain,
% 4.49/4.72 ((~hskp12) | c3_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[849, 844])).
% 4.49/4.72 tff(851,plain,
% 4.49/4.72 (c3_1(a1666)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[850, 837])).
% 4.49/4.72 tff(852,plain,
% 4.49/4.72 (((~hskp12) | c2_1(a1666)) <=> ((~hskp12) | c2_1(a1666))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(853,axiom,((~hskp12) | c2_1(a1666)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 4.49/4.72 tff(854,plain,
% 4.49/4.72 ((~hskp12) | c2_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[853, 852])).
% 4.49/4.72 tff(855,plain,
% 4.49/4.72 ((~hskp12) | c2_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[854, 852])).
% 4.49/4.72 tff(856,plain,
% 4.49/4.72 ((~hskp12) | c2_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[855, 852])).
% 4.49/4.72 tff(857,plain,
% 4.49/4.72 ((~hskp12) | c2_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[856, 852])).
% 4.49/4.72 tff(858,plain,
% 4.49/4.72 ((~hskp12) | c2_1(a1666)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[857, 852])).
% 4.49/4.72 tff(859,plain,
% 4.49/4.72 (c2_1(a1666)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[858, 837])).
% 4.49/4.72 tff(860,plain,
% 4.49/4.72 (c0_1(a1654)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[480, 818])).
% 4.49/4.72 tff(861,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(862,plain,
% 4.49/4.72 ((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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(863,plain,
% 4.49/4.72 (((~![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))))),
% 4.49/4.72 inference(monotonicity,[status(thm)],[862])).
% 4.49/4.72 tff(864,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(transitivity,[status(thm)],[863, 861])).
% 4.49/4.72 tff(865,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.72 inference(quant_inst,[status(thm)],[])).
% 4.49/4.72 tff(866,plain,
% 4.49/4.72 ((~![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))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[865, 864])).
% 4.49/4.72 tff(867,plain,
% 4.49/4.72 (hskp26),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[866, 197, 860, 832, 831, 859, 851, 843, 20])).
% 4.49/4.72 tff(868,plain,
% 4.49/4.72 (~c2_1(a1691)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[612, 867])).
% 4.49/4.72 tff(869,plain,
% 4.49/4.72 (~c1_1(a1691)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[618, 867])).
% 4.49/4.72 tff(870,plain,
% 4.49/4.72 (~c3_1(a1691)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[632, 867])).
% 4.49/4.72 tff(871,assumption,(c0_1(a1691)), introduced(assumption)).
% 4.49/4.72 tff(872,plain,
% 4.49/4.72 (^[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))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(873,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[872])).
% 4.49/4.72 tff(874,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(875,plain,
% 4.49/4.72 (^[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)))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(876,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[875])).
% 4.49/4.72 tff(877,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')).
% 4.49/4.72 tff(878,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[877, 876])).
% 4.49/4.72 tff(879,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[878, 874])).
% 4.49/4.72 tff(880,plain,(
% 4.49/4.72 ![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)))),
% 4.49/4.72 inference(skolemize,[status(sab)],[879])).
% 4.49/4.72 tff(881,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[880, 873])).
% 4.49/4.72 tff(882,plain,
% 4.49/4.72 (^[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))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(883,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[882])).
% 4.49/4.72 tff(884,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(885,plain,
% 4.49/4.72 (^[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))) | (~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)))))),
% 4.49/4.72 inference(bind,[status(th)],[])).
% 4.49/4.72 tff(886,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(quant_intro,[status(thm)],[885])).
% 4.49/4.72 tff(887,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')).
% 4.49/4.72 tff(888,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[887, 886])).
% 4.49/4.72 tff(889,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[888, 884])).
% 4.49/4.72 tff(890,plain,(
% 4.49/4.72 ![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)))),
% 4.49/4.72 inference(skolemize,[status(sab)],[889])).
% 4.49/4.72 tff(891,plain,
% 4.49/4.72 (![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)))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[890, 883])).
% 4.49/4.72 tff(892,assumption,(~c1_1(a1691)), introduced(assumption)).
% 4.49/4.72 tff(893,assumption,(~c3_1(a1691)), introduced(assumption)).
% 4.49/4.72 tff(894,assumption,(~hskp0), introduced(assumption)).
% 4.49/4.72 tff(895,assumption,(~c2_1(a1691)), introduced(assumption)).
% 4.49/4.72 tff(896,assumption,(hskp38), introduced(assumption)).
% 4.49/4.72 tff(897,plain,
% 4.49/4.72 (((~hskp38) | (~c2_1(a1718))) <=> ((~hskp38) | (~c2_1(a1718)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(898,plain,
% 4.49/4.72 (((~c2_1(a1718)) | (~hskp38)) <=> ((~hskp38) | (~c2_1(a1718)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(899,axiom,((~c2_1(a1718)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause231')).
% 4.49/4.72 tff(900,plain,
% 4.49/4.72 ((~hskp38) | (~c2_1(a1718))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[899, 898])).
% 4.49/4.72 tff(901,plain,
% 4.49/4.72 ((~hskp38) | (~c2_1(a1718))),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[900, 897])).
% 4.49/4.72 tff(902,plain,
% 4.49/4.72 (~c2_1(a1718)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[901, 896])).
% 4.49/4.72 tff(903,plain,
% 4.49/4.72 (((~hskp38) | c3_1(a1718)) <=> ((~hskp38) | c3_1(a1718))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(904,axiom,((~hskp38) | c3_1(a1718)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 4.49/4.72 tff(905,plain,
% 4.49/4.72 ((~hskp38) | c3_1(a1718)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[904, 903])).
% 4.49/4.72 tff(906,plain,
% 4.49/4.72 ((~hskp38) | c3_1(a1718)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[905, 903])).
% 4.49/4.72 tff(907,plain,
% 4.49/4.72 ((~hskp38) | c3_1(a1718)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[906, 903])).
% 4.49/4.72 tff(908,plain,
% 4.49/4.72 ((~hskp38) | c3_1(a1718)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[907, 903])).
% 4.49/4.72 tff(909,plain,
% 4.49/4.72 ((~hskp38) | c3_1(a1718)),
% 4.49/4.72 inference(modus_ponens,[status(thm)],[908, 903])).
% 4.49/4.72 tff(910,plain,
% 4.49/4.72 (c3_1(a1718)),
% 4.49/4.72 inference(unit_resolution,[status(thm)],[909, 896])).
% 4.49/4.72 tff(911,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(912,plain,
% 4.49/4.72 ((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)))),
% 4.49/4.72 inference(rewrite,[status(thm)],[])).
% 4.49/4.72 tff(913,plain,
% 4.49/4.72 (((~![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))))),
% 4.49/4.72 inference(monotonicity,[status(thm)],[912])).
% 4.49/4.72 tff(914,plain,
% 4.49/4.72 (((~![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)))),
% 4.49/4.72 inference(transitivity,[status(thm)],[913, 911])).
% 4.49/4.72 tff(915,plain,
% 4.49/4.72 ((~![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)))),
% 4.49/4.73 inference(quant_inst,[status(thm)],[])).
% 4.49/4.73 tff(916,plain,
% 4.49/4.73 ((~![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))),
% 4.49/4.73 inference(modus_ponens,[status(thm)],[915, 914])).
% 4.49/4.73 tff(917,plain,
% 4.49/4.73 (~c1_1(a1718)),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[916, 197, 894, 560, 559, 910, 902, 881, 819])).
% 4.49/4.73 tff(918,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(919,plain,
% 4.49/4.73 ((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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(920,plain,
% 4.49/4.73 (((~![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))))),
% 4.49/4.73 inference(monotonicity,[status(thm)],[919])).
% 4.49/4.73 tff(921,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(transitivity,[status(thm)],[920, 918])).
% 4.49/4.73 tff(922,plain,
% 4.49/4.73 ((~![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)))),
% 4.49/4.73 inference(quant_inst,[status(thm)],[])).
% 4.49/4.73 tff(923,plain,
% 4.49/4.73 ((~![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))),
% 4.49/4.73 inference(modus_ponens,[status(thm)],[922, 921])).
% 4.49/4.73 tff(924,plain,
% 4.49/4.73 (hskp75),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[923, 197, 771, 333, 910, 334, 902, 398, 917])).
% 4.49/4.73 tff(925,plain,
% 4.49/4.73 (~c2_1(a1724)),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[411, 924])).
% 4.49/4.73 tff(926,plain,
% 4.49/4.73 (c0_1(a1724)),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[443, 924])).
% 4.49/4.73 tff(927,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(928,plain,
% 4.49/4.73 (((~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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(929,plain,
% 4.49/4.73 (((~![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))))),
% 4.49/4.73 inference(monotonicity,[status(thm)],[928])).
% 4.49/4.73 tff(930,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(transitivity,[status(thm)],[929, 927])).
% 4.49/4.73 tff(931,plain,
% 4.49/4.73 ((~![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)))),
% 4.49/4.73 inference(quant_inst,[status(thm)],[])).
% 4.49/4.73 tff(932,plain,
% 4.49/4.73 ((~![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))),
% 4.49/4.73 inference(modus_ponens,[status(thm)],[931, 930])).
% 4.49/4.73 tff(933,plain,
% 4.49/4.73 (c1_1(a1724)),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[932, 197, 926, 560, 558, 910, 925, 902, 590, 819, 917])).
% 4.49/4.73 tff(934,plain,
% 4.49/4.73 (c3_1(a1724)),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[435, 924])).
% 4.49/4.73 tff(935,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(936,plain,
% 4.49/4.73 (((~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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(937,plain,
% 4.49/4.73 (((~![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))))),
% 4.49/4.73 inference(monotonicity,[status(thm)],[936])).
% 4.49/4.73 tff(938,plain,
% 4.49/4.73 (((~![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)))),
% 4.49/4.73 inference(transitivity,[status(thm)],[937, 935])).
% 4.49/4.73 tff(939,plain,
% 4.49/4.73 ((~![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)))),
% 4.49/4.73 inference(quant_inst,[status(thm)],[])).
% 4.49/4.73 tff(940,plain,
% 4.49/4.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))),
% 4.49/4.73 inference(modus_ponens,[status(thm)],[939, 938])).
% 4.49/4.73 tff(941,plain,
% 4.49/4.73 ($false),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[940, 197, 926, 934, 910, 902, 892, 895, 590, 933, 917, 871])).
% 4.49/4.73 tff(942,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,[]))).
% 4.49/4.73 tff(943,plain,
% 4.49/4.73 (~hskp38),
% 4.49/4.73 inference(unit_resolution,[status(thm)],[942, 894, 895, 871, 860, 831, 819, 771, 333, 334, 892, 832])).
% 4.49/4.73 tff(944,plain,
% 4.49/4.73 (^[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))))),
% 4.49/4.73 inference(bind,[status(th)],[])).
% 4.49/4.73 tff(945,plain,
% 4.49/4.73 (![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)))),
% 4.49/4.73 inference(quant_intro,[status(thm)],[944])).
% 4.49/4.73 tff(946,plain,
% 4.49/4.73 (![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)))),
% 4.49/4.73 inference(rewrite,[status(thm)],[])).
% 4.49/4.73 tff(947,plain,
% 4.49/4.73 (^[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)))))),
% 4.57/4.73 inference(bind,[status(th)],[])).
% 4.57/4.73 tff(948,plain,
% 4.57/4.73 (![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)))),
% 4.57/4.73 inference(quant_intro,[status(thm)],[947])).
% 4.57/4.73 tff(949,axiom,(![U: $i] : ((((((~c3_1(U)) | (~c2_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp74) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause333')).
% 4.57/4.73 tff(950,plain,
% 4.57/4.73 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[949, 948])).
% 4.57/4.73 tff(951,plain,
% 4.57/4.73 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[950, 946])).
% 4.57/4.73 tff(952,plain,(
% 4.57/4.73 ![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(skolemize,[status(sab)],[951])).
% 4.57/4.73 tff(953,plain,
% 4.57/4.73 (![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[952, 945])).
% 4.57/4.73 tff(954,assumption,(~hskp38), introduced(assumption)).
% 4.57/4.73 tff(955,assumption,(~hskp74), introduced(assumption)).
% 4.57/4.73 tff(956,plain,
% 4.57/4.73 (((~![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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(957,plain,
% 4.57/4.73 ((~![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)))),
% 4.57/4.73 inference(quant_inst,[status(thm)],[])).
% 4.57/4.73 tff(958,plain,
% 4.57/4.73 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[957, 956])).
% 4.57/4.73 tff(959,plain,
% 4.57/4.73 ($false),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[958, 197, 955, 954, 860, 832, 831, 953])).
% 4.57/4.73 tff(960,plain,((~hskp52) | hskp74 | hskp38), inference(lemma,lemma(discharge,[]))).
% 4.57/4.73 tff(961,plain,
% 4.57/4.73 (hskp74),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[960, 943, 818])).
% 4.57/4.73 tff(962,plain,
% 4.57/4.73 (^[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))))),
% 4.57/4.73 inference(bind,[status(th)],[])).
% 4.57/4.73 tff(963,plain,
% 4.57/4.73 (![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)))),
% 4.57/4.73 inference(quant_intro,[status(thm)],[962])).
% 4.57/4.73 tff(964,plain,
% 4.57/4.73 (![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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(965,plain,
% 4.57/4.73 (^[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)))))),
% 4.57/4.73 inference(bind,[status(th)],[])).
% 4.57/4.73 tff(966,plain,
% 4.57/4.73 (![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)))),
% 4.57/4.73 inference(quant_intro,[status(thm)],[965])).
% 4.57/4.73 tff(967,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause322')).
% 4.57/4.73 tff(968,plain,
% 4.57/4.73 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[967, 966])).
% 4.57/4.73 tff(969,plain,
% 4.57/4.73 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[968, 964])).
% 4.57/4.73 tff(970,plain,(
% 4.57/4.73 ![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(skolemize,[status(sab)],[969])).
% 4.57/4.73 tff(971,plain,
% 4.57/4.73 (![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[970, 963])).
% 4.57/4.73 tff(972,assumption,(hskp74), introduced(assumption)).
% 4.57/4.73 tff(973,plain,
% 4.57/4.73 (((~hskp74) | (~c3_1(a1717))) <=> ((~hskp74) | (~c3_1(a1717)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(974,plain,
% 4.57/4.73 (((~c3_1(a1717)) | (~hskp74)) <=> ((~hskp74) | (~c3_1(a1717)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(975,axiom,((~c3_1(a1717)) | (~hskp74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 4.57/4.73 tff(976,plain,
% 4.57/4.73 ((~hskp74) | (~c3_1(a1717))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[975, 974])).
% 4.57/4.73 tff(977,plain,
% 4.57/4.73 ((~hskp74) | (~c3_1(a1717))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[976, 973])).
% 4.57/4.73 tff(978,plain,
% 4.57/4.73 (~c3_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[977, 972])).
% 4.57/4.73 tff(979,plain,
% 4.57/4.73 (((~hskp74) | c2_1(a1717)) <=> ((~hskp74) | c2_1(a1717))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(980,axiom,((~hskp74) | c2_1(a1717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 4.57/4.73 tff(981,plain,
% 4.57/4.73 ((~hskp74) | c2_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[980, 979])).
% 4.57/4.73 tff(982,plain,
% 4.57/4.73 ((~hskp74) | c2_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[981, 979])).
% 4.57/4.73 tff(983,plain,
% 4.57/4.73 ((~hskp74) | c2_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[982, 979])).
% 4.57/4.73 tff(984,plain,
% 4.57/4.73 ((~hskp74) | c2_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[983, 979])).
% 4.57/4.73 tff(985,plain,
% 4.57/4.73 ((~hskp74) | c2_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[984, 979])).
% 4.57/4.73 tff(986,plain,
% 4.57/4.73 (c2_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[985, 972])).
% 4.57/4.73 tff(987,plain,
% 4.57/4.73 (((~hskp74) | c0_1(a1717)) <=> ((~hskp74) | c0_1(a1717))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(988,axiom,((~hskp74) | c0_1(a1717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 4.57/4.73 tff(989,plain,
% 4.57/4.73 ((~hskp74) | c0_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[988, 987])).
% 4.57/4.73 tff(990,plain,
% 4.57/4.73 ((~hskp74) | c0_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[989, 987])).
% 4.57/4.73 tff(991,plain,
% 4.57/4.73 ((~hskp74) | c0_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[990, 987])).
% 4.57/4.73 tff(992,plain,
% 4.57/4.73 ((~hskp74) | c0_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[991, 987])).
% 4.57/4.73 tff(993,plain,
% 4.57/4.73 ((~hskp74) | c0_1(a1717)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[992, 987])).
% 4.57/4.73 tff(994,plain,
% 4.57/4.73 (c0_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[993, 972])).
% 4.57/4.73 tff(995,assumption,(~hskp42), introduced(assumption)).
% 4.57/4.73 tff(996,plain,
% 4.57/4.73 (((~![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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(997,plain,
% 4.57/4.73 ((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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(998,plain,
% 4.57/4.73 (((~![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))))),
% 4.57/4.73 inference(monotonicity,[status(thm)],[997])).
% 4.57/4.73 tff(999,plain,
% 4.57/4.73 (((~![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)))),
% 4.57/4.73 inference(transitivity,[status(thm)],[998, 996])).
% 4.57/4.73 tff(1000,plain,
% 4.57/4.73 ((~![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)))),
% 4.57/4.73 inference(quant_inst,[status(thm)],[])).
% 4.57/4.73 tff(1001,plain,
% 4.57/4.73 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1717) | (~ndr1_0) | (~c2_1(a1717)) | (~c0_1(a1717))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1000, 999])).
% 4.57/4.73 tff(1002,plain,
% 4.57/4.73 ($false),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1001, 197, 995, 894, 994, 986, 978, 971])).
% 4.57/4.73 tff(1003,plain,((~hskp74) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.57/4.73 tff(1004,plain,
% 4.57/4.73 (hskp42),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1003, 961, 894])).
% 4.57/4.73 tff(1005,plain,
% 4.57/4.73 (((~hskp42) | (~c3_1(a1638))) <=> ((~hskp42) | (~c3_1(a1638)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1006,plain,
% 4.57/4.73 (((~c3_1(a1638)) | (~hskp42)) <=> ((~hskp42) | (~c3_1(a1638)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1007,axiom,((~c3_1(a1638)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause226')).
% 4.57/4.73 tff(1008,plain,
% 4.57/4.73 ((~hskp42) | (~c3_1(a1638))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 4.57/4.73 tff(1009,plain,
% 4.57/4.73 ((~hskp42) | (~c3_1(a1638))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 4.57/4.73 tff(1010,plain,
% 4.57/4.73 (~c3_1(a1638)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1009, 1004])).
% 4.57/4.73 tff(1011,plain,
% 4.57/4.73 (((~hskp42) | c0_1(a1638)) <=> ((~hskp42) | c0_1(a1638))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1012,axiom,((~hskp42) | c0_1(a1638)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 4.57/4.73 tff(1013,plain,
% 4.57/4.73 ((~hskp42) | c0_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 4.57/4.73 tff(1014,plain,
% 4.57/4.73 ((~hskp42) | c0_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1013, 1011])).
% 4.57/4.73 tff(1015,plain,
% 4.57/4.73 ((~hskp42) | c0_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 4.57/4.73 tff(1016,plain,
% 4.57/4.73 ((~hskp42) | c0_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1015, 1011])).
% 4.57/4.73 tff(1017,plain,
% 4.57/4.73 ((~hskp42) | c0_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1016, 1011])).
% 4.57/4.73 tff(1018,plain,
% 4.57/4.73 (c0_1(a1638)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1017, 1004])).
% 4.57/4.73 tff(1019,plain,
% 4.57/4.73 (((~hskp42) | c1_1(a1638)) <=> ((~hskp42) | c1_1(a1638))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1020,axiom,((~hskp42) | c1_1(a1638)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 4.57/4.73 tff(1021,plain,
% 4.57/4.73 ((~hskp42) | c1_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 4.57/4.73 tff(1022,plain,
% 4.57/4.73 ((~hskp42) | c1_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1021, 1019])).
% 4.57/4.73 tff(1023,plain,
% 4.57/4.73 ((~hskp42) | c1_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 4.57/4.73 tff(1024,plain,
% 4.57/4.73 ((~hskp42) | c1_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 4.57/4.73 tff(1025,plain,
% 4.57/4.73 ((~hskp42) | c1_1(a1638)),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1024, 1019])).
% 4.57/4.73 tff(1026,plain,
% 4.57/4.73 (c1_1(a1638)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1025, 1004])).
% 4.57/4.73 tff(1027,plain,
% 4.57/4.73 (((~![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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1028,plain,
% 4.57/4.73 ((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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1029,plain,
% 4.57/4.73 (((~![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))))),
% 4.57/4.73 inference(monotonicity,[status(thm)],[1028])).
% 4.57/4.73 tff(1030,plain,
% 4.57/4.73 (((~![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)))),
% 4.57/4.73 inference(transitivity,[status(thm)],[1029, 1027])).
% 4.57/4.73 tff(1031,plain,
% 4.57/4.73 ((~![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)))),
% 4.57/4.73 inference(quant_inst,[status(thm)],[])).
% 4.57/4.73 tff(1032,plain,
% 4.57/4.73 ((~![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))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 4.57/4.73 tff(1033,plain,
% 4.57/4.73 (hskp2),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1032, 197, 1026, 1018, 1010, 893, 892, 891, 871])).
% 4.57/4.73 tff(1034,plain,
% 4.57/4.73 (((~hskp2) | (~c0_1(a1645))) <=> ((~hskp2) | (~c0_1(a1645)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1035,plain,
% 4.57/4.73 (((~c0_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1645)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1036,axiom,((~c0_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause308')).
% 4.57/4.73 tff(1037,plain,
% 4.57/4.73 ((~hskp2) | (~c0_1(a1645))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 4.57/4.73 tff(1038,plain,
% 4.57/4.73 ((~hskp2) | (~c0_1(a1645))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1037, 1034])).
% 4.57/4.73 tff(1039,plain,
% 4.57/4.73 (~c0_1(a1645)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1038, 1033])).
% 4.57/4.73 tff(1040,plain,
% 4.57/4.73 (((~hskp2) | (~c1_1(a1645))) <=> ((~hskp2) | (~c1_1(a1645)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1041,plain,
% 4.57/4.73 (((~c1_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1645)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1042,axiom,((~c1_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause307')).
% 4.57/4.73 tff(1043,plain,
% 4.57/4.73 ((~hskp2) | (~c1_1(a1645))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 4.57/4.73 tff(1044,plain,
% 4.57/4.73 ((~hskp2) | (~c1_1(a1645))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1043, 1040])).
% 4.57/4.73 tff(1045,plain,
% 4.57/4.73 (~c1_1(a1645)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1044, 1033])).
% 4.57/4.73 tff(1046,plain,
% 4.57/4.73 (~c3_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[977, 961])).
% 4.57/4.73 tff(1047,plain,
% 4.57/4.73 (c2_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[985, 961])).
% 4.57/4.73 tff(1048,plain,
% 4.57/4.73 (c0_1(a1717)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[993, 961])).
% 4.57/4.73 tff(1049,plain,
% 4.57/4.73 (((~![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(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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1050,plain,
% 4.57/4.73 (((~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)))),
% 4.57/4.73 inference(rewrite,[status(thm)],[])).
% 4.57/4.73 tff(1051,plain,
% 4.57/4.73 (((~![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(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))))),
% 4.57/4.73 inference(monotonicity,[status(thm)],[1050])).
% 4.57/4.73 tff(1052,plain,
% 4.57/4.73 (((~![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(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)))),
% 4.57/4.73 inference(transitivity,[status(thm)],[1051, 1049])).
% 4.57/4.73 tff(1053,plain,
% 4.57/4.73 ((~![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(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))),
% 4.57/4.73 inference(quant_inst,[status(thm)],[])).
% 4.57/4.73 tff(1054,plain,
% 4.57/4.73 ((~![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(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))),
% 4.57/4.73 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 4.57/4.73 tff(1055,plain,
% 4.57/4.73 (c2_1(a1645)),
% 4.57/4.73 inference(unit_resolution,[status(thm)],[1054, 197, 1048, 1047, 1046, 893, 892, 895, 1045, 1039, 30])).
% 4.57/4.74 tff(1056,plain,
% 4.57/4.74 (((~hskp2) | (~c3_1(a1645))) <=> ((~hskp2) | (~c3_1(a1645)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1057,plain,
% 4.57/4.74 (((~c3_1(a1645)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1645)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1058,axiom,((~c3_1(a1645)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause309')).
% 4.57/4.74 tff(1059,plain,
% 4.57/4.74 ((~hskp2) | (~c3_1(a1645))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 4.57/4.74 tff(1060,plain,
% 4.57/4.74 ((~hskp2) | (~c3_1(a1645))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1059, 1056])).
% 4.57/4.74 tff(1061,plain,
% 4.57/4.74 (~c3_1(a1645)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1060, 1033])).
% 4.57/4.74 tff(1062,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1063,plain,
% 4.57/4.74 ((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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1064,plain,
% 4.57/4.74 (((~![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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1063])).
% 4.57/4.74 tff(1065,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1064, 1062])).
% 4.57/4.74 tff(1066,plain,
% 4.57/4.74 ((~![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)))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1067,plain,
% 4.57/4.74 ((~![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))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 4.57/4.74 tff(1068,plain,
% 4.57/4.74 (hskp40),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1067, 197, 860, 831, 1045, 1061, 671, 819, 1055])).
% 4.57/4.74 tff(1069,plain,
% 4.57/4.74 (~c2_1(a1725)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[684, 1068])).
% 4.57/4.74 tff(1070,plain,
% 4.57/4.74 (c3_1(a1725)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[692, 1068])).
% 4.57/4.74 tff(1071,plain,
% 4.57/4.74 (c1_1(a1725)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[700, 1068])).
% 4.57/4.74 tff(1072,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1073,plain,
% 4.57/4.74 ((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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1074,plain,
% 4.57/4.74 (((~![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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1073])).
% 4.57/4.74 tff(1075,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1074, 1072])).
% 4.57/4.74 tff(1076,plain,
% 4.57/4.74 ((~![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)))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1077,plain,
% 4.57/4.74 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 4.57/4.74 tff(1078,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1077, 197, 894, 860, 832, 1071, 1070, 1069, 881, 819])).
% 4.57/4.74 tff(1079,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,[]))).
% 4.57/4.74 tff(1080,plain,
% 4.57/4.74 (hskp0),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1079, 871, 870, 869, 868, 819, 818, 771, 333, 334])).
% 4.57/4.74 tff(1081,plain,
% 4.57/4.74 (((~hskp0) | (~c2_1(a1637))) <=> ((~hskp0) | (~c2_1(a1637)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1082,plain,
% 4.57/4.74 (((~c2_1(a1637)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1637)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1083,axiom,((~c2_1(a1637)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause312')).
% 4.57/4.74 tff(1084,plain,
% 4.57/4.74 ((~hskp0) | (~c2_1(a1637))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 4.57/4.74 tff(1085,plain,
% 4.57/4.74 ((~hskp0) | (~c2_1(a1637))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1084, 1081])).
% 4.57/4.74 tff(1086,plain,
% 4.57/4.74 (~c2_1(a1637)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1085, 1080])).
% 4.57/4.74 tff(1087,plain,
% 4.57/4.74 (((~hskp0) | c0_1(a1637)) <=> ((~hskp0) | c0_1(a1637))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1088,axiom,((~hskp0) | c0_1(a1637)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 4.57/4.74 tff(1089,plain,
% 4.57/4.74 ((~hskp0) | c0_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 4.57/4.74 tff(1090,plain,
% 4.57/4.74 ((~hskp0) | c0_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1089, 1087])).
% 4.57/4.74 tff(1091,plain,
% 4.57/4.74 ((~hskp0) | c0_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1090, 1087])).
% 4.57/4.74 tff(1092,plain,
% 4.57/4.74 ((~hskp0) | c0_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1091, 1087])).
% 4.57/4.74 tff(1093,plain,
% 4.57/4.74 ((~hskp0) | c0_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1092, 1087])).
% 4.57/4.74 tff(1094,plain,
% 4.57/4.74 (c0_1(a1637)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1093, 1080])).
% 4.57/4.74 tff(1095,assumption,(hskp61), introduced(assumption)).
% 4.57/4.74 tff(1096,plain,
% 4.57/4.74 (((~hskp61) | (~c2_1(a1674))) <=> ((~hskp61) | (~c2_1(a1674)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1097,plain,
% 4.57/4.74 (((~c2_1(a1674)) | (~hskp61)) <=> ((~hskp61) | (~c2_1(a1674)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1098,axiom,((~c2_1(a1674)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 4.57/4.74 tff(1099,plain,
% 4.57/4.74 ((~hskp61) | (~c2_1(a1674))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 4.57/4.74 tff(1100,plain,
% 4.57/4.74 ((~hskp61) | (~c2_1(a1674))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 4.57/4.74 tff(1101,plain,
% 4.57/4.74 (~c2_1(a1674)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1100, 1095])).
% 4.57/4.74 tff(1102,plain,
% 4.57/4.74 (((~hskp61) | (~c1_1(a1674))) <=> ((~hskp61) | (~c1_1(a1674)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1103,plain,
% 4.57/4.74 (((~c1_1(a1674)) | (~hskp61)) <=> ((~hskp61) | (~c1_1(a1674)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1104,axiom,((~c1_1(a1674)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 4.57/4.74 tff(1105,plain,
% 4.57/4.74 ((~hskp61) | (~c1_1(a1674))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 4.57/4.74 tff(1106,plain,
% 4.57/4.74 ((~hskp61) | (~c1_1(a1674))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1105, 1102])).
% 4.57/4.74 tff(1107,plain,
% 4.57/4.74 (~c1_1(a1674)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1106, 1095])).
% 4.57/4.74 tff(1108,plain,
% 4.57/4.74 (((~hskp61) | c3_1(a1674)) <=> ((~hskp61) | c3_1(a1674))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1109,axiom,((~hskp61) | c3_1(a1674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 4.57/4.74 tff(1110,plain,
% 4.57/4.74 ((~hskp61) | c3_1(a1674)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 4.57/4.74 tff(1111,plain,
% 4.57/4.74 ((~hskp61) | c3_1(a1674)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1110, 1108])).
% 4.57/4.74 tff(1112,plain,
% 4.57/4.74 ((~hskp61) | c3_1(a1674)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1111, 1108])).
% 4.57/4.74 tff(1113,plain,
% 4.57/4.74 ((~hskp61) | c3_1(a1674)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1112, 1108])).
% 4.57/4.74 tff(1114,plain,
% 4.57/4.74 ((~hskp61) | c3_1(a1674)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1113, 1108])).
% 4.57/4.74 tff(1115,plain,
% 4.57/4.74 (c3_1(a1674)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1114, 1095])).
% 4.57/4.74 tff(1116,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1117,plain,
% 4.57/4.74 (((~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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1118,plain,
% 4.57/4.74 (((~![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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1117])).
% 4.57/4.74 tff(1119,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1118, 1116])).
% 4.57/4.74 tff(1120,plain,
% 4.57/4.74 ((~![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)))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1121,plain,
% 4.57/4.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 4.57/4.74 tff(1122,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1121, 197, 1115, 560, 558, 1107, 1101, 892, 895, 590, 819, 871])).
% 4.57/4.74 tff(1123,plain,((~hskp61) | (~c0_1(a1654)) | (~c3_1(a1654)) | c1_1(a1691) | c2_1(a1691) | (~c1_1(a1654)) | (~c0_1(a1691))), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1124,plain,
% 4.57/4.74 (~hskp61),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1123, 871, 831, 869, 868, 819, 860])).
% 4.57/4.74 tff(1125,plain,
% 4.57/4.74 (((~hskp0) | c1_1(a1637)) <=> ((~hskp0) | c1_1(a1637))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1126,axiom,((~hskp0) | c1_1(a1637)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 4.57/4.74 tff(1127,plain,
% 4.57/4.74 ((~hskp0) | c1_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 4.57/4.74 tff(1128,plain,
% 4.57/4.74 ((~hskp0) | c1_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1127, 1125])).
% 4.57/4.74 tff(1129,plain,
% 4.57/4.74 ((~hskp0) | c1_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1128, 1125])).
% 4.57/4.74 tff(1130,plain,
% 4.57/4.74 ((~hskp0) | c1_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1129, 1125])).
% 4.57/4.74 tff(1131,plain,
% 4.57/4.74 ((~hskp0) | c1_1(a1637)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1130, 1125])).
% 4.57/4.74 tff(1132,plain,
% 4.57/4.74 (c1_1(a1637)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1131, 1080])).
% 4.57/4.74 tff(1133,assumption,(c3_1(a1637)), introduced(assumption)).
% 4.57/4.74 tff(1134,assumption,(~c2_1(a1637)), introduced(assumption)).
% 4.57/4.74 tff(1135,assumption,(c0_1(a1637)), introduced(assumption)).
% 4.57/4.74 tff(1136,assumption,(c1_1(a1637)), introduced(assumption)).
% 4.57/4.74 tff(1137,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1138,plain,
% 4.57/4.74 ((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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1139,plain,
% 4.57/4.74 (((~![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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1138])).
% 4.57/4.74 tff(1140,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1139, 1137])).
% 4.57/4.74 tff(1141,plain,
% 4.57/4.74 ((~![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)))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1142,plain,
% 4.57/4.74 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1637) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 4.57/4.74 tff(1143,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1142, 197, 820, 1136, 1135, 1134, 266, 1133])).
% 4.57/4.74 tff(1144,plain,((~c3_1(a1637)) | hskp13 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1145,plain,
% 4.57/4.74 (~c3_1(a1637)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1144, 1132, 820, 1094, 1086])).
% 4.57/4.74 tff(1146,assumption,(~c3_1(a1637)), introduced(assumption)).
% 4.57/4.74 tff(1147,plain,
% 4.57/4.74 (^[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))))),
% 4.57/4.74 inference(bind,[status(th)],[])).
% 4.57/4.74 tff(1148,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(quant_intro,[status(thm)],[1147])).
% 4.57/4.74 tff(1149,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1150,plain,
% 4.57/4.74 (^[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)))))),
% 4.57/4.74 inference(bind,[status(th)],[])).
% 4.57/4.74 tff(1151,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(quant_intro,[status(thm)],[1150])).
% 4.57/4.74 tff(1152,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')).
% 4.57/4.74 tff(1153,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 4.57/4.74 tff(1154,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1153, 1149])).
% 4.57/4.74 tff(1155,plain,(
% 4.57/4.74 ![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)))),
% 4.57/4.74 inference(skolemize,[status(sab)],[1154])).
% 4.57/4.74 tff(1156,plain,
% 4.57/4.74 (![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)))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1155, 1148])).
% 4.57/4.74 tff(1157,assumption,(~hskp61), introduced(assumption)).
% 4.57/4.74 tff(1158,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1159,plain,
% 4.57/4.74 ((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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1160,plain,
% 4.57/4.74 (((~![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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1159])).
% 4.57/4.74 tff(1161,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1160, 1158])).
% 4.57/4.74 tff(1162,plain,
% 4.57/4.74 ((~![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)))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1163,plain,
% 4.57/4.74 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c0_1(a1637))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 4.57/4.74 tff(1164,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1163, 197, 1157, 1136, 1135, 1134, 1156, 1146])).
% 4.57/4.74 tff(1165,plain,(c3_1(a1637) | hskp61 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1166,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1165, 1145, 1132, 1124, 1094, 1086])).
% 4.57/4.74 tff(1167,plain,((~c0_1(a1691)) | hskp13 | (~c1_1(a1654)) | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1168,plain,
% 4.57/4.74 (~c0_1(a1691)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1167, 820, 819, 818, 771, 333, 334])).
% 4.57/4.74 tff(1169,plain,
% 4.57/4.74 (hskp37 | c0_1(a1691)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[639, 197, 503, 870, 868, 526])).
% 4.57/4.74 tff(1170,plain,
% 4.57/4.74 (hskp37),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1169, 1168])).
% 4.57/4.74 tff(1171,plain,
% 4.57/4.74 (~c1_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[540, 1170])).
% 4.57/4.74 tff(1172,plain,
% 4.57/4.74 (c0_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[548, 1170])).
% 4.57/4.74 tff(1173,plain,
% 4.57/4.74 (c2_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[556, 1170])).
% 4.57/4.74 tff(1174,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[650, 197, 860, 832, 831, 1173, 1172, 1171, 870, 868, 514, 1168])).
% 4.57/4.74 tff(1175,plain,(hskp13 | (~c1_1(a1654)) | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1176,plain,
% 4.57/4.74 (hskp13),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1175, 817, 812, 770, 333, 334])).
% 4.57/4.74 tff(1177,plain,
% 4.57/4.74 (~c1_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[279, 1176])).
% 4.57/4.74 tff(1178,plain,
% 4.57/4.74 (c3_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[287, 1176])).
% 4.57/4.74 tff(1179,plain,
% 4.57/4.74 (c0_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[295, 1176])).
% 4.57/4.74 tff(1180,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[807, 197, 770, 333, 1179, 1178, 334, 224, 218, 1177, 90, 816])).
% 4.57/4.74 tff(1181,plain,((~hskp17) | c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1182,plain,
% 4.57/4.74 (~hskp17),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1181, 333, 334, 126])).
% 4.57/4.74 tff(1183,plain,
% 4.57/4.74 (hskp17 | hskp16 | c1_1(a1654)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[659, 197, 860, 831, 10])).
% 4.57/4.74 tff(1184,plain,
% 4.57/4.74 (c1_1(a1654)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1183, 247, 248])).
% 4.57/4.74 tff(1185,plain,
% 4.57/4.74 (hskp13),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1175, 1184, 818, 771, 333, 334])).
% 4.57/4.74 tff(1186,plain,
% 4.57/4.74 (~c1_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[279, 1185])).
% 4.57/4.74 tff(1187,plain,
% 4.57/4.74 (c3_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[287, 1185])).
% 4.57/4.74 tff(1188,plain,
% 4.57/4.74 (c0_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[295, 1185])).
% 4.57/4.74 tff(1189,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[302, 197, 247, 248, 1188, 1187, 1186, 10])).
% 4.57/4.74 tff(1190,plain,(hskp17 | hskp16 | (~hskp52) | (~c1_1(a1715)) | c3_1(a1715) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1191,plain,
% 4.57/4.74 (hskp16),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1190, 1182, 812, 770, 333, 334])).
% 4.57/4.74 tff(1192,plain,
% 4.57/4.74 (~c0_1(a1677)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[111, 1191])).
% 4.57/4.74 tff(1193,plain,
% 4.57/4.74 (~c2_1(a1677)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[105, 1191])).
% 4.57/4.74 tff(1194,plain,
% 4.57/4.74 (c3_1(a1677)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[735, 1193, 503, 814, 815, 1192, 813])).
% 4.57/4.74 tff(1195,plain,
% 4.57/4.74 (~c1_1(a1677)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[99, 1191])).
% 4.57/4.74 tff(1196,plain,
% 4.57/4.74 (c1_1(a1654)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[745, 1194, 126, 814, 813, 1195, 1192])).
% 4.57/4.74 tff(1197,plain,
% 4.57/4.74 (hskp13),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1175, 1196, 812, 770, 333, 334])).
% 4.57/4.74 tff(1198,plain,
% 4.57/4.74 (~c1_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[279, 1197])).
% 4.57/4.74 tff(1199,plain,
% 4.57/4.74 (c3_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[287, 1197])).
% 4.57/4.74 tff(1200,plain,
% 4.57/4.74 (c0_1(a1667)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[295, 1197])).
% 4.57/4.74 tff(1201,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[790, 197, 770, 333, 1200, 1199, 334, 1192, 1195, 1198, 90, 1194])).
% 4.57/4.74 tff(1202,plain,(c3_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.57/4.74 tff(1203,plain,
% 4.57/4.74 (~c2_1(a1715)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1202, 333, 126])).
% 4.57/4.74 tff(1204,assumption,(~c0_1(a1715)), introduced(assumption)).
% 4.57/4.74 tff(1205,plain,
% 4.57/4.74 (((~hskp72) | c3_1(a1715)) <=> ((~hskp72) | c3_1(a1715))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1206,axiom,((~hskp72) | c3_1(a1715)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 4.57/4.74 tff(1207,plain,
% 4.57/4.74 ((~hskp72) | c3_1(a1715)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 4.57/4.74 tff(1208,plain,
% 4.57/4.74 ((~hskp72) | c3_1(a1715)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1207, 1205])).
% 4.57/4.74 tff(1209,plain,
% 4.57/4.74 ((~hskp72) | c3_1(a1715)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1208, 1205])).
% 4.57/4.74 tff(1210,plain,
% 4.57/4.74 ((~hskp72) | c3_1(a1715)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 4.57/4.74 tff(1211,plain,
% 4.57/4.74 ((~hskp72) | c3_1(a1715)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1210, 1205])).
% 4.57/4.74 tff(1212,plain,
% 4.57/4.74 (~hskp72),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1211, 333])).
% 4.57/4.74 tff(1213,assumption,(~c2_1(a1715)), introduced(assumption)).
% 4.57/4.74 tff(1214,plain,
% 4.57/4.74 (((~![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))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1215,plain,
% 4.57/4.74 ((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))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1216,plain,
% 4.57/4.74 (((~![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)))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1215])).
% 4.57/4.74 tff(1217,plain,
% 4.57/4.74 (((~![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))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1216, 1214])).
% 4.57/4.74 tff(1218,plain,
% 4.57/4.74 ((~![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))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1219,plain,
% 4.57/4.74 ((~![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)),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 4.57/4.74 tff(1220,plain,
% 4.57/4.74 (hskp72 | hskp37 | c3_1(a1715)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1219, 197, 1213, 526, 1204])).
% 4.57/4.74 tff(1221,plain,
% 4.57/4.74 (hskp37),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1220, 1212, 333])).
% 4.57/4.74 tff(1222,plain,
% 4.57/4.74 (~c1_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[540, 1221])).
% 4.57/4.74 tff(1223,plain,
% 4.57/4.74 (c0_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[548, 1221])).
% 4.57/4.74 tff(1224,plain,
% 4.57/4.74 (c2_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[556, 1221])).
% 4.57/4.74 tff(1225,assumption,(c3_1(a1714)), introduced(assumption)).
% 4.57/4.74 tff(1226,assumption,(~c1_1(a1714)), introduced(assumption)).
% 4.57/4.74 tff(1227,assumption,(c0_1(a1714)), introduced(assumption)).
% 4.57/4.74 tff(1228,assumption,(c2_1(a1714)), introduced(assumption)).
% 4.57/4.74 tff(1229,assumption,(ndr1_0), introduced(assumption)).
% 4.57/4.74 tff(1230,plain,
% 4.57/4.74 (((~![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))) | (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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1231,plain,
% 4.57/4.74 (((~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)))),
% 4.57/4.74 inference(rewrite,[status(thm)],[])).
% 4.57/4.74 tff(1232,plain,
% 4.57/4.74 (((~![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))) | ((~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))))),
% 4.57/4.74 inference(monotonicity,[status(thm)],[1231])).
% 4.57/4.74 tff(1233,plain,
% 4.57/4.74 (((~![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))) | ((~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)))),
% 4.57/4.74 inference(transitivity,[status(thm)],[1232, 1230])).
% 4.57/4.74 tff(1234,plain,
% 4.57/4.74 ((~![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))) | ((~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))),
% 4.57/4.74 inference(quant_inst,[status(thm)],[])).
% 4.57/4.74 tff(1235,plain,
% 4.57/4.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 4.57/4.74 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 4.57/4.74 tff(1236,plain,
% 4.57/4.74 ($false),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1235, 1229, 333, 1228, 1227, 1213, 1226, 514, 1204, 1225])).
% 4.57/4.74 tff(1237,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,[]))).
% 4.57/4.74 tff(1238,plain,
% 4.57/4.74 ((~c3_1(a1714)) | c3_1(a1715) | (~c2_1(a1714)) | (~c0_1(a1714)) | c2_1(a1715) | c1_1(a1714) | c0_1(a1715)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1237, 197])).
% 4.57/4.74 tff(1239,plain,
% 4.57/4.74 (~c3_1(a1714)),
% 4.57/4.74 inference(unit_resolution,[status(thm)],[1238, 1224, 1204, 333, 1223, 1213, 1222])).
% 4.57/4.75 tff(1240,plain,
% 4.57/4.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1241,plain,
% 4.57/4.75 (((~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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1242,plain,
% 4.57/4.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1241])).
% 4.57/4.75 tff(1243,plain,
% 4.57/4.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1242, 1240])).
% 4.57/4.75 tff(1244,plain,
% 4.57/4.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1245,plain,
% 4.57/4.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 4.57/4.75 tff(1246,plain,
% 4.57/4.75 (c1_1(a1715)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1245, 197, 333, 1224, 1223, 1213, 30, 1204, 1239])).
% 4.57/4.75 tff(1247,plain,
% 4.57/4.75 (hskp72 | hskp37 | c3_1(a1715) | c0_1(a1715)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1219, 197, 1213, 526])).
% 4.57/4.75 tff(1248,plain,
% 4.57/4.75 (hskp37),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1247, 1204, 333, 1212])).
% 4.57/4.75 tff(1249,assumption,(~hskp21), introduced(assumption)).
% 4.57/4.75 tff(1250,plain,
% 4.57/4.75 (c2_1(a1714)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[556, 1248])).
% 4.57/4.75 tff(1251,plain,
% 4.57/4.75 (c0_1(a1714)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[548, 1248])).
% 4.57/4.75 tff(1252,plain,
% 4.57/4.75 (^[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))))),
% 4.57/4.75 inference(bind,[status(th)],[])).
% 4.57/4.75 tff(1253,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(quant_intro,[status(thm)],[1252])).
% 4.57/4.75 tff(1254,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1255,plain,
% 4.57/4.75 (^[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)))))),
% 4.57/4.75 inference(bind,[status(th)],[])).
% 4.57/4.75 tff(1256,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(quant_intro,[status(thm)],[1255])).
% 4.57/4.75 tff(1257,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')).
% 4.57/4.75 tff(1258,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 4.57/4.75 tff(1259,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1258, 1254])).
% 4.57/4.75 tff(1260,plain,(
% 4.57/4.75 ![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)))),
% 4.57/4.75 inference(skolemize,[status(sab)],[1259])).
% 4.57/4.75 tff(1261,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1260, 1253])).
% 4.57/4.75 tff(1262,plain,
% 4.57/4.75 (~c3_1(a1714)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1237, 1204, 1229, 333, 1227, 1213, 1226, 1228])).
% 4.57/4.75 tff(1263,plain,
% 4.57/4.75 (c1_1(a1715)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1245, 1229, 333, 1228, 1227, 1213, 30, 1204, 1262])).
% 4.57/4.75 tff(1264,plain,
% 4.57/4.75 (((~![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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1265,plain,
% 4.57/4.75 ((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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1266,plain,
% 4.57/4.75 (((~![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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1265])).
% 4.57/4.75 tff(1267,plain,
% 4.57/4.75 (((~![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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1266, 1264])).
% 4.57/4.75 tff(1268,plain,
% 4.57/4.75 ((~![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)))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1269,plain,
% 4.57/4.75 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 4.57/4.75 tff(1270,plain,
% 4.57/4.75 ($false),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1269, 1229, 1249, 1263, 333, 1213, 1261, 1204])).
% 4.57/4.75 tff(1271,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,[]))).
% 4.57/4.75 tff(1272,plain,
% 4.57/4.75 ($false),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1271, 1251, 1250, 1249, 333, 1213, 1226, 1204, 197])).
% 4.57/4.75 tff(1273,plain,(c0_1(a1715) | hskp21 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714)), inference(lemma,lemma(discharge,[]))).
% 4.57/4.75 tff(1274,plain,
% 4.57/4.75 (c1_1(a1714)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1273, 1204, 333, 1213, 1249])).
% 4.57/4.75 tff(1275,plain,
% 4.57/4.75 ($false),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[540, 1274, 1248])).
% 4.57/4.75 tff(1276,plain,(c0_1(a1715) | c3_1(a1715) | c2_1(a1715) | hskp21), inference(lemma,lemma(discharge,[]))).
% 4.57/4.75 tff(1277,plain,
% 4.57/4.75 (hskp21),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1276, 333, 1204, 1213])).
% 4.57/4.75 tff(1278,plain,
% 4.57/4.75 (((~hskp21) | c2_1(a1683)) <=> ((~hskp21) | c2_1(a1683))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1279,axiom,((~hskp21) | c2_1(a1683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 4.57/4.75 tff(1280,plain,
% 4.57/4.75 ((~hskp21) | c2_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 4.57/4.75 tff(1281,plain,
% 4.57/4.75 ((~hskp21) | c2_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1280, 1278])).
% 4.57/4.75 tff(1282,plain,
% 4.57/4.75 ((~hskp21) | c2_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1281, 1278])).
% 4.57/4.75 tff(1283,plain,
% 4.57/4.75 ((~hskp21) | c2_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 4.57/4.75 tff(1284,plain,
% 4.57/4.75 ((~hskp21) | c2_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1283, 1278])).
% 4.57/4.75 tff(1285,plain,
% 4.57/4.75 (c2_1(a1683)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1284, 1277])).
% 4.57/4.75 tff(1286,plain,
% 4.57/4.75 (((~hskp21) | c3_1(a1683)) <=> ((~hskp21) | c3_1(a1683))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1287,axiom,((~hskp21) | c3_1(a1683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 4.57/4.75 tff(1288,plain,
% 4.57/4.75 ((~hskp21) | c3_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 4.57/4.75 tff(1289,plain,
% 4.57/4.75 ((~hskp21) | c3_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1288, 1286])).
% 4.57/4.75 tff(1290,plain,
% 4.57/4.75 ((~hskp21) | c3_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1289, 1286])).
% 4.57/4.75 tff(1291,plain,
% 4.57/4.75 ((~hskp21) | c3_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1290, 1286])).
% 4.57/4.75 tff(1292,plain,
% 4.57/4.75 ((~hskp21) | c3_1(a1683)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1291, 1286])).
% 4.57/4.75 tff(1293,plain,
% 4.57/4.75 (c3_1(a1683)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1292, 1277])).
% 4.57/4.75 tff(1294,plain,
% 4.57/4.75 (((~![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))) | (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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1295,plain,
% 4.57/4.75 (((~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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1296,plain,
% 4.57/4.75 (((~![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(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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1295])).
% 4.57/4.75 tff(1297,plain,
% 4.57/4.75 (((~![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(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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1296, 1294])).
% 4.57/4.75 tff(1298,plain,
% 4.57/4.75 ((~![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(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))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1299,plain,
% 4.57/4.75 ((~![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))) | 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))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 4.57/4.75 tff(1300,plain,
% 4.57/4.75 (~c0_1(a1683)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1299, 197, 333, 1224, 1223, 1293, 1285, 1213, 1222, 514, 1204])).
% 4.57/4.75 tff(1301,plain,
% 4.57/4.75 (^[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))))),
% 4.57/4.75 inference(bind,[status(th)],[])).
% 4.57/4.75 tff(1302,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(quant_intro,[status(thm)],[1301])).
% 4.57/4.75 tff(1303,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1304,plain,
% 4.57/4.75 (^[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)))))),
% 4.57/4.75 inference(bind,[status(th)],[])).
% 4.57/4.75 tff(1305,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(quant_intro,[status(thm)],[1304])).
% 4.57/4.75 tff(1306,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')).
% 4.57/4.75 tff(1307,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 4.57/4.75 tff(1308,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 4.57/4.75 tff(1309,plain,(
% 4.57/4.75 ![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)))),
% 4.57/4.75 inference(skolemize,[status(sab)],[1308])).
% 4.57/4.75 tff(1310,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 4.57/4.75 tff(1311,plain,
% 4.57/4.75 (((~hskp21) | (~c1_1(a1683))) <=> ((~hskp21) | (~c1_1(a1683)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1312,plain,
% 4.57/4.75 (((~c1_1(a1683)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1683)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1313,axiom,((~c1_1(a1683)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 4.57/4.75 tff(1314,plain,
% 4.57/4.75 ((~hskp21) | (~c1_1(a1683))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 4.57/4.75 tff(1315,plain,
% 4.57/4.75 ((~hskp21) | (~c1_1(a1683))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1314, 1311])).
% 4.57/4.75 tff(1316,plain,
% 4.57/4.75 (~c1_1(a1683)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1315, 1277])).
% 4.57/4.75 tff(1317,plain,
% 4.57/4.75 (((~![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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1318,plain,
% 4.57/4.75 ((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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1319,plain,
% 4.57/4.75 (((~![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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1318])).
% 4.57/4.75 tff(1320,plain,
% 4.57/4.75 (((~![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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1319, 1317])).
% 4.57/4.75 tff(1321,plain,
% 4.57/4.75 ((~![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)))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1322,plain,
% 4.57/4.75 ((~![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))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 4.57/4.75 tff(1323,plain,
% 4.57/4.75 (hskp69 | (~c1_1(a1715))),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1322, 197, 333, 1293, 1213, 1316, 1310, 1300])).
% 4.57/4.75 tff(1324,plain,
% 4.57/4.75 (hskp69),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1323, 1246])).
% 4.57/4.75 tff(1325,plain,
% 4.57/4.75 (((~hskp69) | (~c1_1(a1709))) <=> ((~hskp69) | (~c1_1(a1709)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1326,plain,
% 4.57/4.75 (((~c1_1(a1709)) | (~hskp69)) <=> ((~hskp69) | (~c1_1(a1709)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1327,axiom,((~c1_1(a1709)) | (~hskp69)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 4.57/4.75 tff(1328,plain,
% 4.57/4.75 ((~hskp69) | (~c1_1(a1709))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 4.57/4.75 tff(1329,plain,
% 4.57/4.75 ((~hskp69) | (~c1_1(a1709))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1328, 1325])).
% 4.57/4.75 tff(1330,plain,
% 4.57/4.75 (~c1_1(a1709)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1329, 1324])).
% 4.57/4.75 tff(1331,plain,
% 4.57/4.75 (((~hskp69) | c3_1(a1709)) <=> ((~hskp69) | c3_1(a1709))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1332,axiom,((~hskp69) | c3_1(a1709)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 4.57/4.75 tff(1333,plain,
% 4.57/4.75 ((~hskp69) | c3_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 4.57/4.75 tff(1334,plain,
% 4.57/4.75 ((~hskp69) | c3_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1333, 1331])).
% 4.57/4.75 tff(1335,plain,
% 4.57/4.75 ((~hskp69) | c3_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1334, 1331])).
% 4.57/4.75 tff(1336,plain,
% 4.57/4.75 ((~hskp69) | c3_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1335, 1331])).
% 4.57/4.75 tff(1337,plain,
% 4.57/4.75 ((~hskp69) | c3_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1336, 1331])).
% 4.57/4.75 tff(1338,plain,
% 4.57/4.75 (c3_1(a1709)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1337, 1324])).
% 4.57/4.75 tff(1339,plain,
% 4.57/4.75 (((~hskp69) | c0_1(a1709)) <=> ((~hskp69) | c0_1(a1709))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1340,axiom,((~hskp69) | c0_1(a1709)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 4.57/4.75 tff(1341,plain,
% 4.57/4.75 ((~hskp69) | c0_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 4.57/4.75 tff(1342,plain,
% 4.57/4.75 ((~hskp69) | c0_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1341, 1339])).
% 4.57/4.75 tff(1343,plain,
% 4.57/4.75 ((~hskp69) | c0_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1342, 1339])).
% 4.57/4.75 tff(1344,plain,
% 4.57/4.75 ((~hskp69) | c0_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1343, 1339])).
% 4.57/4.75 tff(1345,plain,
% 4.57/4.75 ((~hskp69) | c0_1(a1709)),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1344, 1339])).
% 4.57/4.75 tff(1346,plain,
% 4.57/4.75 (c0_1(a1709)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1345, 1324])).
% 4.57/4.75 tff(1347,plain,
% 4.57/4.75 (((~![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))) | (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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1348,plain,
% 4.57/4.75 (((~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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1349,plain,
% 4.57/4.75 (((~![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(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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1348])).
% 4.57/4.75 tff(1350,plain,
% 4.57/4.75 (((~![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(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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1349, 1347])).
% 4.57/4.75 tff(1351,plain,
% 4.57/4.75 ((~![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(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))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1352,plain,
% 4.57/4.75 ((~![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))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1709) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709)) | (~c2_1(a1709))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 4.57/4.75 tff(1353,plain,
% 4.57/4.75 (~c2_1(a1709)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1352, 197, 333, 1346, 1338, 1213, 1330, 514, 1204])).
% 4.57/4.75 tff(1354,plain,
% 4.57/4.75 (((~![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(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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1355,plain,
% 4.57/4.75 ((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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1356,plain,
% 4.57/4.75 (((~![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(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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1355])).
% 4.57/4.75 tff(1357,plain,
% 4.57/4.75 (((~![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(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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1356, 1354])).
% 4.57/4.75 tff(1358,plain,
% 4.57/4.75 ((~![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(a1714) | c1_1(a1714) | (~c2_1(a1714)) | c0_1(a1683) | c1_1(a1683) | (~c3_1(a1683)))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1359,plain,
% 4.57/4.75 ((~![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(a1714) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | c3_1(a1714) | (~c2_1(a1714))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 4.57/4.75 tff(1360,plain,
% 4.57/4.75 (hskp60),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1359, 197, 1224, 1293, 1222, 1316, 356, 1239, 1300])).
% 4.57/4.75 tff(1361,plain,
% 4.57/4.75 (~c1_1(a1673)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[369, 1360])).
% 4.57/4.75 tff(1362,plain,
% 4.57/4.75 (c2_1(a1673)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[419, 1360])).
% 4.57/4.75 tff(1363,plain,
% 4.57/4.75 (c3_1(a1673)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[427, 1360])).
% 4.57/4.75 tff(1364,plain,
% 4.57/4.75 (((~![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))) | (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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1365,plain,
% 4.57/4.75 (((~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)))),
% 4.57/4.75 inference(rewrite,[status(thm)],[])).
% 4.57/4.75 tff(1366,plain,
% 4.57/4.75 (((~![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(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))))),
% 4.57/4.75 inference(monotonicity,[status(thm)],[1365])).
% 4.57/4.75 tff(1367,plain,
% 4.57/4.75 (((~![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(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)))),
% 4.57/4.75 inference(transitivity,[status(thm)],[1366, 1364])).
% 4.57/4.75 tff(1368,plain,
% 4.57/4.75 ((~![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(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))),
% 4.57/4.75 inference(quant_inst,[status(thm)],[])).
% 4.57/4.75 tff(1369,plain,
% 4.57/4.75 ((~![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))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1673)) | (~c0_1(a1673)) | (~c2_1(a1673))),
% 4.57/4.75 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 4.57/4.75 tff(1370,plain,
% 4.57/4.75 (~c0_1(a1673)),
% 4.57/4.75 inference(unit_resolution,[status(thm)],[1369, 197, 333, 1363, 1362, 1213, 1361, 514, 1204])).
% 4.57/4.75 tff(1371,plain,
% 4.57/4.75 (^[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))))),
% 4.57/4.75 inference(bind,[status(th)],[])).
% 4.57/4.75 tff(1372,plain,
% 4.57/4.75 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1371])).
% 4.57/4.76 tff(1373,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1374,plain,
% 4.57/4.76 (^[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)))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1375,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1374])).
% 4.57/4.76 tff(1376,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')).
% 4.57/4.76 tff(1377,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 4.57/4.76 tff(1378,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1377, 1373])).
% 4.57/4.76 tff(1379,plain,(
% 4.57/4.76 ![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)))),
% 4.57/4.76 inference(skolemize,[status(sab)],[1378])).
% 4.57/4.76 tff(1380,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1379, 1372])).
% 4.57/4.76 tff(1381,plain,
% 4.57/4.76 (((~![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))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1382,plain,
% 4.57/4.76 ((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))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1383,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(monotonicity,[status(thm)],[1382])).
% 4.57/4.76 tff(1384,plain,
% 4.57/4.76 (((~![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))),
% 4.57/4.76 inference(transitivity,[status(thm)],[1383, 1381])).
% 4.57/4.76 tff(1385,plain,
% 4.57/4.76 ((~![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)))),
% 4.57/4.76 inference(quant_inst,[status(thm)],[])).
% 4.57/4.76 tff(1386,plain,
% 4.57/4.76 ((~![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)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 4.57/4.76 tff(1387,plain,
% 4.57/4.76 (hskp39),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1386, 197, 1346, 1338, 1363, 1362, 1380, 1370, 1353])).
% 4.57/4.76 tff(1388,plain,
% 4.57/4.76 (((~hskp39) | (~c0_1(a1721))) <=> ((~hskp39) | (~c0_1(a1721)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1389,plain,
% 4.57/4.76 (((~c0_1(a1721)) | (~hskp39)) <=> ((~hskp39) | (~c0_1(a1721)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1390,axiom,((~c0_1(a1721)) | (~hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause230')).
% 4.57/4.76 tff(1391,plain,
% 4.57/4.76 ((~hskp39) | (~c0_1(a1721))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 4.57/4.76 tff(1392,plain,
% 4.57/4.76 ((~hskp39) | (~c0_1(a1721))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1391, 1388])).
% 4.57/4.76 tff(1393,plain,
% 4.57/4.76 (~c0_1(a1721)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1392, 1387])).
% 4.57/4.76 tff(1394,plain,
% 4.57/4.76 (((~hskp39) | (~c1_1(a1721))) <=> ((~hskp39) | (~c1_1(a1721)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1395,plain,
% 4.57/4.76 (((~c1_1(a1721)) | (~hskp39)) <=> ((~hskp39) | (~c1_1(a1721)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1396,axiom,((~c1_1(a1721)) | (~hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause229')).
% 4.57/4.76 tff(1397,plain,
% 4.57/4.76 ((~hskp39) | (~c1_1(a1721))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 4.57/4.76 tff(1398,plain,
% 4.57/4.76 ((~hskp39) | (~c1_1(a1721))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1397, 1394])).
% 4.57/4.76 tff(1399,plain,
% 4.57/4.76 (~c1_1(a1721)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1398, 1387])).
% 4.57/4.76 tff(1400,plain,
% 4.57/4.76 (^[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))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1401,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1400])).
% 4.57/4.76 tff(1402,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1403,plain,
% 4.57/4.76 (^[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)))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1404,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1403])).
% 4.57/4.76 tff(1405,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')).
% 4.57/4.76 tff(1406,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 4.57/4.76 tff(1407,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1406, 1402])).
% 4.57/4.76 tff(1408,plain,(
% 4.57/4.76 ![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)))),
% 4.57/4.76 inference(skolemize,[status(sab)],[1407])).
% 4.57/4.76 tff(1409,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1408, 1401])).
% 4.57/4.76 tff(1410,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1411,plain,
% 4.57/4.76 ((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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1412,plain,
% 4.57/4.76 (((~![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))))),
% 4.57/4.76 inference(monotonicity,[status(thm)],[1411])).
% 4.57/4.76 tff(1413,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(transitivity,[status(thm)],[1412, 1410])).
% 4.57/4.76 tff(1414,plain,
% 4.57/4.76 ((~![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)))),
% 4.57/4.76 inference(quant_inst,[status(thm)],[])).
% 4.57/4.76 tff(1415,plain,
% 4.57/4.76 ((~![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))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 4.57/4.76 tff(1416,plain,
% 4.57/4.76 (hskp67),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1415, 197, 1346, 1338, 1363, 1362, 1330, 1361, 1409])).
% 4.57/4.76 tff(1417,plain,
% 4.57/4.76 (((~hskp67) | c3_1(a1702)) <=> ((~hskp67) | c3_1(a1702))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1418,axiom,((~hskp67) | c3_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 4.57/4.76 tff(1419,plain,
% 4.57/4.76 ((~hskp67) | c3_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 4.57/4.76 tff(1420,plain,
% 4.57/4.76 ((~hskp67) | c3_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1419, 1417])).
% 4.57/4.76 tff(1421,plain,
% 4.57/4.76 ((~hskp67) | c3_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1420, 1417])).
% 4.57/4.76 tff(1422,plain,
% 4.57/4.76 ((~hskp67) | c3_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1421, 1417])).
% 4.57/4.76 tff(1423,plain,
% 4.57/4.76 ((~hskp67) | c3_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1422, 1417])).
% 4.57/4.76 tff(1424,plain,
% 4.57/4.76 (c3_1(a1702)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1423, 1416])).
% 4.57/4.76 tff(1425,plain,
% 4.57/4.76 (((~hskp67) | c1_1(a1702)) <=> ((~hskp67) | c1_1(a1702))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1426,axiom,((~hskp67) | c1_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 4.57/4.76 tff(1427,plain,
% 4.57/4.76 ((~hskp67) | c1_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 4.57/4.76 tff(1428,plain,
% 4.57/4.76 ((~hskp67) | c1_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1427, 1425])).
% 4.57/4.76 tff(1429,plain,
% 4.57/4.76 ((~hskp67) | c1_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1428, 1425])).
% 4.57/4.76 tff(1430,plain,
% 4.57/4.76 ((~hskp67) | c1_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1429, 1425])).
% 4.57/4.76 tff(1431,plain,
% 4.57/4.76 ((~hskp67) | c1_1(a1702)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1430, 1425])).
% 4.57/4.76 tff(1432,plain,
% 4.57/4.76 (c1_1(a1702)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1431, 1416])).
% 4.57/4.76 tff(1433,plain,
% 4.57/4.76 (((~![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(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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1434,plain,
% 4.57/4.76 (((~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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1435,plain,
% 4.57/4.76 (((~![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(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))))),
% 4.57/4.76 inference(monotonicity,[status(thm)],[1434])).
% 4.57/4.76 tff(1436,plain,
% 4.57/4.76 (((~![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(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)))),
% 4.57/4.76 inference(transitivity,[status(thm)],[1435, 1433])).
% 4.57/4.76 tff(1437,plain,
% 4.57/4.76 ((~![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(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)))),
% 4.57/4.76 inference(quant_inst,[status(thm)],[])).
% 4.57/4.76 tff(1438,plain,
% 4.57/4.76 ((~![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(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c2_1(a1709) | (~c3_1(a1702)) | (~c1_1(a1702)) | (~c0_1(a1702))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 4.57/4.76 tff(1439,plain,
% 4.57/4.76 (~c0_1(a1702)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1438, 197, 1346, 1338, 1432, 1424, 1330, 590, 1353])).
% 4.57/4.76 tff(1440,plain,
% 4.57/4.76 (^[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))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1441,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1440])).
% 4.57/4.76 tff(1442,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1443,plain,
% 4.57/4.76 (^[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)))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1444,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1443])).
% 4.57/4.76 tff(1445,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')).
% 4.57/4.76 tff(1446,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 4.57/4.76 tff(1447,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1446, 1442])).
% 4.57/4.76 tff(1448,plain,(
% 4.57/4.76 ![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)))),
% 4.57/4.76 inference(skolemize,[status(sab)],[1447])).
% 4.57/4.76 tff(1449,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1448, 1441])).
% 4.57/4.76 tff(1450,plain,
% 4.57/4.76 (((~![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))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1451,plain,
% 4.57/4.76 ((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))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1452,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(monotonicity,[status(thm)],[1451])).
% 4.57/4.76 tff(1453,plain,
% 4.57/4.76 (((~![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))),
% 4.57/4.76 inference(transitivity,[status(thm)],[1452, 1450])).
% 4.57/4.76 tff(1454,plain,
% 4.57/4.76 ((~![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)))),
% 4.57/4.76 inference(quant_inst,[status(thm)],[])).
% 4.57/4.76 tff(1455,plain,
% 4.57/4.76 ((~![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)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 4.57/4.76 tff(1456,plain,
% 4.57/4.76 (hskp73),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1455, 197, 1432, 1424, 1363, 1362, 1361, 1449, 1439])).
% 4.57/4.76 tff(1457,plain,
% 4.57/4.76 (((~hskp73) | (~c3_1(a1716))) <=> ((~hskp73) | (~c3_1(a1716)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1458,plain,
% 4.57/4.76 (((~c3_1(a1716)) | (~hskp73)) <=> ((~hskp73) | (~c3_1(a1716)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1459,axiom,((~c3_1(a1716)) | (~hskp73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 4.57/4.76 tff(1460,plain,
% 4.57/4.76 ((~hskp73) | (~c3_1(a1716))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 4.57/4.76 tff(1461,plain,
% 4.57/4.76 ((~hskp73) | (~c3_1(a1716))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1460, 1457])).
% 4.57/4.76 tff(1462,plain,
% 4.57/4.76 (~c3_1(a1716)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1461, 1456])).
% 4.57/4.76 tff(1463,plain,
% 4.57/4.76 (((~hskp39) | c3_1(a1721)) <=> ((~hskp39) | c3_1(a1721))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1464,axiom,((~hskp39) | c3_1(a1721)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 4.57/4.76 tff(1465,plain,
% 4.57/4.76 ((~hskp39) | c3_1(a1721)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 4.57/4.76 tff(1466,plain,
% 4.57/4.76 ((~hskp39) | c3_1(a1721)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1465, 1463])).
% 4.57/4.76 tff(1467,plain,
% 4.57/4.76 ((~hskp39) | c3_1(a1721)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1466, 1463])).
% 4.57/4.76 tff(1468,plain,
% 4.57/4.76 ((~hskp39) | c3_1(a1721)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1467, 1463])).
% 4.57/4.76 tff(1469,plain,
% 4.57/4.76 ((~hskp39) | c3_1(a1721)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1468, 1463])).
% 4.57/4.76 tff(1470,plain,
% 4.57/4.76 (c3_1(a1721)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1469, 1387])).
% 4.57/4.76 tff(1471,plain,
% 4.57/4.76 (((~hskp73) | c2_1(a1716)) <=> ((~hskp73) | c2_1(a1716))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1472,axiom,((~hskp73) | c2_1(a1716)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 4.57/4.76 tff(1473,plain,
% 4.57/4.76 ((~hskp73) | c2_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 4.57/4.76 tff(1474,plain,
% 4.57/4.76 ((~hskp73) | c2_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1473, 1471])).
% 4.57/4.76 tff(1475,plain,
% 4.57/4.76 ((~hskp73) | c2_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1474, 1471])).
% 4.57/4.76 tff(1476,plain,
% 4.57/4.76 ((~hskp73) | c2_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1475, 1471])).
% 4.57/4.76 tff(1477,plain,
% 4.57/4.76 ((~hskp73) | c2_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1476, 1471])).
% 4.57/4.76 tff(1478,plain,
% 4.57/4.76 (c2_1(a1716)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1477, 1456])).
% 4.57/4.76 tff(1479,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1480,plain,
% 4.57/4.76 (((~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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1481,plain,
% 4.57/4.76 (((~![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))))),
% 4.57/4.76 inference(monotonicity,[status(thm)],[1480])).
% 4.57/4.76 tff(1482,plain,
% 4.57/4.76 (((~![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)))),
% 4.57/4.76 inference(transitivity,[status(thm)],[1481, 1479])).
% 4.57/4.76 tff(1483,plain,
% 4.57/4.76 ((~![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)))),
% 4.57/4.76 inference(quant_inst,[status(thm)],[])).
% 4.57/4.76 tff(1484,plain,
% 4.57/4.76 ((~![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))),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 4.57/4.76 tff(1485,plain,
% 4.57/4.76 (~c1_1(a1716)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1484, 197, 1478, 1346, 1338, 1470, 1462, 1330, 1399, 1393, 90])).
% 4.57/4.76 tff(1486,plain,
% 4.57/4.76 (((~hskp73) | c0_1(a1716)) <=> ((~hskp73) | c0_1(a1716))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1487,axiom,((~hskp73) | c0_1(a1716)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 4.57/4.76 tff(1488,plain,
% 4.57/4.76 ((~hskp73) | c0_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 4.57/4.76 tff(1489,plain,
% 4.57/4.76 ((~hskp73) | c0_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1488, 1486])).
% 4.57/4.76 tff(1490,plain,
% 4.57/4.76 ((~hskp73) | c0_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1489, 1486])).
% 4.57/4.76 tff(1491,plain,
% 4.57/4.76 ((~hskp73) | c0_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1490, 1486])).
% 4.57/4.76 tff(1492,plain,
% 4.57/4.76 ((~hskp73) | c0_1(a1716)),
% 4.57/4.76 inference(modus_ponens,[status(thm)],[1491, 1486])).
% 4.57/4.76 tff(1493,plain,
% 4.57/4.76 (c0_1(a1716)),
% 4.57/4.76 inference(unit_resolution,[status(thm)],[1492, 1456])).
% 4.57/4.76 tff(1494,assumption,(~c1_1(a1716)), introduced(assumption)).
% 4.57/4.76 tff(1495,plain,
% 4.57/4.76 (^[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))))),
% 4.57/4.76 inference(bind,[status(th)],[])).
% 4.57/4.76 tff(1496,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(quant_intro,[status(thm)],[1495])).
% 4.57/4.76 tff(1497,plain,
% 4.57/4.76 (![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)))),
% 4.57/4.76 inference(rewrite,[status(thm)],[])).
% 4.57/4.76 tff(1498,plain,
% 4.57/4.76 (^[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)))))),
% 4.57/4.77 inference(bind,[status(th)],[])).
% 4.57/4.77 tff(1499,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(quant_intro,[status(thm)],[1498])).
% 4.57/4.77 tff(1500,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')).
% 4.57/4.77 tff(1501,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 4.57/4.77 tff(1502,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1501, 1497])).
% 4.57/4.77 tff(1503,plain,(
% 4.57/4.77 ![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)))),
% 4.57/4.77 inference(skolemize,[status(sab)],[1502])).
% 4.57/4.77 tff(1504,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1503, 1496])).
% 4.57/4.77 tff(1505,assumption,(~hskp57), introduced(assumption)).
% 4.57/4.77 tff(1506,assumption,(~c2_1(a1709)), introduced(assumption)).
% 4.57/4.77 tff(1507,plain,
% 4.57/4.77 (^[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))))),
% 4.57/4.77 inference(bind,[status(th)],[])).
% 4.57/4.77 tff(1508,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(quant_intro,[status(thm)],[1507])).
% 4.57/4.77 tff(1509,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1510,plain,
% 4.57/4.77 (^[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)))))),
% 4.57/4.77 inference(bind,[status(th)],[])).
% 4.57/4.77 tff(1511,plain,
% 4.57/4.77 (![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)))),
% 4.57/4.77 inference(quant_intro,[status(thm)],[1510])).
% 4.57/4.77 tff(1512,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause326')).
% 4.57/4.77 tff(1513,plain,
% 4.57/4.77 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 4.57/4.77 tff(1514,plain,
% 4.57/4.77 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1513, 1509])).
% 4.57/4.77 tff(1515,plain,(
% 4.57/4.77 ![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.57/4.77 inference(skolemize,[status(sab)],[1514])).
% 4.57/4.77 tff(1516,plain,
% 4.57/4.77 (![U: $i] : (hskp57 | hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1515, 1508])).
% 4.57/4.77 tff(1517,assumption,(c3_1(a1709)), introduced(assumption)).
% 4.57/4.77 tff(1518,assumption,(c0_1(a1709)), introduced(assumption)).
% 4.57/4.77 tff(1519,plain,
% 4.57/4.77 (((~![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))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1520,plain,
% 4.57/4.77 ((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))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1521,plain,
% 4.57/4.77 (((~![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)))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1520])).
% 4.57/4.77 tff(1522,plain,
% 4.57/4.77 (((~![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))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1521, 1519])).
% 4.57/4.77 tff(1523,plain,
% 4.57/4.77 ((~![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)))),
% 4.57/4.77 inference(quant_inst,[status(thm)],[])).
% 4.57/4.77 tff(1524,plain,
% 4.57/4.77 ((~![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)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 4.57/4.77 tff(1525,plain,
% 4.57/4.77 (hskp57 | hskp11),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1524, 197, 1518, 1517, 1516, 1506])).
% 4.57/4.77 tff(1526,plain,
% 4.57/4.77 (hskp11),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1525, 1505])).
% 4.57/4.77 tff(1527,plain,
% 4.57/4.77 (((~hskp11) | (~c2_1(a1664))) <=> ((~hskp11) | (~c2_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1528,plain,
% 4.57/4.77 (((~c2_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1529,axiom,((~c2_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause287')).
% 4.57/4.77 tff(1530,plain,
% 4.57/4.77 ((~hskp11) | (~c2_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 4.57/4.77 tff(1531,plain,
% 4.57/4.77 ((~hskp11) | (~c2_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1530, 1527])).
% 4.57/4.77 tff(1532,plain,
% 4.57/4.77 (~c2_1(a1664)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1531, 1526])).
% 4.57/4.77 tff(1533,plain,
% 4.57/4.77 (((~hskp11) | (~c3_1(a1664))) <=> ((~hskp11) | (~c3_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1534,plain,
% 4.57/4.77 (((~c3_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1535,axiom,((~c3_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 4.57/4.77 tff(1536,plain,
% 4.57/4.77 ((~hskp11) | (~c3_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 4.57/4.77 tff(1537,plain,
% 4.57/4.77 ((~hskp11) | (~c3_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1536, 1533])).
% 4.57/4.77 tff(1538,plain,
% 4.57/4.77 (~c3_1(a1664)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1537, 1526])).
% 4.57/4.77 tff(1539,assumption,(~c3_1(a1716)), introduced(assumption)).
% 4.57/4.77 tff(1540,assumption,(c2_1(a1716)), introduced(assumption)).
% 4.57/4.77 tff(1541,plain,
% 4.57/4.77 (((~![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))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1542,plain,
% 4.57/4.77 ((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))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1543,plain,
% 4.57/4.77 (((~![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)))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1542])).
% 4.57/4.77 tff(1544,plain,
% 4.57/4.77 (((~![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))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1543, 1541])).
% 4.57/4.77 tff(1545,plain,
% 4.57/4.77 ((~![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)))),
% 4.57/4.77 inference(quant_inst,[status(thm)],[])).
% 4.57/4.77 tff(1546,plain,
% 4.57/4.77 ((~![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)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 4.57/4.77 tff(1547,plain,
% 4.57/4.77 (~c0_1(a1664)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1546, 197, 1505, 1540, 1539, 1538, 1532, 1504, 1494])).
% 4.57/4.77 tff(1548,plain,
% 4.57/4.77 (((~hskp11) | (~c1_1(a1664))) <=> ((~hskp11) | (~c1_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1549,plain,
% 4.57/4.77 (((~c1_1(a1664)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a1664)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1550,axiom,((~c1_1(a1664)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 4.57/4.77 tff(1551,plain,
% 4.57/4.77 ((~hskp11) | (~c1_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 4.57/4.77 tff(1552,plain,
% 4.57/4.77 ((~hskp11) | (~c1_1(a1664))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1551, 1548])).
% 4.57/4.77 tff(1553,plain,
% 4.57/4.77 (~c1_1(a1664)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1552, 1526])).
% 4.57/4.77 tff(1554,assumption,(c0_1(a1716)), introduced(assumption)).
% 4.57/4.77 tff(1555,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1556,plain,
% 4.57/4.77 (((~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1557,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1556])).
% 4.57/4.77 tff(1558,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1557, 1555])).
% 4.57/4.77 tff(1559,plain,
% 4.57/4.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.57/4.77 inference(quant_inst,[status(thm)],[])).
% 4.57/4.77 tff(1560,plain,
% 4.57/4.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | c0_1(a1664) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 4.57/4.77 tff(1561,plain,
% 4.57/4.77 ($false),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1560, 197, 1540, 1554, 1539, 1538, 1532, 1553, 30, 1547])).
% 4.57/4.77 tff(1562,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,[]))).
% 4.57/4.77 tff(1563,plain,
% 4.57/4.77 (hskp57),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1562, 1478, 1493, 1462, 1485, 1346, 1338, 1353])).
% 4.57/4.77 tff(1564,plain,
% 4.57/4.77 (~c1_1(a1665)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[59, 1563])).
% 4.57/4.77 tff(1565,plain,
% 4.57/4.77 (c3_1(a1665)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[67, 1563])).
% 4.57/4.77 tff(1566,plain,
% 4.57/4.77 (c0_1(a1665)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[78, 1563])).
% 4.57/4.77 tff(1567,plain,
% 4.57/4.77 (((~![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))) | (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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1568,plain,
% 4.57/4.77 (((~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1569,plain,
% 4.57/4.77 (((~![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(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))))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1568])).
% 4.57/4.77 tff(1570,plain,
% 4.57/4.77 (((~![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(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)))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1569, 1567])).
% 4.57/4.77 tff(1571,plain,
% 4.57/4.77 ((~![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(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))),
% 4.57/4.77 inference(quant_inst,[status(thm)],[])).
% 4.57/4.77 tff(1572,plain,
% 4.57/4.77 ((~![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))) | c3_1(a1715) | c2_1(a1715) | c1_1(a1665) | (~ndr1_0) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 4.57/4.77 tff(1573,plain,
% 4.57/4.77 (~c2_1(a1665)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1572, 197, 333, 1566, 1565, 1213, 1564, 514, 1204])).
% 4.57/4.77 tff(1574,assumption,(~c1_1(a1673)), introduced(assumption)).
% 4.57/4.77 tff(1575,assumption,(hskp71), introduced(assumption)).
% 4.57/4.77 tff(1576,plain,
% 4.57/4.77 (((~hskp71) | (~c2_1(a1713))) <=> ((~hskp71) | (~c2_1(a1713)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1577,plain,
% 4.57/4.77 (((~c2_1(a1713)) | (~hskp71)) <=> ((~hskp71) | (~c2_1(a1713)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1578,axiom,((~c2_1(a1713)) | (~hskp71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 4.57/4.77 tff(1579,plain,
% 4.57/4.77 ((~hskp71) | (~c2_1(a1713))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 4.57/4.77 tff(1580,plain,
% 4.57/4.77 ((~hskp71) | (~c2_1(a1713))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1579, 1576])).
% 4.57/4.77 tff(1581,plain,
% 4.57/4.77 (~c2_1(a1713)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1580, 1575])).
% 4.57/4.77 tff(1582,assumption,(c2_1(a1673)), introduced(assumption)).
% 4.57/4.77 tff(1583,assumption,(c3_1(a1673)), introduced(assumption)).
% 4.57/4.77 tff(1584,plain,
% 4.57/4.77 (((~hskp71) | c0_1(a1713)) <=> ((~hskp71) | c0_1(a1713))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1585,axiom,((~hskp71) | c0_1(a1713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 4.57/4.77 tff(1586,plain,
% 4.57/4.77 ((~hskp71) | c0_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 4.57/4.77 tff(1587,plain,
% 4.57/4.77 ((~hskp71) | c0_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1586, 1584])).
% 4.57/4.77 tff(1588,plain,
% 4.57/4.77 ((~hskp71) | c0_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1587, 1584])).
% 4.57/4.77 tff(1589,plain,
% 4.57/4.77 ((~hskp71) | c0_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1588, 1584])).
% 4.57/4.77 tff(1590,plain,
% 4.57/4.77 ((~hskp71) | c0_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1589, 1584])).
% 4.57/4.77 tff(1591,plain,
% 4.57/4.77 (c0_1(a1713)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1590, 1575])).
% 4.57/4.77 tff(1592,plain,
% 4.57/4.77 (((~hskp71) | c3_1(a1713)) <=> ((~hskp71) | c3_1(a1713))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1593,axiom,((~hskp71) | c3_1(a1713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 4.57/4.77 tff(1594,plain,
% 4.57/4.77 ((~hskp71) | c3_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 4.57/4.77 tff(1595,plain,
% 4.57/4.77 ((~hskp71) | c3_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1594, 1592])).
% 4.57/4.77 tff(1596,plain,
% 4.57/4.77 ((~hskp71) | c3_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1595, 1592])).
% 4.57/4.77 tff(1597,plain,
% 4.57/4.77 ((~hskp71) | c3_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1596, 1592])).
% 4.57/4.77 tff(1598,plain,
% 4.57/4.77 ((~hskp71) | c3_1(a1713)),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1597, 1592])).
% 4.57/4.77 tff(1599,plain,
% 4.57/4.77 (c3_1(a1713)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1598, 1575])).
% 4.57/4.77 tff(1600,assumption,(~c2_1(a1713)), introduced(assumption)).
% 4.57/4.77 tff(1601,assumption,(c0_1(a1713)), introduced(assumption)).
% 4.57/4.77 tff(1602,assumption,(c3_1(a1713)), introduced(assumption)).
% 4.57/4.77 tff(1603,plain,
% 4.57/4.77 (((~![W: $i, 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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1604,plain,
% 4.57/4.77 (((~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1605,plain,
% 4.57/4.77 (((~![W: $i, 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))))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1604])).
% 4.57/4.77 tff(1606,plain,
% 4.57/4.77 (((~![W: $i, 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)))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1605, 1603])).
% 4.57/4.77 tff(1607,plain,
% 4.57/4.77 ((~![W: $i, 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)))),
% 4.57/4.77 inference(quant_inst,[status(thm)],[])).
% 4.57/4.77 tff(1608,plain,
% 4.57/4.77 ((~![W: $i, 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))),
% 4.57/4.77 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 4.57/4.77 tff(1609,plain,
% 4.57/4.77 (~c3_1(a1678)),
% 4.57/4.77 inference(unit_resolution,[status(thm)],[1608, 197, 1602, 1601, 1583, 1582, 1600, 1574, 224, 237, 346])).
% 4.57/4.77 tff(1610,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1611,plain,
% 4.57/4.77 (((~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)))),
% 4.57/4.77 inference(rewrite,[status(thm)],[])).
% 4.57/4.77 tff(1612,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.57/4.77 inference(monotonicity,[status(thm)],[1611])).
% 4.57/4.77 tff(1613,plain,
% 4.57/4.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.57/4.77 inference(transitivity,[status(thm)],[1612, 1610])).
% 4.57/4.77 tff(1614,plain,
% 4.61/4.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.77 inference(quant_inst,[status(thm)],[])).
% 4.61/4.77 tff(1615,plain,
% 4.61/4.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.61/4.77 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 4.61/4.77 tff(1616,plain,
% 4.61/4.77 ($false),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[1615, 197, 1540, 1554, 1539, 224, 218, 237, 30, 1609])).
% 4.61/4.77 tff(1617,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,[]))).
% 4.61/4.77 tff(1618,plain,
% 4.61/4.77 (~hskp17),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[1617, 1599, 1554, 1539, 1540, 1591, 1583, 1582, 1581, 1574])).
% 4.61/4.77 tff(1619,assumption,(~c1_1(a1709)), introduced(assumption)).
% 4.61/4.77 tff(1620,plain,
% 4.61/4.77 (((~![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)))),
% 4.61/4.77 inference(rewrite,[status(thm)],[])).
% 4.61/4.77 tff(1621,plain,
% 4.61/4.77 ((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)))),
% 4.61/4.77 inference(rewrite,[status(thm)],[])).
% 4.61/4.77 tff(1622,plain,
% 4.61/4.77 (((~![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))))),
% 4.61/4.77 inference(monotonicity,[status(thm)],[1621])).
% 4.61/4.77 tff(1623,plain,
% 4.61/4.77 (((~![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)))),
% 4.61/4.77 inference(transitivity,[status(thm)],[1622, 1620])).
% 4.61/4.77 tff(1624,plain,
% 4.61/4.77 ((~![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)))),
% 4.61/4.77 inference(quant_inst,[status(thm)],[])).
% 4.61/4.77 tff(1625,plain,
% 4.61/4.77 ((~![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))),
% 4.61/4.77 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 4.61/4.77 tff(1626,plain,
% 4.61/4.77 (hskp17 | hskp16),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[1625, 197, 1518, 1517, 1619, 10])).
% 4.61/4.77 tff(1627,plain,
% 4.61/4.77 (hskp16),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[1626, 1618])).
% 4.61/4.77 tff(1628,plain,
% 4.61/4.77 (~c2_1(a1677)),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[105, 1627])).
% 4.61/4.77 tff(1629,plain,
% 4.61/4.77 (~c0_1(a1677)),
% 4.61/4.77 inference(unit_resolution,[status(thm)],[111, 1627])).
% 4.61/4.77 tff(1630,plain,
% 4.61/4.77 (((~![W: $i, 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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1631,plain,
% 4.61/4.78 (((~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1632,plain,
% 4.61/4.78 (((~![W: $i, 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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1631])).
% 4.61/4.78 tff(1633,plain,
% 4.61/4.78 (((~![W: $i, 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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1632, 1630])).
% 4.61/4.78 tff(1634,plain,
% 4.61/4.78 ((~![W: $i, 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)))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1635,plain,
% 4.61/4.78 ((~![W: $i, 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))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 4.61/4.78 tff(1636,plain,
% 4.61/4.78 (~c3_1(a1677)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1635, 197, 1599, 1591, 1583, 1582, 1581, 1574, 1629, 1628, 346])).
% 4.61/4.78 tff(1637,plain,
% 4.61/4.78 (~c1_1(a1677)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[99, 1627])).
% 4.61/4.78 tff(1638,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1639,plain,
% 4.61/4.78 (((~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1640,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1639])).
% 4.61/4.78 tff(1641,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1640, 1638])).
% 4.61/4.78 tff(1642,plain,
% 4.61/4.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1643,plain,
% 4.61/4.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 4.61/4.78 tff(1644,plain,
% 4.61/4.78 ($false),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1643, 197, 1540, 1554, 1539, 1629, 1628, 1637, 30, 1636])).
% 4.61/4.78 tff(1645,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,[]))).
% 4.61/4.78 tff(1646,plain,
% 4.61/4.78 (~hskp71),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1645, 1478, 1493, 1462, 1363, 1362, 1361, 1346, 1338, 1330])).
% 4.61/4.78 tff(1647,plain,
% 4.61/4.78 (^[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))))),
% 4.61/4.78 inference(bind,[status(th)],[])).
% 4.61/4.78 tff(1648,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(quant_intro,[status(thm)],[1647])).
% 4.61/4.78 tff(1649,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1650,plain,
% 4.61/4.78 (^[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)))))),
% 4.61/4.78 inference(bind,[status(th)],[])).
% 4.61/4.78 tff(1651,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(quant_intro,[status(thm)],[1650])).
% 4.61/4.78 tff(1652,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause320')).
% 4.61/4.78 tff(1653,plain,
% 4.61/4.78 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 4.61/4.78 tff(1654,plain,
% 4.61/4.78 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1653, 1649])).
% 4.61/4.78 tff(1655,plain,(
% 4.61/4.78 ![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 4.61/4.78 inference(skolemize,[status(sab)],[1654])).
% 4.61/4.78 tff(1656,plain,
% 4.61/4.78 (![U: $i] : (hskp71 | hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1655, 1648])).
% 4.61/4.78 tff(1657,plain,
% 4.61/4.78 (((~![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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1658,plain,
% 4.61/4.78 ((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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1659,plain,
% 4.61/4.78 (((~![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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1658])).
% 4.61/4.78 tff(1660,plain,
% 4.61/4.78 (((~![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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1659, 1657])).
% 4.61/4.78 tff(1661,plain,
% 4.61/4.78 ((~![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)))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1662,plain,
% 4.61/4.78 ((~![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))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 4.61/4.78 tff(1663,plain,
% 4.61/4.78 (hskp71 | hskp36 | (~c1_1(a1715))),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1662, 197, 1213, 1656, 1204])).
% 4.61/4.78 tff(1664,plain,
% 4.61/4.78 (hskp36),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1663, 1646, 1246])).
% 4.61/4.78 tff(1665,plain,
% 4.61/4.78 (((~hskp36) | (~c0_1(a1712))) <=> ((~hskp36) | (~c0_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1666,plain,
% 4.61/4.78 (((~c0_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c0_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1667,axiom,((~c0_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 4.61/4.78 tff(1668,plain,
% 4.61/4.78 ((~hskp36) | (~c0_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 4.61/4.78 tff(1669,plain,
% 4.61/4.78 ((~hskp36) | (~c0_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1668, 1665])).
% 4.61/4.78 tff(1670,plain,
% 4.61/4.78 (~c0_1(a1712)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1669, 1664])).
% 4.61/4.78 tff(1671,plain,
% 4.61/4.78 (((~hskp36) | (~c2_1(a1712))) <=> ((~hskp36) | (~c2_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1672,plain,
% 4.61/4.78 (((~c2_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c2_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1673,axiom,((~c2_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause234')).
% 4.61/4.78 tff(1674,plain,
% 4.61/4.78 ((~hskp36) | (~c2_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 4.61/4.78 tff(1675,plain,
% 4.61/4.78 ((~hskp36) | (~c2_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1674, 1671])).
% 4.61/4.78 tff(1676,plain,
% 4.61/4.78 (~c2_1(a1712)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1675, 1664])).
% 4.61/4.78 tff(1677,plain,
% 4.61/4.78 (((~hskp36) | (~c1_1(a1712))) <=> ((~hskp36) | (~c1_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1678,plain,
% 4.61/4.78 (((~c1_1(a1712)) | (~hskp36)) <=> ((~hskp36) | (~c1_1(a1712)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1679,axiom,((~c1_1(a1712)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 4.61/4.78 tff(1680,plain,
% 4.61/4.78 ((~hskp36) | (~c1_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 4.61/4.78 tff(1681,plain,
% 4.61/4.78 ((~hskp36) | (~c1_1(a1712))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1680, 1677])).
% 4.61/4.78 tff(1682,plain,
% 4.61/4.78 (~c1_1(a1712)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1681, 1664])).
% 4.61/4.78 tff(1683,assumption,(~c2_1(a1712)), introduced(assumption)).
% 4.61/4.78 tff(1684,assumption,(~c2_1(a1665)), introduced(assumption)).
% 4.61/4.78 tff(1685,assumption,(~c0_1(a1712)), introduced(assumption)).
% 4.61/4.78 tff(1686,plain,
% 4.61/4.78 (((~![W: $i, 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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1687,plain,
% 4.61/4.78 (((~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1688,plain,
% 4.61/4.78 (((~![W: $i, 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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1687])).
% 4.61/4.78 tff(1689,plain,
% 4.61/4.78 (((~![W: $i, 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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1688, 1686])).
% 4.61/4.78 tff(1690,plain,
% 4.61/4.78 ((~![W: $i, 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)))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1691,plain,
% 4.61/4.78 ((~![W: $i, 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))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 4.61/4.78 tff(1692,plain,
% 4.61/4.78 (c2_1(a1712) | (~c3_1(a1712))),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1691, 197, 1583, 1582, 93, 92, 1574, 1685, 346, 1684])).
% 4.61/4.78 tff(1693,plain,
% 4.61/4.78 (~c3_1(a1712)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1692, 1683])).
% 4.61/4.78 tff(1694,assumption,(~c1_1(a1712)), introduced(assumption)).
% 4.61/4.78 tff(1695,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1696,plain,
% 4.61/4.78 (((~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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1697,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1696])).
% 4.61/4.78 tff(1698,plain,
% 4.61/4.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1697, 1695])).
% 4.61/4.78 tff(1699,plain,
% 4.61/4.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1700,plain,
% 4.61/4.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c2_1(a1712) | c0_1(a1712) | c1_1(a1712) | (~ndr1_0) | c3_1(a1712) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 4.61/4.78 tff(1701,plain,
% 4.61/4.78 ($false),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1700, 197, 1540, 1554, 1539, 1683, 1685, 1694, 30, 1693])).
% 4.61/4.78 tff(1702,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,[]))).
% 4.61/4.78 tff(1703,plain,
% 4.61/4.78 ($false),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1702, 1682, 1676, 1493, 1462, 1670, 1478, 1363, 1362, 1566, 1565, 1361, 1573])).
% 4.61/4.78 tff(1704,plain,(c3_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.78 tff(1705,plain,
% 4.61/4.78 (c0_1(a1715)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1704, 1203, 333])).
% 4.61/4.78 tff(1706,assumption,(c0_1(a1715)), introduced(assumption)).
% 4.61/4.78 tff(1707,assumption,(c1_1(a1655)), introduced(assumption)).
% 4.61/4.78 tff(1708,plain,
% 4.61/4.78 (hskp13),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[273, 1707])).
% 4.61/4.78 tff(1709,plain,
% 4.61/4.78 (~c1_1(a1667)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[279, 1708])).
% 4.61/4.78 tff(1710,plain,
% 4.61/4.78 (^[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))))),
% 4.61/4.78 inference(bind,[status(th)],[])).
% 4.61/4.78 tff(1711,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(quant_intro,[status(thm)],[1710])).
% 4.61/4.78 tff(1712,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1713,plain,
% 4.61/4.78 (^[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)))))),
% 4.61/4.78 inference(bind,[status(th)],[])).
% 4.61/4.78 tff(1714,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(quant_intro,[status(thm)],[1713])).
% 4.61/4.78 tff(1715,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')).
% 4.61/4.78 tff(1716,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 4.61/4.78 tff(1717,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1716, 1712])).
% 4.61/4.78 tff(1718,plain,(
% 4.61/4.78 ![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)))),
% 4.61/4.78 inference(skolemize,[status(sab)],[1717])).
% 4.61/4.78 tff(1719,plain,
% 4.61/4.78 (![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)))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1718, 1711])).
% 4.61/4.78 tff(1720,plain,
% 4.61/4.78 (((~![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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1721,plain,
% 4.61/4.78 ((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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1722,plain,
% 4.61/4.78 (((~![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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1721])).
% 4.61/4.78 tff(1723,plain,
% 4.61/4.78 (((~![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)))),
% 4.61/4.78 inference(transitivity,[status(thm)],[1722, 1720])).
% 4.61/4.78 tff(1724,plain,
% 4.61/4.78 ((~![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)))),
% 4.61/4.78 inference(quant_inst,[status(thm)],[])).
% 4.61/4.78 tff(1725,plain,
% 4.61/4.78 ((~![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))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 4.61/4.78 tff(1726,plain,
% 4.61/4.78 (hskp47 | (~c1_1(a1655))),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1725, 197, 333, 69, 71, 1213, 1719, 1706])).
% 4.61/4.78 tff(1727,plain,
% 4.61/4.78 (hskp47),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1726, 1707])).
% 4.61/4.78 tff(1728,plain,
% 4.61/4.78 (((~hskp47) | (~c0_1(a1644))) <=> ((~hskp47) | (~c0_1(a1644)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1729,plain,
% 4.61/4.78 (((~c0_1(a1644)) | (~hskp47)) <=> ((~hskp47) | (~c0_1(a1644)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1730,axiom,((~c0_1(a1644)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause220')).
% 4.61/4.78 tff(1731,plain,
% 4.61/4.78 ((~hskp47) | (~c0_1(a1644))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 4.61/4.78 tff(1732,plain,
% 4.61/4.78 ((~hskp47) | (~c0_1(a1644))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1731, 1728])).
% 4.61/4.78 tff(1733,plain,
% 4.61/4.78 (~c0_1(a1644)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1732, 1727])).
% 4.61/4.78 tff(1734,plain,
% 4.61/4.78 (((~hskp47) | (~c1_1(a1644))) <=> ((~hskp47) | (~c1_1(a1644)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1735,plain,
% 4.61/4.78 (((~c1_1(a1644)) | (~hskp47)) <=> ((~hskp47) | (~c1_1(a1644)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1736,axiom,((~c1_1(a1644)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 4.61/4.78 tff(1737,plain,
% 4.61/4.78 ((~hskp47) | (~c1_1(a1644))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 4.61/4.78 tff(1738,plain,
% 4.61/4.78 ((~hskp47) | (~c1_1(a1644))),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1737, 1734])).
% 4.61/4.78 tff(1739,plain,
% 4.61/4.78 (~c1_1(a1644)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1738, 1727])).
% 4.61/4.78 tff(1740,plain,
% 4.61/4.78 (c3_1(a1667)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[287, 1708])).
% 4.61/4.78 tff(1741,plain,
% 4.61/4.78 (c0_1(a1667)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[295, 1708])).
% 4.61/4.78 tff(1742,plain,
% 4.61/4.78 (((~hskp47) | c3_1(a1644)) <=> ((~hskp47) | c3_1(a1644))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1743,axiom,((~hskp47) | c3_1(a1644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 4.61/4.78 tff(1744,plain,
% 4.61/4.78 ((~hskp47) | c3_1(a1644)),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 4.61/4.78 tff(1745,plain,
% 4.61/4.78 ((~hskp47) | c3_1(a1644)),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1744, 1742])).
% 4.61/4.78 tff(1746,plain,
% 4.61/4.78 ((~hskp47) | c3_1(a1644)),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1745, 1742])).
% 4.61/4.78 tff(1747,plain,
% 4.61/4.78 ((~hskp47) | c3_1(a1644)),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1746, 1742])).
% 4.61/4.78 tff(1748,plain,
% 4.61/4.78 ((~hskp47) | c3_1(a1644)),
% 4.61/4.78 inference(modus_ponens,[status(thm)],[1747, 1742])).
% 4.61/4.78 tff(1749,plain,
% 4.61/4.78 (c3_1(a1644)),
% 4.61/4.78 inference(unit_resolution,[status(thm)],[1748, 1727])).
% 4.61/4.78 tff(1750,plain,
% 4.61/4.78 (((~![V: $i, 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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1751,plain,
% 4.61/4.78 ((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)))),
% 4.61/4.78 inference(rewrite,[status(thm)],[])).
% 4.61/4.78 tff(1752,plain,
% 4.61/4.78 (((~![V: $i, 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))))),
% 4.61/4.78 inference(monotonicity,[status(thm)],[1751])).
% 4.61/4.78 tff(1753,plain,
% 4.61/4.78 (((~![V: $i, 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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1752, 1750])).
% 4.61/4.79 tff(1754,plain,
% 4.61/4.79 ((~![V: $i, 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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1755,plain,
% 4.61/4.79 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1644) | c0_1(a1644) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1644))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 4.61/4.79 tff(1756,plain,
% 4.61/4.79 ($false),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1755, 197, 126, 1749, 1741, 1740, 1739, 1733, 1709, 125])).
% 4.61/4.79 tff(1757,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,[]))).
% 4.61/4.79 tff(1758,plain,
% 4.61/4.79 (~c1_1(a1655)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1757, 206, 333, 126, 205, 1213, 1706, 207])).
% 4.61/4.79 tff(1759,plain,
% 4.61/4.79 (~hskp17),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[245, 158, 144, 150, 126, 206, 205, 1758])).
% 4.61/4.79 tff(1760,plain,
% 4.61/4.79 (hskp17 | hskp16 | c1_1(a1655)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[254, 197, 206, 205, 10])).
% 4.61/4.79 tff(1761,plain,
% 4.61/4.79 (hskp16),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1760, 1759, 1758])).
% 4.61/4.79 tff(1762,plain,
% 4.61/4.79 (~c1_1(a1677)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[99, 1761])).
% 4.61/4.79 tff(1763,plain,
% 4.61/4.79 (~c0_1(a1677)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[111, 1761])).
% 4.61/4.79 tff(1764,plain,
% 4.61/4.79 (~c3_1(a1677)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[325, 197, 126, 206, 205, 1763, 1762, 125, 1758])).
% 4.61/4.79 tff(1765,plain,
% 4.61/4.79 (~c2_1(a1677)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[105, 1761])).
% 4.61/4.79 tff(1766,plain,
% 4.61/4.79 ($false),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[316, 197, 158, 144, 150, 1763, 1765, 1762, 30, 1764])).
% 4.61/4.79 tff(1767,plain,(hskp52 | hskp29 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.61/4.79 tff(1768,plain,
% 4.61/4.79 (hskp52),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1767, 1203, 126, 333, 1705])).
% 4.61/4.79 tff(1769,plain,
% 4.61/4.79 (hskp52),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1767, 333, 126, 1213, 1706])).
% 4.61/4.79 tff(1770,plain,
% 4.61/4.79 (c0_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[480, 1769])).
% 4.61/4.79 tff(1771,plain,
% 4.61/4.79 (c3_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[488, 1769])).
% 4.61/4.79 tff(1772,plain,
% 4.61/4.79 (c2_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[496, 1769])).
% 4.61/4.79 tff(1773,plain,
% 4.61/4.79 (c3_1(a1677)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[735, 112, 559, 558, 560, 106, 1212])).
% 4.61/4.79 tff(1774,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1775,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1776,plain,
% 4.61/4.79 (((~![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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1775])).
% 4.61/4.79 tff(1777,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1776, 1774])).
% 4.61/4.79 tff(1778,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1779,plain,
% 4.61/4.79 ((~![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))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 4.61/4.79 tff(1780,plain,
% 4.61/4.79 (hskp69 | (~c3_1(a1677))),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1779, 197, 771, 333, 1213, 112, 100, 1310])).
% 4.61/4.79 tff(1781,plain,
% 4.61/4.79 (hskp69),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1780, 1773])).
% 4.61/4.79 tff(1782,plain,
% 4.61/4.79 (~c1_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1329, 1781])).
% 4.61/4.79 tff(1783,plain,
% 4.61/4.79 (c3_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1337, 1781])).
% 4.61/4.79 tff(1784,plain,
% 4.61/4.79 (c0_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1345, 1781])).
% 4.61/4.79 tff(1785,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1786,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1787,plain,
% 4.61/4.79 (((~![V: $i, 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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1786])).
% 4.61/4.79 tff(1788,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1787, 1785])).
% 4.61/4.79 tff(1789,plain,
% 4.61/4.79 ((~![V: $i, 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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1790,plain,
% 4.61/4.79 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 4.61/4.79 tff(1791,plain,
% 4.61/4.79 ($false),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1790, 197, 126, 1784, 1783, 1782, 112, 100, 125, 1773])).
% 4.61/4.79 tff(1792,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,[]))).
% 4.61/4.79 tff(1793,plain,
% 4.61/4.79 (~hskp16),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1792, 333, 771, 126, 1213, 1772, 1771, 1770])).
% 4.61/4.79 tff(1794,plain,
% 4.61/4.79 (hskp17 | hskp16 | c1_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[659, 197, 1770, 1771, 10])).
% 4.61/4.79 tff(1795,plain,
% 4.61/4.79 (c1_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1794, 248, 247])).
% 4.61/4.79 tff(1796,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1797,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1798,plain,
% 4.61/4.79 (((~![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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1797])).
% 4.61/4.79 tff(1799,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1798, 1796])).
% 4.61/4.79 tff(1800,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1801,plain,
% 4.61/4.79 ((~![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))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 4.61/4.79 tff(1802,plain,
% 4.61/4.79 (hskp47 | (~c1_1(a1654))),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1801, 197, 333, 1770, 1771, 1213, 1719, 1706])).
% 4.61/4.79 tff(1803,plain,
% 4.61/4.79 (hskp47),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1802, 1795])).
% 4.61/4.79 tff(1804,plain,
% 4.61/4.79 (~c0_1(a1644)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1732, 1803])).
% 4.61/4.79 tff(1805,plain,
% 4.61/4.79 (~c1_1(a1644)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1738, 1803])).
% 4.61/4.79 tff(1806,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1807,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1808,plain,
% 4.61/4.79 (((~![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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1807])).
% 4.61/4.79 tff(1809,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1808, 1806])).
% 4.61/4.79 tff(1810,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1811,plain,
% 4.61/4.79 ((~![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))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 4.61/4.79 tff(1812,plain,
% 4.61/4.79 (hskp61),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1811, 197, 771, 333, 1213, 1156, 1706])).
% 4.61/4.79 tff(1813,plain,
% 4.61/4.79 (~c1_1(a1674)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1106, 1812])).
% 4.61/4.79 tff(1814,plain,
% 4.61/4.79 (c3_1(a1674)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1114, 1812])).
% 4.61/4.79 tff(1815,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1816,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1817,plain,
% 4.61/4.79 (((~![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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1816])).
% 4.61/4.79 tff(1818,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1817, 1815])).
% 4.61/4.79 tff(1819,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1820,plain,
% 4.61/4.79 ((~![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))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 4.61/4.79 tff(1821,plain,
% 4.61/4.79 (hskp17 | hskp16 | (~c0_1(a1674))),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1820, 197, 1814, 1813, 10])).
% 4.61/4.79 tff(1822,plain,
% 4.61/4.79 (~c0_1(a1674)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1821, 248, 247])).
% 4.61/4.79 tff(1823,plain,
% 4.61/4.79 (((~![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))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1824,plain,
% 4.61/4.79 ((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))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1825,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1824])).
% 4.61/4.79 tff(1826,plain,
% 4.61/4.79 (((~![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))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1825, 1823])).
% 4.61/4.79 tff(1827,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1828,plain,
% 4.61/4.79 ((~![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)),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 4.61/4.79 tff(1829,plain,
% 4.61/4.79 (hskp69),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1828, 197, 771, 333, 1814, 1213, 1813, 1310, 1822])).
% 4.61/4.79 tff(1830,plain,
% 4.61/4.79 (~c1_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1329, 1829])).
% 4.61/4.79 tff(1831,plain,
% 4.61/4.79 (c3_1(a1644)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1748, 1803])).
% 4.61/4.79 tff(1832,plain,
% 4.61/4.79 (c3_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1337, 1829])).
% 4.61/4.79 tff(1833,plain,
% 4.61/4.79 (c0_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1345, 1829])).
% 4.61/4.79 tff(1834,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1835,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1836,plain,
% 4.61/4.79 (((~![V: $i, 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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1835])).
% 4.61/4.79 tff(1837,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1836, 1834])).
% 4.61/4.79 tff(1838,plain,
% 4.61/4.79 ((~![V: $i, 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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1839,plain,
% 4.61/4.79 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 4.61/4.79 tff(1840,plain,
% 4.61/4.79 ($false),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1839, 197, 126, 1833, 1832, 1831, 1830, 1805, 1804, 125])).
% 4.61/4.79 tff(1841,plain,(hskp16 | hskp29 | (~c1_1(a1715)) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 4.61/4.79 tff(1842,plain,
% 4.61/4.79 (hskp17),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1841, 1793, 771, 333, 1213, 1706, 126])).
% 4.61/4.79 tff(1843,plain,
% 4.61/4.79 (~c2_1(a1678)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[236, 1842])).
% 4.61/4.79 tff(1844,plain,
% 4.61/4.79 (~c0_1(a1678)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[223, 1842])).
% 4.61/4.79 tff(1845,plain,
% 4.61/4.79 (c3_1(a1678)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[568, 1770, 1772, 1771, 1844, 1843, 1212])).
% 4.61/4.79 tff(1846,plain,
% 4.61/4.79 (~c1_1(a1678)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[217, 1842])).
% 4.61/4.79 tff(1847,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1848,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1849,plain,
% 4.61/4.79 (((~![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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1848])).
% 4.61/4.79 tff(1850,plain,
% 4.61/4.79 (((~![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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1849, 1847])).
% 4.61/4.79 tff(1851,plain,
% 4.61/4.79 ((~![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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1852,plain,
% 4.61/4.79 ((~![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))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 4.61/4.79 tff(1853,plain,
% 4.61/4.79 (hskp69 | (~c3_1(a1678))),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1852, 197, 771, 333, 1213, 1844, 1846, 1310])).
% 4.61/4.79 tff(1854,plain,
% 4.61/4.79 (hskp69),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1853, 1845])).
% 4.61/4.79 tff(1855,plain,
% 4.61/4.79 (~c1_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1329, 1854])).
% 4.61/4.79 tff(1856,plain,
% 4.61/4.79 (c3_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1337, 1854])).
% 4.61/4.79 tff(1857,plain,
% 4.61/4.79 (c0_1(a1709)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1345, 1854])).
% 4.61/4.79 tff(1858,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1859,plain,
% 4.61/4.79 ((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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1860,plain,
% 4.61/4.79 (((~![V: $i, 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))))),
% 4.61/4.79 inference(monotonicity,[status(thm)],[1859])).
% 4.61/4.79 tff(1861,plain,
% 4.61/4.79 (((~![V: $i, 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)))),
% 4.61/4.79 inference(transitivity,[status(thm)],[1860, 1858])).
% 4.61/4.79 tff(1862,plain,
% 4.61/4.79 ((~![V: $i, 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)))),
% 4.61/4.79 inference(quant_inst,[status(thm)],[])).
% 4.61/4.79 tff(1863,plain,
% 4.61/4.79 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 4.61/4.79 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 4.61/4.79 tff(1864,plain,
% 4.61/4.79 ($false),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1863, 197, 126, 1857, 1856, 1855, 1844, 1846, 125, 1845])).
% 4.61/4.79 tff(1865,plain,(c3_1(a1715) | hskp29 | (~c1_1(a1715)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.61/4.79 tff(1866,plain,
% 4.61/4.79 (~c1_1(a1715)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[1865, 1203, 126, 333, 1705])).
% 4.61/4.79 tff(1867,plain,
% 4.61/4.79 (c2_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[496, 1768])).
% 4.61/4.79 tff(1868,plain,
% 4.61/4.79 (c3_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[488, 1768])).
% 4.61/4.79 tff(1869,plain,
% 4.61/4.79 (c0_1(a1654)),
% 4.61/4.79 inference(unit_resolution,[status(thm)],[480, 1768])).
% 4.61/4.79 tff(1870,plain,
% 4.61/4.79 (^[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))))),
% 4.61/4.79 inference(bind,[status(th)],[])).
% 4.61/4.79 tff(1871,plain,
% 4.61/4.79 (![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)))),
% 4.61/4.79 inference(quant_intro,[status(thm)],[1870])).
% 4.61/4.79 tff(1872,plain,
% 4.61/4.79 (![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)))),
% 4.61/4.79 inference(rewrite,[status(thm)],[])).
% 4.61/4.79 tff(1873,plain,
% 4.61/4.79 (^[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)))))),
% 4.61/4.80 inference(bind,[status(th)],[])).
% 4.61/4.80 tff(1874,plain,
% 4.61/4.80 (![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)))),
% 4.61/4.80 inference(quant_intro,[status(thm)],[1873])).
% 4.61/4.80 tff(1875,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')).
% 4.61/4.80 tff(1876,plain,
% 4.61/4.80 (![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)))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 4.61/4.80 tff(1877,plain,
% 4.61/4.80 (![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)))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1876, 1872])).
% 4.61/4.80 tff(1878,plain,(
% 4.61/4.80 ![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)))),
% 4.61/4.80 inference(skolemize,[status(sab)],[1877])).
% 4.61/4.80 tff(1879,plain,
% 4.61/4.80 (![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)))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1878, 1871])).
% 4.61/4.80 tff(1880,plain,
% 4.61/4.80 (((~![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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1881,plain,
% 4.61/4.80 ((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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1882,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1881])).
% 4.61/4.80 tff(1883,plain,
% 4.61/4.80 (((~![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))),
% 4.61/4.80 inference(transitivity,[status(thm)],[1882, 1880])).
% 4.61/4.80 tff(1884,plain,
% 4.61/4.80 ((~![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)))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(1885,plain,
% 4.61/4.80 ((~![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)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 4.61/4.80 tff(1886,plain,
% 4.61/4.80 (hskp67),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1885, 197, 560, 559, 558, 1409, 570])).
% 4.61/4.80 tff(1887,plain,
% 4.61/4.80 (c3_1(a1702)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1423, 1886])).
% 4.61/4.80 tff(1888,plain,
% 4.61/4.80 (((~hskp67) | c2_1(a1702)) <=> ((~hskp67) | c2_1(a1702))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1889,axiom,((~hskp67) | c2_1(a1702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 4.61/4.80 tff(1890,plain,
% 4.61/4.80 ((~hskp67) | c2_1(a1702)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 4.61/4.80 tff(1891,plain,
% 4.61/4.80 ((~hskp67) | c2_1(a1702)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1890, 1888])).
% 4.61/4.80 tff(1892,plain,
% 4.61/4.80 ((~hskp67) | c2_1(a1702)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1891, 1888])).
% 4.61/4.80 tff(1893,plain,
% 4.61/4.80 ((~hskp67) | c2_1(a1702)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1892, 1888])).
% 4.61/4.80 tff(1894,plain,
% 4.61/4.80 ((~hskp67) | c2_1(a1702)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1893, 1888])).
% 4.61/4.80 tff(1895,plain,
% 4.61/4.80 (c2_1(a1702)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1894, 1886])).
% 4.61/4.80 tff(1896,plain,
% 4.61/4.80 (c1_1(a1702)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1431, 1886])).
% 4.61/4.80 tff(1897,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1898,plain,
% 4.61/4.80 ((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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1899,plain,
% 4.61/4.80 (((~![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))))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1898])).
% 4.61/4.80 tff(1900,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(transitivity,[status(thm)],[1899, 1897])).
% 4.61/4.80 tff(1901,plain,
% 4.61/4.80 ((~![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)))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(1902,plain,
% 4.61/4.80 ((~![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 4.61/4.80 tff(1903,plain,
% 4.61/4.80 (hskp63),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1902, 197, 1896, 1895, 1887, 560, 558, 1879, 570])).
% 4.61/4.80 tff(1904,plain,
% 4.61/4.80 (((~hskp63) | (~c0_1(a1676))) <=> ((~hskp63) | (~c0_1(a1676)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1905,plain,
% 4.61/4.80 (((~c0_1(a1676)) | (~hskp63)) <=> ((~hskp63) | (~c0_1(a1676)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1906,axiom,((~c0_1(a1676)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 4.61/4.80 tff(1907,plain,
% 4.61/4.80 ((~hskp63) | (~c0_1(a1676))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 4.61/4.80 tff(1908,plain,
% 4.61/4.80 ((~hskp63) | (~c0_1(a1676))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1907, 1904])).
% 4.61/4.80 tff(1909,plain,
% 4.61/4.80 (~c0_1(a1676)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1908, 1903])).
% 4.61/4.80 tff(1910,plain,
% 4.61/4.80 (((~hskp63) | c3_1(a1676)) <=> ((~hskp63) | c3_1(a1676))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1911,axiom,((~hskp63) | c3_1(a1676)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 4.61/4.80 tff(1912,plain,
% 4.61/4.80 ((~hskp63) | c3_1(a1676)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 4.61/4.80 tff(1913,plain,
% 4.61/4.80 ((~hskp63) | c3_1(a1676)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1912, 1910])).
% 4.61/4.80 tff(1914,plain,
% 4.61/4.80 ((~hskp63) | c3_1(a1676)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1913, 1910])).
% 4.61/4.80 tff(1915,plain,
% 4.61/4.80 ((~hskp63) | c3_1(a1676)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1914, 1910])).
% 4.61/4.80 tff(1916,plain,
% 4.61/4.80 ((~hskp63) | c3_1(a1676)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1915, 1910])).
% 4.61/4.80 tff(1917,plain,
% 4.61/4.80 (c3_1(a1676)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1916, 1903])).
% 4.61/4.80 tff(1918,assumption,(~hskp75), introduced(assumption)).
% 4.61/4.80 tff(1919,assumption,(~c2_1(a1716)), introduced(assumption)).
% 4.61/4.80 tff(1920,assumption,(hskp29), introduced(assumption)).
% 4.61/4.80 tff(1921,plain,
% 4.61/4.80 (((~hskp29) | (~c3_1(a1695))) <=> ((~hskp29) | (~c3_1(a1695)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1922,plain,
% 4.61/4.80 (((~c3_1(a1695)) | (~hskp29)) <=> ((~hskp29) | (~c3_1(a1695)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1923,axiom,((~c3_1(a1695)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause248')).
% 4.61/4.80 tff(1924,plain,
% 4.61/4.80 ((~hskp29) | (~c3_1(a1695))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 4.61/4.80 tff(1925,plain,
% 4.61/4.80 ((~hskp29) | (~c3_1(a1695))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1924, 1921])).
% 4.61/4.80 tff(1926,plain,
% 4.61/4.80 (~c3_1(a1695)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1925, 1920])).
% 4.61/4.80 tff(1927,plain,
% 4.61/4.80 (((~hskp29) | c0_1(a1695)) <=> ((~hskp29) | c0_1(a1695))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1928,axiom,((~hskp29) | c0_1(a1695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 4.61/4.80 tff(1929,plain,
% 4.61/4.80 ((~hskp29) | c0_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 4.61/4.80 tff(1930,plain,
% 4.61/4.80 ((~hskp29) | c0_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1929, 1927])).
% 4.61/4.80 tff(1931,plain,
% 4.61/4.80 ((~hskp29) | c0_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1930, 1927])).
% 4.61/4.80 tff(1932,plain,
% 4.61/4.80 ((~hskp29) | c0_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1931, 1927])).
% 4.61/4.80 tff(1933,plain,
% 4.61/4.80 ((~hskp29) | c0_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1932, 1927])).
% 4.61/4.80 tff(1934,plain,
% 4.61/4.80 (c0_1(a1695)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1933, 1920])).
% 4.61/4.80 tff(1935,plain,
% 4.61/4.80 (((~hskp29) | c2_1(a1695)) <=> ((~hskp29) | c2_1(a1695))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1936,axiom,((~hskp29) | c2_1(a1695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 4.61/4.80 tff(1937,plain,
% 4.61/4.80 ((~hskp29) | c2_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 4.61/4.80 tff(1938,plain,
% 4.61/4.80 ((~hskp29) | c2_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1937, 1935])).
% 4.61/4.80 tff(1939,plain,
% 4.61/4.80 ((~hskp29) | c2_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1938, 1935])).
% 4.61/4.80 tff(1940,plain,
% 4.61/4.80 ((~hskp29) | c2_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1939, 1935])).
% 4.61/4.80 tff(1941,plain,
% 4.61/4.80 ((~hskp29) | c2_1(a1695)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1940, 1935])).
% 4.61/4.80 tff(1942,plain,
% 4.61/4.80 (c2_1(a1695)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1941, 1920])).
% 4.61/4.80 tff(1943,plain,
% 4.61/4.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1944,plain,
% 4.61/4.80 (((~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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1945,plain,
% 4.61/4.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1944])).
% 4.61/4.80 tff(1946,plain,
% 4.61/4.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.80 inference(transitivity,[status(thm)],[1945, 1943])).
% 4.61/4.80 tff(1947,plain,
% 4.61/4.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(1948,plain,
% 4.61/4.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1715) | c1_1(a1716)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 4.61/4.80 tff(1949,plain,
% 4.61/4.80 ($false),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1948, 197, 1919, 335, 1942, 1934, 1539, 1213, 1926, 30, 1204, 1494])).
% 4.61/4.80 tff(1950,plain,((~hskp29) | c2_1(a1716) | c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.80 tff(1951,plain,
% 4.61/4.80 (~hskp29),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1950, 1494, 335, 1539, 1213, 1204, 1919])).
% 4.61/4.80 tff(1952,plain,
% 4.61/4.80 (c3_1(a1715)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1704, 1213, 1204])).
% 4.61/4.80 tff(1953,assumption,(~c0_1(a1716)), introduced(assumption)).
% 4.61/4.80 tff(1954,plain,
% 4.61/4.80 (~hskp73),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1492, 1953])).
% 4.61/4.80 tff(1955,assumption,(hskp21), introduced(assumption)).
% 4.61/4.80 tff(1956,plain,
% 4.61/4.80 (~c1_1(a1683)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1315, 1955])).
% 4.61/4.80 tff(1957,plain,
% 4.61/4.80 (c2_1(a1683)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1284, 1955])).
% 4.61/4.80 tff(1958,plain,
% 4.61/4.80 (c3_1(a1683)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1292, 1955])).
% 4.61/4.80 tff(1959,assumption,(c3_1(a1715)), introduced(assumption)).
% 4.61/4.80 tff(1960,assumption,(~hskp73), introduced(assumption)).
% 4.61/4.80 tff(1961,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1962,plain,
% 4.61/4.80 ((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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1963,plain,
% 4.61/4.80 (((~![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))))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1962])).
% 4.61/4.80 tff(1964,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(transitivity,[status(thm)],[1963, 1961])).
% 4.61/4.80 tff(1965,plain,
% 4.61/4.80 ((~![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)))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(1966,plain,
% 4.61/4.80 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c1_1(a1715))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 4.61/4.80 tff(1967,plain,
% 4.61/4.80 ($false),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1966, 197, 1960, 771, 1959, 1958, 1957, 1956, 1449, 1204])).
% 4.61/4.80 tff(1968,plain,((~hskp21) | hskp73 | (~c1_1(a1715)) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.80 tff(1969,plain,
% 4.61/4.80 (~hskp21),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1968, 771, 1954, 1952, 1204])).
% 4.61/4.80 tff(1970,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1971,plain,
% 4.61/4.80 ((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)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1972,plain,
% 4.61/4.80 (((~![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))))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1971])).
% 4.61/4.80 tff(1973,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(transitivity,[status(thm)],[1972, 1970])).
% 4.61/4.80 tff(1974,plain,
% 4.61/4.80 ((~![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)))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(1975,plain,
% 4.61/4.80 ((~![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 4.61/4.80 tff(1976,plain,
% 4.61/4.80 (hskp21 | c2_1(a1716) | (~c1_1(a1715)) | (~c1_1(a1716))),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1975, 197, 1539, 1213, 1261, 1204])).
% 4.61/4.80 tff(1977,plain,
% 4.61/4.80 (~c1_1(a1716)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[1976, 1969, 1919, 771])).
% 4.61/4.80 tff(1978,plain,
% 4.61/4.80 (^[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)))),
% 4.61/4.80 inference(bind,[status(th)],[])).
% 4.61/4.80 tff(1979,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(quant_intro,[status(thm)],[1978])).
% 4.61/4.80 tff(1980,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1981,plain,
% 4.61/4.80 (^[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))))),
% 4.61/4.80 inference(bind,[status(th)],[])).
% 4.61/4.80 tff(1982,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(quant_intro,[status(thm)],[1981])).
% 4.61/4.80 tff(1983,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')).
% 4.61/4.80 tff(1984,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 4.61/4.80 tff(1985,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1984, 1980])).
% 4.61/4.80 tff(1986,plain,(
% 4.61/4.80 ![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))),
% 4.61/4.80 inference(skolemize,[status(sab)],[1985])).
% 4.61/4.80 tff(1987,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1986, 1979])).
% 4.61/4.80 tff(1988,plain,
% 4.61/4.80 (^[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)))),
% 4.61/4.80 inference(bind,[status(th)],[])).
% 4.61/4.80 tff(1989,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(quant_intro,[status(thm)],[1988])).
% 4.61/4.80 tff(1990,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1991,plain,
% 4.61/4.80 (^[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))))),
% 4.61/4.80 inference(bind,[status(th)],[])).
% 4.61/4.80 tff(1992,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(quant_intro,[status(thm)],[1991])).
% 4.61/4.80 tff(1993,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')).
% 4.61/4.80 tff(1994,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 4.61/4.80 tff(1995,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1994, 1990])).
% 4.61/4.80 tff(1996,plain,(
% 4.61/4.80 ![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))),
% 4.61/4.80 inference(skolemize,[status(sab)],[1995])).
% 4.61/4.80 tff(1997,plain,
% 4.61/4.80 (![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))),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[1996, 1989])).
% 4.61/4.80 tff(1998,plain,
% 4.61/4.80 (((~![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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(1999,plain,
% 4.61/4.80 ((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))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(2000,plain,
% 4.61/4.80 (((~![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)))),
% 4.61/4.80 inference(monotonicity,[status(thm)],[1999])).
% 4.61/4.80 tff(2001,plain,
% 4.61/4.80 (((~![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))),
% 4.61/4.80 inference(transitivity,[status(thm)],[2000, 1998])).
% 4.61/4.80 tff(2002,plain,
% 4.61/4.80 ((~![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))),
% 4.61/4.80 inference(quant_inst,[status(thm)],[])).
% 4.61/4.80 tff(2003,plain,
% 4.61/4.80 ((~![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)),
% 4.61/4.80 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 4.61/4.80 tff(2004,plain,
% 4.61/4.80 (hskp25 | c0_1(a1716) | (~c1_1(a1715)) | c1_1(a1716)),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[2003, 197, 1952, 1539, 1997, 1204])).
% 4.61/4.80 tff(2005,plain,
% 4.61/4.80 (hskp25),
% 4.61/4.80 inference(unit_resolution,[status(thm)],[2004, 1977, 1953, 771])).
% 4.61/4.80 tff(2006,plain,
% 4.61/4.80 (((~hskp25) | (~c1_1(a1690))) <=> ((~hskp25) | (~c1_1(a1690)))),
% 4.61/4.80 inference(rewrite,[status(thm)],[])).
% 4.61/4.80 tff(2007,plain,
% 4.61/4.80 (((~c1_1(a1690)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a1690)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2008,axiom,((~c1_1(a1690)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 4.61/4.81 tff(2009,plain,
% 4.61/4.81 ((~hskp25) | (~c1_1(a1690))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 4.61/4.81 tff(2010,plain,
% 4.61/4.81 ((~hskp25) | (~c1_1(a1690))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2009, 2006])).
% 4.61/4.81 tff(2011,plain,
% 4.61/4.81 (~c1_1(a1690)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2010, 2005])).
% 4.61/4.81 tff(2012,plain,
% 4.61/4.81 (((~hskp25) | (~c0_1(a1690))) <=> ((~hskp25) | (~c0_1(a1690)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2013,plain,
% 4.61/4.81 (((~c0_1(a1690)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1690)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2014,axiom,((~c0_1(a1690)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause257')).
% 4.61/4.81 tff(2015,plain,
% 4.61/4.81 ((~hskp25) | (~c0_1(a1690))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 4.61/4.81 tff(2016,plain,
% 4.61/4.81 ((~hskp25) | (~c0_1(a1690))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2015, 2012])).
% 4.61/4.81 tff(2017,plain,
% 4.61/4.81 (~c0_1(a1690)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2016, 2005])).
% 4.61/4.81 tff(2018,plain,
% 4.61/4.81 (((~hskp25) | c2_1(a1690)) <=> ((~hskp25) | c2_1(a1690))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2019,axiom,((~hskp25) | c2_1(a1690)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 4.61/4.81 tff(2020,plain,
% 4.61/4.81 ((~hskp25) | c2_1(a1690)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 4.61/4.81 tff(2021,plain,
% 4.61/4.81 ((~hskp25) | c2_1(a1690)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2020, 2018])).
% 4.61/4.81 tff(2022,plain,
% 4.61/4.81 ((~hskp25) | c2_1(a1690)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2021, 2018])).
% 4.61/4.81 tff(2023,plain,
% 4.61/4.81 ((~hskp25) | c2_1(a1690)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2022, 2018])).
% 4.61/4.81 tff(2024,plain,
% 4.61/4.81 ((~hskp25) | c2_1(a1690)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2023, 2018])).
% 4.61/4.81 tff(2025,plain,
% 4.61/4.81 (c2_1(a1690)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2024, 2005])).
% 4.61/4.81 tff(2026,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2027,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2028,plain,
% 4.61/4.81 (((~![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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2027])).
% 4.61/4.81 tff(2029,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2028, 2026])).
% 4.61/4.81 tff(2030,plain,
% 4.61/4.81 ((~![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))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2031,plain,
% 4.61/4.81 ((~![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))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 4.61/4.81 tff(2032,plain,
% 4.61/4.81 (hskp70),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2031, 197, 1919, 1953, 2025, 1539, 2017, 2011, 1987])).
% 4.61/4.81 tff(2033,plain,
% 4.61/4.81 (((~hskp70) | (~c3_1(a1710))) <=> ((~hskp70) | (~c3_1(a1710)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2034,plain,
% 4.61/4.81 (((~c3_1(a1710)) | (~hskp70)) <=> ((~hskp70) | (~c3_1(a1710)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2035,axiom,((~c3_1(a1710)) | (~hskp70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 4.61/4.81 tff(2036,plain,
% 4.61/4.81 ((~hskp70) | (~c3_1(a1710))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 4.61/4.81 tff(2037,plain,
% 4.61/4.81 ((~hskp70) | (~c3_1(a1710))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2036, 2033])).
% 4.61/4.81 tff(2038,plain,
% 4.61/4.81 (~c3_1(a1710)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2037, 2032])).
% 4.61/4.81 tff(2039,plain,
% 4.61/4.81 (((~hskp70) | (~c0_1(a1710))) <=> ((~hskp70) | (~c0_1(a1710)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2040,plain,
% 4.61/4.81 (((~c0_1(a1710)) | (~hskp70)) <=> ((~hskp70) | (~c0_1(a1710)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2041,axiom,((~c0_1(a1710)) | (~hskp70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 4.61/4.81 tff(2042,plain,
% 4.61/4.81 ((~hskp70) | (~c0_1(a1710))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 4.61/4.81 tff(2043,plain,
% 4.61/4.81 ((~hskp70) | (~c0_1(a1710))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2042, 2039])).
% 4.61/4.81 tff(2044,plain,
% 4.61/4.81 (~c0_1(a1710)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2043, 2032])).
% 4.61/4.81 tff(2045,plain,
% 4.61/4.81 (((~hskp70) | c1_1(a1710)) <=> ((~hskp70) | c1_1(a1710))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2046,axiom,((~hskp70) | c1_1(a1710)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 4.61/4.81 tff(2047,plain,
% 4.61/4.81 ((~hskp70) | c1_1(a1710)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 4.61/4.81 tff(2048,plain,
% 4.61/4.81 ((~hskp70) | c1_1(a1710)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2047, 2045])).
% 4.61/4.81 tff(2049,plain,
% 4.61/4.81 ((~hskp70) | c1_1(a1710)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2048, 2045])).
% 4.61/4.81 tff(2050,plain,
% 4.61/4.81 ((~hskp70) | c1_1(a1710)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2049, 2045])).
% 4.61/4.81 tff(2051,plain,
% 4.61/4.81 ((~hskp70) | c1_1(a1710)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2050, 2045])).
% 4.61/4.81 tff(2052,plain,
% 4.61/4.81 (c1_1(a1710)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2051, 2032])).
% 4.61/4.81 tff(2053,plain,
% 4.61/4.81 (((~![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 | 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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2054,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2055,plain,
% 4.61/4.81 (((~![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(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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2054])).
% 4.61/4.81 tff(2056,plain,
% 4.61/4.81 (((~![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(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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2055, 2053])).
% 4.61/4.81 tff(2057,plain,
% 4.61/4.81 ((~![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(a1710) | c2_1(a1710) | (~c1_1(a1710)) | c0_1(a1710) | c2_1(a1710) | (~c1_1(a1710)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2058,plain,
% 4.61/4.81 ((~![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 | c0_1(a1710) | c3_1(a1710) | (~ndr1_0) | c2_1(a1710) | (~c1_1(a1710))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 4.61/4.81 tff(2059,plain,
% 4.61/4.81 (c2_1(a1710)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2058, 197, 1969, 2052, 2044, 2038, 1261])).
% 4.61/4.81 tff(2060,plain,
% 4.61/4.81 (^[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))))),
% 4.61/4.81 inference(bind,[status(th)],[])).
% 4.61/4.81 tff(2061,plain,
% 4.61/4.81 (![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)))),
% 4.61/4.81 inference(quant_intro,[status(thm)],[2060])).
% 4.61/4.81 tff(2062,plain,
% 4.61/4.81 (![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2063,plain,
% 4.61/4.81 (^[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)))))),
% 4.61/4.81 inference(bind,[status(th)],[])).
% 4.61/4.81 tff(2064,plain,
% 4.61/4.81 (![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)))),
% 4.61/4.81 inference(quant_intro,[status(thm)],[2063])).
% 4.61/4.81 tff(2065,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp61) | hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause327')).
% 4.61/4.81 tff(2066,plain,
% 4.61/4.81 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 4.61/4.81 tff(2067,plain,
% 4.61/4.81 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2066, 2062])).
% 4.61/4.81 tff(2068,plain,(
% 4.61/4.81 ![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 4.61/4.81 inference(skolemize,[status(sab)],[2067])).
% 4.61/4.81 tff(2069,plain,
% 4.61/4.81 (![U: $i] : (hskp62 | hskp61 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2068, 2061])).
% 4.61/4.81 tff(2070,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2071,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2072,plain,
% 4.61/4.81 (((~![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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2071])).
% 4.61/4.81 tff(2073,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2072, 2070])).
% 4.61/4.81 tff(2074,plain,
% 4.61/4.81 ((~![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)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2075,plain,
% 4.61/4.81 ((~![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))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 4.61/4.81 tff(2076,plain,
% 4.61/4.81 (hskp62 | hskp61 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2075, 197, 2069, 1204])).
% 4.61/4.81 tff(2077,plain,
% 4.61/4.81 (hskp62),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2076, 1157, 1959, 771])).
% 4.61/4.81 tff(2078,plain,
% 4.61/4.81 (((~hskp62) | c0_1(a1675)) <=> ((~hskp62) | c0_1(a1675))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2079,axiom,((~hskp62) | c0_1(a1675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 4.61/4.81 tff(2080,plain,
% 4.61/4.81 ((~hskp62) | c0_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 4.61/4.81 tff(2081,plain,
% 4.61/4.81 ((~hskp62) | c0_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2080, 2078])).
% 4.61/4.81 tff(2082,plain,
% 4.61/4.81 ((~hskp62) | c0_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2081, 2078])).
% 4.61/4.81 tff(2083,plain,
% 4.61/4.81 ((~hskp62) | c0_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2082, 2078])).
% 4.61/4.81 tff(2084,plain,
% 4.61/4.81 ((~hskp62) | c0_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2083, 2078])).
% 4.61/4.81 tff(2085,plain,
% 4.61/4.81 (c0_1(a1675)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2084, 2077])).
% 4.61/4.81 tff(2086,plain,
% 4.61/4.81 (((~hskp62) | c1_1(a1675)) <=> ((~hskp62) | c1_1(a1675))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2087,axiom,((~hskp62) | c1_1(a1675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 4.61/4.81 tff(2088,plain,
% 4.61/4.81 ((~hskp62) | c1_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 4.61/4.81 tff(2089,plain,
% 4.61/4.81 ((~hskp62) | c1_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2088, 2086])).
% 4.61/4.81 tff(2090,plain,
% 4.61/4.81 ((~hskp62) | c1_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2089, 2086])).
% 4.61/4.81 tff(2091,plain,
% 4.61/4.81 ((~hskp62) | c1_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2090, 2086])).
% 4.61/4.81 tff(2092,plain,
% 4.61/4.81 ((~hskp62) | c1_1(a1675)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2091, 2086])).
% 4.61/4.81 tff(2093,plain,
% 4.61/4.81 (c1_1(a1675)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2092, 2077])).
% 4.61/4.81 tff(2094,plain,
% 4.61/4.81 (((~hskp62) | (~c3_1(a1675))) <=> ((~hskp62) | (~c3_1(a1675)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2095,plain,
% 4.61/4.81 (((~c3_1(a1675)) | (~hskp62)) <=> ((~hskp62) | (~c3_1(a1675)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2096,axiom,((~c3_1(a1675)) | (~hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 4.61/4.81 tff(2097,plain,
% 4.61/4.81 ((~hskp62) | (~c3_1(a1675))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 4.61/4.81 tff(2098,plain,
% 4.61/4.81 ((~hskp62) | (~c3_1(a1675))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2097, 2094])).
% 4.61/4.81 tff(2099,plain,
% 4.61/4.81 (~c3_1(a1675)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2098, 2077])).
% 4.61/4.81 tff(2100,assumption,(~c2_1(a1675)), introduced(assumption)).
% 4.61/4.81 tff(2101,assumption,(~c3_1(a1675)), introduced(assumption)).
% 4.61/4.81 tff(2102,assumption,(c0_1(a1675)), introduced(assumption)).
% 4.61/4.81 tff(2103,assumption,(c1_1(a1675)), introduced(assumption)).
% 4.61/4.81 tff(2104,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2105,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2106,plain,
% 4.61/4.81 (((~![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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2105])).
% 4.61/4.81 tff(2107,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2106, 2104])).
% 4.61/4.81 tff(2108,plain,
% 4.61/4.81 ((~![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)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2109,plain,
% 4.61/4.81 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1675) | (~ndr1_0) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 4.61/4.81 tff(2110,plain,
% 4.61/4.81 ($false),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2109, 197, 1157, 2103, 2102, 2101, 1156, 2100])).
% 4.61/4.81 tff(2111,plain,(c2_1(a1675) | hskp61 | (~c1_1(a1675)) | (~c0_1(a1675)) | c3_1(a1675)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.81 tff(2112,plain,
% 4.61/4.81 (c2_1(a1675)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2111, 2099, 2093, 2085, 1157])).
% 4.61/4.81 tff(2113,plain,
% 4.61/4.81 (((~![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))) | (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))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2114,plain,
% 4.61/4.81 (((~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))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2115,plain,
% 4.61/4.81 (((~![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(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)))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2114])).
% 4.61/4.81 tff(2116,plain,
% 4.61/4.81 (((~![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(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))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2115, 2113])).
% 4.61/4.81 tff(2117,plain,
% 4.61/4.81 ((~![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(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))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2118,plain,
% 4.61/4.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1675) | (~ndr1_0) | (~c2_1(a1675)) | (~c0_1(a1675)) | c1_1(a1716)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 4.61/4.81 tff(2119,plain,
% 4.61/4.81 ($false),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2118, 197, 1919, 1953, 2085, 1539, 2099, 30, 1494, 2112])).
% 4.61/4.81 tff(2120,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,[]))).
% 4.61/4.81 tff(2121,plain,
% 4.61/4.81 (hskp61),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2120, 1977, 1953, 1539, 1919, 1952, 771, 1204])).
% 4.61/4.81 tff(2122,plain,
% 4.61/4.81 (~c2_1(a1674)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[1100, 2121])).
% 4.61/4.81 tff(2123,plain,
% 4.61/4.81 (~c1_1(a1674)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[1106, 2121])).
% 4.61/4.81 tff(2124,plain,
% 4.61/4.81 (c3_1(a1674)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[1114, 2121])).
% 4.61/4.81 tff(2125,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2126,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2127,plain,
% 4.61/4.81 (((~![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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2126])).
% 4.61/4.81 tff(2128,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2127, 2125])).
% 4.61/4.81 tff(2129,plain,
% 4.61/4.81 ((~![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)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2130,plain,
% 4.61/4.81 ((~![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))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 4.61/4.81 tff(2131,plain,
% 4.61/4.81 (hskp75),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2130, 197, 2052, 2124, 2038, 2123, 2122, 398, 2059])).
% 4.61/4.81 tff(2132,plain,
% 4.61/4.81 (~c2_1(a1724)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[411, 2131])).
% 4.61/4.81 tff(2133,plain,
% 4.61/4.81 (c3_1(a1724)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[435, 2131])).
% 4.61/4.81 tff(2134,plain,
% 4.61/4.81 (c0_1(a1724)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[443, 2131])).
% 4.61/4.81 tff(2135,assumption,(c2_1(a1710)), introduced(assumption)).
% 4.61/4.81 tff(2136,assumption,(~c0_1(a1674)), introduced(assumption)).
% 4.61/4.81 tff(2137,assumption,(c0_1(a1724)), introduced(assumption)).
% 4.61/4.81 tff(2138,assumption,(~c1_1(a1674)), introduced(assumption)).
% 4.61/4.81 tff(2139,assumption,(~c3_1(a1710)), introduced(assumption)).
% 4.61/4.81 tff(2140,assumption,(c3_1(a1674)), introduced(assumption)).
% 4.61/4.81 tff(2141,assumption,(c1_1(a1710)), introduced(assumption)).
% 4.61/4.81 tff(2142,assumption,(c3_1(a1724)), introduced(assumption)).
% 4.61/4.81 tff(2143,assumption,(~c1_1(a1724)), introduced(assumption)).
% 4.61/4.81 tff(2144,plain,
% 4.61/4.81 (((~![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))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2145,plain,
% 4.61/4.81 (((~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))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2146,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2145])).
% 4.61/4.81 tff(2147,plain,
% 4.61/4.81 (((~![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))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2146, 2144])).
% 4.61/4.81 tff(2148,plain,
% 4.61/4.81 ((~![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)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2149,plain,
% 4.61/4.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 4.61/4.81 tff(2150,plain,
% 4.61/4.81 ($false),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2149, 197, 2137, 2142, 2141, 2140, 2139, 2138, 90, 2136, 2135, 2143])).
% 4.61/4.81 tff(2151,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,[]))).
% 4.61/4.81 tff(2152,plain,
% 4.61/4.81 (c1_1(a1724)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2151, 2136, 2142, 2141, 2140, 2139, 2138, 2135, 2137])).
% 4.61/4.81 tff(2153,assumption,(~c2_1(a1724)), introduced(assumption)).
% 4.61/4.81 tff(2154,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2155,plain,
% 4.61/4.81 ((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)))),
% 4.61/4.81 inference(rewrite,[status(thm)],[])).
% 4.61/4.81 tff(2156,plain,
% 4.61/4.81 (((~![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))))),
% 4.61/4.81 inference(monotonicity,[status(thm)],[2155])).
% 4.61/4.81 tff(2157,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.81 inference(transitivity,[status(thm)],[2156, 2154])).
% 4.61/4.81 tff(2158,plain,
% 4.61/4.81 ((~![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)))),
% 4.61/4.81 inference(quant_inst,[status(thm)],[])).
% 4.61/4.81 tff(2159,plain,
% 4.61/4.81 ((~![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))),
% 4.61/4.81 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 4.61/4.81 tff(2160,plain,
% 4.61/4.81 (hskp13 | (~c1_1(a1724))),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2159, 197, 2137, 2142, 2153, 266])).
% 4.61/4.81 tff(2161,plain,
% 4.61/4.81 (hskp13),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[2160, 2152])).
% 4.61/4.81 tff(2162,plain,
% 4.61/4.81 (~c1_1(a1667)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[279, 2161])).
% 4.61/4.81 tff(2163,plain,
% 4.61/4.81 (c3_1(a1667)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[287, 2161])).
% 4.61/4.81 tff(2164,plain,
% 4.61/4.81 (c0_1(a1667)),
% 4.61/4.81 inference(unit_resolution,[status(thm)],[295, 2161])).
% 4.61/4.81 tff(2165,plain,
% 4.61/4.81 (((~![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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2166,plain,
% 4.61/4.82 (((~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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2167,plain,
% 4.61/4.82 (((~![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))))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2166])).
% 4.61/4.82 tff(2168,plain,
% 4.61/4.82 (((~![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)))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2167, 2165])).
% 4.61/4.82 tff(2169,plain,
% 4.61/4.82 ((~![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)))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2170,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1710) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1710)) | (~c1_1(a1710))),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 4.61/4.82 tff(2171,plain,
% 4.61/4.82 ($false),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2170, 197, 2141, 2140, 2164, 2163, 2139, 2138, 2162, 90, 2136, 2135])).
% 4.61/4.82 tff(2172,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,[]))).
% 4.61/4.82 tff(2173,plain,
% 4.61/4.82 (c0_1(a1674)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2172, 2052, 2124, 2038, 2123, 2059, 2134, 2133, 2132])).
% 4.61/4.82 tff(2174,plain,
% 4.61/4.82 (((~![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(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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2175,plain,
% 4.61/4.82 (((~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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2176,plain,
% 4.61/4.82 (((~![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(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))))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2175])).
% 4.61/4.82 tff(2177,plain,
% 4.61/4.82 (((~![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(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)))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2176, 2174])).
% 4.61/4.82 tff(2178,plain,
% 4.61/4.82 ((~![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(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)))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2179,plain,
% 4.61/4.82 ((~![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(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c1_1(a1724))),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 4.61/4.82 tff(2180,plain,
% 4.61/4.82 ((~c0_1(a1674)) | (~c1_1(a1724))),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2179, 197, 2134, 2133, 2124, 2123, 2122, 590])).
% 4.61/4.82 tff(2181,plain,
% 4.61/4.82 (~c1_1(a1724)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2180, 2173])).
% 4.61/4.82 tff(2182,assumption,(~c2_1(a1674)), introduced(assumption)).
% 4.61/4.82 tff(2183,plain,
% 4.61/4.82 (((~![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)))) | (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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2184,plain,
% 4.61/4.82 (((~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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2185,plain,
% 4.61/4.82 (((~![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(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))))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2184])).
% 4.61/4.82 tff(2186,plain,
% 4.61/4.82 (((~![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(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)))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2185, 2183])).
% 4.61/4.82 tff(2187,plain,
% 4.61/4.82 ((~![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(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)))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2188,plain,
% 4.61/4.82 ((~![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)))) | 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))),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 4.61/4.82 tff(2189,plain,
% 4.61/4.82 (~c1_1(a1654)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2188, 197, 2137, 2140, 860, 831, 2153, 2138, 2182, 590, 2143])).
% 4.61/4.82 tff(2190,plain,
% 4.61/4.82 (((~![W: $i, 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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2191,plain,
% 4.61/4.82 (((~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2192,plain,
% 4.61/4.82 (((~![W: $i, 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)))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2191])).
% 4.61/4.82 tff(2193,plain,
% 4.61/4.82 (((~![W: $i, 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))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2192, 2190])).
% 4.61/4.82 tff(2194,plain,
% 4.61/4.82 ((~![W: $i, 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)))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2195,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 4.61/4.82 tff(2196,plain,
% 4.61/4.82 ($false),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2195, 197, 2137, 2142, 1952, 832, 831, 2153, 1213, 346, 1204, 2189])).
% 4.61/4.82 tff(2197,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,[]))).
% 4.61/4.82 tff(2198,plain,
% 4.61/4.82 (~hskp52),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2197, 2134, 2133, 2132, 1213, 1204, 2124, 2123, 2122, 2181])).
% 4.61/4.82 tff(2199,assumption,(hskp53), introduced(assumption)).
% 4.61/4.82 tff(2200,plain,
% 4.61/4.82 (~c3_1(a1656)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[149, 2199])).
% 4.61/4.82 tff(2201,plain,
% 4.61/4.82 (c0_1(a1656)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[143, 2199])).
% 4.61/4.82 tff(2202,plain,
% 4.61/4.82 (c2_1(a1656)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[157, 2199])).
% 4.61/4.82 tff(2203,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2204,plain,
% 4.61/4.82 (((~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2205,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2204])).
% 4.61/4.82 tff(2206,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2205, 2203])).
% 4.61/4.82 tff(2207,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2208,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656)) | c1_1(a1716)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 4.61/4.82 tff(2209,plain,
% 4.61/4.82 ($false),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2208, 197, 1919, 1953, 2202, 2201, 1539, 2200, 30, 1494])).
% 4.61/4.82 tff(2210,plain,((~hskp53) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.82 tff(2211,plain,
% 4.61/4.82 (~hskp53),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2210, 1977, 1953, 1539, 1919])).
% 4.61/4.82 tff(2212,plain,
% 4.61/4.82 (hskp29),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[135, 2211, 2198])).
% 4.61/4.82 tff(2213,plain,
% 4.61/4.82 (~c3_1(a1695)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[1925, 2212])).
% 4.61/4.82 tff(2214,plain,
% 4.61/4.82 (c0_1(a1695)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[1933, 2212])).
% 4.61/4.82 tff(2215,plain,
% 4.61/4.82 (c2_1(a1695)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[1941, 2212])).
% 4.61/4.82 tff(2216,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2217,plain,
% 4.61/4.82 (((~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2218,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2217])).
% 4.61/4.82 tff(2219,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2218, 2216])).
% 4.61/4.82 tff(2220,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2221,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c1_1(a1716)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 4.61/4.82 tff(2222,plain,
% 4.61/4.82 ($false),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2221, 197, 1919, 1953, 2215, 2214, 1539, 2213, 30, 1977])).
% 4.61/4.82 tff(2223,plain,((~c1_1(a1715)) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.82 tff(2224,plain,
% 4.61/4.82 (~c1_1(a1715)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2223, 1919, 1953, 1539, 1213, 1204])).
% 4.61/4.82 tff(2225,assumption,(~hskp69), introduced(assumption)).
% 4.61/4.82 tff(2226,plain,
% 4.61/4.82 (((~![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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2227,plain,
% 4.61/4.82 ((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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2228,plain,
% 4.61/4.82 (((~![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))))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2227])).
% 4.61/4.82 tff(2229,plain,
% 4.61/4.82 (((~![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)))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2228, 2226])).
% 4.61/4.82 tff(2230,plain,
% 4.61/4.82 ((~![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)))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2231,plain,
% 4.61/4.82 ((~![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))),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 4.61/4.82 tff(2232,plain,
% 4.61/4.82 (hskp69 | c2_1(a1716) | c1_1(a1715) | (~c1_1(a1716))),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2231, 197, 1959, 1539, 1310, 1204])).
% 4.61/4.82 tff(2233,plain,
% 4.61/4.82 (~c1_1(a1716)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2232, 335, 1919, 2225])).
% 4.61/4.82 tff(2234,plain,
% 4.61/4.82 (((~hskp72) | c1_1(a1715)) <=> ((~hskp72) | c1_1(a1715))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2235,axiom,((~hskp72) | c1_1(a1715)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 4.61/4.82 tff(2236,plain,
% 4.61/4.82 ((~hskp72) | c1_1(a1715)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2235, 2234])).
% 4.61/4.82 tff(2237,plain,
% 4.61/4.82 ((~hskp72) | c1_1(a1715)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2236, 2234])).
% 4.61/4.82 tff(2238,plain,
% 4.61/4.82 ((~hskp72) | c1_1(a1715)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2237, 2234])).
% 4.61/4.82 tff(2239,plain,
% 4.61/4.82 ((~hskp72) | c1_1(a1715)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2238, 2234])).
% 4.61/4.82 tff(2240,plain,
% 4.61/4.82 ((~hskp72) | c1_1(a1715)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2239, 2234])).
% 4.61/4.82 tff(2241,plain,
% 4.61/4.82 (~hskp72),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2240, 335])).
% 4.61/4.82 tff(2242,plain,
% 4.61/4.82 (((~![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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2243,plain,
% 4.61/4.82 ((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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2244,plain,
% 4.61/4.82 (((~![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)))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2243])).
% 4.61/4.82 tff(2245,plain,
% 4.61/4.82 (((~![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))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2244, 2242])).
% 4.61/4.82 tff(2246,plain,
% 4.61/4.82 ((~![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))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2247,plain,
% 4.61/4.82 ((~![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)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 4.61/4.82 tff(2248,plain,
% 4.61/4.82 (hskp72 | hskp37 | c2_1(a1716) | c0_1(a1716)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2247, 197, 1539, 526])).
% 4.61/4.82 tff(2249,plain,
% 4.61/4.82 (hskp37),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2248, 2241, 1919, 1953])).
% 4.61/4.82 tff(2250,plain,
% 4.61/4.82 (c0_1(a1714)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[548, 2249])).
% 4.61/4.82 tff(2251,plain,
% 4.61/4.82 (c2_1(a1714)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[556, 2249])).
% 4.61/4.82 tff(2252,assumption,(~c3_1(a1714)), introduced(assumption)).
% 4.61/4.82 tff(2253,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2254,plain,
% 4.61/4.82 (((~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))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2255,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.61/4.82 inference(monotonicity,[status(thm)],[2254])).
% 4.61/4.82 tff(2256,plain,
% 4.61/4.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(transitivity,[status(thm)],[2255, 2253])).
% 4.61/4.82 tff(2257,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.61/4.82 inference(quant_inst,[status(thm)],[])).
% 4.61/4.82 tff(2258,plain,
% 4.61/4.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | c3_1(a1714) | (~c0_1(a1714)) | (~c2_1(a1714)) | c1_1(a1716)),
% 4.61/4.82 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 4.61/4.82 tff(2259,plain,
% 4.61/4.82 ($false),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2258, 197, 1919, 1953, 1228, 1227, 1539, 30, 2252, 1494])).
% 4.61/4.82 tff(2260,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,[]))).
% 4.61/4.82 tff(2261,plain,
% 4.61/4.82 (c3_1(a1714)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[2260, 2251, 1953, 1919, 2250, 1539, 2233])).
% 4.61/4.82 tff(2262,plain,
% 4.61/4.82 (~c1_1(a1714)),
% 4.61/4.82 inference(unit_resolution,[status(thm)],[540, 2249])).
% 4.61/4.82 tff(2263,plain,
% 4.61/4.82 (((~![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))) | (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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2264,plain,
% 4.61/4.82 (((~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)))),
% 4.61/4.82 inference(rewrite,[status(thm)],[])).
% 4.61/4.82 tff(2265,plain,
% 4.61/4.82 (((~![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(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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2264])).
% 4.61/4.83 tff(2266,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2265, 2263])).
% 4.61/4.83 tff(2267,plain,
% 4.61/4.83 ((~![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))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2268,plain,
% 4.61/4.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 4.61/4.83 tff(2269,plain,
% 4.61/4.83 ($false),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2268, 197, 1919, 1953, 2251, 2250, 1539, 2262, 514, 2261])).
% 4.61/4.83 tff(2270,plain,(c1_1(a1715) | c2_1(a1716) | c0_1(a1716) | c3_1(a1716) | hskp69 | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.83 tff(2271,plain,
% 4.61/4.83 (hskp69),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2270, 2224, 1953, 1539, 1919, 1952, 1204])).
% 4.61/4.83 tff(2272,plain,
% 4.61/4.83 (~c1_1(a1709)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1329, 2271])).
% 4.61/4.83 tff(2273,plain,
% 4.61/4.83 (c3_1(a1709)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1337, 2271])).
% 4.61/4.83 tff(2274,plain,
% 4.61/4.83 (c0_1(a1709)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1345, 2271])).
% 4.61/4.83 tff(2275,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2276,plain,
% 4.61/4.83 (((~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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2277,plain,
% 4.61/4.83 (((~![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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2276])).
% 4.61/4.83 tff(2278,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2277, 2275])).
% 4.61/4.83 tff(2279,plain,
% 4.61/4.83 ((~![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))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2280,plain,
% 4.61/4.83 ((~![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))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 4.61/4.83 tff(2281,plain,
% 4.61/4.83 (~c2_1(a1709)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2280, 197, 1919, 1953, 2274, 2273, 1539, 2272, 514])).
% 4.61/4.83 tff(2282,plain,
% 4.61/4.83 (((~![V: $i, 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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2283,plain,
% 4.61/4.83 ((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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2284,plain,
% 4.61/4.83 (((~![V: $i, 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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2283])).
% 4.61/4.83 tff(2285,plain,
% 4.61/4.83 (((~![V: $i, 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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2284, 2282])).
% 4.61/4.83 tff(2286,plain,
% 4.61/4.83 ((~![V: $i, 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)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2287,plain,
% 4.61/4.83 ((~![V: $i, 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))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 4.61/4.83 tff(2288,plain,
% 4.61/4.83 (hskp29),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2287, 197, 2224, 1952, 2274, 2273, 2272, 125, 1204])).
% 4.61/4.83 tff(2289,plain,
% 4.61/4.83 (~c3_1(a1695)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1925, 2288])).
% 4.61/4.83 tff(2290,plain,
% 4.61/4.83 (c0_1(a1695)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1933, 2288])).
% 4.61/4.83 tff(2291,plain,
% 4.61/4.83 (((~![W: $i, 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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2292,plain,
% 4.61/4.83 (((~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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2293,plain,
% 4.61/4.83 (((~![W: $i, 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)))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2292])).
% 4.61/4.83 tff(2294,plain,
% 4.61/4.83 (((~![W: $i, 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))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2293, 2291])).
% 4.61/4.83 tff(2295,plain,
% 4.61/4.83 ((~![W: $i, 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)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2296,plain,
% 4.61/4.83 ((~![W: $i, 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)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 4.61/4.83 tff(2297,plain,
% 4.61/4.83 (c1_1(a1695)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2296, 197, 1952, 2274, 2273, 2290, 1213, 2289, 380, 1204, 2281])).
% 4.61/4.83 tff(2298,plain,
% 4.61/4.83 (c2_1(a1695)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1941, 2288])).
% 4.61/4.83 tff(2299,plain,
% 4.61/4.83 (((~![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)))) | (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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2300,plain,
% 4.61/4.83 (((~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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2301,plain,
% 4.61/4.83 (((~![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(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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2300])).
% 4.61/4.83 tff(2302,plain,
% 4.61/4.83 (((~![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(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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2301, 2299])).
% 4.61/4.83 tff(2303,plain,
% 4.61/4.83 ((~![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(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)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2304,plain,
% 4.61/4.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 4.61/4.83 tff(2305,plain,
% 4.61/4.83 ($false),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2304, 197, 2224, 1952, 2274, 2273, 2298, 2272, 2289, 90, 1204, 2297])).
% 4.61/4.83 tff(2306,plain,(c2_1(a1716) | c0_1(a1715) | c2_1(a1715) | c0_1(a1716) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.83 tff(2307,plain,
% 4.61/4.83 (c2_1(a1716)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2306, 1953, 1213, 1204, 1539])).
% 4.61/4.83 tff(2308,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2309,plain,
% 4.61/4.83 ((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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2310,plain,
% 4.61/4.83 (((~![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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2309])).
% 4.61/4.83 tff(2311,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2310, 2308])).
% 4.61/4.83 tff(2312,plain,
% 4.61/4.83 ((~![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)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2313,plain,
% 4.61/4.83 ((~![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))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 4.61/4.83 tff(2314,plain,
% 4.61/4.83 (hskp75 | c1_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2313, 197, 1952, 1539, 1213, 398])).
% 4.61/4.83 tff(2315,plain,
% 4.61/4.83 (~c1_1(a1716)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2314, 335, 1540, 1918])).
% 4.61/4.83 tff(2316,plain,
% 4.61/4.83 (((~![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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2317,plain,
% 4.61/4.83 ((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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2318,plain,
% 4.61/4.83 (((~![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)))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2317])).
% 4.61/4.83 tff(2319,plain,
% 4.61/4.83 (((~![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))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2318, 2316])).
% 4.61/4.83 tff(2320,plain,
% 4.61/4.83 ((~![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)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2321,plain,
% 4.61/4.83 ((~![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)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 4.61/4.83 tff(2322,plain,
% 4.61/4.83 (hskp60 | c1_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2321, 197, 1952, 1539, 356, 1204])).
% 4.61/4.83 tff(2323,plain,
% 4.61/4.83 (hskp60),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2322, 335, 1540, 2315])).
% 4.61/4.83 tff(2324,plain,
% 4.61/4.83 (~c1_1(a1673)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[369, 2323])).
% 4.61/4.83 tff(2325,plain,
% 4.61/4.83 (c2_1(a1673)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[419, 2323])).
% 4.61/4.83 tff(2326,plain,
% 4.61/4.83 (c3_1(a1673)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[427, 2323])).
% 4.61/4.83 tff(2327,assumption,(hskp30), introduced(assumption)).
% 4.61/4.83 tff(2328,plain,
% 4.61/4.83 (((~hskp30) | (~c0_1(a1698))) <=> ((~hskp30) | (~c0_1(a1698)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2329,plain,
% 4.61/4.83 (((~c0_1(a1698)) | (~hskp30)) <=> ((~hskp30) | (~c0_1(a1698)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2330,axiom,((~c0_1(a1698)) | (~hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 4.61/4.83 tff(2331,plain,
% 4.61/4.83 ((~hskp30) | (~c0_1(a1698))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 4.61/4.83 tff(2332,plain,
% 4.61/4.83 ((~hskp30) | (~c0_1(a1698))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2331, 2328])).
% 4.61/4.83 tff(2333,plain,
% 4.61/4.83 (~c0_1(a1698)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2332, 2327])).
% 4.61/4.83 tff(2334,plain,
% 4.61/4.83 (((~hskp30) | c3_1(a1698)) <=> ((~hskp30) | c3_1(a1698))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2335,axiom,((~hskp30) | c3_1(a1698)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 4.61/4.83 tff(2336,plain,
% 4.61/4.83 ((~hskp30) | c3_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 4.61/4.83 tff(2337,plain,
% 4.61/4.83 ((~hskp30) | c3_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2336, 2334])).
% 4.61/4.83 tff(2338,plain,
% 4.61/4.83 ((~hskp30) | c3_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2337, 2334])).
% 4.61/4.83 tff(2339,plain,
% 4.61/4.83 ((~hskp30) | c3_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2338, 2334])).
% 4.61/4.83 tff(2340,plain,
% 4.61/4.83 ((~hskp30) | c3_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2339, 2334])).
% 4.61/4.83 tff(2341,plain,
% 4.61/4.83 (c3_1(a1698)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2340, 2327])).
% 4.61/4.83 tff(2342,plain,
% 4.61/4.83 (((~hskp30) | c1_1(a1698)) <=> ((~hskp30) | c1_1(a1698))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2343,axiom,((~hskp30) | c1_1(a1698)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 4.61/4.83 tff(2344,plain,
% 4.61/4.83 ((~hskp30) | c1_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 4.61/4.83 tff(2345,plain,
% 4.61/4.83 ((~hskp30) | c1_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2344, 2342])).
% 4.61/4.83 tff(2346,plain,
% 4.61/4.83 ((~hskp30) | c1_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2345, 2342])).
% 4.61/4.83 tff(2347,plain,
% 4.61/4.83 ((~hskp30) | c1_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2346, 2342])).
% 4.61/4.83 tff(2348,plain,
% 4.61/4.83 ((~hskp30) | c1_1(a1698)),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2347, 2342])).
% 4.61/4.83 tff(2349,plain,
% 4.61/4.83 (c1_1(a1698)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2348, 2327])).
% 4.61/4.83 tff(2350,plain,
% 4.61/4.83 (((~![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) | 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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2351,plain,
% 4.61/4.83 ((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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2352,plain,
% 4.61/4.83 (((~![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(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))))),
% 4.61/4.83 inference(monotonicity,[status(thm)],[2351])).
% 4.61/4.83 tff(2353,plain,
% 4.61/4.83 (((~![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(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)))),
% 4.61/4.83 inference(transitivity,[status(thm)],[2352, 2350])).
% 4.61/4.83 tff(2354,plain,
% 4.61/4.83 ((~![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(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))),
% 4.61/4.83 inference(quant_inst,[status(thm)],[])).
% 4.61/4.83 tff(2355,plain,
% 4.61/4.83 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1673) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 4.61/4.83 tff(2356,plain,
% 4.61/4.83 ($false),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2355, 197, 1960, 1583, 1582, 2349, 2341, 1574, 2333, 1449])).
% 4.61/4.83 tff(2357,plain,((~hskp30) | hskp73 | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.83 tff(2358,plain,
% 4.61/4.83 (~hskp30),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[2357, 2326, 1960, 2325, 2324])).
% 4.61/4.83 tff(2359,plain,
% 4.61/4.83 (^[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))))),
% 4.61/4.83 inference(bind,[status(th)],[])).
% 4.61/4.83 tff(2360,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(quant_intro,[status(thm)],[2359])).
% 4.61/4.83 tff(2361,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2362,plain,
% 4.61/4.83 (^[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)))))),
% 4.61/4.83 inference(bind,[status(th)],[])).
% 4.61/4.83 tff(2363,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(quant_intro,[status(thm)],[2362])).
% 4.61/4.83 tff(2364,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')).
% 4.61/4.83 tff(2365,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 4.61/4.83 tff(2366,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2365, 2361])).
% 4.61/4.83 tff(2367,plain,(
% 4.61/4.83 ![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)))),
% 4.61/4.83 inference(skolemize,[status(sab)],[2366])).
% 4.61/4.83 tff(2368,plain,
% 4.61/4.83 (![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)))),
% 4.61/4.83 inference(modus_ponens,[status(thm)],[2367, 2360])).
% 4.61/4.83 tff(2369,assumption,(hskp0), introduced(assumption)).
% 4.61/4.83 tff(2370,plain,
% 4.61/4.83 (~c2_1(a1637)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1085, 2369])).
% 4.61/4.83 tff(2371,plain,
% 4.61/4.83 (c0_1(a1637)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1093, 2369])).
% 4.61/4.83 tff(2372,plain,
% 4.61/4.83 (c1_1(a1637)),
% 4.61/4.83 inference(unit_resolution,[status(thm)],[1131, 2369])).
% 4.61/4.83 tff(2373,assumption,(~hskp30), introduced(assumption)).
% 4.61/4.83 tff(2374,plain,
% 4.61/4.83 (((~![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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.83 tff(2375,plain,
% 4.61/4.83 ((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))),
% 4.61/4.83 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2376,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2375])).
% 4.61/4.84 tff(2377,plain,
% 4.61/4.84 (((~![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))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2376, 2374])).
% 4.61/4.84 tff(2378,plain,
% 4.61/4.84 ((~![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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2379,plain,
% 4.61/4.84 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 4.61/4.84 tff(2380,plain,
% 4.61/4.84 ($false),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2379, 197, 2373, 335, 1959, 2372, 2371, 2370, 2368, 1204])).
% 4.61/4.84 tff(2381,plain,((~hskp0) | hskp30 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.84 tff(2382,plain,
% 4.61/4.84 (~hskp0),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2381, 2358, 335, 1952, 1204])).
% 4.61/4.84 tff(2383,assumption,(hskp42), introduced(assumption)).
% 4.61/4.84 tff(2384,plain,
% 4.61/4.84 (~c3_1(a1638)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[1009, 2383])).
% 4.61/4.84 tff(2385,plain,
% 4.61/4.84 (c1_1(a1638)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[1025, 2383])).
% 4.61/4.84 tff(2386,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2387,plain,
% 4.61/4.84 ((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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2388,plain,
% 4.61/4.84 (((~![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))))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2387])).
% 4.61/4.84 tff(2389,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2388, 2386])).
% 4.61/4.84 tff(2390,plain,
% 4.61/4.84 ((~![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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2391,plain,
% 4.61/4.84 ((~![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))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 4.61/4.84 tff(2392,plain,
% 4.61/4.84 (~c2_1(a1638)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2391, 1918, 197, 335, 1952, 2385, 1213, 2384, 398])).
% 4.61/4.84 tff(2393,plain,
% 4.61/4.84 (c0_1(a1638)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[1017, 2383])).
% 4.61/4.84 tff(2394,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2395,plain,
% 4.61/4.84 ((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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2396,plain,
% 4.61/4.84 (((~![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))))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2395])).
% 4.61/4.84 tff(2397,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2396, 2394])).
% 4.61/4.84 tff(2398,plain,
% 4.61/4.84 ((~![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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2399,plain,
% 4.61/4.84 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 4.61/4.84 tff(2400,plain,
% 4.61/4.84 ($false),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2399, 197, 2373, 335, 1952, 2385, 2393, 2368, 1204, 2392])).
% 4.61/4.84 tff(2401,plain,((~hskp42) | hskp30 | c1_1(a1715) | c0_1(a1715) | hskp75 | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.61/4.84 tff(2402,plain,
% 4.61/4.84 (~hskp42),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2401, 2358, 335, 1204, 1918, 1213])).
% 4.61/4.84 tff(2403,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2404,plain,
% 4.61/4.84 ((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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2405,plain,
% 4.61/4.84 (((~![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))))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2404])).
% 4.61/4.84 tff(2406,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2405, 2403])).
% 4.61/4.84 tff(2407,plain,
% 4.61/4.84 ((~![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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2408,plain,
% 4.61/4.84 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 4.61/4.84 tff(2409,plain,
% 4.61/4.84 ($false),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2408, 197, 995, 894, 1942, 1934, 1926, 971])).
% 4.61/4.84 tff(2410,plain,((~hskp29) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.61/4.84 tff(2411,plain,
% 4.61/4.84 (~hskp29),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2410, 2402, 2382])).
% 4.61/4.84 tff(2412,plain,
% 4.61/4.84 (~hskp74),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[1003, 894, 995])).
% 4.61/4.84 tff(2413,plain,
% 4.61/4.84 (hskp38),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[960, 2412, 818])).
% 4.61/4.84 tff(2414,plain,
% 4.61/4.84 (((~hskp38) | (~c0_1(a1718))) <=> ((~hskp38) | (~c0_1(a1718)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2415,plain,
% 4.61/4.84 (((~c0_1(a1718)) | (~hskp38)) <=> ((~hskp38) | (~c0_1(a1718)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2416,axiom,((~c0_1(a1718)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 4.61/4.84 tff(2417,plain,
% 4.61/4.84 ((~hskp38) | (~c0_1(a1718))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 4.61/4.84 tff(2418,plain,
% 4.61/4.84 ((~hskp38) | (~c0_1(a1718))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2417, 2414])).
% 4.61/4.84 tff(2419,plain,
% 4.61/4.84 (~c0_1(a1718)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2418, 2413])).
% 4.61/4.84 tff(2420,plain,
% 4.61/4.84 (c3_1(a1718)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[909, 2413])).
% 4.61/4.84 tff(2421,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2422,plain,
% 4.61/4.84 ((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)))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2423,plain,
% 4.61/4.84 (((~![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))))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2422])).
% 4.61/4.84 tff(2424,plain,
% 4.61/4.84 (((~![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)))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2423, 2421])).
% 4.61/4.84 tff(2425,plain,
% 4.61/4.84 ((~![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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2426,plain,
% 4.61/4.84 ((~![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))),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 4.61/4.84 tff(2427,plain,
% 4.61/4.84 (~c1_1(a1718)),
% 4.61/4.84 inference(unit_resolution,[status(thm)],[2426, 197, 1960, 1583, 1582, 2420, 1574, 2419, 1449])).
% 4.61/4.84 tff(2428,assumption,(~c1_1(a1718)), introduced(assumption)).
% 4.61/4.84 tff(2429,assumption,(~c0_1(a1718)), introduced(assumption)).
% 4.61/4.84 tff(2430,assumption,(c3_1(a1718)), introduced(assumption)).
% 4.61/4.84 tff(2431,plain,
% 4.61/4.84 (((~![V: $i, 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))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2432,plain,
% 4.61/4.84 ((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))),
% 4.61/4.84 inference(rewrite,[status(thm)],[])).
% 4.61/4.84 tff(2433,plain,
% 4.61/4.84 (((~![V: $i, 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)))),
% 4.61/4.84 inference(monotonicity,[status(thm)],[2432])).
% 4.61/4.84 tff(2434,plain,
% 4.61/4.84 (((~![V: $i, 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))),
% 4.61/4.84 inference(transitivity,[status(thm)],[2433, 2431])).
% 4.61/4.84 tff(2435,plain,
% 4.61/4.84 ((~![V: $i, 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)))),
% 4.61/4.84 inference(quant_inst,[status(thm)],[])).
% 4.61/4.84 tff(2436,plain,
% 4.61/4.84 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 4.61/4.84 inference(modus_ponens,[status(thm)],[2435, 2434])).
% 4.68/4.84 tff(2437,plain,
% 4.68/4.84 ($false),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2436, 197, 126, 560, 558, 2430, 2429, 125, 570, 2428])).
% 4.68/4.84 tff(2438,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c3_1(a1718)) | c0_1(a1718) | c1_1(a1718)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.84 tff(2439,plain,
% 4.68/4.84 (c1_1(a1654)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2438, 2420, 860, 831, 126, 2419, 2427])).
% 4.68/4.84 tff(2440,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2441,plain,
% 4.68/4.84 ((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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2442,plain,
% 4.68/4.84 (((~![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))))),
% 4.68/4.84 inference(monotonicity,[status(thm)],[2441])).
% 4.68/4.84 tff(2443,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(transitivity,[status(thm)],[2442, 2440])).
% 4.68/4.84 tff(2444,plain,
% 4.68/4.84 ((~![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)))),
% 4.68/4.84 inference(quant_inst,[status(thm)],[])).
% 4.68/4.84 tff(2445,plain,
% 4.68/4.84 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp40 | c3_1(a1716) | (~ndr1_0) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.68/4.84 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 4.68/4.84 tff(2446,plain,
% 4.68/4.84 (hskp40 | (~c1_1(a1654))),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2445, 197, 1540, 860, 831, 1539, 671, 1494])).
% 4.68/4.84 tff(2447,plain,
% 4.68/4.84 (hskp40),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2446, 2439])).
% 4.68/4.84 tff(2448,plain,
% 4.68/4.84 (~c2_1(a1725)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[684, 2447])).
% 4.68/4.84 tff(2449,plain,
% 4.68/4.84 (c3_1(a1725)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[692, 2447])).
% 4.68/4.84 tff(2450,plain,
% 4.68/4.84 (c1_1(a1725)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[700, 2447])).
% 4.68/4.84 tff(2451,plain,
% 4.68/4.84 ($false),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[1077, 197, 894, 860, 832, 2450, 2449, 2448, 881, 2439])).
% 4.68/4.84 tff(2452,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,[]))).
% 4.68/4.84 tff(2453,plain,
% 4.68/4.84 (~hskp52),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2452, 995, 1539, 1494, 894, 1960, 1583, 1582, 1574, 126, 1540])).
% 4.68/4.84 tff(2454,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2455,plain,
% 4.68/4.84 ((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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2456,plain,
% 4.68/4.84 (((~![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))))),
% 4.68/4.84 inference(monotonicity,[status(thm)],[2455])).
% 4.68/4.84 tff(2457,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(transitivity,[status(thm)],[2456, 2454])).
% 4.68/4.84 tff(2458,plain,
% 4.68/4.84 ((~![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)))),
% 4.68/4.84 inference(quant_inst,[status(thm)],[])).
% 4.68/4.84 tff(2459,plain,
% 4.68/4.84 ((~![U: $i] : (hskp42 | hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp42 | hskp0 | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.68/4.84 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 4.68/4.84 tff(2460,plain,
% 4.68/4.84 ($false),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2459, 197, 995, 894, 2202, 2201, 2200, 971])).
% 4.68/4.84 tff(2461,plain,((~hskp53) | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.68/4.84 tff(2462,plain,
% 4.68/4.84 (~hskp53),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2461, 995, 894])).
% 4.68/4.84 tff(2463,plain,
% 4.68/4.84 ($false),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[135, 2462, 2453, 126])).
% 4.68/4.84 tff(2464,plain,(hskp42 | hskp29 | hskp0 | c3_1(a1716) | c1_1(a1716) | hskp73 | (~c3_1(a1673)) | (~c2_1(a1673)) | c1_1(a1673) | (~c2_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 4.68/4.84 tff(2465,plain,
% 4.68/4.84 ($false),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2464, 2411, 2402, 2382, 1539, 2315, 1960, 2326, 2325, 2324, 1540])).
% 4.68/4.84 tff(2466,plain,(c1_1(a1715) | c3_1(a1716) | hskp73 | (~c2_1(a1716)) | c0_1(a1715) | hskp75 | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.84 tff(2467,plain,
% 4.68/4.84 (c1_1(a1715)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2466, 1918, 1960, 1540, 1204, 1539, 1213])).
% 4.68/4.84 tff(2468,plain,
% 4.68/4.84 (c3_1(a1637)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[1165, 1157, 1136, 1135, 1134])).
% 4.68/4.84 tff(2469,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2470,plain,
% 4.68/4.84 ((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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2471,plain,
% 4.68/4.84 (((~![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))))),
% 4.68/4.84 inference(monotonicity,[status(thm)],[2470])).
% 4.68/4.84 tff(2472,plain,
% 4.68/4.84 (((~![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)))),
% 4.68/4.84 inference(transitivity,[status(thm)],[2471, 2469])).
% 4.68/4.84 tff(2473,plain,
% 4.68/4.84 ((~![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)))),
% 4.68/4.84 inference(quant_inst,[status(thm)],[])).
% 4.68/4.84 tff(2474,plain,
% 4.68/4.84 ((~![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))),
% 4.68/4.84 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 4.68/4.84 tff(2475,plain,
% 4.68/4.84 (hskp13),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[2474, 197, 771, 1959, 1136, 1135, 1213, 266, 2468])).
% 4.68/4.84 tff(2476,plain,
% 4.68/4.84 (~c1_1(a1667)),
% 4.68/4.84 inference(unit_resolution,[status(thm)],[279, 2475])).
% 4.68/4.84 tff(2477,plain,
% 4.68/4.84 (^[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))))),
% 4.68/4.84 inference(bind,[status(th)],[])).
% 4.68/4.84 tff(2478,plain,
% 4.68/4.84 (![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)))),
% 4.68/4.84 inference(quant_intro,[status(thm)],[2477])).
% 4.68/4.84 tff(2479,plain,
% 4.68/4.84 (![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)))),
% 4.68/4.84 inference(rewrite,[status(thm)],[])).
% 4.68/4.84 tff(2480,plain,
% 4.68/4.84 (^[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)))))),
% 4.68/4.84 inference(bind,[status(th)],[])).
% 4.68/4.84 tff(2481,plain,
% 4.68/4.84 (![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)))),
% 4.68/4.84 inference(quant_intro,[status(thm)],[2480])).
% 4.68/4.84 tff(2482,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp61) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause330')).
% 4.68/4.84 tff(2483,plain,
% 4.68/4.84 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 4.68/4.85 tff(2484,plain,
% 4.68/4.85 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2483, 2479])).
% 4.68/4.85 tff(2485,plain,(
% 4.68/4.85 ![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.68/4.85 inference(skolemize,[status(sab)],[2484])).
% 4.68/4.85 tff(2486,plain,
% 4.68/4.85 (![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2485, 2478])).
% 4.68/4.85 tff(2487,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2488,plain,
% 4.68/4.85 ((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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2489,plain,
% 4.68/4.85 (((~![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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2488])).
% 4.68/4.85 tff(2490,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2489, 2487])).
% 4.68/4.85 tff(2491,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2492,plain,
% 4.68/4.85 ((~![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))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 4.68/4.85 tff(2493,plain,
% 4.68/4.85 (hskp61 | hskp33 | (~c3_1(a1637))),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2492, 197, 1135, 1134, 2486])).
% 4.68/4.85 tff(2494,plain,
% 4.68/4.85 (hskp33),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2493, 2468, 1157])).
% 4.68/4.85 tff(2495,plain,
% 4.68/4.85 (((~hskp33) | (~c2_1(a1704))) <=> ((~hskp33) | (~c2_1(a1704)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2496,plain,
% 4.68/4.85 (((~c2_1(a1704)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a1704)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2497,axiom,((~c2_1(a1704)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 4.68/4.85 tff(2498,plain,
% 4.68/4.85 ((~hskp33) | (~c2_1(a1704))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 4.68/4.85 tff(2499,plain,
% 4.68/4.85 ((~hskp33) | (~c2_1(a1704))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2498, 2495])).
% 4.68/4.85 tff(2500,plain,
% 4.68/4.85 (~c2_1(a1704)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2499, 2494])).
% 4.68/4.85 tff(2501,plain,
% 4.68/4.85 (((~hskp33) | (~c0_1(a1704))) <=> ((~hskp33) | (~c0_1(a1704)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2502,plain,
% 4.68/4.85 (((~c0_1(a1704)) | (~hskp33)) <=> ((~hskp33) | (~c0_1(a1704)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2503,axiom,((~c0_1(a1704)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 4.68/4.85 tff(2504,plain,
% 4.68/4.85 ((~hskp33) | (~c0_1(a1704))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 4.68/4.85 tff(2505,plain,
% 4.68/4.85 ((~hskp33) | (~c0_1(a1704))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2504, 2501])).
% 4.68/4.85 tff(2506,plain,
% 4.68/4.85 (~c0_1(a1704)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2505, 2494])).
% 4.68/4.85 tff(2507,plain,
% 4.68/4.85 (c3_1(a1667)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[287, 2475])).
% 4.68/4.85 tff(2508,plain,
% 4.68/4.85 (((~hskp33) | c3_1(a1704)) <=> ((~hskp33) | c3_1(a1704))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2509,axiom,((~hskp33) | c3_1(a1704)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 4.68/4.85 tff(2510,plain,
% 4.68/4.85 ((~hskp33) | c3_1(a1704)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 4.68/4.85 tff(2511,plain,
% 4.68/4.85 ((~hskp33) | c3_1(a1704)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2510, 2508])).
% 4.68/4.85 tff(2512,plain,
% 4.68/4.85 ((~hskp33) | c3_1(a1704)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2511, 2508])).
% 4.68/4.85 tff(2513,plain,
% 4.68/4.85 ((~hskp33) | c3_1(a1704)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2512, 2508])).
% 4.68/4.85 tff(2514,plain,
% 4.68/4.85 ((~hskp33) | c3_1(a1704)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2513, 2508])).
% 4.68/4.85 tff(2515,plain,
% 4.68/4.85 (c3_1(a1704)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2514, 2494])).
% 4.68/4.85 tff(2516,plain,
% 4.68/4.85 (((~![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)))) | (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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2517,plain,
% 4.68/4.85 (((~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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2518,plain,
% 4.68/4.85 (((~![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(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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2517])).
% 4.68/4.85 tff(2519,plain,
% 4.68/4.85 (((~![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(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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2518, 2516])).
% 4.68/4.85 tff(2520,plain,
% 4.68/4.85 ((~![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(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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2521,plain,
% 4.68/4.85 ((~![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)))) | 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))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 4.68/4.85 tff(2522,plain,
% 4.68/4.85 (~c2_1(a1667)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2521, 197, 2515, 2507, 1135, 2506, 2500, 2476, 1134, 346, 2468])).
% 4.68/4.85 tff(2523,plain,
% 4.68/4.85 (c0_1(a1667)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[295, 2475])).
% 4.68/4.85 tff(2524,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2525,plain,
% 4.68/4.85 (((~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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2526,plain,
% 4.68/4.85 (((~![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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2525])).
% 4.68/4.85 tff(2527,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2526, 2524])).
% 4.68/4.85 tff(2528,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2529,plain,
% 4.68/4.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 4.68/4.85 tff(2530,plain,
% 4.68/4.85 ($false),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2529, 197, 2523, 2507, 1136, 1135, 2476, 590, 2468, 2522])).
% 4.68/4.85 tff(2531,plain,(hskp61 | (~c1_1(a1637)) | (~c0_1(a1637)) | c2_1(a1637) | (~c1_1(a1715)) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.85 tff(2532,plain,
% 4.68/4.85 (hskp61),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2531, 2372, 2371, 2370, 2467, 1952, 1213])).
% 4.68/4.85 tff(2533,plain,
% 4.68/4.85 (~c2_1(a1674)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[1100, 2532])).
% 4.68/4.85 tff(2534,plain,
% 4.68/4.85 (~c1_1(a1674)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[1106, 2532])).
% 4.68/4.85 tff(2535,plain,
% 4.68/4.85 (c3_1(a1674)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[1114, 2532])).
% 4.68/4.85 tff(2536,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2537,plain,
% 4.68/4.85 ((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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2538,plain,
% 4.68/4.85 (((~![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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2537])).
% 4.68/4.85 tff(2539,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2538, 2536])).
% 4.68/4.85 tff(2540,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2541,plain,
% 4.68/4.85 ((~![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))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 4.68/4.85 tff(2542,plain,
% 4.68/4.85 (~c1_1(a1716)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2541, 1918, 197, 1540, 2535, 1539, 2534, 2533, 398])).
% 4.68/4.85 tff(2543,assumption,(~hskp60), introduced(assumption)).
% 4.68/4.85 tff(2544,plain,
% 4.68/4.85 (((~![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))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2545,plain,
% 4.68/4.85 ((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))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2546,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2545])).
% 4.68/4.85 tff(2547,plain,
% 4.68/4.85 (((~![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))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2546, 2544])).
% 4.68/4.85 tff(2548,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2549,plain,
% 4.68/4.85 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c3_1(a1716) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 4.68/4.85 tff(2550,plain,
% 4.68/4.85 ($false),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2549, 197, 2543, 1540, 2140, 1539, 2138, 356, 2136, 1494])).
% 4.68/4.85 tff(2551,plain,(c0_1(a1674) | hskp60 | (~c2_1(a1716)) | (~c3_1(a1674)) | c3_1(a1716) | c1_1(a1674) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.85 tff(2552,plain,
% 4.68/4.85 (hskp60),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2551, 2136, 1540, 2140, 1539, 2138, 1494])).
% 4.68/4.85 tff(2553,plain,
% 4.68/4.85 (~c1_1(a1673)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[369, 2552])).
% 4.68/4.85 tff(2554,plain,
% 4.68/4.85 (c3_1(a1673)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[427, 2552])).
% 4.68/4.85 tff(2555,plain,
% 4.68/4.85 (c2_1(a1673)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[419, 2552])).
% 4.68/4.85 tff(2556,plain,
% 4.68/4.85 (~hskp30),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2357, 2555, 1960, 2554, 2553])).
% 4.68/4.85 tff(2557,plain,
% 4.68/4.85 (((~![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))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2558,plain,
% 4.68/4.85 ((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))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2559,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2558])).
% 4.68/4.85 tff(2560,plain,
% 4.68/4.85 (((~![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))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2559, 2557])).
% 4.68/4.85 tff(2561,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2562,plain,
% 4.68/4.85 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp30 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 4.68/4.85 tff(2563,plain,
% 4.68/4.85 ($false),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2562, 197, 2556, 2140, 1136, 1135, 2138, 1134, 2368, 2136])).
% 4.68/4.85 tff(2564,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,[]))).
% 4.68/4.85 tff(2565,plain,
% 4.68/4.85 (c0_1(a1674)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2564, 2535, 2372, 2371, 2534, 2370, 1960, 1540, 1539, 2542])).
% 4.68/4.85 tff(2566,assumption,(c0_1(a1674)), introduced(assumption)).
% 4.68/4.85 tff(2567,plain,
% 4.68/4.85 (((~![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)) | 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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2568,plain,
% 4.68/4.85 (((~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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2569,plain,
% 4.68/4.85 (((~![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)) | 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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2568])).
% 4.68/4.85 tff(2570,plain,
% 4.68/4.85 (((~![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)) | 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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2569, 2567])).
% 4.68/4.85 tff(2571,plain,
% 4.68/4.85 ((~![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)) | 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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2572,plain,
% 4.68/4.85 ((~![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)) | 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))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2571, 2570])).
% 4.68/4.85 tff(2573,plain,
% 4.68/4.85 (c1_1(a1656)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2572, 197, 1952, 2140, 2201, 1213, 2182, 2200, 380, 1204, 2566])).
% 4.68/4.85 tff(2574,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2575,plain,
% 4.68/4.85 ((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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2576,plain,
% 4.68/4.85 (((~![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))))),
% 4.68/4.85 inference(monotonicity,[status(thm)],[2575])).
% 4.68/4.85 tff(2577,plain,
% 4.68/4.85 (((~![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)))),
% 4.68/4.85 inference(transitivity,[status(thm)],[2576, 2574])).
% 4.68/4.85 tff(2578,plain,
% 4.68/4.85 ((~![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)))),
% 4.68/4.85 inference(quant_inst,[status(thm)],[])).
% 4.68/4.85 tff(2579,plain,
% 4.68/4.85 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1656) | (~ndr1_0) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674))),
% 4.68/4.85 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 4.68/4.85 tff(2580,plain,
% 4.68/4.85 ($false),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2579, 1918, 197, 2140, 2202, 2138, 2182, 2200, 398, 2573])).
% 4.68/4.85 tff(2581,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,[]))).
% 4.68/4.85 tff(2582,plain,
% 4.68/4.85 (~hskp53),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[2581, 2566, 2140, 2138, 2182, 1213, 1204, 1918])).
% 4.68/4.85 tff(2583,plain,
% 4.68/4.85 (hskp52),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[135, 126, 2582])).
% 4.68/4.85 tff(2584,plain,
% 4.68/4.85 (c0_1(a1654)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[480, 2583])).
% 4.68/4.85 tff(2585,plain,
% 4.68/4.85 (hskp52),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[135, 2582, 126])).
% 4.68/4.85 tff(2586,plain,
% 4.68/4.85 (hskp74),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[960, 2585, 954])).
% 4.68/4.85 tff(2587,plain,
% 4.68/4.85 (~c3_1(a1717)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[977, 2586])).
% 4.68/4.85 tff(2588,plain,
% 4.68/4.85 (c0_1(a1717)),
% 4.68/4.85 inference(unit_resolution,[status(thm)],[993, 2586])).
% 4.68/4.85 tff(2589,plain,
% 4.68/4.85 (((~![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)) | 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)))),
% 4.68/4.85 inference(rewrite,[status(thm)],[])).
% 4.68/4.85 tff(2590,plain,
% 4.68/4.85 (((~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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2591,plain,
% 4.68/4.86 (((~![W: $i, 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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2590])).
% 4.68/4.86 tff(2592,plain,
% 4.68/4.86 (((~![W: $i, 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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2591, 2589])).
% 4.68/4.86 tff(2593,plain,
% 4.68/4.86 ((~![W: $i, 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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2594,plain,
% 4.68/4.86 ((~![W: $i, 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))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 4.68/4.86 tff(2595,plain,
% 4.68/4.86 (c1_1(a1717)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2594, 197, 2588, 1952, 2140, 2587, 1213, 2182, 380, 1204, 2566])).
% 4.68/4.86 tff(2596,plain,
% 4.68/4.86 (c2_1(a1717)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[985, 2586])).
% 4.68/4.86 tff(2597,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2598,plain,
% 4.68/4.86 ((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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2599,plain,
% 4.68/4.86 (((~![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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2598])).
% 4.68/4.86 tff(2600,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2599, 2597])).
% 4.68/4.86 tff(2601,plain,
% 4.68/4.86 ((~![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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2602,plain,
% 4.68/4.86 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c3_1(a1717) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | (~c2_1(a1717)) | (~c1_1(a1717))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 4.68/4.86 tff(2603,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2602, 1918, 197, 2596, 2140, 2587, 2138, 2182, 398, 2595])).
% 4.68/4.86 tff(2604,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,[]))).
% 4.68/4.86 tff(2605,plain,
% 4.68/4.86 (hskp38),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2604, 126, 2140, 2138, 2182, 1213, 1204, 1918, 2566])).
% 4.68/4.86 tff(2606,plain,
% 4.68/4.86 (~c0_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2418, 2605])).
% 4.68/4.86 tff(2607,plain,
% 4.68/4.86 (~c2_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[901, 2605])).
% 4.68/4.86 tff(2608,plain,
% 4.68/4.86 (c2_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[496, 2583])).
% 4.68/4.86 tff(2609,plain,
% 4.68/4.86 (c3_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[909, 2605])).
% 4.68/4.86 tff(2610,plain,
% 4.68/4.86 (c3_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[488, 2583])).
% 4.68/4.86 tff(2611,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2612,plain,
% 4.68/4.86 (((~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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2613,plain,
% 4.68/4.86 (((~![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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2612])).
% 4.68/4.86 tff(2614,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2613, 2611])).
% 4.68/4.86 tff(2615,plain,
% 4.68/4.86 ((~![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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2616,plain,
% 4.68/4.86 ((~![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))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 4.68/4.86 tff(2617,plain,
% 4.68/4.86 ((~c0_1(a1674)) | (~c1_1(a1654))),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2616, 197, 2140, 560, 558, 2138, 2182, 590])).
% 4.68/4.86 tff(2618,plain,
% 4.68/4.86 (~c1_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2617, 2566])).
% 4.68/4.86 tff(2619,assumption,(~c2_1(a1718)), introduced(assumption)).
% 4.68/4.86 tff(2620,plain,
% 4.68/4.86 (((~![W: $i, 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))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2621,plain,
% 4.68/4.86 (((~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))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2622,plain,
% 4.68/4.86 (((~![W: $i, 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)))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2621])).
% 4.68/4.86 tff(2623,plain,
% 4.68/4.86 (((~![W: $i, 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))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2622, 2620])).
% 4.68/4.86 tff(2624,plain,
% 4.68/4.86 ((~![W: $i, 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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2625,plain,
% 4.68/4.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1674) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c3_1(a1674)) | (~c0_1(a1674)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2624, 2623])).
% 4.68/4.86 tff(2626,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2625, 197, 2140, 559, 558, 2430, 2182, 2619, 2429, 346, 2566, 2618])).
% 4.68/4.86 tff(2627,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,[]))).
% 4.68/4.86 tff(2628,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2627, 2610, 2609, 2140, 2566, 2608, 2182, 2607, 2606, 2584, 2138])).
% 4.68/4.86 tff(2629,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,[]))).
% 4.68/4.86 tff(2630,plain,
% 4.68/4.86 (hskp29),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2629, 2535, 2565, 2533, 2534, 1213, 1204, 1918])).
% 4.68/4.86 tff(2631,plain,
% 4.68/4.86 (~c3_1(a1695)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1925, 2630])).
% 4.68/4.86 tff(2632,plain,
% 4.68/4.86 (c0_1(a1695)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1933, 2630])).
% 4.68/4.86 tff(2633,plain,
% 4.68/4.86 (((~![W: $i, 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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2634,plain,
% 4.68/4.86 (((~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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2635,plain,
% 4.68/4.86 (((~![W: $i, 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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2634])).
% 4.68/4.86 tff(2636,plain,
% 4.68/4.86 (((~![W: $i, 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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2635, 2633])).
% 4.68/4.86 tff(2637,plain,
% 4.68/4.86 ((~![W: $i, 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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2638,plain,
% 4.68/4.86 ((~![W: $i, 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))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 4.68/4.86 tff(2639,plain,
% 4.68/4.86 (c1_1(a1695)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2638, 197, 1952, 2535, 2632, 1213, 2533, 2631, 380, 1204, 2565])).
% 4.68/4.86 tff(2640,plain,
% 4.68/4.86 (c2_1(a1695)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1941, 2630])).
% 4.68/4.86 tff(2641,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2642,plain,
% 4.68/4.86 ((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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2643,plain,
% 4.68/4.86 (((~![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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2642])).
% 4.68/4.86 tff(2644,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2643, 2641])).
% 4.68/4.86 tff(2645,plain,
% 4.68/4.86 ((~![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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2646,plain,
% 4.68/4.86 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1674))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 4.68/4.86 tff(2647,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2646, 1918, 197, 2535, 2640, 2534, 2533, 2631, 398, 2639])).
% 4.68/4.86 tff(2648,plain,((~hskp0) | hskp75 | c2_1(a1715) | c0_1(a1715) | hskp73 | (~c2_1(a1716)) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.86 tff(2649,plain,
% 4.68/4.86 (~hskp0),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2648, 1918, 1213, 1204, 1960, 1540, 1539])).
% 4.68/4.86 tff(2650,plain,
% 4.68/4.86 (hskp62),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2076, 1157, 1952, 771])).
% 4.68/4.86 tff(2651,plain,
% 4.68/4.86 (c0_1(a1675)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2084, 2650])).
% 4.68/4.86 tff(2652,plain,
% 4.68/4.86 (c1_1(a1675)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2092, 2650])).
% 4.68/4.86 tff(2653,plain,
% 4.68/4.86 (~c3_1(a1675)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2098, 2650])).
% 4.68/4.86 tff(2654,plain,
% 4.68/4.86 (c2_1(a1675)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2111, 2653, 2652, 2651, 1157])).
% 4.68/4.86 tff(2655,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2656,plain,
% 4.68/4.86 ((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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2657,plain,
% 4.68/4.86 (((~![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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2656])).
% 4.68/4.86 tff(2658,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2657, 2655])).
% 4.68/4.86 tff(2659,plain,
% 4.68/4.86 ((~![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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2660,plain,
% 4.68/4.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 4.68/4.86 tff(2661,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2660, 197, 894, 771, 1952, 2652, 2651, 1213, 881, 2654])).
% 4.68/4.86 tff(2662,plain,(hskp61 | hskp0 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.86 tff(2663,plain,
% 4.68/4.86 (hskp61),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2662, 894, 2467, 1213, 1204])).
% 4.68/4.86 tff(2664,plain,
% 4.68/4.86 (~c2_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1100, 2663])).
% 4.68/4.86 tff(2665,plain,
% 4.68/4.86 (~c1_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1106, 2663])).
% 4.68/4.86 tff(2666,plain,
% 4.68/4.86 (c3_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1114, 2663])).
% 4.68/4.86 tff(2667,plain,
% 4.68/4.86 (~c1_1(a1716)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2541, 1918, 197, 1540, 2666, 1539, 2665, 2664, 398])).
% 4.68/4.86 tff(2668,plain,
% 4.68/4.86 (~hskp29),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2410, 894, 995])).
% 4.68/4.86 tff(2669,plain,
% 4.68/4.86 (~hskp53),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2461, 894, 995])).
% 4.68/4.86 tff(2670,plain,
% 4.68/4.86 (hskp52),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[135, 2669, 2668])).
% 4.68/4.86 tff(2671,plain,
% 4.68/4.86 (c0_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[480, 2670])).
% 4.68/4.86 tff(2672,plain,
% 4.68/4.86 (hskp38),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[960, 2670, 2412])).
% 4.68/4.86 tff(2673,plain,
% 4.68/4.86 (~c0_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2418, 2672])).
% 4.68/4.86 tff(2674,plain,
% 4.68/4.86 (~c2_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[901, 2672])).
% 4.68/4.86 tff(2675,plain,
% 4.68/4.86 (c3_1(a1718)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[909, 2672])).
% 4.68/4.86 tff(2676,plain,
% 4.68/4.86 (c3_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[488, 2670])).
% 4.68/4.86 tff(2677,plain,
% 4.68/4.86 (c2_1(a1654)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[496, 2670])).
% 4.68/4.86 tff(2678,plain,
% 4.68/4.86 (~c0_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2627, 2666, 2677, 2676, 2675, 2664, 2674, 2673, 2671, 2665])).
% 4.68/4.86 tff(2679,plain,
% 4.68/4.86 (hskp60),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2551, 2678, 1540, 2666, 1539, 2665, 2667])).
% 4.68/4.86 tff(2680,plain,
% 4.68/4.86 (~c1_1(a1673)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[369, 2679])).
% 4.68/4.86 tff(2681,plain,
% 4.68/4.86 (c3_1(a1673)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[427, 2679])).
% 4.68/4.86 tff(2682,plain,
% 4.68/4.86 (c2_1(a1673)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[419, 2679])).
% 4.68/4.86 tff(2683,plain,
% 4.68/4.86 ($false),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2464, 2682, 2681, 995, 1539, 894, 1960, 2668, 2667, 2680, 1540])).
% 4.68/4.86 tff(2684,plain,(hskp0 | hskp42 | c3_1(a1716) | hskp73 | (~c2_1(a1716)) | hskp75 | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.68/4.86 tff(2685,plain,
% 4.68/4.86 (hskp42),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2684, 2649, 1539, 1960, 1540, 1918, 1213, 1204])).
% 4.68/4.86 tff(2686,plain,
% 4.68/4.86 (~c3_1(a1638)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1009, 2685])).
% 4.68/4.86 tff(2687,plain,
% 4.68/4.86 (hskp61),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2662, 2649, 2467, 1213, 1204])).
% 4.68/4.86 tff(2688,plain,
% 4.68/4.86 (~c2_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1100, 2687])).
% 4.68/4.86 tff(2689,plain,
% 4.68/4.86 (~c1_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1106, 2687])).
% 4.68/4.86 tff(2690,plain,
% 4.68/4.86 (c1_1(a1638)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1025, 2685])).
% 4.68/4.86 tff(2691,plain,
% 4.68/4.86 (c3_1(a1674)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1114, 2687])).
% 4.68/4.86 tff(2692,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2693,plain,
% 4.68/4.86 ((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)))),
% 4.68/4.86 inference(rewrite,[status(thm)],[])).
% 4.68/4.86 tff(2694,plain,
% 4.68/4.86 (((~![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))))),
% 4.68/4.86 inference(monotonicity,[status(thm)],[2693])).
% 4.68/4.86 tff(2695,plain,
% 4.68/4.86 (((~![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)))),
% 4.68/4.86 inference(transitivity,[status(thm)],[2694, 2692])).
% 4.68/4.86 tff(2696,plain,
% 4.68/4.86 ((~![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)))),
% 4.68/4.86 inference(quant_inst,[status(thm)],[])).
% 4.68/4.86 tff(2697,plain,
% 4.68/4.86 ((~![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))),
% 4.68/4.86 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 4.68/4.86 tff(2698,plain,
% 4.68/4.86 (~c2_1(a1638)),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[2697, 1918, 197, 2691, 2690, 2689, 2688, 2686, 398])).
% 4.68/4.86 tff(2699,plain,
% 4.68/4.86 (~hskp21),
% 4.68/4.86 inference(unit_resolution,[status(thm)],[1968, 2467, 1960, 1952, 1204])).
% 4.70/4.86 tff(2700,plain,
% 4.70/4.86 (((~![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)))),
% 4.70/4.86 inference(rewrite,[status(thm)],[])).
% 4.70/4.86 tff(2701,plain,
% 4.70/4.86 ((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)))),
% 4.70/4.86 inference(rewrite,[status(thm)],[])).
% 4.70/4.86 tff(2702,plain,
% 4.70/4.86 (((~![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))))),
% 4.70/4.86 inference(monotonicity,[status(thm)],[2701])).
% 4.70/4.86 tff(2703,plain,
% 4.70/4.86 (((~![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)))),
% 4.70/4.86 inference(transitivity,[status(thm)],[2702, 2700])).
% 4.70/4.86 tff(2704,plain,
% 4.70/4.86 ((~![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)))),
% 4.70/4.86 inference(quant_inst,[status(thm)],[])).
% 4.70/4.86 tff(2705,plain,
% 4.70/4.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c3_1(a1638) | (~ndr1_0) | c0_1(a1715) | (~c1_1(a1715)) | c2_1(a1638) | (~c1_1(a1638))),
% 4.70/4.86 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 4.70/4.86 tff(2706,plain,
% 4.70/4.86 ($false),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[2705, 197, 2699, 2467, 2690, 1213, 2686, 1261, 1204, 2698])).
% 4.70/4.86 tff(2707,plain,(hskp75 | c2_1(a1715) | c0_1(a1715) | c3_1(a1716) | hskp73 | (~c2_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.86 tff(2708,plain,
% 4.70/4.86 (hskp75),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[2707, 1954, 1204, 1539, 1213, 2307])).
% 4.70/4.86 tff(2709,plain,
% 4.70/4.86 (~c2_1(a1724)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[411, 2708])).
% 4.70/4.86 tff(2710,plain,
% 4.70/4.86 (c3_1(a1724)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[435, 2708])).
% 4.70/4.86 tff(2711,plain,
% 4.70/4.86 (c0_1(a1724)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[443, 2708])).
% 4.70/4.86 tff(2712,assumption,(hskp60), introduced(assumption)).
% 4.70/4.86 tff(2713,plain,
% 4.70/4.86 (~c1_1(a1673)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[369, 2712])).
% 4.70/4.86 tff(2714,plain,
% 4.70/4.86 (c2_1(a1673)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[419, 2712])).
% 4.70/4.86 tff(2715,plain,
% 4.70/4.86 (c3_1(a1673)),
% 4.70/4.86 inference(unit_resolution,[status(thm)],[427, 2712])).
% 4.70/4.86 tff(2716,plain,
% 4.70/4.86 (((~![W: $i, 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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2717,plain,
% 4.70/4.87 (((~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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2718,plain,
% 4.70/4.87 (((~![W: $i, 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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2717])).
% 4.70/4.87 tff(2719,plain,
% 4.70/4.87 (((~![W: $i, 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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2718, 2716])).
% 4.70/4.87 tff(2720,plain,
% 4.70/4.87 ((~![W: $i, 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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2721,plain,
% 4.70/4.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1673) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 4.70/4.87 tff(2722,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2721, 197, 2137, 2142, 1952, 2715, 2714, 2153, 1213, 2713, 346, 1204])).
% 4.70/4.87 tff(2723,plain,((~hskp60) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.87 tff(2724,plain,
% 4.70/4.87 (~hskp60),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2723, 2711, 2710, 2709, 1213, 1204])).
% 4.70/4.87 tff(2725,assumption,(c1_1(a1716)), introduced(assumption)).
% 4.70/4.87 tff(2726,plain,
% 4.70/4.87 (((~![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))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2727,plain,
% 4.70/4.87 (((~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))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2728,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2727])).
% 4.70/4.87 tff(2729,plain,
% 4.70/4.87 (((~![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))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2728, 2726])).
% 4.70/4.87 tff(2730,plain,
% 4.70/4.87 ((~![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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2731,plain,
% 4.70/4.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 4.70/4.87 tff(2732,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2731, 197, 2137, 2142, 1540, 335, 1959, 1539, 90, 1204, 2143, 2725])).
% 4.70/4.87 tff(2733,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,[]))).
% 4.70/4.87 tff(2734,plain,
% 4.70/4.87 (c1_1(a1724)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2733, 2725, 2142, 1540, 335, 1959, 1539, 1204, 2137])).
% 4.70/4.87 tff(2735,plain,
% 4.70/4.87 (hskp13),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2160, 2734])).
% 4.70/4.87 tff(2736,plain,
% 4.70/4.87 (~c1_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[279, 2735])).
% 4.70/4.87 tff(2737,plain,
% 4.70/4.87 (c3_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[287, 2735])).
% 4.70/4.87 tff(2738,plain,
% 4.70/4.87 (c0_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[295, 2735])).
% 4.70/4.87 tff(2739,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2740,plain,
% 4.70/4.87 (((~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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2741,plain,
% 4.70/4.87 (((~![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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2740])).
% 4.70/4.87 tff(2742,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2741, 2739])).
% 4.70/4.87 tff(2743,plain,
% 4.70/4.87 ((~![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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2744,plain,
% 4.70/4.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1716) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 4.70/4.87 tff(2745,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2744, 197, 1540, 335, 1959, 2738, 2737, 1539, 2736, 90, 1204, 2725])).
% 4.70/4.87 tff(2746,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,[]))).
% 4.70/4.87 tff(2747,plain,
% 4.70/4.87 (~c1_1(a1716)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2746, 335, 1540, 1959, 1539, 1204, 2137, 2142, 2153])).
% 4.70/4.87 tff(2748,plain,
% 4.70/4.87 (hskp60 | c1_1(a1715) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2321, 197, 1959, 1539, 356, 1204])).
% 4.70/4.87 tff(2749,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2748, 2747, 335, 1540, 2543])).
% 4.70/4.87 tff(2750,plain,(c1_1(a1715) | (~c2_1(a1716)) | hskp60 | (~c3_1(a1715)) | c3_1(a1716) | c0_1(a1715) | (~c0_1(a1724)) | (~c3_1(a1724)) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.87 tff(2751,plain,
% 4.70/4.87 (c1_1(a1715)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2750, 2307, 2724, 1952, 1539, 1204, 2711, 2710, 2709])).
% 4.70/4.87 tff(2752,plain,
% 4.70/4.87 (hskp0),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2662, 771, 1157, 1213, 1204])).
% 4.70/4.87 tff(2753,plain,
% 4.70/4.87 (~c2_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1085, 2752])).
% 4.70/4.87 tff(2754,plain,
% 4.70/4.87 (c1_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1131, 2752])).
% 4.70/4.87 tff(2755,plain,
% 4.70/4.87 (c0_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1093, 2752])).
% 4.70/4.87 tff(2756,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2531, 2755, 2754, 1157, 2753, 771, 1952, 1213])).
% 4.70/4.87 tff(2757,plain,((~c1_1(a1715)) | hskp61 | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.87 tff(2758,plain,
% 4.70/4.87 (hskp61),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2757, 2751, 1213, 1204])).
% 4.70/4.87 tff(2759,plain,
% 4.70/4.87 (~c2_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1100, 2758])).
% 4.70/4.87 tff(2760,plain,
% 4.70/4.87 (~c1_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1106, 2758])).
% 4.70/4.87 tff(2761,plain,
% 4.70/4.87 (c3_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1114, 2758])).
% 4.70/4.87 tff(2762,assumption,(c1_1(a1724)), introduced(assumption)).
% 4.70/4.87 tff(2763,plain,
% 4.70/4.87 ((~c0_1(a1674)) | (~c1_1(a1724))),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2179, 197, 2137, 2142, 2140, 2138, 2182, 590])).
% 4.70/4.87 tff(2764,plain,
% 4.70/4.87 (~c0_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2763, 2762])).
% 4.70/4.87 tff(2765,plain,
% 4.70/4.87 (c1_1(a1716)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2551, 2764, 1540, 2543, 1539, 2138, 2140])).
% 4.70/4.87 tff(2766,plain,
% 4.70/4.87 (hskp13),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2160, 2762])).
% 4.70/4.87 tff(2767,plain,
% 4.70/4.87 (~c1_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[279, 2766])).
% 4.70/4.87 tff(2768,plain,
% 4.70/4.87 (c3_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[287, 2766])).
% 4.70/4.87 tff(2769,plain,
% 4.70/4.87 (c0_1(a1667)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[295, 2766])).
% 4.70/4.87 tff(2770,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2771,plain,
% 4.70/4.87 (((~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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2772,plain,
% 4.70/4.87 (((~![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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2771])).
% 4.70/4.87 tff(2773,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2772, 2770])).
% 4.70/4.87 tff(2774,plain,
% 4.70/4.87 ((~![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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2775,plain,
% 4.70/4.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1716) | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 4.70/4.87 tff(2776,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2775, 197, 1540, 2140, 2769, 2768, 1539, 2138, 2767, 90, 2764, 2765])).
% 4.70/4.87 tff(2777,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,[]))).
% 4.70/4.87 tff(2778,plain,
% 4.70/4.87 (~c1_1(a1724)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2777, 2307, 2761, 1539, 2760, 2724, 2711, 2710, 2759, 2709])).
% 4.70/4.87 tff(2779,plain,
% 4.70/4.87 (~hskp21),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1968, 2751, 1954, 1952, 1204])).
% 4.70/4.87 tff(2780,plain,
% 4.70/4.87 (hskp61),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2757, 771, 1213, 1204])).
% 4.70/4.87 tff(2781,plain,
% 4.70/4.87 (~c2_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1100, 2780])).
% 4.70/4.87 tff(2782,plain,
% 4.70/4.87 (~c1_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1106, 2780])).
% 4.70/4.87 tff(2783,plain,
% 4.70/4.87 (c3_1(a1674)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1114, 2780])).
% 4.70/4.87 tff(2784,plain,
% 4.70/4.87 (~hskp52),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2197, 2143, 2142, 2153, 1213, 1204, 2137, 2782, 2783, 2781])).
% 4.70/4.87 tff(2785,plain,
% 4.70/4.87 (hskp53),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[135, 2784, 126])).
% 4.70/4.87 tff(2786,plain,
% 4.70/4.87 (~c3_1(a1656)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[149, 2785])).
% 4.70/4.87 tff(2787,plain,
% 4.70/4.87 (c0_1(a1656)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[143, 2785])).
% 4.70/4.87 tff(2788,plain,
% 4.70/4.87 (((~![W: $i, 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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2789,plain,
% 4.70/4.87 (((~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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2790,plain,
% 4.70/4.87 (((~![W: $i, 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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2789])).
% 4.70/4.87 tff(2791,plain,
% 4.70/4.87 (((~![W: $i, 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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2790, 2788])).
% 4.70/4.87 tff(2792,plain,
% 4.70/4.87 ((~![W: $i, 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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2793,plain,
% 4.70/4.87 ((~![W: $i, 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))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 4.70/4.87 tff(2794,plain,
% 4.70/4.87 (c1_1(a1656)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2793, 197, 2137, 2142, 1952, 2787, 2153, 1213, 2786, 380, 1204])).
% 4.70/4.87 tff(2795,plain,
% 4.70/4.87 (c2_1(a1656)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[157, 2785])).
% 4.70/4.87 tff(2796,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2797,plain,
% 4.70/4.87 ((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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2798,plain,
% 4.70/4.87 (((~![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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2797])).
% 4.70/4.87 tff(2799,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2798, 2796])).
% 4.70/4.87 tff(2800,plain,
% 4.70/4.87 ((~![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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2801,plain,
% 4.70/4.87 ((~![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))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 4.70/4.87 tff(2802,plain,
% 4.70/4.87 (hskp0),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2801, 197, 771, 1952, 2795, 2787, 1213, 881, 2794])).
% 4.70/4.87 tff(2803,plain,
% 4.70/4.87 (c0_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1093, 2802])).
% 4.70/4.87 tff(2804,plain,
% 4.70/4.87 (c1_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1131, 2802])).
% 4.70/4.87 tff(2805,plain,
% 4.70/4.87 (((~![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))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2806,plain,
% 4.70/4.87 (((~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))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2807,plain,
% 4.70/4.87 (((~![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)))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2806])).
% 4.70/4.87 tff(2808,plain,
% 4.70/4.87 (((~![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))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2807, 2805])).
% 4.70/4.87 tff(2809,plain,
% 4.70/4.87 ((~![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)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2810,plain,
% 4.70/4.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1724) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c3_1(a1674)) | (~c0_1(a1724)) | c1_1(a1724)),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 4.70/4.87 tff(2811,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2810, 197, 2137, 2140, 1136, 1135, 2153, 2138, 2182, 590, 1133, 2143])).
% 4.70/4.87 tff(2812,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,[]))).
% 4.70/4.87 tff(2813,plain,
% 4.70/4.87 (~c3_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2812, 2804, 2783, 2137, 2803, 2153, 2782, 2781, 2143])).
% 4.70/4.87 tff(2814,plain,
% 4.70/4.87 (~c2_1(a1637)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1085, 2802])).
% 4.70/4.87 tff(2815,plain,
% 4.70/4.87 (((~![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(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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2816,plain,
% 4.70/4.87 ((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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2817,plain,
% 4.70/4.87 (((~![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(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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2816])).
% 4.70/4.87 tff(2818,plain,
% 4.70/4.87 (((~![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(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)))),
% 4.70/4.87 inference(transitivity,[status(thm)],[2817, 2815])).
% 4.70/4.87 tff(2819,plain,
% 4.70/4.87 ((~![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(a1637) | c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | c2_1(a1715) | (~c1_1(a1715)))),
% 4.70/4.87 inference(quant_inst,[status(thm)],[])).
% 4.70/4.87 tff(2820,plain,
% 4.70/4.87 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | c0_1(a1715) | (~c1_1(a1715))),
% 4.70/4.87 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 4.70/4.87 tff(2821,plain,
% 4.70/4.87 ($false),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2820, 197, 1249, 771, 2804, 1213, 2814, 1261, 2813, 1204])).
% 4.70/4.87 tff(2822,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,[]))).
% 4.70/4.87 tff(2823,plain,
% 4.70/4.87 (hskp29),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[2822, 2778, 2751, 1213, 1204, 2711, 2709, 2710, 2779])).
% 4.70/4.87 tff(2824,plain,
% 4.70/4.87 (~c3_1(a1695)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1925, 2823])).
% 4.70/4.87 tff(2825,plain,
% 4.70/4.87 (c0_1(a1695)),
% 4.70/4.87 inference(unit_resolution,[status(thm)],[1933, 2823])).
% 4.70/4.87 tff(2826,plain,
% 4.70/4.87 (((~![W: $i, 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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2827,plain,
% 4.70/4.87 (((~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)))),
% 4.70/4.87 inference(rewrite,[status(thm)],[])).
% 4.70/4.87 tff(2828,plain,
% 4.70/4.87 (((~![W: $i, 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))))),
% 4.70/4.87 inference(monotonicity,[status(thm)],[2827])).
% 4.70/4.87 tff(2829,plain,
% 4.70/4.87 (((~![W: $i, 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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2828, 2826])).
% 4.70/4.88 tff(2830,plain,
% 4.70/4.88 ((~![W: $i, 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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2831,plain,
% 4.70/4.88 ((~![W: $i, 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))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2830, 2829])).
% 4.70/4.88 tff(2832,plain,
% 4.70/4.88 (c1_1(a1695)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2831, 197, 2711, 2710, 1952, 2825, 2709, 1213, 2824, 380, 1204])).
% 4.70/4.88 tff(2833,plain,
% 4.70/4.88 (c2_1(a1695)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1941, 2823])).
% 4.70/4.88 tff(2834,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2835,plain,
% 4.70/4.88 ((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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2836,plain,
% 4.70/4.88 (((~![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))))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2835])).
% 4.70/4.88 tff(2837,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2836, 2834])).
% 4.70/4.88 tff(2838,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2839,plain,
% 4.70/4.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c0_1(a1695)) | (~c3_1(a1715)) | (~c1_1(a1715))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 4.70/4.88 tff(2840,plain,
% 4.70/4.88 (hskp0),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2839, 197, 2751, 1952, 2833, 2825, 1213, 881, 2832])).
% 4.70/4.88 tff(2841,plain,
% 4.70/4.88 (c0_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1093, 2840])).
% 4.70/4.88 tff(2842,plain,
% 4.70/4.88 (c1_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1131, 2840])).
% 4.70/4.88 tff(2843,plain,
% 4.70/4.88 (~c3_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2812, 2842, 2761, 2711, 2841, 2709, 2760, 2759, 2778])).
% 4.70/4.88 tff(2844,plain,
% 4.70/4.88 (~c2_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1085, 2840])).
% 4.70/4.88 tff(2845,plain,
% 4.70/4.88 ($false),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2820, 197, 2779, 2751, 2842, 1213, 2844, 1261, 2843, 1204])).
% 4.70/4.88 tff(2846,plain,(c0_1(a1716) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.88 tff(2847,plain,
% 4.70/4.88 (c0_1(a1716)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2846, 1539, 1204, 1213])).
% 4.70/4.88 tff(2848,plain,
% 4.70/4.88 (~hskp74),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1003, 995, 894])).
% 4.70/4.88 tff(2849,plain,
% 4.70/4.88 (hskp52),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[135, 2462, 126])).
% 4.70/4.88 tff(2850,plain,
% 4.70/4.88 (hskp38),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[960, 2849, 2848])).
% 4.70/4.88 tff(2851,plain,
% 4.70/4.88 (~c0_1(a1718)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2418, 2850])).
% 4.70/4.88 tff(2852,plain,
% 4.70/4.88 (c3_1(a1718)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[909, 2850])).
% 4.70/4.88 tff(2853,plain,
% 4.70/4.88 (c3_1(a1654)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[488, 2849])).
% 4.70/4.88 tff(2854,plain,
% 4.70/4.88 (c0_1(a1654)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[480, 2849])).
% 4.70/4.88 tff(2855,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2856,plain,
% 4.70/4.88 (((~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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2857,plain,
% 4.70/4.88 (((~![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))))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2856])).
% 4.70/4.88 tff(2858,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2857, 2855])).
% 4.70/4.88 tff(2859,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2860,plain,
% 4.70/4.88 ((~![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))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2859, 2858])).
% 4.70/4.88 tff(2861,plain,
% 4.70/4.88 (~c1_1(a1654)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2860, 197, 1919, 1554, 335, 1959, 2854, 2853, 1213, 590, 1494])).
% 4.70/4.88 tff(2862,plain,
% 4.70/4.88 (c1_1(a1718)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2438, 2861, 2854, 2853, 2852, 2851, 126])).
% 4.70/4.88 tff(2863,plain,
% 4.70/4.88 (c2_1(a1654)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[496, 2849])).
% 4.70/4.88 tff(2864,plain,
% 4.70/4.88 (~hskp73),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1477, 1919])).
% 4.70/4.88 tff(2865,plain,
% 4.70/4.88 (((~![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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2866,plain,
% 4.70/4.88 ((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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2867,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2866])).
% 4.70/4.88 tff(2868,plain,
% 4.70/4.88 (((~![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))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2867, 2865])).
% 4.70/4.88 tff(2869,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2870,plain,
% 4.70/4.88 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1718)) | (~c1_1(a1718)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 4.70/4.88 tff(2871,plain,
% 4.70/4.88 ($false),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2870, 197, 2864, 2863, 2853, 2852, 2851, 1449, 2861, 2862])).
% 4.70/4.88 tff(2872,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,[]))).
% 4.70/4.88 tff(2873,plain,
% 4.70/4.88 (hskp42),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2872, 126, 1919, 2847, 335, 1952, 1213, 1494, 894])).
% 4.70/4.88 tff(2874,plain,
% 4.70/4.88 (~c3_1(a1638)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1009, 2873])).
% 4.70/4.88 tff(2875,plain,
% 4.70/4.88 (c0_1(a1638)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1017, 2873])).
% 4.70/4.88 tff(2876,plain,
% 4.70/4.88 (((~![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) | 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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2877,plain,
% 4.70/4.88 (((~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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2878,plain,
% 4.70/4.88 (((~![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(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)))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2877])).
% 4.70/4.88 tff(2879,plain,
% 4.70/4.88 (((~![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(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))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2878, 2876])).
% 4.70/4.88 tff(2880,plain,
% 4.70/4.88 ((~![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(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))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2881,plain,
% 4.70/4.88 ((~![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) | 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)),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 4.70/4.88 tff(2882,plain,
% 4.70/4.88 (~c2_1(a1638)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2881, 197, 1919, 335, 2875, 1539, 1213, 2874, 30, 1204, 1494])).
% 4.70/4.88 tff(2883,plain,
% 4.70/4.88 (c1_1(a1638)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1025, 2873])).
% 4.70/4.88 tff(2884,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2885,plain,
% 4.70/4.88 ((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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2886,plain,
% 4.70/4.88 (((~![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))))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2885])).
% 4.70/4.88 tff(2887,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2886, 2884])).
% 4.70/4.88 tff(2888,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2889,plain,
% 4.70/4.88 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1638) | (~c1_1(a1638))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 4.70/4.88 tff(2890,plain,
% 4.70/4.88 (hskp69),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2889, 197, 335, 1952, 2883, 2874, 1310, 1204, 2882])).
% 4.70/4.88 tff(2891,plain,
% 4.70/4.88 (~c1_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1329, 2890])).
% 4.70/4.88 tff(2892,plain,
% 4.70/4.88 (c3_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1337, 2890])).
% 4.70/4.88 tff(2893,plain,
% 4.70/4.88 (c0_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1345, 2890])).
% 4.70/4.88 tff(2894,plain,
% 4.70/4.88 ($false),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2287, 197, 126, 335, 1952, 2893, 2892, 2891, 125, 1204])).
% 4.70/4.88 tff(2895,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,[]))).
% 4.70/4.88 tff(2896,plain,
% 4.70/4.88 (hskp0),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2895, 1951, 1204, 1919, 1539, 1213, 1494, 335])).
% 4.70/4.88 tff(2897,plain,
% 4.70/4.88 (~c2_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1085, 2896])).
% 4.70/4.88 tff(2898,plain,
% 4.70/4.88 (c0_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1093, 2896])).
% 4.70/4.88 tff(2899,plain,
% 4.70/4.88 (((~![W: $i, 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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2900,plain,
% 4.70/4.88 (((~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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2901,plain,
% 4.70/4.88 (((~![W: $i, 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))))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2900])).
% 4.70/4.88 tff(2902,plain,
% 4.70/4.88 (((~![W: $i, 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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2901, 2899])).
% 4.70/4.88 tff(2903,plain,
% 4.70/4.88 ((~![W: $i, 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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2904,plain,
% 4.70/4.88 ((~![W: $i, 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))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 4.70/4.88 tff(2905,plain,
% 4.70/4.88 (~c3_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2904, 197, 2847, 1952, 2898, 1539, 1213, 2897, 380, 1204, 1494])).
% 4.70/4.88 tff(2906,plain,
% 4.70/4.88 (c1_1(a1637)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1131, 2896])).
% 4.70/4.88 tff(2907,plain,
% 4.70/4.88 (((~![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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2908,plain,
% 4.70/4.88 ((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))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2909,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2908])).
% 4.70/4.88 tff(2910,plain,
% 4.70/4.88 (((~![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))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2909, 2907])).
% 4.70/4.88 tff(2911,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2912,plain,
% 4.70/4.88 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1715) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1715)) | c0_1(a1715)),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 4.70/4.88 tff(2913,plain,
% 4.70/4.88 (hskp69),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2912, 197, 335, 1952, 2906, 2897, 1310, 2905, 1204])).
% 4.70/4.88 tff(2914,plain,
% 4.70/4.88 (~c1_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1329, 2913])).
% 4.70/4.88 tff(2915,plain,
% 4.70/4.88 (c3_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1337, 2913])).
% 4.70/4.88 tff(2916,plain,
% 4.70/4.88 (c0_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1345, 2913])).
% 4.70/4.88 tff(2917,plain,
% 4.70/4.88 ($false),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2287, 197, 1951, 335, 1952, 2916, 2915, 2914, 125, 1204])).
% 4.70/4.88 tff(2918,plain,(c1_1(a1716) | c1_1(a1715) | c0_1(a1715) | c3_1(a1716) | c2_1(a1715) | c2_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.88 tff(2919,plain,
% 4.70/4.88 (c1_1(a1716)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2918, 1919, 1204, 1539, 1213, 335])).
% 4.70/4.88 tff(2920,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2921,plain,
% 4.70/4.88 ((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)))),
% 4.70/4.88 inference(rewrite,[status(thm)],[])).
% 4.70/4.88 tff(2922,plain,
% 4.70/4.88 (((~![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))))),
% 4.70/4.88 inference(monotonicity,[status(thm)],[2921])).
% 4.70/4.88 tff(2923,plain,
% 4.70/4.88 (((~![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)))),
% 4.70/4.88 inference(transitivity,[status(thm)],[2922, 2920])).
% 4.70/4.88 tff(2924,plain,
% 4.70/4.88 ((~![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)))),
% 4.70/4.88 inference(quant_inst,[status(thm)],[])).
% 4.70/4.88 tff(2925,plain,
% 4.70/4.88 ((~![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))),
% 4.70/4.88 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 4.70/4.88 tff(2926,plain,
% 4.70/4.88 (hskp30 | (~c1_1(a1716))),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2925, 197, 1919, 2847, 335, 1952, 2368, 1204])).
% 4.70/4.88 tff(2927,plain,
% 4.70/4.88 (hskp30),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2926, 2919])).
% 4.70/4.88 tff(2928,plain,
% 4.70/4.88 (~c0_1(a1698)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2332, 2927])).
% 4.70/4.88 tff(2929,plain,
% 4.70/4.88 (hskp69 | c2_1(a1716) | c1_1(a1715) | (~c1_1(a1716))),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2231, 197, 1952, 1539, 1310, 1204])).
% 4.70/4.88 tff(2930,plain,
% 4.70/4.88 (hskp69),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[2929, 2919, 1919, 335])).
% 4.70/4.88 tff(2931,plain,
% 4.70/4.88 (~c1_1(a1709)),
% 4.70/4.88 inference(unit_resolution,[status(thm)],[1329, 2930])).
% 4.70/4.89 tff(2932,plain,
% 4.70/4.89 (c3_1(a1698)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2340, 2927])).
% 4.70/4.89 tff(2933,plain,
% 4.70/4.89 (c1_1(a1698)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2348, 2927])).
% 4.70/4.89 tff(2934,plain,
% 4.70/4.89 (c3_1(a1709)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1337, 2930])).
% 4.70/4.89 tff(2935,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2936,plain,
% 4.70/4.89 ((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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2937,plain,
% 4.70/4.89 (((~![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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2936])).
% 4.70/4.89 tff(2938,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[2937, 2935])).
% 4.70/4.89 tff(2939,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(2940,plain,
% 4.70/4.89 ((~![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))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[2939, 2938])).
% 4.70/4.89 tff(2941,plain,
% 4.70/4.89 (~c2_1(a1709)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2940, 197, 2864, 2934, 2933, 2932, 2931, 2928, 1449])).
% 4.70/4.89 tff(2942,plain,
% 4.70/4.89 (c0_1(a1709)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1345, 2930])).
% 4.70/4.89 tff(2943,plain,
% 4.70/4.89 (hskp29),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2287, 197, 335, 1952, 2942, 2934, 2931, 125, 1204])).
% 4.70/4.89 tff(2944,plain,
% 4.70/4.89 (~c3_1(a1695)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1925, 2943])).
% 4.70/4.89 tff(2945,plain,
% 4.70/4.89 (c0_1(a1695)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1933, 2943])).
% 4.70/4.89 tff(2946,plain,
% 4.70/4.89 (c1_1(a1695)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2296, 197, 1952, 2942, 2934, 2945, 1213, 2944, 380, 1204, 2941])).
% 4.70/4.89 tff(2947,plain,
% 4.70/4.89 (c2_1(a1695)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1941, 2943])).
% 4.70/4.89 tff(2948,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2949,plain,
% 4.70/4.89 ((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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2950,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2949])).
% 4.70/4.89 tff(2951,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(transitivity,[status(thm)],[2950, 2948])).
% 4.70/4.89 tff(2952,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(2953,plain,
% 4.70/4.89 ((~![V: $i, U: $i] : (hskp75 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp75 | c1_1(a1709) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1709)) | c2_1(a1709)),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 4.70/4.89 tff(2954,plain,
% 4.70/4.89 ($false),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2953, 1918, 197, 2934, 2947, 2931, 2944, 398, 2941, 2946])).
% 4.70/4.89 tff(2955,plain,(c2_1(a1716) | hskp75 | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.89 tff(2956,plain,
% 4.70/4.89 (c2_1(a1716)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2955, 335, 1213, 1204, 1918, 1539])).
% 4.70/4.89 tff(2957,plain,
% 4.70/4.89 (~c1_1(a1716)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2314, 2956, 1918, 335])).
% 4.70/4.89 tff(2958,plain,
% 4.70/4.89 (hskp60),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2322, 2956, 335, 2957])).
% 4.70/4.89 tff(2959,plain,
% 4.70/4.89 (~c1_1(a1673)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[369, 2958])).
% 4.70/4.89 tff(2960,plain,
% 4.70/4.89 (c2_1(a1673)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[419, 2958])).
% 4.70/4.89 tff(2961,plain,
% 4.70/4.89 (c3_1(a1673)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[427, 2958])).
% 4.70/4.89 tff(2962,plain,
% 4.70/4.89 (((~![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(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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2963,plain,
% 4.70/4.89 (((~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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2964,plain,
% 4.70/4.89 (((~![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(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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2963])).
% 4.70/4.89 tff(2965,plain,
% 4.70/4.89 (((~![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(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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[2964, 2962])).
% 4.70/4.89 tff(2966,plain,
% 4.70/4.89 ((~![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(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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(2967,plain,
% 4.70/4.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1715) | c1_1(a1673) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1673)) | (~c2_1(a1673))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 4.70/4.89 tff(2968,plain,
% 4.70/4.89 ($false),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2967, 197, 1952, 1583, 1582, 39, 53, 1213, 1574, 45, 346, 1204])).
% 4.70/4.89 tff(2969,plain,((~hskp7) | (~c3_1(a1673)) | (~c2_1(a1673)) | c2_1(a1715) | c1_1(a1673) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.89 tff(2970,plain,
% 4.70/4.89 (~hskp7),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2969, 2961, 2960, 1213, 2959, 1204])).
% 4.70/4.89 tff(2971,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2972,plain,
% 4.70/4.89 ((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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2973,plain,
% 4.70/4.89 (((~![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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2972])).
% 4.70/4.89 tff(2974,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[2973, 2971])).
% 4.70/4.89 tff(2975,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(2976,plain,
% 4.70/4.89 ((~![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))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 4.70/4.89 tff(2977,plain,
% 4.70/4.89 (hskp52 | hskp7 | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2976, 197, 1539, 168])).
% 4.70/4.89 tff(2978,plain,
% 4.70/4.89 (hskp52),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2977, 2970, 2847, 2956])).
% 4.70/4.89 tff(2979,plain,
% 4.70/4.89 (c3_1(a1654)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[488, 2978])).
% 4.70/4.89 tff(2980,plain,
% 4.70/4.89 (c2_1(a1654)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[496, 2978])).
% 4.70/4.89 tff(2981,plain,
% 4.70/4.89 (c0_1(a1654)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[480, 2978])).
% 4.70/4.89 tff(2982,plain,
% 4.70/4.89 (hskp26),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[606, 197, 2961, 2960, 2981, 2980, 2979, 2959, 20])).
% 4.70/4.89 tff(2983,plain,
% 4.70/4.89 (~c2_1(a1691)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[612, 2982])).
% 4.70/4.89 tff(2984,plain,
% 4.70/4.89 (~c3_1(a1691)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[632, 2982])).
% 4.70/4.89 tff(2985,plain,
% 4.70/4.89 (~c1_1(a1691)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[618, 2982])).
% 4.70/4.89 tff(2986,plain,
% 4.70/4.89 (((~![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))) | (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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2987,plain,
% 4.70/4.89 (((~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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2988,plain,
% 4.70/4.89 (((~![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(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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2987])).
% 4.70/4.89 tff(2989,plain,
% 4.70/4.89 (((~![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(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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[2988, 2986])).
% 4.70/4.89 tff(2990,plain,
% 4.70/4.89 ((~![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(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))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(2991,plain,
% 4.70/4.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 4.70/4.89 tff(2992,plain,
% 4.70/4.89 ($false),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2991, 197, 1540, 1554, 1539, 893, 892, 895, 224, 218, 237, 30])).
% 4.70/4.89 tff(2993,plain,((~hskp17) | (~c2_1(a1716)) | (~c0_1(a1716)) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.89 tff(2994,plain,
% 4.70/4.89 (~hskp17),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2993, 2985, 2847, 1539, 2956, 2984, 2983])).
% 4.70/4.89 tff(2995,plain,
% 4.70/4.89 (hskp75 | c1_1(a1715) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2313, 197, 1959, 1539, 1213, 398])).
% 4.70/4.89 tff(2996,plain,
% 4.70/4.89 (~c1_1(a1716)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2995, 1540, 1918, 335])).
% 4.70/4.89 tff(2997,plain,
% 4.70/4.89 (~c2_1(a1638)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[2391, 1918, 197, 335, 1959, 2385, 1213, 2384, 398])).
% 4.70/4.89 tff(2998,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(2999,plain,
% 4.70/4.89 ((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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3000,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[2999])).
% 4.70/4.89 tff(3001,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(transitivity,[status(thm)],[3000, 2998])).
% 4.70/4.89 tff(3002,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(3003,plain,
% 4.70/4.89 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 4.70/4.89 tff(3004,plain,
% 4.70/4.89 ($false),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3003, 197, 1505, 1540, 2393, 1539, 2384, 1504, 2997, 2996])).
% 4.70/4.89 tff(3005,plain,((~hskp42) | hskp57 | (~c2_1(a1716)) | c3_1(a1716) | hskp75 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.89 tff(3006,plain,
% 4.70/4.89 (~hskp42),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3005, 1505, 2956, 1539, 1918, 335, 1952, 1213])).
% 4.70/4.89 tff(3007,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3008,plain,
% 4.70/4.89 ((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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3009,plain,
% 4.70/4.89 (((~![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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[3008])).
% 4.70/4.89 tff(3010,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[3009, 3007])).
% 4.70/4.89 tff(3011,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(3012,plain,
% 4.70/4.89 ((~![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))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 4.70/4.89 tff(3013,plain,
% 4.70/4.89 (hskp42 | hskp0 | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3012, 197, 1539, 971])).
% 4.70/4.89 tff(3014,plain,
% 4.70/4.89 (hskp0),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3013, 3006, 2847, 2956])).
% 4.70/4.89 tff(3015,plain,
% 4.70/4.89 (~c2_1(a1637)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1085, 3014])).
% 4.70/4.89 tff(3016,plain,
% 4.70/4.89 (c0_1(a1637)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[1093, 3014])).
% 4.70/4.89 tff(3017,plain,
% 4.70/4.89 (((~![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(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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3018,plain,
% 4.70/4.89 (((~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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3019,plain,
% 4.70/4.89 (((~![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(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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[3018])).
% 4.70/4.89 tff(3020,plain,
% 4.70/4.89 (((~![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(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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[3019, 3017])).
% 4.70/4.89 tff(3021,plain,
% 4.70/4.89 ((~![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(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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(3022,plain,
% 4.70/4.89 ((~![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(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))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[3021, 3020])).
% 4.70/4.89 tff(3023,plain,
% 4.70/4.89 (~c3_1(a1637)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3022, 197, 1952, 2961, 2960, 3016, 1213, 2959, 3015, 346, 1204])).
% 4.70/4.89 tff(3024,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3025,plain,
% 4.70/4.89 ((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))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3026,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[3025])).
% 4.70/4.89 tff(3027,plain,
% 4.70/4.89 (((~![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))),
% 4.70/4.89 inference(transitivity,[status(thm)],[3026, 3024])).
% 4.70/4.89 tff(3028,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(3029,plain,
% 4.70/4.89 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c0_1(a1637)) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[3028, 3027])).
% 4.70/4.89 tff(3030,plain,
% 4.70/4.89 ($false),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3029, 197, 1505, 2956, 3016, 1539, 3015, 1504, 3023, 2957])).
% 4.70/4.89 tff(3031,plain,(hskp57 | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | hskp75 | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.89 tff(3032,plain,
% 4.70/4.89 (hskp57),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3031, 335, 1213, 1204, 1918, 1539])).
% 4.70/4.89 tff(3033,plain,
% 4.70/4.89 (~c1_1(a1665)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[59, 3032])).
% 4.70/4.89 tff(3034,plain,
% 4.70/4.89 (c3_1(a1665)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[67, 3032])).
% 4.70/4.89 tff(3035,plain,
% 4.70/4.89 (c0_1(a1665)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[78, 3032])).
% 4.70/4.89 tff(3036,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3037,plain,
% 4.70/4.89 ((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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3038,plain,
% 4.70/4.89 (((~![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))))),
% 4.70/4.89 inference(monotonicity,[status(thm)],[3037])).
% 4.70/4.89 tff(3039,plain,
% 4.70/4.89 (((~![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)))),
% 4.70/4.89 inference(transitivity,[status(thm)],[3038, 3036])).
% 4.70/4.89 tff(3040,plain,
% 4.70/4.89 ((~![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)))),
% 4.70/4.89 inference(quant_inst,[status(thm)],[])).
% 4.70/4.89 tff(3041,plain,
% 4.70/4.89 ((~![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))),
% 4.70/4.89 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 4.70/4.89 tff(3042,plain,
% 4.70/4.89 (hskp17 | hskp16),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3041, 197, 3035, 3034, 3033, 10])).
% 4.70/4.89 tff(3043,plain,
% 4.70/4.89 (hskp16),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[3042, 2994])).
% 4.70/4.89 tff(3044,plain,
% 4.70/4.89 (~c1_1(a1677)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[99, 3043])).
% 4.70/4.89 tff(3045,plain,
% 4.70/4.89 (~c2_1(a1677)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[105, 3043])).
% 4.70/4.89 tff(3046,plain,
% 4.70/4.89 (~c0_1(a1677)),
% 4.70/4.89 inference(unit_resolution,[status(thm)],[111, 3043])).
% 4.70/4.89 tff(3047,plain,
% 4.70/4.89 (((~![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))) | (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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3048,plain,
% 4.70/4.89 (((~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)))),
% 4.70/4.89 inference(rewrite,[status(thm)],[])).
% 4.70/4.89 tff(3049,plain,
% 4.70/4.89 (((~![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(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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3048])).
% 4.70/4.90 tff(3050,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3049, 3047])).
% 4.70/4.90 tff(3051,plain,
% 4.70/4.90 ((~![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(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))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3052,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 4.70/4.90 tff(3053,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3052, 197, 2956, 2847, 1539, 2984, 2985, 2983, 3046, 3045, 3044, 30])).
% 4.70/4.90 tff(3054,plain,(c1_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | hskp75), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3055,plain,
% 4.70/4.90 (c1_1(a1715)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3054, 1918, 1213, 1204, 1539])).
% 4.70/4.90 tff(3056,plain,
% 4.70/4.90 (~hskp21),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1968, 2864, 771, 1952, 1204])).
% 4.70/4.90 tff(3057,plain,
% 4.70/4.90 (~c1_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1976, 3056, 771, 1919])).
% 4.70/4.90 tff(3058,plain,
% 4.70/4.90 (((~![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)))) | (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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3059,plain,
% 4.70/4.90 (((~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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3060,plain,
% 4.70/4.90 (((~![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(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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3059])).
% 4.70/4.90 tff(3061,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3060, 3058])).
% 4.70/4.90 tff(3062,plain,
% 4.70/4.90 ((~![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(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)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3063,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1716) | c2_1(a1715) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1674)) | (~c0_1(a1674)) | c1_1(a1716) | (~c0_1(a1716))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 4.70/4.90 tff(3064,plain,
% 4.70/4.90 ((~c0_1(a1674)) | c1_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3063, 197, 2847, 1952, 2783, 1539, 1213, 2781, 380, 1204])).
% 4.70/4.90 tff(3065,plain,
% 4.70/4.90 (~c0_1(a1674)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3064, 3057])).
% 4.70/4.90 tff(3066,plain,
% 4.70/4.90 (~c3_1(a1637)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2904, 197, 2847, 1952, 2371, 1539, 1213, 2370, 380, 1204, 1494])).
% 4.70/4.90 tff(3067,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2820, 197, 1249, 771, 2372, 1213, 2370, 1261, 3066, 1204])).
% 4.70/4.90 tff(3068,plain,((~hskp0) | hskp21 | (~c1_1(a1715)) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3069,plain,
% 4.70/4.90 (~hskp0),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3068, 3056, 771, 1213, 1204, 1539, 3057])).
% 4.70/4.90 tff(3070,plain,
% 4.70/4.90 (hskp38),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[960, 2848, 2849])).
% 4.70/4.90 tff(3071,plain,
% 4.70/4.90 (~c0_1(a1718)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2418, 3070])).
% 4.70/4.90 tff(3072,plain,
% 4.70/4.90 (c3_1(a1718)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[909, 3070])).
% 4.70/4.90 tff(3073,plain,
% 4.70/4.90 (((~![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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3074,plain,
% 4.70/4.90 (((~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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3075,plain,
% 4.70/4.90 (((~![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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3074])).
% 4.70/4.90 tff(3076,plain,
% 4.70/4.90 (((~![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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3075, 3073])).
% 4.70/4.90 tff(3077,plain,
% 4.70/4.90 ((~![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)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3078,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1716) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3077, 3076])).
% 4.70/4.90 tff(3079,plain,
% 4.70/4.90 (~c1_1(a1654)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3078, 197, 1919, 1554, 2140, 2854, 2853, 2138, 2182, 590, 1494])).
% 4.70/4.90 tff(3080,plain,
% 4.70/4.90 (c1_1(a1718)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2438, 3079, 2854, 2853, 3072, 3071, 126])).
% 4.70/4.90 tff(3081,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2870, 197, 2864, 2863, 2853, 3072, 3071, 1449, 3079, 3080])).
% 4.70/4.90 tff(3082,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,[]))).
% 4.70/4.90 tff(3083,plain,
% 4.70/4.90 (hskp42),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3082, 894, 1919, 1554, 2783, 2782, 2781, 1494, 126])).
% 4.70/4.90 tff(3084,plain,
% 4.70/4.90 (c0_1(a1638)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1017, 3083])).
% 4.70/4.90 tff(3085,plain,
% 4.70/4.90 (c1_1(a1638)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1025, 3083])).
% 4.70/4.90 tff(3086,plain,
% 4.70/4.90 (((~![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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3087,plain,
% 4.70/4.90 ((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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3088,plain,
% 4.70/4.90 (((~![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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3087])).
% 4.70/4.90 tff(3089,plain,
% 4.70/4.90 (((~![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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3088, 3086])).
% 4.70/4.90 tff(3090,plain,
% 4.70/4.90 ((~![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)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3091,plain,
% 4.70/4.90 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3090, 3089])).
% 4.70/4.90 tff(3092,plain,
% 4.70/4.90 (~c2_1(a1638)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3091, 197, 894, 771, 1952, 3085, 3084, 1213, 881])).
% 4.70/4.90 tff(3093,plain,
% 4.70/4.90 (~c3_1(a1638)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1009, 3083])).
% 4.70/4.90 tff(3094,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2705, 197, 3056, 771, 3085, 1213, 3093, 1261, 1204, 3092])).
% 4.70/4.90 tff(3095,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,[]))).
% 4.70/4.90 tff(3096,plain,
% 4.70/4.90 (hskp29),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3095, 3069, 1213, 1204, 1919, 2847, 3057, 771])).
% 4.70/4.90 tff(3097,plain,
% 4.70/4.90 (~c3_1(a1695)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1925, 3096])).
% 4.70/4.90 tff(3098,plain,
% 4.70/4.90 (c0_1(a1695)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1933, 3096])).
% 4.70/4.90 tff(3099,plain,
% 4.70/4.90 (c2_1(a1695)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1941, 3096])).
% 4.70/4.90 tff(3100,plain,
% 4.70/4.90 (((~![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) | 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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3101,plain,
% 4.70/4.90 (((~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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3102,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3101])).
% 4.70/4.90 tff(3103,plain,
% 4.70/4.90 (((~![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(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))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3102, 3100])).
% 4.70/4.90 tff(3104,plain,
% 4.70/4.90 ((~![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(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))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3105,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a1716) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695)) | c0_1(a1674) | c1_1(a1716)),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3104, 3103])).
% 4.70/4.90 tff(3106,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3105, 197, 1919, 3099, 3098, 1539, 2782, 2781, 3097, 30, 3065, 3057])).
% 4.70/4.90 tff(3107,plain,(c2_1(a1716) | c3_1(a1716) | c2_1(a1715) | c0_1(a1715) | (~c1_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3108,plain,
% 4.70/4.90 (c2_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3107, 3055, 1213, 1204, 1539])).
% 4.70/4.90 tff(3109,plain,
% 4.70/4.90 (hskp61),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2757, 3055, 1213, 1204])).
% 4.70/4.90 tff(3110,plain,
% 4.70/4.90 (~c2_1(a1674)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1100, 3109])).
% 4.70/4.90 tff(3111,plain,
% 4.70/4.90 (~c1_1(a1674)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1106, 3109])).
% 4.70/4.90 tff(3112,plain,
% 4.70/4.90 (c3_1(a1674)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1114, 3109])).
% 4.70/4.90 tff(3113,plain,
% 4.70/4.90 ((~c2_1(a1716)) | (~c1_1(a1716))),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2541, 1918, 197, 3112, 1539, 3111, 3110, 398])).
% 4.70/4.90 tff(3114,plain,
% 4.70/4.90 (~c1_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3113, 3108])).
% 4.70/4.90 tff(3115,plain,
% 4.70/4.90 ((~c0_1(a1674)) | c1_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3063, 197, 2847, 1952, 3112, 1539, 1213, 3110, 380, 1204])).
% 4.70/4.90 tff(3116,plain,
% 4.70/4.90 (~c0_1(a1674)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3115, 3114])).
% 4.70/4.90 tff(3117,plain,
% 4.70/4.90 (hskp60),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2551, 3114, 3108, 3116, 1539, 3111, 3112])).
% 4.70/4.90 tff(3118,plain,
% 4.70/4.90 (~c1_1(a1673)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[369, 3117])).
% 4.70/4.90 tff(3119,plain,
% 4.70/4.90 (c2_1(a1673)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[419, 3117])).
% 4.70/4.90 tff(3120,plain,
% 4.70/4.90 (c3_1(a1673)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[427, 3117])).
% 4.70/4.90 tff(3121,plain,
% 4.70/4.90 (~hskp7),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2969, 3120, 3119, 1213, 3118, 1204])).
% 4.70/4.90 tff(3122,plain,
% 4.70/4.90 (hskp52),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2977, 3121, 2847, 3108])).
% 4.70/4.90 tff(3123,plain,
% 4.70/4.90 (c3_1(a1654)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[488, 3122])).
% 4.70/4.90 tff(3124,plain,
% 4.70/4.90 (c2_1(a1654)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[496, 3122])).
% 4.70/4.90 tff(3125,plain,
% 4.70/4.90 (c0_1(a1654)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[480, 3122])).
% 4.70/4.90 tff(3126,plain,
% 4.70/4.90 (hskp26),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[606, 197, 3120, 3119, 3125, 3124, 3123, 3118, 20])).
% 4.70/4.90 tff(3127,plain,
% 4.70/4.90 (~c2_1(a1691)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[612, 3126])).
% 4.70/4.90 tff(3128,plain,
% 4.70/4.90 (~c1_1(a1691)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[618, 3126])).
% 4.70/4.90 tff(3129,plain,
% 4.70/4.90 (~c3_1(a1691)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[632, 3126])).
% 4.70/4.90 tff(3130,plain,
% 4.70/4.90 (((~![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))) | (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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3131,plain,
% 4.70/4.90 (((~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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3132,plain,
% 4.70/4.90 (((~![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(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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3131])).
% 4.70/4.90 tff(3133,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3132, 3130])).
% 4.70/4.90 tff(3134,plain,
% 4.70/4.90 ((~![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(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))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3135,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1716) | c1_1(a1674) | c2_1(a1674) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1674) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 4.70/4.90 tff(3136,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3135, 197, 3108, 2847, 1539, 3111, 3110, 3129, 3128, 3127, 30, 3116])).
% 4.70/4.90 tff(3137,plain,(hskp75 | c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3138,plain,
% 4.70/4.90 (hskp75),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3137, 1539, 1213, 1204])).
% 4.70/4.90 tff(3139,plain,
% 4.70/4.90 (~c2_1(a1724)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[411, 3138])).
% 4.70/4.90 tff(3140,plain,
% 4.70/4.90 (c0_1(a1724)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[443, 3138])).
% 4.70/4.90 tff(3141,plain,
% 4.70/4.90 (c3_1(a1724)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[435, 3138])).
% 4.70/4.90 tff(3142,assumption,(hskp13), introduced(assumption)).
% 4.70/4.90 tff(3143,plain,
% 4.70/4.90 (~c1_1(a1667)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[279, 3142])).
% 4.70/4.90 tff(3144,plain,
% 4.70/4.90 (c3_1(a1667)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[287, 3142])).
% 4.70/4.90 tff(3145,plain,
% 4.70/4.90 (c0_1(a1667)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[295, 3142])).
% 4.70/4.90 tff(3146,plain,
% 4.70/4.90 (((~![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(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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3147,plain,
% 4.70/4.90 ((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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3148,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3147])).
% 4.70/4.90 tff(3149,plain,
% 4.70/4.90 (((~![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(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))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3148, 3146])).
% 4.70/4.90 tff(3150,plain,
% 4.70/4.90 ((~![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(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3151,plain,
% 4.70/4.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1715)) | c0_1(a1715)),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 4.70/4.90 tff(3152,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3151, 197, 126, 335, 1959, 3145, 3144, 3143, 125, 1204])).
% 4.70/4.90 tff(3153,plain,((~hskp13) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3154,plain,
% 4.70/4.90 (~hskp13),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3153, 126, 335, 1959, 1204])).
% 4.70/4.90 tff(3155,plain,
% 4.70/4.90 (~c1_1(a1724)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2160, 3154])).
% 4.70/4.90 tff(3156,plain,
% 4.70/4.90 (((~![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) | (~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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3157,plain,
% 4.70/4.90 ((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))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3158,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3157])).
% 4.70/4.90 tff(3159,plain,
% 4.70/4.90 (((~![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(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))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3158, 3156])).
% 4.70/4.90 tff(3160,plain,
% 4.70/4.90 ((~![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(a1724) | (~c3_1(a1724)) | (~c0_1(a1724)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3161,plain,
% 4.70/4.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 4.70/4.90 tff(3162,plain,
% 4.70/4.90 ($false),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3161, 197, 126, 2137, 2142, 335, 1959, 125, 1204, 3155])).
% 4.70/4.90 tff(3163,plain,(hskp29 | (~c0_1(a1724)) | (~c3_1(a1724)) | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715) | c2_1(a1724)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.90 tff(3164,plain,
% 4.70/4.90 (hskp29),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3163, 335, 3141, 3140, 1952, 1204, 3139])).
% 4.70/4.90 tff(3165,plain,
% 4.70/4.90 (~c3_1(a1695)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[1925, 3164])).
% 4.70/4.90 tff(3166,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3167,plain,
% 4.70/4.90 (((~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)))),
% 4.70/4.90 inference(rewrite,[status(thm)],[])).
% 4.70/4.90 tff(3168,plain,
% 4.70/4.90 (((~![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(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))))),
% 4.70/4.90 inference(monotonicity,[status(thm)],[3167])).
% 4.70/4.90 tff(3169,plain,
% 4.70/4.90 (((~![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(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)))),
% 4.70/4.90 inference(transitivity,[status(thm)],[3168, 3166])).
% 4.70/4.90 tff(3170,plain,
% 4.70/4.90 ((~![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(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)))),
% 4.70/4.90 inference(quant_inst,[status(thm)],[])).
% 4.70/4.90 tff(3171,plain,
% 4.70/4.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1724) | c3_1(a1716) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716)) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 4.70/4.90 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 4.70/4.90 tff(3172,plain,
% 4.70/4.90 (c1_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[3171, 197, 3140, 3141, 2847, 1952, 3139, 1539, 1213, 380, 1204])).
% 4.70/4.90 tff(3173,plain,
% 4.70/4.90 (~c2_1(a1716)),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2746, 335, 3172, 1952, 1539, 1204, 3140, 3141, 3139])).
% 4.70/4.90 tff(3174,plain,
% 4.70/4.90 (hskp69),
% 4.70/4.90 inference(unit_resolution,[status(thm)],[2929, 3173, 3172, 335])).
% 4.70/4.91 tff(3175,plain,
% 4.70/4.91 (~c1_1(a1709)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1329, 3174])).
% 4.70/4.91 tff(3176,plain,
% 4.70/4.91 (c2_1(a1695)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1941, 3164])).
% 4.70/4.91 tff(3177,plain,
% 4.70/4.91 (c3_1(a1709)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1337, 3174])).
% 4.70/4.91 tff(3178,plain,
% 4.70/4.91 (c0_1(a1709)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1345, 3174])).
% 4.70/4.91 tff(3179,plain,
% 4.70/4.91 (~c1_1(a1695)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2304, 197, 335, 1952, 3178, 3177, 3176, 3175, 3165, 90, 1204])).
% 4.70/4.91 tff(3180,plain,
% 4.70/4.91 (c0_1(a1695)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1933, 3164])).
% 4.70/4.91 tff(3181,plain,
% 4.70/4.91 ($false),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2831, 197, 3140, 3141, 1952, 3180, 3139, 1213, 3165, 380, 1204, 3179])).
% 4.70/4.91 tff(3182,plain,(c1_1(a1715) | c2_1(a1715) | c0_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.91 tff(3183,plain,
% 4.70/4.91 (c1_1(a1715)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3182, 1539, 1204, 1213])).
% 4.70/4.91 tff(3184,plain,
% 4.70/4.91 (hskp61),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2757, 3183, 1213, 1204])).
% 4.70/4.91 tff(3185,plain,
% 4.70/4.91 (~c2_1(a1674)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1100, 3184])).
% 4.70/4.91 tff(3186,plain,
% 4.70/4.91 (c2_1(a1716)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3107, 3183, 1213, 1204, 1539])).
% 4.70/4.91 tff(3187,plain,
% 4.70/4.91 (~c1_1(a1674)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1106, 3184])).
% 4.70/4.91 tff(3188,plain,
% 4.70/4.91 (~hskp60),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2723, 3140, 3141, 3139, 1213, 1204])).
% 4.70/4.91 tff(3189,plain,
% 4.70/4.91 (c3_1(a1674)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1114, 3184])).
% 4.70/4.91 tff(3190,plain,
% 4.70/4.91 (~c1_1(a1724)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2777, 3189, 3188, 1539, 3187, 3186, 3140, 3141, 3185, 3139])).
% 4.70/4.91 tff(3191,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3192,plain,
% 4.70/4.91 ((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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3193,plain,
% 4.70/4.91 (((~![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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3192])).
% 4.70/4.91 tff(3194,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3193, 3191])).
% 4.70/4.91 tff(3195,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3196,plain,
% 4.70/4.91 ((~![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))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 4.70/4.91 tff(3197,plain,
% 4.70/4.91 (hskp0 | (~c1_1(a1715)) | (~c2_1(a1716))),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3196, 197, 2847, 1952, 1213, 881, 3172])).
% 4.70/4.91 tff(3198,plain,
% 4.70/4.91 (hskp0),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3197, 3186, 3183])).
% 4.70/4.91 tff(3199,plain,
% 4.70/4.91 (c0_1(a1637)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1093, 3198])).
% 4.70/4.91 tff(3200,plain,
% 4.70/4.91 (c1_1(a1637)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1131, 3198])).
% 4.70/4.91 tff(3201,plain,
% 4.70/4.91 (~c3_1(a1637)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2812, 3200, 3140, 3189, 3199, 3139, 3187, 3185, 3190])).
% 4.70/4.91 tff(3202,plain,
% 4.70/4.91 (~c2_1(a1637)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1085, 3198])).
% 4.70/4.91 tff(3203,plain,
% 4.70/4.91 (hskp21),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2820, 197, 3183, 3200, 1213, 3202, 1261, 3201, 1204])).
% 4.70/4.91 tff(3204,plain,
% 4.70/4.91 (~c1_1(a1683)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1315, 3203])).
% 4.70/4.91 tff(3205,plain,
% 4.70/4.91 (c2_1(a1683)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1284, 3203])).
% 4.70/4.91 tff(3206,plain,
% 4.70/4.91 (c3_1(a1683)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1292, 3203])).
% 4.70/4.91 tff(3207,plain,
% 4.70/4.91 (((~![W: $i, 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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3208,plain,
% 4.70/4.91 (((~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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3209,plain,
% 4.70/4.91 (((~![W: $i, 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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3208])).
% 4.70/4.91 tff(3210,plain,
% 4.70/4.91 (((~![W: $i, 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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3209, 3207])).
% 4.70/4.91 tff(3211,plain,
% 4.70/4.91 ((~![W: $i, 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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3212,plain,
% 4.70/4.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | c2_1(a1715) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 4.70/4.91 tff(3213,plain,
% 4.70/4.91 ($false),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3212, 197, 3140, 3141, 1952, 3206, 3205, 3139, 1213, 3204, 346, 1204])).
% 4.70/4.91 tff(3214,plain,(c3_1(a1716) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.91 tff(3215,plain,
% 4.70/4.91 (c0_1(a1715)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3214, 1213, 1539])).
% 4.70/4.91 tff(3216,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3217,plain,
% 4.70/4.91 (((~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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3218,plain,
% 4.70/4.91 (((~![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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3217])).
% 4.70/4.91 tff(3219,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3218, 3216])).
% 4.70/4.91 tff(3220,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3221,plain,
% 4.70/4.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c0_1(a1715)) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 4.70/4.91 tff(3222,plain,
% 4.70/4.91 ($false),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3221, 197, 335, 1115, 560, 558, 1213, 1107, 1101, 590, 1706, 819])).
% 4.70/4.91 tff(3223,plain,((~hskp61) | c1_1(a1715) | (~c0_1(a1654)) | (~c3_1(a1654)) | c2_1(a1715) | (~c0_1(a1715)) | (~c1_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.91 tff(3224,plain,
% 4.70/4.91 (~hskp61),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3223, 819, 860, 831, 1213, 1706, 335])).
% 4.70/4.91 tff(3225,plain,
% 4.70/4.91 (hskp61 | (~c0_1(a1715)) | (~c1_1(a1715))),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1811, 197, 333, 1213, 1156])).
% 4.70/4.91 tff(3226,plain,
% 4.70/4.91 (~c1_1(a1715)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3225, 1157, 1706])).
% 4.70/4.91 tff(3227,assumption,(~c2_1(a1638)), introduced(assumption)).
% 4.70/4.91 tff(3228,assumption,(c0_1(a1638)), introduced(assumption)).
% 4.70/4.91 tff(3229,assumption,(c1_1(a1638)), introduced(assumption)).
% 4.70/4.91 tff(3230,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3231,plain,
% 4.70/4.91 ((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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3232,plain,
% 4.70/4.91 (((~![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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3231])).
% 4.70/4.91 tff(3233,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3232, 3230])).
% 4.70/4.91 tff(3234,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3235,plain,
% 4.70/4.91 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 4.70/4.91 tff(3236,plain,
% 4.70/4.91 ($false),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3235, 197, 1157, 333, 3229, 3228, 1213, 1156, 1706, 3227])).
% 4.70/4.91 tff(3237,plain,(c2_1(a1638) | hskp61 | c3_1(a1715) | (~c1_1(a1638)) | (~c0_1(a1638)) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.91 tff(3238,plain,
% 4.70/4.91 (c2_1(a1638)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3237, 2385, 333, 1157, 2393, 1213, 1706])).
% 4.70/4.91 tff(3239,assumption,(~hskp2), introduced(assumption)).
% 4.70/4.91 tff(3240,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3241,plain,
% 4.70/4.91 ((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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3242,plain,
% 4.70/4.91 (((~![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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3241])).
% 4.70/4.91 tff(3243,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3242, 3240])).
% 4.70/4.91 tff(3244,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3245,plain,
% 4.70/4.91 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1715) | c3_1(a1715) | c3_1(a1638) | (~ndr1_0) | (~c0_1(a1715)) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3244, 3243])).
% 4.70/4.91 tff(3246,plain,
% 4.70/4.91 ($false),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3245, 197, 3239, 335, 333, 2385, 2393, 2384, 891, 1706])).
% 4.70/4.91 tff(3247,plain,((~hskp42) | hskp2 | c1_1(a1715) | c3_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.91 tff(3248,plain,
% 4.70/4.91 (hskp2),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3247, 2383, 3226, 333, 1706])).
% 4.70/4.91 tff(3249,plain,
% 4.70/4.91 (~c0_1(a1645)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1038, 3248])).
% 4.70/4.91 tff(3250,plain,
% 4.70/4.91 (~c1_1(a1645)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1044, 3248])).
% 4.70/4.91 tff(3251,plain,
% 4.70/4.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3252,plain,
% 4.70/4.91 (((~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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3253,plain,
% 4.70/4.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3252])).
% 4.70/4.91 tff(3254,plain,
% 4.70/4.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3253, 3251])).
% 4.70/4.91 tff(3255,plain,
% 4.70/4.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3256,plain,
% 4.70/4.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 4.70/4.91 tff(3257,plain,
% 4.70/4.91 (c2_1(a1645) | (~c2_1(a1638))),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3256, 197, 3226, 333, 2393, 1213, 2384, 3250, 3249, 30])).
% 4.70/4.91 tff(3258,plain,
% 4.70/4.91 (c2_1(a1645)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3257, 3238])).
% 4.70/4.91 tff(3259,plain,
% 4.70/4.91 (~c3_1(a1645)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[1060, 3248])).
% 4.70/4.91 tff(3260,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3261,plain,
% 4.70/4.91 ((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)))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3262,plain,
% 4.70/4.91 (((~![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))))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3261])).
% 4.70/4.91 tff(3263,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3262, 3260])).
% 4.70/4.91 tff(3264,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3265,plain,
% 4.70/4.91 ((~![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))),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 4.70/4.91 tff(3266,plain,
% 4.70/4.91 (hskp57 | (~c2_1(a1645))),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3265, 197, 333, 1213, 3250, 3259, 1504, 1706])).
% 4.70/4.91 tff(3267,plain,
% 4.70/4.91 (hskp57),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3266, 3258])).
% 4.70/4.91 tff(3268,plain,
% 4.70/4.91 (c0_1(a1665)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[78, 3267])).
% 4.70/4.91 tff(3269,plain,
% 4.70/4.91 (c3_1(a1665)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[67, 3267])).
% 4.70/4.91 tff(3270,plain,
% 4.70/4.91 (((~![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))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3271,plain,
% 4.70/4.91 ((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))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3272,plain,
% 4.70/4.91 (((~![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)))),
% 4.70/4.91 inference(monotonicity,[status(thm)],[3271])).
% 4.70/4.91 tff(3273,plain,
% 4.70/4.91 (((~![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))),
% 4.70/4.91 inference(transitivity,[status(thm)],[3272, 3270])).
% 4.70/4.91 tff(3274,plain,
% 4.70/4.91 ((~![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)))),
% 4.70/4.91 inference(quant_inst,[status(thm)],[])).
% 4.70/4.91 tff(3275,plain,
% 4.70/4.91 ((~![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)),
% 4.70/4.91 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 4.70/4.91 tff(3276,plain,
% 4.70/4.91 (hskp33 | c2_1(a1665)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3275, 197, 1157, 93, 92, 2486])).
% 4.70/4.91 tff(3277,plain,
% 4.70/4.91 (hskp33),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[3276, 1684])).
% 4.70/4.91 tff(3278,plain,
% 4.70/4.91 (~c2_1(a1704)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2499, 3277])).
% 4.70/4.91 tff(3279,plain,
% 4.70/4.91 (~c0_1(a1704)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2505, 3277])).
% 4.70/4.91 tff(3280,plain,
% 4.70/4.91 (c3_1(a1704)),
% 4.70/4.91 inference(unit_resolution,[status(thm)],[2514, 3277])).
% 4.70/4.91 tff(3281,plain,
% 4.70/4.91 (((~![W: $i, 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))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3282,plain,
% 4.70/4.91 (((~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))),
% 4.70/4.91 inference(rewrite,[status(thm)],[])).
% 4.70/4.91 tff(3283,plain,
% 4.70/4.91 (((~![W: $i, 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)))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3282])).
% 4.70/4.92 tff(3284,plain,
% 4.70/4.92 (((~![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)) | 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))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3283, 3281])).
% 4.70/4.92 tff(3285,plain,
% 4.70/4.92 ((~![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)) | 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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3286,plain,
% 4.70/4.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c0_1(a1715)) | (~c3_1(a1665)) | (~c0_1(a1665)) | c2_1(a1665)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 4.70/4.92 tff(3287,plain,
% 4.70/4.92 ($false),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3286, 197, 335, 333, 93, 92, 3280, 3279, 3278, 380, 1706, 1684])).
% 4.70/4.92 tff(3288,plain,(c2_1(a1665) | c1_1(a1715) | c3_1(a1715) | (~c0_1(a1665)) | (~c3_1(a1665)) | (~c0_1(a1715)) | hskp61), inference(lemma,lemma(discharge,[]))).
% 4.70/4.92 tff(3289,plain,
% 4.70/4.92 (c2_1(a1665)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3288, 3269, 333, 3268, 3226, 1706, 1157])).
% 4.70/4.92 tff(3290,plain,
% 4.70/4.92 (~c1_1(a1665)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[59, 3267])).
% 4.70/4.92 tff(3291,assumption,(c2_1(a1638)), introduced(assumption)).
% 4.70/4.92 tff(3292,assumption,(~c3_1(a1638)), introduced(assumption)).
% 4.70/4.92 tff(3293,assumption,(hskp58), introduced(assumption)).
% 4.70/4.92 tff(3294,plain,
% 4.70/4.92 (((~hskp58) | (~c1_1(a1668))) <=> ((~hskp58) | (~c1_1(a1668)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3295,plain,
% 4.70/4.92 (((~c1_1(a1668)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a1668)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3296,axiom,((~c1_1(a1668)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 4.70/4.92 tff(3297,plain,
% 4.70/4.92 ((~hskp58) | (~c1_1(a1668))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 4.70/4.92 tff(3298,plain,
% 4.70/4.92 ((~hskp58) | (~c1_1(a1668))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3297, 3294])).
% 4.70/4.92 tff(3299,plain,
% 4.70/4.92 (~c1_1(a1668)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3298, 3293])).
% 4.70/4.92 tff(3300,plain,
% 4.70/4.92 (((~hskp58) | (~c0_1(a1668))) <=> ((~hskp58) | (~c0_1(a1668)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3301,plain,
% 4.70/4.92 (((~c0_1(a1668)) | (~hskp58)) <=> ((~hskp58) | (~c0_1(a1668)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3302,axiom,((~c0_1(a1668)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 4.70/4.92 tff(3303,plain,
% 4.70/4.92 ((~hskp58) | (~c0_1(a1668))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 4.70/4.92 tff(3304,plain,
% 4.70/4.92 ((~hskp58) | (~c0_1(a1668))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3303, 3300])).
% 4.70/4.92 tff(3305,plain,
% 4.70/4.92 (~c0_1(a1668)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3304, 3293])).
% 4.70/4.92 tff(3306,plain,
% 4.70/4.92 (((~hskp58) | c3_1(a1668)) <=> ((~hskp58) | c3_1(a1668))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3307,axiom,((~hskp58) | c3_1(a1668)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 4.70/4.92 tff(3308,plain,
% 4.70/4.92 ((~hskp58) | c3_1(a1668)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3307, 3306])).
% 4.70/4.92 tff(3309,plain,
% 4.70/4.92 ((~hskp58) | c3_1(a1668)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3308, 3306])).
% 4.70/4.92 tff(3310,plain,
% 4.70/4.92 ((~hskp58) | c3_1(a1668)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3309, 3306])).
% 4.70/4.92 tff(3311,plain,
% 4.70/4.92 ((~hskp58) | c3_1(a1668)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3310, 3306])).
% 4.70/4.92 tff(3312,plain,
% 4.70/4.92 ((~hskp58) | c3_1(a1668)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3311, 3306])).
% 4.70/4.92 tff(3313,plain,
% 4.70/4.92 (c3_1(a1668)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3312, 3293])).
% 4.70/4.92 tff(3314,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3315,plain,
% 4.70/4.92 (((~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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3316,plain,
% 4.70/4.92 (((~![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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3315])).
% 4.70/4.92 tff(3317,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3316, 3314])).
% 4.70/4.92 tff(3318,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3319,plain,
% 4.70/4.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1668) | c1_1(a1668) | c1_1(a1665) | c3_1(a1638) | (~ndr1_0) | (~c3_1(a1668)) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 4.70/4.92 tff(3320,plain,
% 4.70/4.92 ($false),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3319, 197, 3313, 93, 92, 3229, 3305, 3299, 91, 3292, 90, 3291])).
% 4.70/4.92 tff(3321,plain,((~hskp58) | (~c0_1(a1665)) | (~c3_1(a1665)) | (~c1_1(a1638)) | c1_1(a1665) | c3_1(a1638) | (~c2_1(a1638))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.92 tff(3322,plain,
% 4.70/4.92 (~hskp58),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3321, 3268, 3269, 2385, 3290, 2384, 3238])).
% 4.70/4.92 tff(3323,plain,
% 4.70/4.92 (^[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))))),
% 4.70/4.92 inference(bind,[status(th)],[])).
% 4.70/4.92 tff(3324,plain,
% 4.70/4.92 (![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)))),
% 4.70/4.92 inference(quant_intro,[status(thm)],[3323])).
% 4.70/4.92 tff(3325,plain,
% 4.70/4.92 (![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3326,plain,
% 4.70/4.92 (^[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)))))),
% 4.70/4.92 inference(bind,[status(th)],[])).
% 4.70/4.92 tff(3327,plain,
% 4.70/4.92 (![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)))),
% 4.70/4.92 inference(quant_intro,[status(thm)],[3326])).
% 4.70/4.92 tff(3328,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp58) | hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause316')).
% 4.70/4.92 tff(3329,plain,
% 4.70/4.92 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 4.70/4.92 tff(3330,plain,
% 4.70/4.92 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3329, 3325])).
% 4.70/4.92 tff(3331,plain,(
% 4.70/4.92 ![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 4.70/4.92 inference(skolemize,[status(sab)],[3330])).
% 4.70/4.92 tff(3332,plain,
% 4.70/4.92 (![U: $i] : (hskp59 | hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3331, 3324])).
% 4.70/4.92 tff(3333,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3334,plain,
% 4.70/4.92 ((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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3335,plain,
% 4.70/4.92 (((~![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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3334])).
% 4.70/4.92 tff(3336,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3335, 3333])).
% 4.70/4.92 tff(3337,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3338,plain,
% 4.70/4.92 ((~![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))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 4.70/4.92 tff(3339,plain,
% 4.70/4.92 (hskp59 | hskp58 | c1_1(a1715) | (~c0_1(a1715))),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3338, 197, 1213, 3332])).
% 4.70/4.92 tff(3340,plain,
% 4.70/4.92 (hskp59),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3339, 3322, 3226, 1706])).
% 4.70/4.92 tff(3341,assumption,(hskp59), introduced(assumption)).
% 4.70/4.92 tff(3342,plain,
% 4.70/4.92 (((~hskp59) | (~c2_1(a1669))) <=> ((~hskp59) | (~c2_1(a1669)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3343,plain,
% 4.70/4.92 (((~c2_1(a1669)) | (~hskp59)) <=> ((~hskp59) | (~c2_1(a1669)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3344,axiom,((~c2_1(a1669)) | (~hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 4.70/4.92 tff(3345,plain,
% 4.70/4.92 ((~hskp59) | (~c2_1(a1669))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 4.70/4.92 tff(3346,plain,
% 4.70/4.92 ((~hskp59) | (~c2_1(a1669))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3345, 3342])).
% 4.70/4.92 tff(3347,plain,
% 4.70/4.92 (~c2_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3346, 3341])).
% 4.70/4.92 tff(3348,plain,
% 4.70/4.92 (((~hskp59) | c0_1(a1669)) <=> ((~hskp59) | c0_1(a1669))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3349,axiom,((~hskp59) | c0_1(a1669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 4.70/4.92 tff(3350,plain,
% 4.70/4.92 ((~hskp59) | c0_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3349, 3348])).
% 4.70/4.92 tff(3351,plain,
% 4.70/4.92 ((~hskp59) | c0_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3350, 3348])).
% 4.70/4.92 tff(3352,plain,
% 4.70/4.92 ((~hskp59) | c0_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3351, 3348])).
% 4.70/4.92 tff(3353,plain,
% 4.70/4.92 ((~hskp59) | c0_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3352, 3348])).
% 4.70/4.92 tff(3354,plain,
% 4.70/4.92 ((~hskp59) | c0_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3353, 3348])).
% 4.70/4.92 tff(3355,plain,
% 4.70/4.92 (c0_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3354, 3341])).
% 4.70/4.92 tff(3356,plain,
% 4.70/4.92 (((~hskp59) | c3_1(a1669)) <=> ((~hskp59) | c3_1(a1669))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3357,axiom,((~hskp59) | c3_1(a1669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 4.70/4.92 tff(3358,plain,
% 4.70/4.92 ((~hskp59) | c3_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 4.70/4.92 tff(3359,plain,
% 4.70/4.92 ((~hskp59) | c3_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3358, 3356])).
% 4.70/4.92 tff(3360,plain,
% 4.70/4.92 ((~hskp59) | c3_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3359, 3356])).
% 4.70/4.92 tff(3361,plain,
% 4.70/4.92 ((~hskp59) | c3_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3360, 3356])).
% 4.70/4.92 tff(3362,plain,
% 4.70/4.92 ((~hskp59) | c3_1(a1669)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3361, 3356])).
% 4.70/4.92 tff(3363,plain,
% 4.70/4.92 (c3_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3362, 3341])).
% 4.70/4.92 tff(3364,assumption,(~hskp33), introduced(assumption)).
% 4.70/4.92 tff(3365,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3366,plain,
% 4.70/4.92 ((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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3367,plain,
% 4.70/4.92 (((~![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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3366])).
% 4.70/4.92 tff(3368,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3367, 3365])).
% 4.70/4.92 tff(3369,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3370,plain,
% 4.70/4.92 ((~![U: $i] : (hskp61 | hskp33 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp61 | hskp33 | c2_1(a1669) | (~ndr1_0) | (~c3_1(a1669)) | (~c0_1(a1669))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 4.70/4.92 tff(3371,plain,
% 4.70/4.92 ($false),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3370, 197, 1157, 3364, 3363, 3355, 3347, 2486])).
% 4.70/4.92 tff(3372,plain,((~hskp59) | hskp61 | hskp33), inference(lemma,lemma(discharge,[]))).
% 4.70/4.92 tff(3373,plain,
% 4.70/4.92 (hskp33),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3372, 3340, 1157])).
% 4.70/4.92 tff(3374,plain,
% 4.70/4.92 (~c2_1(a1704)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[2499, 3373])).
% 4.70/4.92 tff(3375,plain,
% 4.70/4.92 (~c0_1(a1704)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[2505, 3373])).
% 4.70/4.92 tff(3376,plain,
% 4.70/4.92 (~c2_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3346, 3340])).
% 4.70/4.92 tff(3377,plain,
% 4.70/4.92 (c3_1(a1704)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[2514, 3373])).
% 4.70/4.92 tff(3378,plain,
% 4.70/4.92 (c0_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3354, 3340])).
% 4.70/4.92 tff(3379,plain,
% 4.70/4.92 (c3_1(a1669)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3362, 3340])).
% 4.70/4.92 tff(3380,plain,
% 4.70/4.92 (((~![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)))) | (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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3381,plain,
% 4.70/4.92 (((~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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3382,plain,
% 4.70/4.92 (((~![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(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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3381])).
% 4.70/4.92 tff(3383,plain,
% 4.70/4.92 (((~![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(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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3382, 3380])).
% 4.70/4.92 tff(3384,plain,
% 4.70/4.92 ((~![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(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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3385,plain,
% 4.70/4.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1669) | c1_1(a1665) | c0_1(a1704) | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1669)) | (~c0_1(a1669))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 4.70/4.92 tff(3386,plain,
% 4.70/4.92 ($false),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3385, 197, 3379, 3378, 3269, 3377, 3376, 3290, 3375, 3374, 346, 3289])).
% 4.70/4.92 tff(3387,plain,((~hskp42) | hskp61 | (~c0_1(a1715)) | c2_1(a1715) | c3_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.70/4.92 tff(3388,plain,
% 4.70/4.92 (~hskp42),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3387, 3224, 1706, 1213, 333])).
% 4.70/4.92 tff(3389,plain,
% 4.70/4.92 (~hskp74),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[1003, 3388, 894])).
% 4.70/4.92 tff(3390,plain,
% 4.70/4.92 (hskp38),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[960, 3389, 818])).
% 4.70/4.92 tff(3391,plain,
% 4.70/4.92 (~c2_1(a1718)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[901, 3390])).
% 4.70/4.92 tff(3392,plain,
% 4.70/4.92 (c3_1(a1718)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[909, 3390])).
% 4.70/4.92 tff(3393,plain,
% 4.70/4.92 (~c1_1(a1718)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[916, 197, 894, 860, 832, 3392, 3391, 881, 819])).
% 4.70/4.92 tff(3394,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3395,plain,
% 4.70/4.92 ((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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3396,plain,
% 4.70/4.92 (((~![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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3395])).
% 4.70/4.92 tff(3397,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3396, 3394])).
% 4.70/4.92 tff(3398,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3399,plain,
% 4.70/4.92 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c0_1(a1637)) | (~c0_1(a1715))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 4.70/4.92 tff(3400,plain,
% 4.70/4.92 ($false),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3399, 197, 1157, 333, 2372, 2371, 1213, 2370, 1156, 1706])).
% 4.70/4.92 tff(3401,plain,((~hskp0) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.92 tff(3402,plain,
% 4.70/4.92 (~hskp0),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3401, 1157, 333, 1213, 1706])).
% 4.70/4.92 tff(3403,plain,
% 4.70/4.92 (~hskp42),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3387, 1157, 1706, 1213, 333])).
% 4.70/4.92 tff(3404,plain,
% 4.70/4.92 (~hskp74),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[1003, 3403, 3402])).
% 4.70/4.92 tff(3405,assumption,(~hskp62), introduced(assumption)).
% 4.70/4.92 tff(3406,assumption,(hskp44), introduced(assumption)).
% 4.70/4.92 tff(3407,plain,
% 4.70/4.92 (((~hskp44) | c2_1(a1640)) <=> ((~hskp44) | c2_1(a1640))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3408,axiom,((~hskp44) | c2_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 4.70/4.92 tff(3409,plain,
% 4.70/4.92 ((~hskp44) | c2_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3408, 3407])).
% 4.70/4.92 tff(3410,plain,
% 4.70/4.92 ((~hskp44) | c2_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3409, 3407])).
% 4.70/4.92 tff(3411,plain,
% 4.70/4.92 ((~hskp44) | c2_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3410, 3407])).
% 4.70/4.92 tff(3412,plain,
% 4.70/4.92 ((~hskp44) | c2_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3411, 3407])).
% 4.70/4.92 tff(3413,plain,
% 4.70/4.92 ((~hskp44) | c2_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3412, 3407])).
% 4.70/4.92 tff(3414,plain,
% 4.70/4.92 (c2_1(a1640)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3413, 3406])).
% 4.70/4.92 tff(3415,plain,
% 4.70/4.92 (((~hskp44) | c3_1(a1640)) <=> ((~hskp44) | c3_1(a1640))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3416,axiom,((~hskp44) | c3_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 4.70/4.92 tff(3417,plain,
% 4.70/4.92 ((~hskp44) | c3_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3416, 3415])).
% 4.70/4.92 tff(3418,plain,
% 4.70/4.92 ((~hskp44) | c3_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3417, 3415])).
% 4.70/4.92 tff(3419,plain,
% 4.70/4.92 ((~hskp44) | c3_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3418, 3415])).
% 4.70/4.92 tff(3420,plain,
% 4.70/4.92 ((~hskp44) | c3_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3419, 3415])).
% 4.70/4.92 tff(3421,plain,
% 4.70/4.92 ((~hskp44) | c3_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3420, 3415])).
% 4.70/4.92 tff(3422,plain,
% 4.70/4.92 (c3_1(a1640)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3421, 3406])).
% 4.70/4.92 tff(3423,plain,
% 4.70/4.92 (((~hskp44) | c1_1(a1640)) <=> ((~hskp44) | c1_1(a1640))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3424,axiom,((~hskp44) | c1_1(a1640)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 4.70/4.92 tff(3425,plain,
% 4.70/4.92 ((~hskp44) | c1_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 4.70/4.92 tff(3426,plain,
% 4.70/4.92 ((~hskp44) | c1_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3425, 3423])).
% 4.70/4.92 tff(3427,plain,
% 4.70/4.92 ((~hskp44) | c1_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3426, 3423])).
% 4.70/4.92 tff(3428,plain,
% 4.70/4.92 ((~hskp44) | c1_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3427, 3423])).
% 4.70/4.92 tff(3429,plain,
% 4.70/4.92 ((~hskp44) | c1_1(a1640)),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3428, 3423])).
% 4.70/4.92 tff(3430,plain,
% 4.70/4.92 (c1_1(a1640)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3429, 3406])).
% 4.70/4.92 tff(3431,assumption,(c1_1(a1640)), introduced(assumption)).
% 4.70/4.92 tff(3432,assumption,(c3_1(a1640)), introduced(assumption)).
% 4.70/4.92 tff(3433,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3434,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3435,plain,
% 4.70/4.92 ((~![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))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3434, 3433])).
% 4.70/4.92 tff(3436,plain,
% 4.70/4.92 (hskp62 | c0_1(a1640)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3435, 197, 1157, 3432, 3431, 2069])).
% 4.70/4.92 tff(3437,plain,
% 4.70/4.92 (c0_1(a1640)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3436, 3405])).
% 4.70/4.92 tff(3438,assumption,(c2_1(a1640)), introduced(assumption)).
% 4.70/4.92 tff(3439,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3440,plain,
% 4.70/4.92 ((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)))),
% 4.70/4.92 inference(rewrite,[status(thm)],[])).
% 4.70/4.92 tff(3441,plain,
% 4.70/4.92 (((~![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))))),
% 4.70/4.92 inference(monotonicity,[status(thm)],[3440])).
% 4.70/4.92 tff(3442,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.92 inference(transitivity,[status(thm)],[3441, 3439])).
% 4.70/4.92 tff(3443,plain,
% 4.70/4.92 ((~![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)))),
% 4.70/4.92 inference(quant_inst,[status(thm)],[])).
% 4.70/4.92 tff(3444,plain,
% 4.70/4.92 ((~![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))),
% 4.70/4.92 inference(modus_ponens,[status(thm)],[3443, 3442])).
% 4.70/4.92 tff(3445,plain,
% 4.70/4.92 (hskp74 | hskp38 | (~c0_1(a1640))),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3444, 197, 3432, 3438, 953])).
% 4.70/4.92 tff(3446,plain,
% 4.70/4.92 (hskp38),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[3445, 3437, 955])).
% 4.70/4.92 tff(3447,plain,
% 4.70/4.92 (~c0_1(a1718)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[2418, 3446])).
% 4.70/4.92 tff(3448,plain,
% 4.70/4.92 (c3_1(a1718)),
% 4.70/4.92 inference(unit_resolution,[status(thm)],[909, 3446])).
% 4.70/4.92 tff(3449,plain,
% 4.70/4.92 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3450,plain,
% 4.70/4.93 ((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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3451,plain,
% 4.70/4.93 (((~![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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3450])).
% 4.70/4.93 tff(3452,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3451, 3449])).
% 4.70/4.93 tff(3453,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3454,plain,
% 4.70/4.93 ((~![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))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 4.70/4.93 tff(3455,plain,
% 4.70/4.93 (~c1_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3454, 197, 3405, 1157, 3448, 3447, 2069])).
% 4.70/4.93 tff(3456,plain,
% 4.70/4.93 (~c2_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[901, 3446])).
% 4.70/4.93 tff(3457,plain,
% 4.70/4.93 (((~![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(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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3458,plain,
% 4.70/4.93 (((~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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3459,plain,
% 4.70/4.93 (((~![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(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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3458])).
% 4.70/4.93 tff(3460,plain,
% 4.70/4.93 (((~![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(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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3459, 3457])).
% 4.70/4.93 tff(3461,plain,
% 4.70/4.93 ((~![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(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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3462,plain,
% 4.70/4.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c2_1(a1718) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c0_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 4.70/4.93 tff(3463,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3462, 197, 335, 3432, 3431, 3448, 1213, 3456, 590, 1706, 3437, 3455])).
% 4.70/4.93 tff(3464,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,[]))).
% 4.70/4.93 tff(3465,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3464, 3430, 3422, 335, 3405, 1213, 1706, 1157, 955, 3414])).
% 4.70/4.93 tff(3466,plain,((~hskp44) | c1_1(a1715) | hskp62 | c2_1(a1715) | (~c0_1(a1715)) | hskp61 | hskp74), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3467,plain,
% 4.70/4.93 (~hskp44),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3466, 3405, 3226, 1213, 1706, 1157, 3404])).
% 4.70/4.93 tff(3468,plain,
% 4.70/4.93 (c2_1(a1665)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3288, 79, 333, 335, 68, 1706, 1157])).
% 4.70/4.93 tff(3469,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3470,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3471,plain,
% 4.70/4.93 ((~![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))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 4.70/4.93 tff(3472,plain,
% 4.70/4.93 (hskp38 | (~c2_1(a1665))),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3471, 197, 955, 79, 68, 953])).
% 4.70/4.93 tff(3473,plain,
% 4.70/4.93 (hskp38),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3472, 3468])).
% 4.70/4.93 tff(3474,plain,
% 4.70/4.93 (~c0_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2418, 3473])).
% 4.70/4.93 tff(3475,plain,
% 4.70/4.93 (c3_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[909, 3473])).
% 4.70/4.93 tff(3476,plain,
% 4.70/4.93 (~c1_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3454, 197, 3405, 1157, 3475, 3474, 2069])).
% 4.70/4.93 tff(3477,plain,
% 4.70/4.93 (((~![V: $i, 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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3478,plain,
% 4.70/4.93 ((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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3479,plain,
% 4.70/4.93 (((~![V: $i, 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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3478])).
% 4.70/4.93 tff(3480,plain,
% 4.70/4.93 (((~![V: $i, 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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3479, 3477])).
% 4.70/4.93 tff(3481,plain,
% 4.70/4.93 ((~![V: $i, 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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3482,plain,
% 4.70/4.93 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 4.70/4.93 tff(3483,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3482, 197, 126, 79, 68, 3475, 60, 3474, 125, 3476])).
% 4.70/4.93 tff(3484,plain,((~hskp57) | hskp29 | hskp62 | hskp61 | hskp74 | c3_1(a1715) | c1_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3485,plain,
% 4.70/4.93 (~hskp57),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3484, 126, 3404, 1157, 3405, 333, 3226, 1706])).
% 4.70/4.93 tff(3486,assumption,(hskp45), introduced(assumption)).
% 4.70/4.93 tff(3487,plain,
% 4.70/4.93 (((~hskp45) | (~c1_1(a1641))) <=> ((~hskp45) | (~c1_1(a1641)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3488,plain,
% 4.70/4.93 (((~c1_1(a1641)) | (~hskp45)) <=> ((~hskp45) | (~c1_1(a1641)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3489,axiom,((~c1_1(a1641)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause224')).
% 4.70/4.93 tff(3490,plain,
% 4.70/4.93 ((~hskp45) | (~c1_1(a1641))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 4.70/4.93 tff(3491,plain,
% 4.70/4.93 ((~hskp45) | (~c1_1(a1641))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3490, 3487])).
% 4.70/4.93 tff(3492,plain,
% 4.70/4.93 (~c1_1(a1641)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3491, 3486])).
% 4.70/4.93 tff(3493,plain,
% 4.70/4.93 (((~hskp45) | (~c3_1(a1641))) <=> ((~hskp45) | (~c3_1(a1641)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3494,plain,
% 4.70/4.93 (((~c3_1(a1641)) | (~hskp45)) <=> ((~hskp45) | (~c3_1(a1641)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3495,axiom,((~c3_1(a1641)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause223')).
% 4.70/4.93 tff(3496,plain,
% 4.70/4.93 ((~hskp45) | (~c3_1(a1641))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 4.70/4.93 tff(3497,plain,
% 4.70/4.93 ((~hskp45) | (~c3_1(a1641))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3496, 3493])).
% 4.70/4.93 tff(3498,plain,
% 4.70/4.93 (~c3_1(a1641)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3497, 3486])).
% 4.70/4.93 tff(3499,plain,
% 4.70/4.93 (((~hskp45) | c2_1(a1641)) <=> ((~hskp45) | c2_1(a1641))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3500,axiom,((~hskp45) | c2_1(a1641)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 4.70/4.93 tff(3501,plain,
% 4.70/4.93 ((~hskp45) | c2_1(a1641)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3500, 3499])).
% 4.70/4.93 tff(3502,plain,
% 4.70/4.93 ((~hskp45) | c2_1(a1641)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3501, 3499])).
% 4.70/4.93 tff(3503,plain,
% 4.70/4.93 ((~hskp45) | c2_1(a1641)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3502, 3499])).
% 4.70/4.93 tff(3504,plain,
% 4.70/4.93 ((~hskp45) | c2_1(a1641)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3503, 3499])).
% 4.70/4.93 tff(3505,plain,
% 4.70/4.93 ((~hskp45) | c2_1(a1641)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3504, 3499])).
% 4.70/4.93 tff(3506,plain,
% 4.70/4.93 (c2_1(a1641)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3505, 3486])).
% 4.70/4.93 tff(3507,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3508,plain,
% 4.70/4.93 ((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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3509,plain,
% 4.70/4.93 (((~![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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3508])).
% 4.70/4.93 tff(3510,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3509, 3507])).
% 4.70/4.93 tff(3511,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3512,plain,
% 4.70/4.93 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c3_1(a1641) | c1_1(a1641) | (~ndr1_0) | (~c0_1(a1715)) | (~c2_1(a1641))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3511, 3510])).
% 4.70/4.93 tff(3513,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3512, 197, 1505, 333, 3506, 1213, 3498, 3492, 1504, 1706])).
% 4.70/4.93 tff(3514,plain,((~hskp45) | hskp57 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3515,plain,
% 4.70/4.93 (~hskp45),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3514, 3485, 333, 1213, 1706])).
% 4.70/4.93 tff(3516,plain,
% 4.70/4.93 ((hskp45 | hskp44 | hskp43) <=> (hskp45 | hskp44 | hskp43)),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3517,plain,
% 4.70/4.93 (((hskp43 | hskp44) | hskp45) <=> (hskp45 | hskp44 | hskp43)),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3518,axiom,((hskp43 | hskp44) | hskp45), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 4.70/4.93 tff(3519,plain,
% 4.70/4.93 (hskp45 | hskp44 | hskp43),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 4.70/4.93 tff(3520,plain,
% 4.70/4.93 (hskp45 | hskp44 | hskp43),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3519, 3516])).
% 4.70/4.93 tff(3521,plain,
% 4.70/4.93 (hskp45 | hskp44 | hskp43),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3520, 3516])).
% 4.70/4.93 tff(3522,plain,
% 4.70/4.93 (hskp45 | hskp44 | hskp43),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3521, 3516])).
% 4.70/4.93 tff(3523,plain,
% 4.70/4.93 (hskp45 | hskp44 | hskp43),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3522, 3516])).
% 4.70/4.93 tff(3524,plain,
% 4.70/4.93 (hskp43),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3523, 3515, 3467])).
% 4.70/4.93 tff(3525,plain,
% 4.70/4.93 (((~hskp43) | c0_1(a1639)) <=> ((~hskp43) | c0_1(a1639))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3526,axiom,((~hskp43) | c0_1(a1639)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 4.70/4.93 tff(3527,plain,
% 4.70/4.93 ((~hskp43) | c0_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 4.70/4.93 tff(3528,plain,
% 4.70/4.93 ((~hskp43) | c0_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3527, 3525])).
% 4.70/4.93 tff(3529,plain,
% 4.70/4.93 ((~hskp43) | c0_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3528, 3525])).
% 4.70/4.93 tff(3530,plain,
% 4.70/4.93 ((~hskp43) | c0_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3529, 3525])).
% 4.70/4.93 tff(3531,plain,
% 4.70/4.93 ((~hskp43) | c0_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3530, 3525])).
% 4.70/4.93 tff(3532,plain,
% 4.70/4.93 (c0_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3531, 3524])).
% 4.70/4.93 tff(3533,plain,
% 4.70/4.93 (((~hskp43) | c2_1(a1639)) <=> ((~hskp43) | c2_1(a1639))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3534,axiom,((~hskp43) | c2_1(a1639)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 4.70/4.93 tff(3535,plain,
% 4.70/4.93 ((~hskp43) | c2_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 4.70/4.93 tff(3536,plain,
% 4.70/4.93 ((~hskp43) | c2_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3535, 3533])).
% 4.70/4.93 tff(3537,plain,
% 4.70/4.93 ((~hskp43) | c2_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3536, 3533])).
% 4.70/4.93 tff(3538,plain,
% 4.70/4.93 ((~hskp43) | c2_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3537, 3533])).
% 4.70/4.93 tff(3539,plain,
% 4.70/4.93 ((~hskp43) | c2_1(a1639)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3538, 3533])).
% 4.70/4.93 tff(3540,plain,
% 4.70/4.93 (c2_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3539, 3524])).
% 4.70/4.93 tff(3541,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3542,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3543,plain,
% 4.70/4.93 ((~![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))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 4.70/4.93 tff(3544,plain,
% 4.70/4.93 (c3_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3543, 197, 3403, 3402, 3540, 3532, 971])).
% 4.70/4.93 tff(3545,assumption,(hskp43), introduced(assumption)).
% 4.70/4.93 tff(3546,plain,
% 4.70/4.93 (c0_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3531, 3545])).
% 4.70/4.93 tff(3547,plain,
% 4.70/4.93 (c2_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3539, 3545])).
% 4.70/4.93 tff(3548,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3549,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3550,plain,
% 4.70/4.93 ((~![U: $i] : (hskp74 | hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp74 | hskp38 | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3549, 3548])).
% 4.70/4.93 tff(3551,plain,
% 4.70/4.93 (~c3_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3550, 197, 2848, 954, 3547, 3546, 953])).
% 4.70/4.93 tff(3552,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3543, 197, 995, 894, 3547, 3546, 971, 3551])).
% 4.70/4.93 tff(3553,plain,((~hskp43) | hskp42 | hskp0 | hskp38), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3554,plain,
% 4.70/4.93 (hskp38),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3553, 3524, 3402, 3403])).
% 4.70/4.93 tff(3555,plain,
% 4.70/4.93 (~c0_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2418, 3554])).
% 4.70/4.93 tff(3556,plain,
% 4.70/4.93 (((~hskp43) | (~c1_1(a1639))) <=> ((~hskp43) | (~c1_1(a1639)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3557,plain,
% 4.70/4.93 (((~c1_1(a1639)) | (~hskp43)) <=> ((~hskp43) | (~c1_1(a1639)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3558,axiom,((~c1_1(a1639)) | (~hskp43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause225')).
% 4.70/4.93 tff(3559,plain,
% 4.70/4.93 ((~hskp43) | (~c1_1(a1639))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3558, 3557])).
% 4.70/4.93 tff(3560,plain,
% 4.70/4.93 ((~hskp43) | (~c1_1(a1639))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3559, 3556])).
% 4.70/4.93 tff(3561,plain,
% 4.70/4.93 (~c1_1(a1639)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3560, 3524])).
% 4.70/4.93 tff(3562,plain,
% 4.70/4.93 (c3_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[909, 3554])).
% 4.70/4.93 tff(3563,plain,
% 4.70/4.93 (((~![V: $i, 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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3564,plain,
% 4.70/4.93 ((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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3565,plain,
% 4.70/4.93 (((~![V: $i, 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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3564])).
% 4.70/4.93 tff(3566,plain,
% 4.70/4.93 (((~![V: $i, 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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3565, 3563])).
% 4.70/4.93 tff(3567,plain,
% 4.70/4.93 ((~![V: $i, 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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3568,plain,
% 4.70/4.93 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1639) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 4.70/4.93 tff(3569,plain,
% 4.70/4.93 (c1_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3568, 197, 126, 3532, 3562, 3561, 3555, 125, 3544])).
% 4.70/4.93 tff(3570,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3454, 197, 3405, 1157, 3562, 3555, 2069, 3569])).
% 4.70/4.93 tff(3571,plain,(hskp29 | hskp62 | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3572,plain,
% 4.70/4.93 (hskp62),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3571, 3224, 333, 126, 1213, 1706])).
% 4.70/4.93 tff(3573,plain,
% 4.70/4.93 (c0_1(a1675)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2084, 3572])).
% 4.70/4.93 tff(3574,plain,
% 4.70/4.93 (~c3_1(a1675)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2098, 3572])).
% 4.70/4.93 tff(3575,plain,
% 4.70/4.93 (c1_1(a1675)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2092, 3572])).
% 4.70/4.93 tff(3576,plain,
% 4.70/4.93 (c2_1(a1675)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2111, 3575, 3574, 3573, 3224])).
% 4.70/4.93 tff(3577,plain,
% 4.70/4.93 (~c0_1(a1718)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2418, 3390])).
% 4.70/4.93 tff(3578,plain,
% 4.70/4.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3579,plain,
% 4.70/4.93 (((~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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3580,plain,
% 4.70/4.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3579])).
% 4.70/4.93 tff(3581,plain,
% 4.70/4.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3580, 3578])).
% 4.70/4.93 tff(3582,plain,
% 4.70/4.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3583,plain,
% 4.70/4.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1675) | c2_1(a1718) | c0_1(a1718) | (~ndr1_0) | c1_1(a1718) | (~c2_1(a1675)) | (~c0_1(a1675))),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3582, 3581])).
% 4.70/4.93 tff(3584,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3583, 197, 335, 333, 3573, 1213, 3574, 3391, 3577, 30, 3576, 3393])).
% 4.70/4.93 tff(3585,plain,((~c1_1(a1654)) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | hskp0 | (~hskp52) | hskp29 | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.70/4.93 tff(3586,plain,
% 4.70/4.93 (~c1_1(a1654)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3585, 818, 333, 1213, 894, 335, 126, 3215])).
% 4.70/4.93 tff(3587,plain,
% 4.70/4.93 (((~![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))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3588,plain,
% 4.70/4.93 ((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))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3589,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(monotonicity,[status(thm)],[3588])).
% 4.70/4.93 tff(3590,plain,
% 4.70/4.93 (((~![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))),
% 4.70/4.93 inference(transitivity,[status(thm)],[3589, 3587])).
% 4.70/4.93 tff(3591,plain,
% 4.70/4.93 ((~![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)))),
% 4.70/4.93 inference(quant_inst,[status(thm)],[])).
% 4.70/4.93 tff(3592,plain,
% 4.70/4.93 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | (~ndr1_0) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.70/4.93 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 4.70/4.93 tff(3593,plain,
% 4.70/4.93 (hskp26),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3592, 197, 860, 832, 831, 20, 3586])).
% 4.70/4.93 tff(3594,plain,
% 4.70/4.93 (~c2_1(a1691)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[612, 3593])).
% 4.70/4.93 tff(3595,plain,
% 4.70/4.93 (~c3_1(a1691)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[632, 3593])).
% 4.70/4.93 tff(3596,plain,
% 4.70/4.93 (~c1_1(a1691)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[618, 3593])).
% 4.70/4.93 tff(3597,plain,
% 4.70/4.93 (hskp37),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2248, 1919, 527, 1953])).
% 4.70/4.93 tff(3598,plain,
% 4.70/4.93 (~c1_1(a1714)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[540, 3597])).
% 4.70/4.93 tff(3599,plain,
% 4.70/4.93 (c0_1(a1714)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[548, 3597])).
% 4.70/4.93 tff(3600,plain,
% 4.70/4.93 (c2_1(a1714)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[556, 3597])).
% 4.70/4.93 tff(3601,plain,
% 4.70/4.93 ($false),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2268, 197, 1919, 1953, 1228, 1227, 1539, 1226, 514, 1225])).
% 4.70/4.93 tff(3602,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,[]))).
% 4.70/4.93 tff(3603,plain,
% 4.70/4.93 (~c3_1(a1714)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[3602, 1919, 1953, 3600, 3599, 1539, 3598])).
% 4.70/4.93 tff(3604,plain,
% 4.70/4.93 (c1_1(a1716)),
% 4.70/4.93 inference(unit_resolution,[status(thm)],[2260, 3603, 1953, 3600, 3599, 1539, 1919])).
% 4.70/4.93 tff(3605,plain,
% 4.70/4.93 (((~![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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3606,plain,
% 4.70/4.93 ((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)))),
% 4.70/4.93 inference(rewrite,[status(thm)],[])).
% 4.70/4.93 tff(3607,plain,
% 4.70/4.93 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3606])).
% 4.77/4.94 tff(3608,plain,
% 4.77/4.94 (((~![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(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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3607, 3605])).
% 4.77/4.94 tff(3609,plain,
% 4.77/4.94 ((~![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(a1716) | c2_1(a1716) | (~c1_1(a1716)) | c0_1(a1716) | c2_1(a1716) | (~c1_1(a1716)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3610,plain,
% 4.77/4.94 ((~![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(a1716) | c0_1(a1716) | c3_1(a1716) | (~ndr1_0) | (~c1_1(a1716))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3609, 3608])).
% 4.77/4.94 tff(3611,plain,
% 4.77/4.94 (hskp21 | c2_1(a1716) | (~c1_1(a1716))),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3610, 197, 1953, 1539, 1261])).
% 4.77/4.94 tff(3612,plain,
% 4.77/4.94 (hskp21),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3611, 3604, 1919])).
% 4.77/4.94 tff(3613,plain,
% 4.77/4.94 (c2_1(a1683)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1284, 3612])).
% 4.77/4.94 tff(3614,plain,
% 4.77/4.94 (c3_1(a1683)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1292, 3612])).
% 4.77/4.94 tff(3615,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3616,plain,
% 4.77/4.94 (((~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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3617,plain,
% 4.77/4.94 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3616])).
% 4.77/4.94 tff(3618,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3617, 3615])).
% 4.77/4.94 tff(3619,plain,
% 4.77/4.94 ((~![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))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3620,plain,
% 4.77/4.94 ((~![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))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 4.77/4.94 tff(3621,plain,
% 4.77/4.94 (~c0_1(a1683)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3620, 197, 1919, 1953, 3600, 3599, 3614, 3613, 1539, 3598, 514])).
% 4.77/4.94 tff(3622,plain,
% 4.77/4.94 (~c1_1(a1683)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1315, 3612])).
% 4.77/4.94 tff(3623,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3624,plain,
% 4.77/4.94 ((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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3625,plain,
% 4.77/4.94 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3624])).
% 4.77/4.94 tff(3626,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3625, 3623])).
% 4.77/4.94 tff(3627,plain,
% 4.77/4.94 ((~![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)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3628,plain,
% 4.77/4.94 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1715) | c2_1(a1715) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1715)) | c3_1(a1714) | (~c2_1(a1714))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 4.77/4.94 tff(3629,plain,
% 4.77/4.94 ($false),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3628, 197, 1505, 333, 1228, 1213, 1226, 1504, 1706, 2252])).
% 4.77/4.94 tff(3630,plain,(c3_1(a1714) | hskp57 | c3_1(a1715) | (~c2_1(a1714)) | c2_1(a1715) | c1_1(a1714) | (~c0_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.77/4.94 tff(3631,plain,
% 4.77/4.94 (hskp57),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3630, 3603, 3215, 333, 1213, 3598, 3600])).
% 4.77/4.94 tff(3632,plain,
% 4.77/4.94 (~c1_1(a1665)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[59, 3631])).
% 4.77/4.94 tff(3633,plain,
% 4.77/4.94 (c3_1(a1665)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[67, 3631])).
% 4.77/4.94 tff(3634,plain,
% 4.77/4.94 (c0_1(a1665)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[78, 3631])).
% 4.77/4.94 tff(3635,plain,
% 4.77/4.94 (((~![V: $i, 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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3636,plain,
% 4.77/4.94 ((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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3637,plain,
% 4.77/4.94 (((~![V: $i, 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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3636])).
% 4.77/4.94 tff(3638,plain,
% 4.77/4.94 (((~![V: $i, 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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3637, 3635])).
% 4.77/4.94 tff(3639,plain,
% 4.77/4.94 ((~![V: $i, 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)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3640,plain,
% 4.77/4.94 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | c0_1(a1683) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 4.77/4.94 tff(3641,plain,
% 4.77/4.94 ($false),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3640, 197, 126, 3634, 3633, 3614, 3632, 3622, 125, 3621])).
% 4.77/4.94 tff(3642,plain,(c2_1(a1716) | hskp29 | c0_1(a1716) | c3_1(a1716) | c3_1(a1715) | c2_1(a1715) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.77/4.94 tff(3643,plain,
% 4.77/4.94 (c2_1(a1716)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3642, 333, 1953, 1539, 126, 1213, 2241])).
% 4.77/4.94 tff(3644,plain,
% 4.77/4.94 (^[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))))),
% 4.77/4.94 inference(bind,[status(th)],[])).
% 4.77/4.94 tff(3645,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(quant_intro,[status(thm)],[3644])).
% 4.77/4.94 tff(3646,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3647,plain,
% 4.77/4.94 (^[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)))))),
% 4.77/4.94 inference(bind,[status(th)],[])).
% 4.77/4.94 tff(3648,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(quant_intro,[status(thm)],[3647])).
% 4.77/4.94 tff(3649,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')).
% 4.77/4.94 tff(3650,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3649, 3648])).
% 4.77/4.94 tff(3651,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3650, 3646])).
% 4.77/4.94 tff(3652,plain,(
% 4.77/4.94 ![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)))),
% 4.77/4.94 inference(skolemize,[status(sab)],[3651])).
% 4.77/4.94 tff(3653,plain,
% 4.77/4.94 (![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)))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3652, 3645])).
% 4.77/4.94 tff(3654,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3655,plain,
% 4.77/4.94 ((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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3656,plain,
% 4.77/4.94 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3655])).
% 4.77/4.94 tff(3657,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3656, 3654])).
% 4.77/4.94 tff(3658,plain,
% 4.77/4.94 ((~![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)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3659,plain,
% 4.77/4.94 ((~![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))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3658, 3657])).
% 4.77/4.94 tff(3660,plain,
% 4.77/4.94 (hskp22 | (~c2_1(a1716))),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3659, 197, 1953, 333, 1539, 1213, 3653, 3215])).
% 4.77/4.94 tff(3661,plain,
% 4.77/4.94 (hskp22),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3660, 3643])).
% 4.77/4.94 tff(3662,plain,
% 4.77/4.94 (((~hskp22) | (~c3_1(a1684))) <=> ((~hskp22) | (~c3_1(a1684)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3663,plain,
% 4.77/4.94 (((~c3_1(a1684)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1684)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3664,axiom,((~c3_1(a1684)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 4.77/4.94 tff(3665,plain,
% 4.77/4.94 ((~hskp22) | (~c3_1(a1684))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3664, 3663])).
% 4.77/4.94 tff(3666,plain,
% 4.77/4.94 ((~hskp22) | (~c3_1(a1684))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3665, 3662])).
% 4.77/4.94 tff(3667,plain,
% 4.77/4.94 (~c3_1(a1684)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3666, 3661])).
% 4.77/4.94 tff(3668,plain,
% 4.77/4.94 (((~hskp22) | c2_1(a1684)) <=> ((~hskp22) | c2_1(a1684))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3669,axiom,((~hskp22) | c2_1(a1684)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 4.77/4.94 tff(3670,plain,
% 4.77/4.94 ((~hskp22) | c2_1(a1684)),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 4.77/4.94 tff(3671,plain,
% 4.77/4.94 ((~hskp22) | c2_1(a1684)),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3670, 3668])).
% 4.77/4.94 tff(3672,plain,
% 4.77/4.94 ((~hskp22) | c2_1(a1684)),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3671, 3668])).
% 4.77/4.94 tff(3673,plain,
% 4.77/4.94 ((~hskp22) | c2_1(a1684)),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3672, 3668])).
% 4.77/4.94 tff(3674,plain,
% 4.77/4.94 ((~hskp22) | c2_1(a1684)),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3673, 3668])).
% 4.77/4.94 tff(3675,plain,
% 4.77/4.94 (c2_1(a1684)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3674, 3661])).
% 4.77/4.94 tff(3676,plain,
% 4.77/4.94 (c1_1(a1718)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[2438, 570, 560, 558, 2430, 2429, 126])).
% 4.77/4.94 tff(3677,plain,
% 4.77/4.94 ($false),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[2870, 197, 1960, 559, 558, 2430, 2429, 1449, 570, 3676])).
% 4.77/4.94 tff(3678,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,[]))).
% 4.77/4.94 tff(3679,plain,
% 4.77/4.94 (c1_1(a1654)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3678, 2863, 126, 2853, 3072, 3071, 2854, 1960])).
% 4.77/4.94 tff(3680,assumption,(~c3_1(a1684)), introduced(assumption)).
% 4.77/4.94 tff(3681,assumption,(c2_1(a1684)), introduced(assumption)).
% 4.77/4.94 tff(3682,plain,
% 4.77/4.94 (~hskp74),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1003, 995, 3402])).
% 4.77/4.94 tff(3683,plain,
% 4.77/4.94 (~hskp57),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3484, 3405, 126, 1157, 3682, 333, 3226, 1706])).
% 4.77/4.94 tff(3684,assumption,(~hskp44), introduced(assumption)).
% 4.77/4.94 tff(3685,plain,
% 4.77/4.94 (~hskp45),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3514, 1505, 333, 1213, 1706])).
% 4.77/4.94 tff(3686,plain,
% 4.77/4.94 (hskp43),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3523, 3685, 3684])).
% 4.77/4.94 tff(3687,plain,
% 4.77/4.94 (c0_1(a1639)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3531, 3686])).
% 4.77/4.94 tff(3688,plain,
% 4.77/4.94 (c2_1(a1639)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3539, 3686])).
% 4.77/4.94 tff(3689,plain,
% 4.77/4.94 (c3_1(a1639)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3543, 197, 995, 3402, 3688, 3687, 971])).
% 4.77/4.94 tff(3690,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3691,plain,
% 4.77/4.94 ((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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3692,plain,
% 4.77/4.94 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3691])).
% 4.77/4.94 tff(3693,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3692, 3690])).
% 4.77/4.94 tff(3694,plain,
% 4.77/4.94 ((~![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)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3695,plain,
% 4.77/4.94 ((~![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))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3694, 3693])).
% 4.77/4.94 tff(3696,plain,
% 4.77/4.94 (hskp57 | c1_1(a1684)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3695, 197, 333, 3681, 1213, 3680, 1504, 1706])).
% 4.77/4.94 tff(3697,plain,
% 4.77/4.94 (c1_1(a1684)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3696, 1505])).
% 4.77/4.94 tff(3698,plain,
% 4.77/4.94 (c3_1(a1639)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3543, 197, 995, 894, 3547, 3546, 971])).
% 4.77/4.94 tff(3699,plain,
% 4.77/4.94 (~c1_1(a1639)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3560, 3545])).
% 4.77/4.94 tff(3700,assumption,(~hskp67), introduced(assumption)).
% 4.77/4.94 tff(3701,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3702,plain,
% 4.77/4.94 ((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)))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3703,plain,
% 4.77/4.94 (((~![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))))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3702])).
% 4.77/4.94 tff(3704,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(transitivity,[status(thm)],[3703, 3701])).
% 4.77/4.94 tff(3705,plain,
% 4.77/4.94 ((~![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)))),
% 4.77/4.94 inference(quant_inst,[status(thm)],[])).
% 4.77/4.94 tff(3706,plain,
% 4.77/4.94 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1639)) | (~c2_1(a1639))),
% 4.77/4.94 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 4.77/4.94 tff(3707,plain,
% 4.77/4.94 ($false),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3706, 197, 3700, 3547, 3546, 3699, 1409, 3698])).
% 4.77/4.94 tff(3708,plain,((~hskp43) | hskp67 | hskp42 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.77/4.94 tff(3709,plain,
% 4.77/4.94 (hskp67),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[3708, 3686, 995, 3402])).
% 4.77/4.94 tff(3710,plain,
% 4.77/4.94 (c3_1(a1702)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1423, 3709])).
% 4.77/4.94 tff(3711,plain,
% 4.77/4.94 (c1_1(a1702)),
% 4.77/4.94 inference(unit_resolution,[status(thm)],[1431, 3709])).
% 4.77/4.94 tff(3712,plain,
% 4.77/4.94 (((~![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))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3713,plain,
% 4.77/4.94 ((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))),
% 4.77/4.94 inference(rewrite,[status(thm)],[])).
% 4.77/4.94 tff(3714,plain,
% 4.77/4.94 (((~![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)))),
% 4.77/4.94 inference(monotonicity,[status(thm)],[3713])).
% 4.77/4.95 tff(3715,plain,
% 4.77/4.95 (((~![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))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3714, 3712])).
% 4.77/4.95 tff(3716,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3717,plain,
% 4.77/4.95 ((~![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)),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3716, 3715])).
% 4.77/4.95 tff(3718,plain,
% 4.77/4.95 (c0_1(a1702)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3717, 197, 3405, 1157, 3711, 3710, 2069])).
% 4.77/4.95 tff(3719,plain,
% 4.77/4.95 (c2_1(a1702)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1894, 3709])).
% 4.77/4.95 tff(3720,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3721,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3722,plain,
% 4.77/4.95 ((~![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))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 4.77/4.95 tff(3723,plain,
% 4.77/4.95 (hskp38),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3722, 197, 3682, 3719, 3710, 953, 3718])).
% 4.77/4.95 tff(3724,plain,
% 4.77/4.95 (~c0_1(a1718)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[2418, 3723])).
% 4.77/4.95 tff(3725,plain,
% 4.77/4.95 (~c1_1(a1639)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3560, 3686])).
% 4.77/4.95 tff(3726,plain,
% 4.77/4.95 (c3_1(a1718)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[909, 3723])).
% 4.77/4.95 tff(3727,plain,
% 4.77/4.95 (((~![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(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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3728,plain,
% 4.77/4.95 (((~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3729,plain,
% 4.77/4.95 (((~![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(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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3728])).
% 4.77/4.95 tff(3730,plain,
% 4.77/4.95 (((~![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(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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3729, 3727])).
% 4.77/4.95 tff(3731,plain,
% 4.77/4.95 ((~![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(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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3732,plain,
% 4.77/4.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1639) | c0_1(a1718) | c3_1(a1684) | (~ndr1_0) | (~c2_1(a1684)) | (~c1_1(a1684)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1639)) | (~c0_1(a1639))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 4.77/4.95 tff(3733,plain,
% 4.77/4.95 (c1_1(a1718)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3732, 197, 3687, 3726, 3681, 3725, 3724, 3680, 90, 3697, 3689])).
% 4.77/4.95 tff(3734,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3454, 197, 3405, 1157, 3726, 3724, 2069, 3733])).
% 4.77/4.95 tff(3735,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,[]))).
% 4.77/4.95 tff(3736,plain,
% 4.77/4.95 (hskp44),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3735, 3683, 1157, 3681, 3680, 995, 3405, 333, 1213, 1706])).
% 4.77/4.95 tff(3737,plain,
% 4.77/4.95 (c2_1(a1640)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3413, 3736])).
% 4.77/4.95 tff(3738,plain,
% 4.77/4.95 (c3_1(a1640)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3421, 3736])).
% 4.77/4.95 tff(3739,plain,
% 4.77/4.95 (c1_1(a1640)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3429, 3736])).
% 4.77/4.95 tff(3740,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3464, 3739, 3738, 3226, 3405, 1213, 1706, 1157, 3682, 3737])).
% 4.77/4.95 tff(3741,plain,(hskp62 | c2_1(a1715) | (~c0_1(a1715)) | hskp61 | (~c2_1(a1684)) | c3_1(a1684) | hskp42 | c3_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.77/4.95 tff(3742,plain,
% 4.77/4.95 (hskp62),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3741, 995, 1706, 1157, 3681, 3680, 1213, 333, 126])).
% 4.77/4.95 tff(3743,plain,
% 4.77/4.95 (~c3_1(a1675)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[2098, 3742])).
% 4.77/4.95 tff(3744,plain,
% 4.77/4.95 (c0_1(a1675)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[2084, 3742])).
% 4.77/4.95 tff(3745,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3746,plain,
% 4.77/4.95 ((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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3747,plain,
% 4.77/4.95 (((~![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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3746])).
% 4.77/4.95 tff(3748,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3747, 3745])).
% 4.77/4.95 tff(3749,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3750,plain,
% 4.77/4.95 ((~![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))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3749, 3748])).
% 4.77/4.95 tff(3751,plain,
% 4.77/4.95 (~c2_1(a1675)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3750, 197, 995, 3402, 3744, 3743, 971])).
% 4.77/4.95 tff(3752,plain,
% 4.77/4.95 (c1_1(a1675)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[2092, 3742])).
% 4.77/4.95 tff(3753,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3754,plain,
% 4.77/4.95 ((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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3755,plain,
% 4.77/4.95 (((~![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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3754])).
% 4.77/4.95 tff(3756,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3755, 3753])).
% 4.77/4.95 tff(3757,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3758,plain,
% 4.77/4.95 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1715) | c2_1(a1715) | (~ndr1_0) | (~c0_1(a1715)) | c2_1(a1675) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3757, 3756])).
% 4.77/4.95 tff(3759,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3758, 197, 1157, 333, 3752, 3744, 1213, 1156, 1706, 3751])).
% 4.77/4.95 tff(3760,plain,(hskp42 | hskp61 | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1715)) | (~c2_1(a1684)) | c3_1(a1684) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.77/4.95 tff(3761,plain,
% 4.77/4.95 (hskp61),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3760, 995, 1706, 1213, 333, 3681, 126, 3680])).
% 4.77/4.95 tff(3762,plain,
% 4.77/4.95 (~c2_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1100, 3761])).
% 4.77/4.95 tff(3763,plain,
% 4.77/4.95 (~c1_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1106, 3761])).
% 4.77/4.95 tff(3764,plain,
% 4.77/4.95 (c3_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1114, 3761])).
% 4.77/4.95 tff(3765,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3221, 197, 335, 3764, 2854, 2853, 1213, 3763, 3762, 590, 1706, 3679])).
% 4.77/4.95 tff(3766,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,[]))).
% 4.77/4.95 tff(3767,plain,
% 4.77/4.95 (hskp42),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3766, 333, 1213, 3215, 126, 1954, 335, 3675, 3667, 894])).
% 4.77/4.95 tff(3768,plain,
% 4.77/4.95 (hskp61),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3387, 3767, 3215, 1213, 333])).
% 4.77/4.95 tff(3769,plain,
% 4.77/4.95 (~c2_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1100, 3768])).
% 4.77/4.95 tff(3770,plain,
% 4.77/4.95 (~c1_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1106, 3768])).
% 4.77/4.95 tff(3771,plain,
% 4.77/4.95 (c3_1(a1674)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1114, 3768])).
% 4.77/4.95 tff(3772,plain,
% 4.77/4.95 (hskp2),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3247, 3767, 335, 333, 3215])).
% 4.77/4.95 tff(3773,plain,
% 4.77/4.95 (~c1_1(a1645)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1044, 3772])).
% 4.77/4.95 tff(3774,plain,
% 4.77/4.95 (~c3_1(a1645)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1060, 3772])).
% 4.77/4.95 tff(3775,plain,
% 4.77/4.95 (~c0_1(a1645)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1038, 3772])).
% 4.77/4.95 tff(3776,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3777,plain,
% 4.77/4.95 (((~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3778,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3777])).
% 4.77/4.95 tff(3779,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3778, 3776])).
% 4.77/4.95 tff(3780,plain,
% 4.77/4.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3781,plain,
% 4.77/4.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3780, 3779])).
% 4.77/4.95 tff(3782,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3781, 197, 335, 333, 208, 210, 1213, 209, 112, 106, 100, 30])).
% 4.77/4.95 tff(3783,plain,((~hskp16) | c1_1(a1715) | c3_1(a1715) | (~c2_1(a1656)) | (~c0_1(a1656)) | c2_1(a1715) | c3_1(a1656)), inference(lemma,lemma(discharge,[]))).
% 4.77/4.95 tff(3784,plain,
% 4.77/4.95 (~hskp16),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3783, 2202, 333, 335, 2201, 1213, 2200])).
% 4.77/4.95 tff(3785,plain,
% 4.77/4.95 (hskp17 | hskp16),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3041, 197, 93, 92, 91, 10])).
% 4.77/4.95 tff(3786,plain,
% 4.77/4.95 (hskp17),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3785, 3784])).
% 4.77/4.95 tff(3787,plain,
% 4.77/4.95 (~c2_1(a1678)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[236, 3786])).
% 4.77/4.95 tff(3788,plain,
% 4.77/4.95 (~c1_1(a1678)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[217, 3786])).
% 4.77/4.95 tff(3789,plain,
% 4.77/4.95 (~c0_1(a1678)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[223, 3786])).
% 4.77/4.95 tff(3790,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3791,plain,
% 4.77/4.95 (((~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3792,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3791])).
% 4.77/4.95 tff(3793,plain,
% 4.77/4.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3792, 3790])).
% 4.77/4.95 tff(3794,plain,
% 4.77/4.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3795,plain,
% 4.77/4.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 4.77/4.95 tff(3796,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3795, 197, 335, 333, 2202, 2201, 1213, 2200, 3789, 3788, 3787, 30])).
% 4.77/4.95 tff(3797,plain,((~hskp53) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 4.77/4.95 tff(3798,plain,
% 4.77/4.95 (~hskp53),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3797, 79, 333, 1213, 335, 68, 60])).
% 4.77/4.95 tff(3799,plain,
% 4.77/4.95 (hskp52),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[135, 3798, 126])).
% 4.77/4.95 tff(3800,plain,
% 4.77/4.95 (c3_1(a1654)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[488, 3799])).
% 4.77/4.95 tff(3801,plain,
% 4.77/4.95 (c0_1(a1654)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[480, 3799])).
% 4.77/4.95 tff(3802,plain,
% 4.77/4.95 (~c1_1(a1654)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3221, 197, 335, 2140, 3801, 3800, 1213, 2138, 2182, 590, 1706])).
% 4.77/4.95 tff(3803,plain,
% 4.77/4.95 (c2_1(a1654)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[496, 3799])).
% 4.77/4.95 tff(3804,plain,
% 4.77/4.95 (((~![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))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3805,plain,
% 4.77/4.95 ((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))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3806,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3805])).
% 4.77/4.95 tff(3807,plain,
% 4.77/4.95 (((~![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))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3806, 3804])).
% 4.77/4.95 tff(3808,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3809,plain,
% 4.77/4.95 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3808, 3807])).
% 4.77/4.95 tff(3810,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3809, 197, 3700, 79, 68, 3803, 3800, 60, 1409, 3802])).
% 4.77/4.95 tff(3811,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,[]))).
% 4.77/4.95 tff(3812,plain,
% 4.77/4.95 (~hskp57),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3811, 3700, 335, 2140, 1213, 2138, 2182, 1706, 126, 333])).
% 4.77/4.95 tff(3813,assumption,(~c3_1(a1645)), introduced(assumption)).
% 4.77/4.95 tff(3814,assumption,(~c1_1(a1645)), introduced(assumption)).
% 4.77/4.95 tff(3815,plain,
% 4.77/4.95 (hskp57 | (~c2_1(a1645))),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3265, 197, 333, 1213, 3814, 3813, 1504, 1706])).
% 4.77/4.95 tff(3816,plain,
% 4.77/4.95 (~c2_1(a1645)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3815, 3812])).
% 4.77/4.95 tff(3817,assumption,(~c0_1(a1645)), introduced(assumption)).
% 4.77/4.95 tff(3818,plain,
% 4.77/4.95 (((~![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))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3819,plain,
% 4.77/4.95 ((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))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3820,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3819])).
% 4.77/4.95 tff(3821,plain,
% 4.77/4.95 (((~![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))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3820, 3818])).
% 4.77/4.95 tff(3822,plain,
% 4.77/4.95 ((~![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))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3823,plain,
% 4.77/4.95 ((~![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)),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3822, 3821])).
% 4.77/4.95 tff(3824,plain,
% 4.77/4.95 (hskp37 | c2_1(a1645)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3823, 197, 2241, 3817, 3813, 526])).
% 4.77/4.95 tff(3825,plain,
% 4.77/4.95 (hskp37),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3824, 3816])).
% 4.77/4.95 tff(3826,plain,
% 4.77/4.95 (c2_1(a1714)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[556, 3825])).
% 4.77/4.95 tff(3827,plain,
% 4.77/4.95 (~c1_1(a1714)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[540, 3825])).
% 4.77/4.95 tff(3828,plain,
% 4.77/4.95 (c3_1(a1714)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3630, 3827, 1706, 333, 1213, 3812, 3826])).
% 4.77/4.95 tff(3829,plain,
% 4.77/4.95 (c0_1(a1714)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[548, 3825])).
% 4.77/4.95 tff(3830,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3831,plain,
% 4.77/4.95 ((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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3832,plain,
% 4.77/4.95 (((~![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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3831])).
% 4.77/4.95 tff(3833,plain,
% 4.77/4.95 (((~![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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3832, 3830])).
% 4.77/4.95 tff(3834,plain,
% 4.77/4.95 ((~![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)))),
% 4.77/4.95 inference(quant_inst,[status(thm)],[])).
% 4.77/4.95 tff(3835,plain,
% 4.77/4.95 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1714))),
% 4.77/4.95 inference(modus_ponens,[status(thm)],[3834, 3833])).
% 4.77/4.95 tff(3836,plain,
% 4.77/4.95 ($false),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3835, 197, 3700, 3826, 3829, 3827, 1409, 3828])).
% 4.77/4.95 tff(3837,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,[]))).
% 4.77/4.95 tff(3838,plain,
% 4.77/4.95 (hskp67),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[3837, 333, 3215, 1213, 3775, 3774, 3773, 335, 3771, 3770, 3769, 126])).
% 4.77/4.95 tff(3839,assumption,(hskp67), introduced(assumption)).
% 4.77/4.95 tff(3840,plain,
% 4.77/4.95 (c3_1(a1702)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1423, 3839])).
% 4.77/4.95 tff(3841,plain,
% 4.77/4.95 (c1_1(a1702)),
% 4.77/4.95 inference(unit_resolution,[status(thm)],[1431, 3839])).
% 4.77/4.95 tff(3842,plain,
% 4.77/4.95 (((~![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)))) | (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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3843,plain,
% 4.77/4.95 (((~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)))),
% 4.77/4.95 inference(rewrite,[status(thm)],[])).
% 4.77/4.95 tff(3844,plain,
% 4.77/4.95 (((~![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(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))))),
% 4.77/4.95 inference(monotonicity,[status(thm)],[3843])).
% 4.77/4.95 tff(3845,plain,
% 4.77/4.95 (((~![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(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)))),
% 4.77/4.95 inference(transitivity,[status(thm)],[3844, 3842])).
% 4.77/4.96 tff(3846,plain,
% 4.77/4.96 ((~![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(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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3847,plain,
% 4.77/4.96 ((~![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)))) | 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))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 4.77/4.96 tff(3848,plain,
% 4.77/4.96 (~c0_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3847, 197, 335, 3841, 3840, 2140, 1213, 2138, 2182, 590, 1706])).
% 4.77/4.96 tff(3849,plain,
% 4.77/4.96 (c2_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1894, 3839])).
% 4.77/4.96 tff(3850,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3851,plain,
% 4.77/4.96 ((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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3852,plain,
% 4.77/4.96 (((~![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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3851])).
% 4.77/4.96 tff(3853,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3852, 3850])).
% 4.77/4.96 tff(3854,plain,
% 4.77/4.96 ((~![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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3855,plain,
% 4.77/4.96 ((~![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))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 4.77/4.96 tff(3856,plain,
% 4.77/4.96 (hskp12),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3855, 197, 820, 3841, 3849, 3840, 830])).
% 4.77/4.96 tff(3857,plain,
% 4.77/4.96 (~c1_1(a1666)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[842, 3856])).
% 4.77/4.96 tff(3858,plain,
% 4.77/4.96 (c3_1(a1666)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[850, 3856])).
% 4.77/4.96 tff(3859,plain,
% 4.77/4.96 (c2_1(a1666)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[858, 3856])).
% 4.77/4.96 tff(3860,plain,
% 4.77/4.96 (((~![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 | 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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3861,plain,
% 4.77/4.96 ((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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3862,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3861])).
% 4.77/4.96 tff(3863,plain,
% 4.77/4.96 (((~![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(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))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3862, 3860])).
% 4.77/4.96 tff(3864,plain,
% 4.77/4.96 ((~![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(a1666) | (~c3_1(a1666)) | (~c2_1(a1666)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3865,plain,
% 4.77/4.96 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3864, 3863])).
% 4.77/4.96 tff(3866,plain,
% 4.77/4.96 ($false),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3865, 197, 1960, 3841, 3840, 3859, 3858, 3857, 1449, 3848])).
% 4.77/4.96 tff(3867,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,[]))).
% 4.77/4.96 tff(3868,plain,
% 4.77/4.96 (hskp13),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3867, 3838, 335, 3771, 1213, 3770, 3769, 3215, 1954])).
% 4.77/4.96 tff(3869,plain,
% 4.77/4.96 (~c1_1(a1667)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[279, 3868])).
% 4.77/4.96 tff(3870,plain,
% 4.77/4.96 (c3_1(a1667)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[287, 3868])).
% 4.77/4.96 tff(3871,plain,
% 4.77/4.96 (c0_1(a1667)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[295, 3868])).
% 4.77/4.96 tff(3872,plain,
% 4.77/4.96 (c3_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1423, 3838])).
% 4.77/4.96 tff(3873,plain,
% 4.77/4.96 (c2_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1894, 3838])).
% 4.77/4.96 tff(3874,plain,
% 4.77/4.96 (c1_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1431, 3838])).
% 4.77/4.96 tff(3875,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3876,plain,
% 4.77/4.96 ((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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3877,plain,
% 4.77/4.96 (((~![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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3876])).
% 4.77/4.96 tff(3878,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3877, 3875])).
% 4.77/4.96 tff(3879,plain,
% 4.77/4.96 ((~![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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3880,plain,
% 4.77/4.96 ((~![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))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 4.77/4.96 tff(3881,plain,
% 4.77/4.96 (hskp63),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3880, 197, 3874, 3873, 3872, 3871, 3870, 3869, 1879])).
% 4.77/4.96 tff(3882,plain,
% 4.77/4.96 (~c0_1(a1676)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1908, 3881])).
% 4.77/4.96 tff(3883,plain,
% 4.77/4.96 (c3_1(a1676)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1916, 3881])).
% 4.77/4.96 tff(3884,plain,
% 4.77/4.96 (((~![V: $i, 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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3885,plain,
% 4.77/4.96 ((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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3886,plain,
% 4.77/4.96 (((~![V: $i, 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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3885])).
% 4.77/4.96 tff(3887,plain,
% 4.77/4.96 (((~![V: $i, 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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3886, 3884])).
% 4.77/4.96 tff(3888,plain,
% 4.77/4.96 ((~![V: $i, 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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3889,plain,
% 4.77/4.96 ((~![V: $i, 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))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 4.77/4.96 tff(3890,plain,
% 4.77/4.96 (c1_1(a1676)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3889, 197, 126, 3883, 3871, 3870, 3882, 3869, 125])).
% 4.77/4.96 tff(3891,plain,
% 4.77/4.96 (~c0_1(a1702)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3847, 197, 335, 3874, 3872, 3771, 1213, 3770, 3769, 590, 3215])).
% 4.77/4.96 tff(3892,plain,
% 4.77/4.96 (((~![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 | 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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3893,plain,
% 4.77/4.96 ((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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3894,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3893])).
% 4.77/4.96 tff(3895,plain,
% 4.77/4.96 (((~![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(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))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3894, 3892])).
% 4.77/4.96 tff(3896,plain,
% 4.77/4.96 ((~![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(a1667) | (~c3_1(a1667)) | (~c2_1(a1667)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3897,plain,
% 4.77/4.96 ((~![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 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3896, 3895])).
% 4.77/4.96 tff(3898,plain,
% 4.77/4.96 (~c2_1(a1667)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3897, 197, 1954, 3874, 3872, 3870, 3869, 1449, 3891])).
% 4.77/4.96 tff(3899,plain,
% 4.77/4.96 (((~hskp63) | c2_1(a1676)) <=> ((~hskp63) | c2_1(a1676))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3900,axiom,((~hskp63) | c2_1(a1676)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 4.77/4.96 tff(3901,plain,
% 4.77/4.96 ((~hskp63) | c2_1(a1676)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 4.77/4.96 tff(3902,plain,
% 4.77/4.96 ((~hskp63) | c2_1(a1676)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3901, 3899])).
% 4.77/4.96 tff(3903,plain,
% 4.77/4.96 ((~hskp63) | c2_1(a1676)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3902, 3899])).
% 4.77/4.96 tff(3904,plain,
% 4.77/4.96 ((~hskp63) | c2_1(a1676)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3903, 3899])).
% 4.77/4.96 tff(3905,plain,
% 4.77/4.96 ((~hskp63) | c2_1(a1676)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3904, 3899])).
% 4.77/4.96 tff(3906,plain,
% 4.77/4.96 (c2_1(a1676)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3905, 3881])).
% 4.77/4.96 tff(3907,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3908,plain,
% 4.77/4.96 ((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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3909,plain,
% 4.77/4.96 (((~![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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3908])).
% 4.77/4.96 tff(3910,plain,
% 4.77/4.96 (((~![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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3909, 3907])).
% 4.77/4.96 tff(3911,plain,
% 4.77/4.96 ((~![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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3912,plain,
% 4.77/4.96 ((~![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))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 4.77/4.96 tff(3913,plain,
% 4.77/4.96 (hskp39),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3912, 197, 3906, 3883, 3871, 3870, 3882, 1380, 3898])).
% 4.77/4.96 tff(3914,plain,
% 4.77/4.96 (~c1_1(a1721)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1398, 3913])).
% 4.77/4.96 tff(3915,plain,
% 4.77/4.96 (c3_1(a1721)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1469, 3913])).
% 4.77/4.96 tff(3916,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3917,plain,
% 4.77/4.96 ((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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3918,plain,
% 4.77/4.96 (((~![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(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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3917])).
% 4.77/4.96 tff(3919,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3918, 3916])).
% 4.77/4.96 tff(3920,plain,
% 4.77/4.96 ((~![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(a1721) | (~c3_1(a1721)) | (~c2_1(a1721)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3921,plain,
% 4.77/4.96 ((~![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(a1676) | c1_1(a1721) | (~ndr1_0) | (~c3_1(a1721)) | (~c2_1(a1721)) | (~c3_1(a1676)) | (~c1_1(a1676))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3920, 3919])).
% 4.77/4.96 tff(3922,plain,
% 4.77/4.96 (~c2_1(a1721)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3921, 197, 1954, 3883, 3915, 3882, 3914, 1449, 3890])).
% 4.77/4.96 tff(3923,plain,
% 4.77/4.96 (~c0_1(a1721)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[1392, 3913])).
% 4.77/4.96 tff(3924,plain,
% 4.77/4.96 (((~![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)))) | (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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3925,plain,
% 4.77/4.96 (((~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))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3926,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3925])).
% 4.77/4.96 tff(3927,plain,
% 4.77/4.96 (((~![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(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))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3926, 3924])).
% 4.77/4.96 tff(3928,plain,
% 4.77/4.96 ((~![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(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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3929,plain,
% 4.77/4.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1715) | c3_1(a1715) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c0_1(a1715)) | (~c3_1(a1721)) | c2_1(a1721)),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 4.77/4.96 tff(3930,plain,
% 4.77/4.96 ($false),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3929, 197, 335, 333, 3915, 3871, 3870, 3923, 380, 3215, 3898, 3922])).
% 4.77/4.96 tff(3931,plain,(c3_1(a1715) | c1_1(a1715) | hskp29 | c2_1(a1715) | hskp0 | c0_1(a1716) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.77/4.96 tff(3932,plain,
% 4.77/4.96 (c3_1(a1715)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3931, 1953, 126, 1213, 894, 335, 1539])).
% 4.77/4.96 tff(3933,assumption,(~c1_1(a1656)), introduced(assumption)).
% 4.77/4.96 tff(3934,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3935,plain,
% 4.77/4.96 (((~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)))),
% 4.77/4.96 inference(rewrite,[status(thm)],[])).
% 4.77/4.96 tff(3936,plain,
% 4.77/4.96 (((~![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(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))))),
% 4.77/4.96 inference(monotonicity,[status(thm)],[3935])).
% 4.77/4.96 tff(3937,plain,
% 4.77/4.96 (((~![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(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)))),
% 4.77/4.96 inference(transitivity,[status(thm)],[3936, 3934])).
% 4.77/4.96 tff(3938,plain,
% 4.77/4.96 ((~![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(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)))),
% 4.77/4.96 inference(quant_inst,[status(thm)],[])).
% 4.77/4.96 tff(3939,plain,
% 4.77/4.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))),
% 4.77/4.96 inference(modus_ponens,[status(thm)],[3938, 3937])).
% 4.77/4.96 tff(3940,plain,
% 4.77/4.96 (~c3_1(a1678)),
% 4.77/4.96 inference(unit_resolution,[status(thm)],[3939, 197, 1959, 210, 1213, 209, 224, 237, 380, 1706, 3933])).
% 4.77/4.96 tff(3941,plain,
% 4.77/4.96 ($false),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[243, 197, 208, 210, 209, 224, 218, 237, 30, 3940])).
% 4.77/4.97 tff(3942,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,[]))).
% 4.77/4.97 tff(3943,plain,
% 4.77/4.97 (~hskp17),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[3942, 3933, 210, 209, 1959, 1213, 1706, 208])).
% 4.77/4.97 tff(3944,plain,
% 4.77/4.97 (((~![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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3945,plain,
% 4.77/4.97 ((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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3946,plain,
% 4.77/4.97 (((~![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))))),
% 4.77/4.97 inference(monotonicity,[status(thm)],[3945])).
% 4.77/4.97 tff(3947,plain,
% 4.77/4.97 (((~![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)))),
% 4.77/4.97 inference(transitivity,[status(thm)],[3946, 3944])).
% 4.77/4.97 tff(3948,plain,
% 4.77/4.97 ((~![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)))),
% 4.77/4.97 inference(quant_inst,[status(thm)],[])).
% 4.77/4.97 tff(3949,plain,
% 4.77/4.97 ((~![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))),
% 4.77/4.97 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 4.77/4.97 tff(3950,plain,
% 4.77/4.97 (hskp17 | hskp16 | c1_1(a1715) | (~c3_1(a1715))),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[3949, 197, 10, 1706])).
% 4.77/4.97 tff(3951,plain,
% 4.77/4.97 (hskp16),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[3950, 3943, 335, 1959])).
% 4.77/4.97 tff(3952,plain,
% 4.77/4.97 (~c2_1(a1677)),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[105, 3951])).
% 4.77/4.97 tff(3953,plain,
% 4.77/4.97 (~c0_1(a1677)),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[111, 3951])).
% 4.77/4.97 tff(3954,plain,
% 4.77/4.97 (((~![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)) | 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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3955,plain,
% 4.77/4.97 (((~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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3956,plain,
% 4.77/4.97 (((~![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)) | 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))))),
% 4.77/4.97 inference(monotonicity,[status(thm)],[3955])).
% 4.77/4.97 tff(3957,plain,
% 4.77/4.97 (((~![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)) | 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)))),
% 4.77/4.97 inference(transitivity,[status(thm)],[3956, 3954])).
% 4.77/4.97 tff(3958,plain,
% 4.77/4.97 ((~![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)) | 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)))),
% 4.77/4.97 inference(quant_inst,[status(thm)],[])).
% 4.77/4.97 tff(3959,plain,
% 4.77/4.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1715) | c3_1(a1656) | c0_1(a1677) | c2_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | c1_1(a1656) | (~c0_1(a1656))),
% 4.77/4.97 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 4.77/4.97 tff(3960,plain,
% 4.77/4.97 (~c3_1(a1677)),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[3959, 197, 1959, 210, 1213, 209, 3953, 3952, 380, 1706, 3933])).
% 4.77/4.97 tff(3961,plain,
% 4.77/4.97 (~c1_1(a1677)),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[99, 3951])).
% 4.77/4.97 tff(3962,plain,
% 4.77/4.97 ($false),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[316, 197, 208, 210, 209, 3953, 3952, 3961, 30, 3960])).
% 4.77/4.97 tff(3963,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,[]))).
% 4.77/4.97 tff(3964,plain,
% 4.77/4.97 (c1_1(a1656)),
% 4.77/4.97 inference(unit_resolution,[status(thm)],[3963, 2202, 2201, 2200, 1959, 1213, 1706, 335])).
% 4.77/4.97 tff(3965,assumption,(c1_1(a1656)), introduced(assumption)).
% 4.77/4.97 tff(3966,plain,
% 4.77/4.97 (((~![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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3967,plain,
% 4.77/4.97 (((~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)))),
% 4.77/4.97 inference(rewrite,[status(thm)],[])).
% 4.77/4.97 tff(3968,plain,
% 4.77/4.97 (((~![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))))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[3967])).
% 4.81/4.97 tff(3969,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(transitivity,[status(thm)],[3968, 3966])).
% 4.81/4.97 tff(3970,plain,
% 4.81/4.97 ((~![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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(3971,plain,
% 4.81/4.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 4.81/4.97 tff(3972,plain,
% 4.81/4.97 (~c3_1(a1677)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3971, 197, 335, 1959, 208, 209, 112, 100, 90, 1706, 3965])).
% 4.81/4.97 tff(3973,plain,
% 4.81/4.97 ($false),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[316, 197, 208, 210, 209, 112, 106, 100, 30, 3972])).
% 4.81/4.97 tff(3974,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,[]))).
% 4.81/4.97 tff(3975,plain,
% 4.81/4.97 (~hskp16),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3974, 2202, 2201, 2200, 335, 1959, 1706, 3964])).
% 4.81/4.97 tff(3976,plain,
% 4.81/4.97 (hskp17),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3950, 3975, 335, 1959])).
% 4.81/4.97 tff(3977,plain,
% 4.81/4.97 (~c1_1(a1678)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[217, 3976])).
% 4.81/4.97 tff(3978,plain,
% 4.81/4.97 (~c0_1(a1678)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[223, 3976])).
% 4.81/4.97 tff(3979,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(3980,plain,
% 4.81/4.97 (((~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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(3981,plain,
% 4.81/4.97 (((~![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))))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[3980])).
% 4.81/4.97 tff(3982,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(transitivity,[status(thm)],[3981, 3979])).
% 4.81/4.97 tff(3983,plain,
% 4.81/4.97 ((~![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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(3984,plain,
% 4.81/4.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | (~ndr1_0) | (~c3_1(a1678)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 4.81/4.97 tff(3985,plain,
% 4.81/4.97 (~c3_1(a1678)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3984, 197, 335, 1959, 2202, 2200, 3978, 3977, 90, 1706, 3964])).
% 4.81/4.97 tff(3986,plain,
% 4.81/4.97 (~c2_1(a1678)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[236, 3976])).
% 4.81/4.97 tff(3987,plain,
% 4.81/4.97 ($false),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[243, 197, 2202, 2201, 2200, 3978, 3977, 3986, 30, 3985])).
% 4.81/4.97 tff(3988,plain,((~hskp53) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.97 tff(3989,plain,
% 4.81/4.97 (~hskp53),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3988, 3932, 335, 3215, 1213])).
% 4.81/4.97 tff(3990,plain,
% 4.81/4.97 (hskp52),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[135, 3989, 126])).
% 4.81/4.97 tff(3991,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(3992,plain,
% 4.81/4.97 (((~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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(3993,plain,
% 4.81/4.97 (((~![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))))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[3992])).
% 4.81/4.97 tff(3994,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(transitivity,[status(thm)],[3993, 3991])).
% 4.81/4.97 tff(3995,plain,
% 4.81/4.97 ((~![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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(3996,plain,
% 4.81/4.97 ((~![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))),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 4.81/4.97 tff(3997,plain,
% 4.81/4.97 (~c1_1(a1654)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3996, 197, 335, 1959, 860, 831, 1213, 590, 1706])).
% 4.81/4.97 tff(3998,plain,
% 4.81/4.97 (((~![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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(3999,plain,
% 4.81/4.97 ((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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4000,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[3999])).
% 4.81/4.97 tff(4001,plain,
% 4.81/4.97 (((~![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))),
% 4.81/4.97 inference(transitivity,[status(thm)],[4000, 3998])).
% 4.81/4.97 tff(4002,plain,
% 4.81/4.97 ((~![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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(4003,plain,
% 4.81/4.97 ((~![V: $i, U: $i] : (hskp67 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp67 | c1_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654)),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[4002, 4001])).
% 4.81/4.97 tff(4004,plain,
% 4.81/4.97 ($false),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4003, 197, 3700, 335, 1959, 832, 831, 1409, 1706, 3997])).
% 4.81/4.97 tff(4005,plain,((~hskp52) | hskp67 | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.97 tff(4006,plain,
% 4.81/4.97 (hskp67),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4005, 3990, 335, 3932, 3215, 1213])).
% 4.81/4.97 tff(4007,plain,
% 4.81/4.97 (c3_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1423, 4006])).
% 4.81/4.97 tff(4008,plain,
% 4.81/4.97 (c1_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1431, 4006])).
% 4.81/4.97 tff(4009,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4010,plain,
% 4.81/4.97 (((~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)))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4011,plain,
% 4.81/4.97 (((~![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))))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[4010])).
% 4.81/4.97 tff(4012,plain,
% 4.81/4.97 (((~![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)))),
% 4.81/4.97 inference(transitivity,[status(thm)],[4011, 4009])).
% 4.81/4.97 tff(4013,plain,
% 4.81/4.97 ((~![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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(4014,plain,
% 4.81/4.97 ((~![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))),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[4013, 4012])).
% 4.81/4.97 tff(4015,plain,
% 4.81/4.97 (~c0_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4014, 197, 335, 3932, 4008, 4007, 1213, 590, 3215])).
% 4.81/4.97 tff(4016,plain,
% 4.81/4.97 (c3_1(a1654)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[488, 3990])).
% 4.81/4.97 tff(4017,plain,
% 4.81/4.97 (c0_1(a1654)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[480, 3990])).
% 4.81/4.97 tff(4018,plain,
% 4.81/4.97 (~c1_1(a1654)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[3996, 197, 335, 3932, 4017, 4016, 1213, 590, 3215])).
% 4.81/4.97 tff(4019,plain,
% 4.81/4.97 (c2_1(a1654)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[496, 3990])).
% 4.81/4.97 tff(4020,plain,
% 4.81/4.97 (((~![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) | (~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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4021,plain,
% 4.81/4.97 ((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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4022,plain,
% 4.81/4.97 (((~![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(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)))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[4021])).
% 4.81/4.97 tff(4023,plain,
% 4.81/4.97 (((~![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(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))),
% 4.81/4.97 inference(transitivity,[status(thm)],[4022, 4020])).
% 4.81/4.97 tff(4024,plain,
% 4.81/4.97 ((~![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(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1702) | (~c3_1(a1702)) | (~c1_1(a1702)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(4025,plain,
% 4.81/4.97 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~ndr1_0) | (~c3_1(a1654)) | (~c2_1(a1654)) | c1_1(a1654) | (~c3_1(a1702)) | (~c1_1(a1702)) | c0_1(a1702)),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 4.81/4.97 tff(4026,plain,
% 4.81/4.97 ($false),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4025, 197, 1954, 4008, 4007, 4019, 4016, 1449, 4018, 4015])).
% 4.81/4.97 tff(4027,plain,(c0_1(a1716) | c1_1(a1715) | c2_1(a1715) | hskp29 | hskp0 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.97 tff(4028,plain,
% 4.81/4.97 (c0_1(a1716)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4027, 894, 1213, 126, 335, 1539])).
% 4.81/4.97 tff(4029,plain,
% 4.81/4.97 (hskp67),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1885, 197, 860, 832, 831, 1409, 3586])).
% 4.81/4.97 tff(4030,plain,
% 4.81/4.97 (c3_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1423, 4029])).
% 4.81/4.97 tff(4031,plain,
% 4.81/4.97 (c2_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1894, 4029])).
% 4.81/4.97 tff(4032,plain,
% 4.81/4.97 (c1_1(a1702)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1431, 4029])).
% 4.81/4.97 tff(4033,plain,
% 4.81/4.97 (hskp63),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1902, 197, 4032, 4031, 4030, 860, 831, 1879, 3586])).
% 4.81/4.97 tff(4034,plain,
% 4.81/4.97 (~c0_1(a1676)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1908, 4033])).
% 4.81/4.97 tff(4035,plain,
% 4.81/4.97 (c3_1(a1676)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[1916, 4033])).
% 4.81/4.97 tff(4036,plain,
% 4.81/4.97 (((~![V: $i, 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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4037,plain,
% 4.81/4.97 ((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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4038,plain,
% 4.81/4.97 (((~![V: $i, 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)))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[4037])).
% 4.81/4.97 tff(4039,plain,
% 4.81/4.97 (((~![V: $i, 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))),
% 4.81/4.97 inference(transitivity,[status(thm)],[4038, 4036])).
% 4.81/4.97 tff(4040,plain,
% 4.81/4.97 ((~![V: $i, 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)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.97 tff(4041,plain,
% 4.81/4.97 ((~![V: $i, 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)),
% 4.81/4.97 inference(modus_ponens,[status(thm)],[4040, 4039])).
% 4.81/4.97 tff(4042,plain,
% 4.81/4.97 (c1_1(a1676)),
% 4.81/4.97 inference(unit_resolution,[status(thm)],[4041, 197, 126, 4035, 860, 831, 4034, 125, 3586])).
% 4.81/4.97 tff(4043,plain,
% 4.81/4.97 (((~![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 | 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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4044,plain,
% 4.81/4.97 ((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))),
% 4.81/4.97 inference(rewrite,[status(thm)],[])).
% 4.81/4.97 tff(4045,plain,
% 4.81/4.97 (((~![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(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)))),
% 4.81/4.97 inference(monotonicity,[status(thm)],[4044])).
% 4.81/4.97 tff(4046,plain,
% 4.81/4.97 (((~![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(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))),
% 4.81/4.97 inference(transitivity,[status(thm)],[4045, 4043])).
% 4.81/4.97 tff(4047,plain,
% 4.81/4.97 ((~![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(a1654) | (~c3_1(a1654)) | (~c2_1(a1654)) | c0_1(a1676) | (~c3_1(a1676)) | (~c1_1(a1676)))),
% 4.81/4.97 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4048,plain,
% 4.81/4.98 ((~![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)),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 4.81/4.98 tff(4049,plain,
% 4.81/4.98 (hskp73 | (~c1_1(a1676))),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4048, 197, 4035, 832, 831, 4034, 1449, 3586])).
% 4.81/4.98 tff(4050,plain,
% 4.81/4.98 (hskp73),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4049, 4042])).
% 4.81/4.98 tff(4051,plain,
% 4.81/4.98 (c2_1(a1716)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1477, 4050])).
% 4.81/4.98 tff(4052,plain,
% 4.81/4.98 (~hskp17),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2993, 4051, 1539, 4028, 3596, 3595, 3594])).
% 4.81/4.98 tff(4053,plain,
% 4.81/4.98 (hskp16),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1183, 4052, 3586])).
% 4.81/4.98 tff(4054,plain,
% 4.81/4.98 (~c1_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[99, 4053])).
% 4.81/4.98 tff(4055,plain,
% 4.81/4.98 (~c2_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[105, 4053])).
% 4.81/4.98 tff(4056,plain,
% 4.81/4.98 (~c0_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[111, 4053])).
% 4.81/4.98 tff(4057,plain,
% 4.81/4.98 (((~![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))) | (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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4058,plain,
% 4.81/4.98 (((~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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4059,plain,
% 4.81/4.98 (((~![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(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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4058])).
% 4.81/4.98 tff(4060,plain,
% 4.81/4.98 (((~![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(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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4059, 4057])).
% 4.81/4.98 tff(4061,plain,
% 4.81/4.98 ((~![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(a1715) | c1_1(a1715) | c2_1(a1715))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4062,plain,
% 4.81/4.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4061, 4060])).
% 4.81/4.98 tff(4063,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4062, 197, 4051, 4028, 335, 333, 1539, 1213, 4056, 4055, 4054, 30])).
% 4.81/4.98 tff(4064,plain,((~hskp52) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | hskp29 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4065,plain,
% 4.81/4.98 (~hskp52),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4064, 333, 335, 1539, 1213, 126, 894])).
% 4.81/4.98 tff(4066,plain,
% 4.81/4.98 (hskp53),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[135, 4065, 126])).
% 4.81/4.98 tff(4067,plain,
% 4.81/4.98 (hskp42),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2461, 4066, 894])).
% 4.81/4.98 tff(4068,plain,
% 4.81/4.98 (hskp2),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3247, 4067, 335, 333, 3215])).
% 4.81/4.98 tff(4069,plain,
% 4.81/4.98 (~c0_1(a1645)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1038, 4068])).
% 4.81/4.98 tff(4070,plain,
% 4.81/4.98 (~c1_1(a1645)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1044, 4068])).
% 4.81/4.98 tff(4071,plain,
% 4.81/4.98 (~c3_1(a1656)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[149, 4066])).
% 4.81/4.98 tff(4072,plain,
% 4.81/4.98 (c0_1(a1656)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[143, 4066])).
% 4.81/4.98 tff(4073,plain,
% 4.81/4.98 (c2_1(a1656)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[157, 4066])).
% 4.81/4.98 tff(4074,plain,
% 4.81/4.98 (((~![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))) | (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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4075,plain,
% 4.81/4.98 (((~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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4076,plain,
% 4.81/4.98 (((~![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(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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4075])).
% 4.81/4.98 tff(4077,plain,
% 4.81/4.98 (((~![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(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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4076, 4074])).
% 4.81/4.98 tff(4078,plain,
% 4.81/4.98 ((~![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(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))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4079,plain,
% 4.81/4.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1715) | c3_1(a1715) | c2_1(a1715) | c3_1(a1656) | c1_1(a1645) | c0_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4078, 4077])).
% 4.81/4.98 tff(4080,plain,
% 4.81/4.98 (c2_1(a1645)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4079, 197, 335, 333, 4073, 4072, 1213, 4071, 4070, 4069, 30])).
% 4.81/4.98 tff(4081,plain,
% 4.81/4.98 (~c3_1(a1645)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1060, 4068])).
% 4.81/4.98 tff(4082,plain,
% 4.81/4.98 (hskp57),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3265, 197, 333, 1213, 4070, 4081, 1504, 3215, 4080])).
% 4.81/4.98 tff(4083,plain,
% 4.81/4.98 (~c1_1(a1665)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[59, 4082])).
% 4.81/4.98 tff(4084,plain,
% 4.81/4.98 (c0_1(a1665)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[78, 4082])).
% 4.81/4.98 tff(4085,plain,
% 4.81/4.98 (c3_1(a1665)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[67, 4082])).
% 4.81/4.98 tff(4086,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3797, 4085, 4084, 333, 1213, 335, 4066, 4083])).
% 4.81/4.98 tff(4087,plain,(c3_1(a1715) | c2_1(a1715) | c1_1(a1715) | hskp0 | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4088,plain,
% 4.81/4.98 (c3_1(a1715)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4087, 894, 335, 1213, 126, 1539])).
% 4.81/4.98 tff(4089,plain,
% 4.81/4.98 (~hskp53),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3988, 4088, 335, 3215, 1213])).
% 4.81/4.98 tff(4090,plain,
% 4.81/4.98 (hskp52),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[135, 4089, 126])).
% 4.81/4.98 tff(4091,plain,
% 4.81/4.98 (c3_1(a1654)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[488, 4090])).
% 4.81/4.98 tff(4092,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4093,plain,
% 4.81/4.98 ((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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4094,plain,
% 4.81/4.98 (((~![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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4093])).
% 4.81/4.98 tff(4095,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4094, 4092])).
% 4.81/4.98 tff(4096,plain,
% 4.81/4.98 ((~![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)))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4097,plain,
% 4.81/4.98 ((~![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))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 4.81/4.98 tff(4098,plain,
% 4.81/4.98 (hskp61 | hskp33 | (~c3_1(a1715))),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4097, 197, 1213, 2486, 1706])).
% 4.81/4.98 tff(4099,plain,
% 4.81/4.98 (hskp33),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4098, 1157, 1959])).
% 4.81/4.98 tff(4100,plain,
% 4.81/4.98 (~c0_1(a1704)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2505, 4099])).
% 4.81/4.98 tff(4101,plain,
% 4.81/4.98 (c3_1(a1704)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2514, 4099])).
% 4.81/4.98 tff(4102,plain,
% 4.81/4.98 (((~![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) | 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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4103,plain,
% 4.81/4.98 ((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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4104,plain,
% 4.81/4.98 (((~![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 | (~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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4103])).
% 4.81/4.98 tff(4105,plain,
% 4.81/4.98 (((~![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 | (~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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4104, 4102])).
% 4.81/4.98 tff(4106,plain,
% 4.81/4.98 ((~![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 | (~ndr1_0) | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1704) | c1_1(a1704) | (~c3_1(a1704)))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4107,plain,
% 4.81/4.98 ((~![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) | c0_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | c1_1(a1704) | (~c3_1(a1715)) | (~c0_1(a1715))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4106, 4105])).
% 4.81/4.98 tff(4108,plain,
% 4.81/4.98 (c1_1(a1704)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4107, 197, 126, 335, 1959, 4101, 4100, 125, 1706])).
% 4.81/4.98 tff(4109,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4110,plain,
% 4.81/4.98 ((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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4111,plain,
% 4.81/4.98 (((~![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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4110])).
% 4.81/4.98 tff(4112,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4111, 4109])).
% 4.81/4.98 tff(4113,plain,
% 4.81/4.98 ((~![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)))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4114,plain,
% 4.81/4.98 ((~![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))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 4.81/4.98 tff(4115,plain,
% 4.81/4.98 (hskp62),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4114, 197, 1157, 4101, 4100, 2069, 4108])).
% 4.81/4.98 tff(4116,plain,
% 4.81/4.98 (c0_1(a1675)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2084, 4115])).
% 4.81/4.98 tff(4117,plain,
% 4.81/4.98 (~c3_1(a1675)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2098, 4115])).
% 4.81/4.98 tff(4118,plain,
% 4.81/4.98 (c1_1(a1675)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2092, 4115])).
% 4.81/4.98 tff(4119,plain,
% 4.81/4.98 (c2_1(a1675)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2111, 4118, 4117, 4116, 1157])).
% 4.81/4.98 tff(4120,plain,
% 4.81/4.98 (~c2_1(a1704)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2499, 4099])).
% 4.81/4.98 tff(4121,plain,
% 4.81/4.98 (((~![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(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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4122,plain,
% 4.81/4.98 ((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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4123,plain,
% 4.81/4.98 (((~![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(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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4122])).
% 4.81/4.98 tff(4124,plain,
% 4.81/4.98 (((~![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(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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4123, 4121])).
% 4.81/4.98 tff(4125,plain,
% 4.81/4.98 ((~![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(a1704) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c1_1(a1675)) | (~c2_1(a1675)) | (~c0_1(a1675)))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4126,plain,
% 4.81/4.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1704) | (~ndr1_0) | (~c3_1(a1704)) | (~c1_1(a1704)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 4.81/4.98 tff(4127,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4126, 197, 894, 4118, 4116, 4101, 4120, 881, 4119, 4108])).
% 4.81/4.98 tff(4128,plain,(hskp61 | hskp0 | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4129,plain,
% 4.81/4.98 (hskp61),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4128, 4088, 126, 335, 894, 3215, 1213])).
% 4.81/4.98 tff(4130,plain,
% 4.81/4.98 (c0_1(a1654)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[480, 4090])).
% 4.81/4.98 tff(4131,plain,
% 4.81/4.98 (~c1_1(a1654)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3223, 4130, 4129, 4091, 1213, 3215, 335])).
% 4.81/4.98 tff(4132,plain,
% 4.81/4.98 (c2_1(a1654)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[496, 4090])).
% 4.81/4.98 tff(4133,plain,
% 4.81/4.98 (hskp26),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3592, 197, 4130, 4132, 4091, 20, 4131])).
% 4.81/4.98 tff(4134,plain,
% 4.81/4.98 (~c2_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[612, 4133])).
% 4.81/4.98 tff(4135,plain,
% 4.81/4.98 (~c3_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[632, 4133])).
% 4.81/4.98 tff(4136,plain,
% 4.81/4.98 (~c1_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[618, 4133])).
% 4.81/4.98 tff(4137,plain,
% 4.81/4.98 (hskp67),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4005, 4090, 335, 4088, 3215, 1213])).
% 4.81/4.98 tff(4138,plain,
% 4.81/4.98 (c3_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1423, 4137])).
% 4.81/4.98 tff(4139,plain,
% 4.81/4.98 (c1_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1431, 4137])).
% 4.81/4.98 tff(4140,plain,
% 4.81/4.98 (~c0_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4014, 197, 335, 4088, 4139, 4138, 1213, 590, 3215])).
% 4.81/4.98 tff(4141,plain,
% 4.81/4.98 (hskp73),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4025, 197, 4139, 4138, 4132, 4091, 1449, 4131, 4140])).
% 4.81/4.98 tff(4142,plain,
% 4.81/4.98 (c2_1(a1716)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1477, 4141])).
% 4.81/4.98 tff(4143,plain,
% 4.81/4.98 (~hskp17),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2993, 4142, 1539, 4028, 4136, 4135, 4134])).
% 4.81/4.98 tff(4144,plain,
% 4.81/4.98 (hskp17 | hskp16 | c1_1(a1715) | (~c3_1(a1715))),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3949, 197, 10, 3215])).
% 4.81/4.98 tff(4145,plain,
% 4.81/4.98 (hskp16),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4144, 4143, 335, 4088])).
% 4.81/4.98 tff(4146,plain,
% 4.81/4.98 (~c1_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[99, 4145])).
% 4.81/4.98 tff(4147,plain,
% 4.81/4.98 (~c2_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[105, 4145])).
% 4.81/4.98 tff(4148,plain,
% 4.81/4.98 (~c0_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[111, 4145])).
% 4.81/4.98 tff(4149,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3052, 197, 4142, 4028, 1539, 4135, 4136, 4134, 4148, 4147, 4146, 30])).
% 4.81/4.98 tff(4150,plain,(hskp0 | c3_1(a1716) | c1_1(a1715) | c2_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4151,plain,
% 4.81/4.98 (hskp0),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4150, 335, 1539, 1213, 126])).
% 4.81/4.98 tff(4152,plain,
% 4.81/4.98 (hskp61),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3401, 333, 3215, 1213, 4151])).
% 4.81/4.98 tff(4153,plain,
% 4.81/4.98 (~c1_1(a1654)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3223, 860, 1095, 831, 1213, 3215, 335])).
% 4.81/4.98 tff(4154,plain,
% 4.81/4.98 (hskp26),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3592, 197, 860, 832, 831, 20, 4153])).
% 4.81/4.98 tff(4155,plain,
% 4.81/4.98 (~c2_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[612, 4154])).
% 4.81/4.98 tff(4156,plain,
% 4.81/4.98 (~c3_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[632, 4154])).
% 4.81/4.98 tff(4157,plain,
% 4.81/4.98 (~c1_1(a1691)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[618, 4154])).
% 4.81/4.98 tff(4158,plain,
% 4.81/4.98 (hskp67),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1885, 197, 860, 832, 831, 1409, 4153])).
% 4.81/4.98 tff(4159,plain,
% 4.81/4.98 (c3_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1423, 4158])).
% 4.81/4.98 tff(4160,plain,
% 4.81/4.98 (c1_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1431, 4158])).
% 4.81/4.98 tff(4161,plain,
% 4.81/4.98 (~c0_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3847, 197, 335, 4160, 4159, 1115, 1213, 1107, 1101, 590, 3215])).
% 4.81/4.98 tff(4162,plain,
% 4.81/4.98 (hskp73),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4025, 197, 4160, 4159, 832, 831, 1449, 4153, 4161])).
% 4.81/4.98 tff(4163,plain,
% 4.81/4.98 (c2_1(a1716)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1477, 4162])).
% 4.81/4.98 tff(4164,plain,
% 4.81/4.98 (c0_1(a1716)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1492, 4162])).
% 4.81/4.98 tff(4165,plain,
% 4.81/4.98 (~hskp17),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[2993, 4164, 1539, 4163, 4157, 4156, 4155])).
% 4.81/4.98 tff(4166,plain,
% 4.81/4.98 (hskp17 | hskp16),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[659, 197, 860, 831, 10, 4153])).
% 4.81/4.98 tff(4167,plain,
% 4.81/4.98 (hskp16),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4166, 4165])).
% 4.81/4.98 tff(4168,plain,
% 4.81/4.98 (~c1_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[99, 4167])).
% 4.81/4.98 tff(4169,plain,
% 4.81/4.98 (~c2_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[105, 4167])).
% 4.81/4.98 tff(4170,plain,
% 4.81/4.98 (~c0_1(a1677)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[111, 4167])).
% 4.81/4.98 tff(4171,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4062, 197, 4163, 4164, 335, 333, 1539, 1213, 4170, 4169, 4168, 30])).
% 4.81/4.98 tff(4172,plain,((~hskp52) | c1_1(a1715) | c3_1(a1715) | c3_1(a1716) | c2_1(a1715) | (~hskp61)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4173,plain,
% 4.81/4.98 (~hskp52),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4172, 333, 335, 1539, 1213, 4152])).
% 4.81/4.98 tff(4174,plain,
% 4.81/4.98 (hskp53),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[135, 4173, 126])).
% 4.81/4.98 tff(4175,plain,
% 4.81/4.98 (~c2_1(a1674)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1100, 4152])).
% 4.81/4.98 tff(4176,plain,
% 4.81/4.98 (~c1_1(a1674)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1106, 4152])).
% 4.81/4.98 tff(4177,plain,
% 4.81/4.98 (c3_1(a1674)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1114, 4152])).
% 4.81/4.98 tff(4178,plain,
% 4.81/4.98 (hskp52 | hskp7 | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[203, 197, 209, 168])).
% 4.81/4.98 tff(4179,plain,
% 4.81/4.98 (hskp7),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4178, 158, 127, 144])).
% 4.81/4.98 tff(4180,plain,
% 4.81/4.98 (c0_1(a1655)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[52, 4179])).
% 4.81/4.98 tff(4181,plain,
% 4.81/4.98 (c3_1(a1655)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[38, 4179])).
% 4.81/4.98 tff(4182,plain,
% 4.81/4.98 (((~![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)))) | (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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4183,plain,
% 4.81/4.98 (((~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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4184,plain,
% 4.81/4.98 (((~![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(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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4183])).
% 4.81/4.98 tff(4185,plain,
% 4.81/4.98 (((~![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(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)))),
% 4.81/4.98 inference(transitivity,[status(thm)],[4184, 4182])).
% 4.81/4.98 tff(4186,plain,
% 4.81/4.98 ((~![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(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)))),
% 4.81/4.98 inference(quant_inst,[status(thm)],[])).
% 4.81/4.98 tff(4187,plain,
% 4.81/4.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1674) | c2_1(a1674) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c1_1(a1655)) | (~c0_1(a1715)) | (~c3_1(a1674))),
% 4.81/4.98 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 4.81/4.98 tff(4188,plain,
% 4.81/4.98 (~c1_1(a1655)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4187, 197, 335, 2140, 4181, 4180, 1213, 2138, 2182, 590, 1706])).
% 4.81/4.98 tff(4189,plain,
% 4.81/4.98 (~hskp16),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3783, 158, 333, 335, 144, 1213, 209])).
% 4.81/4.98 tff(4190,plain,
% 4.81/4.98 (hskp17 | c1_1(a1655)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[254, 197, 4189, 4181, 4180, 10])).
% 4.81/4.98 tff(4191,plain,
% 4.81/4.98 (hskp17),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4190, 4188])).
% 4.81/4.98 tff(4192,plain,
% 4.81/4.98 (~c2_1(a1678)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[236, 4191])).
% 4.81/4.98 tff(4193,plain,
% 4.81/4.98 (~c1_1(a1678)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[217, 4191])).
% 4.81/4.98 tff(4194,plain,
% 4.81/4.98 (~c0_1(a1678)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[223, 4191])).
% 4.81/4.98 tff(4195,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3795, 197, 335, 333, 158, 144, 1213, 209, 4194, 4193, 4192, 30])).
% 4.81/4.98 tff(4196,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,[]))).
% 4.81/4.98 tff(4197,plain,
% 4.81/4.98 (c3_1(a1656)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4196, 4173, 333, 1213, 335, 4177, 4176, 4175, 3215, 126])).
% 4.81/4.98 tff(4198,plain,
% 4.81/4.98 ($false),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[149, 4197, 4174])).
% 4.81/4.98 tff(4199,plain,(c3_1(a1715) | c2_1(a1715) | c1_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.98 tff(4200,plain,
% 4.81/4.98 (c3_1(a1715)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4199, 335, 1213, 126, 1539])).
% 4.81/4.98 tff(4201,plain,
% 4.81/4.98 (~hskp53),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[3988, 4200, 335, 3215, 1213])).
% 4.81/4.98 tff(4202,plain,
% 4.81/4.98 (hskp52),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[135, 4201, 126])).
% 4.81/4.98 tff(4203,plain,
% 4.81/4.98 (hskp67),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4005, 4202, 335, 4200, 3215, 1213])).
% 4.81/4.98 tff(4204,plain,
% 4.81/4.98 (c3_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1423, 4203])).
% 4.81/4.98 tff(4205,plain,
% 4.81/4.98 (c1_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1431, 4203])).
% 4.81/4.98 tff(4206,plain,
% 4.81/4.98 (~c0_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[4014, 197, 335, 4200, 4205, 4204, 1213, 590, 3215])).
% 4.81/4.98 tff(4207,plain,
% 4.81/4.98 (c2_1(a1702)),
% 4.81/4.98 inference(unit_resolution,[status(thm)],[1894, 4203])).
% 4.81/4.98 tff(4208,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4209,plain,
% 4.81/4.98 ((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)))),
% 4.81/4.98 inference(rewrite,[status(thm)],[])).
% 4.81/4.98 tff(4210,plain,
% 4.81/4.98 (((~![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))))),
% 4.81/4.98 inference(monotonicity,[status(thm)],[4209])).
% 4.81/4.98 tff(4211,plain,
% 4.81/4.98 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4210, 4208])).
% 4.81/4.99 tff(4212,plain,
% 4.81/4.99 ((~![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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4213,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 4.81/4.99 tff(4214,plain,
% 4.81/4.99 (hskp39),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4213, 197, 4200, 4207, 4204, 1213, 1380, 3215, 4206])).
% 4.81/4.99 tff(4215,plain,
% 4.81/4.99 (~c0_1(a1721)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1392, 4214])).
% 4.81/4.99 tff(4216,plain,
% 4.81/4.99 (~c1_1(a1721)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1398, 4214])).
% 4.81/4.99 tff(4217,plain,
% 4.81/4.99 (c3_1(a1721)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1469, 4214])).
% 4.81/4.99 tff(4218,plain,
% 4.81/4.99 (((~![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(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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4219,plain,
% 4.81/4.99 ((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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4220,plain,
% 4.81/4.99 (((~![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(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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4219])).
% 4.81/4.99 tff(4221,plain,
% 4.81/4.99 (((~![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(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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4220, 4218])).
% 4.81/4.99 tff(4222,plain,
% 4.81/4.99 ((~![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(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4223,plain,
% 4.81/4.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1721) | c0_1(a1721) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1721))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4222, 4221])).
% 4.81/4.99 tff(4224,plain,
% 4.81/4.99 ($false),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4223, 197, 126, 335, 4200, 4217, 4216, 4215, 125, 3215])).
% 4.81/4.99 tff(4225,plain,(c1_1(a1715) | hskp29 | c2_1(a1715) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/4.99 tff(4226,plain,
% 4.81/4.99 (c1_1(a1715)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4225, 1213, 126, 1539])).
% 4.81/4.99 tff(4227,plain,
% 4.81/4.99 (c3_1(a1715)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1865, 4226, 126, 1213, 3215])).
% 4.81/4.99 tff(4228,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4229,plain,
% 4.81/4.99 ((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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4230,plain,
% 4.81/4.99 (((~![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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4229])).
% 4.81/4.99 tff(4231,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4230, 4228])).
% 4.81/4.99 tff(4232,plain,
% 4.81/4.99 ((~![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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4233,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4232, 4231])).
% 4.81/4.99 tff(4234,plain,
% 4.81/4.99 (hskp13),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4233, 197, 4226, 4227, 1213, 266, 3215])).
% 4.81/4.99 tff(4235,plain,
% 4.81/4.99 (~c1_1(a1667)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[279, 4234])).
% 4.81/4.99 tff(4236,plain,
% 4.81/4.99 (c3_1(a1667)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[287, 4234])).
% 4.81/4.99 tff(4237,plain,
% 4.81/4.99 (c0_1(a1667)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[295, 4234])).
% 4.81/4.99 tff(4238,assumption,(~c2_1(a1667)), introduced(assumption)).
% 4.81/4.99 tff(4239,assumption,(~c1_1(a1667)), introduced(assumption)).
% 4.81/4.99 tff(4240,assumption,(c3_1(a1667)), introduced(assumption)).
% 4.81/4.99 tff(4241,assumption,(c0_1(a1667)), introduced(assumption)).
% 4.81/4.99 tff(4242,plain,
% 4.81/4.99 (((~![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(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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4243,plain,
% 4.81/4.99 (((~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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4244,plain,
% 4.81/4.99 (((~![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(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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4243])).
% 4.81/4.99 tff(4245,plain,
% 4.81/4.99 (((~![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(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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4244, 4242])).
% 4.81/4.99 tff(4246,plain,
% 4.81/4.99 ((~![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(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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4247,plain,
% 4.81/4.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 4.81/4.99 tff(4248,plain,
% 4.81/4.99 ($false),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4247, 197, 771, 1959, 4241, 4240, 4239, 590, 1706, 4238])).
% 4.81/4.99 tff(4249,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,[]))).
% 4.81/4.99 tff(4250,plain,
% 4.81/4.99 (c2_1(a1667)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4249, 4226, 4227, 4237, 4236, 4235, 3215])).
% 4.81/4.99 tff(4251,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4252,plain,
% 4.81/4.99 ((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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4253,plain,
% 4.81/4.99 (((~![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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4252])).
% 4.81/4.99 tff(4254,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4253, 4251])).
% 4.81/4.99 tff(4255,plain,
% 4.81/4.99 ((~![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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4256,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 4.81/4.99 tff(4257,plain,
% 4.81/4.99 (hskp26 | (~c2_1(a1667))),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4256, 197, 4237, 4236, 4235, 20])).
% 4.81/4.99 tff(4258,plain,
% 4.81/4.99 (hskp26),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4257, 4250])).
% 4.81/4.99 tff(4259,plain,
% 4.81/4.99 (~c2_1(a1691)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[612, 4258])).
% 4.81/4.99 tff(4260,plain,
% 4.81/4.99 (~c3_1(a1691)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[632, 4258])).
% 4.81/4.99 tff(4261,plain,
% 4.81/4.99 (c1_1(a1656)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[3942, 212, 1959, 209, 210, 1213, 1706, 208])).
% 4.81/4.99 tff(4262,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4263,plain,
% 4.81/4.99 (((~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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4264,plain,
% 4.81/4.99 (((~![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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4263])).
% 4.81/4.99 tff(4265,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4264, 4262])).
% 4.81/4.99 tff(4266,plain,
% 4.81/4.99 ((~![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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4267,plain,
% 4.81/4.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1656) | c0_1(a1678) | c1_1(a1678) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1678)) | (~c2_1(a1656)) | (~c1_1(a1656))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 4.81/4.99 tff(4268,plain,
% 4.81/4.99 (~c3_1(a1678)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4267, 197, 208, 4241, 4240, 209, 224, 218, 4239, 90, 4261])).
% 4.81/4.99 tff(4269,plain,
% 4.81/4.99 ($false),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[243, 197, 208, 210, 209, 224, 218, 237, 30, 4268])).
% 4.81/4.99 tff(4270,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,[]))).
% 4.81/4.99 tff(4271,plain,
% 4.81/4.99 (~hskp17),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4270, 2202, 2201, 2200, 4241, 4240, 4239, 1959, 1213, 1706])).
% 4.81/4.99 tff(4272,plain,
% 4.81/4.99 (hskp17 | hskp16),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[302, 197, 4241, 4240, 4239, 10])).
% 4.81/4.99 tff(4273,plain,
% 4.81/4.99 (hskp16),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4272, 4271])).
% 4.81/4.99 tff(4274,plain,
% 4.81/4.99 (~c1_1(a1677)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[99, 4273])).
% 4.81/4.99 tff(4275,plain,
% 4.81/4.99 (~c0_1(a1677)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[111, 4273])).
% 4.81/4.99 tff(4276,plain,
% 4.81/4.99 (((~![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 | 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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4277,plain,
% 4.81/4.99 ((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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4278,plain,
% 4.81/4.99 (((~![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(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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4277])).
% 4.81/4.99 tff(4279,plain,
% 4.81/4.99 (((~![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(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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4278, 4276])).
% 4.81/4.99 tff(4280,plain,
% 4.81/4.99 ((~![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(a1677) | c1_1(a1677) | (~c3_1(a1677)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4281,plain,
% 4.81/4.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1677) | c1_1(a1677) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1677))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4280, 4279])).
% 4.81/4.99 tff(4282,plain,
% 4.81/4.99 (~c3_1(a1677)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4281, 197, 126, 4241, 4240, 4275, 4274, 4239, 125])).
% 4.81/4.99 tff(4283,plain,
% 4.81/4.99 (~c2_1(a1677)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[105, 4273])).
% 4.81/4.99 tff(4284,plain,
% 4.81/4.99 ($false),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[316, 197, 2202, 2201, 2200, 4275, 4283, 4274, 30, 4282])).
% 4.81/4.99 tff(4285,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,[]))).
% 4.81/4.99 tff(4286,plain,
% 4.81/4.99 (~hskp53),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4285, 4237, 126, 4236, 4235, 4227, 1213, 3215])).
% 4.81/4.99 tff(4287,plain,
% 4.81/4.99 (hskp52),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[135, 4286, 126])).
% 4.81/4.99 tff(4288,plain,
% 4.81/4.99 (c3_1(a1654)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[488, 4287])).
% 4.81/4.99 tff(4289,plain,
% 4.81/4.99 (c2_1(a1654)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[496, 4287])).
% 4.81/4.99 tff(4290,plain,
% 4.81/4.99 (c0_1(a1654)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[480, 4287])).
% 4.81/4.99 tff(4291,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4292,plain,
% 4.81/4.99 (((~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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4293,plain,
% 4.81/4.99 (((~![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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4292])).
% 4.81/4.99 tff(4294,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4293, 4291])).
% 4.81/4.99 tff(4295,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4296,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4295, 4294])).
% 4.81/4.99 tff(4297,plain,
% 4.81/4.99 (c0_1(a1691)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4296, 197, 4290, 4289, 4288, 4237, 4260, 4259, 4235, 514, 4250])).
% 4.81/4.99 tff(4298,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4299,plain,
% 4.81/4.99 ((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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4300,plain,
% 4.81/4.99 (((~![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))))),
% 4.81/4.99 inference(monotonicity,[status(thm)],[4299])).
% 4.81/4.99 tff(4301,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/4.99 inference(transitivity,[status(thm)],[4300, 4298])).
% 4.81/4.99 tff(4302,plain,
% 4.81/4.99 ((~![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)))),
% 4.81/4.99 inference(quant_inst,[status(thm)],[])).
% 4.81/4.99 tff(4303,plain,
% 4.81/4.99 ((~![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))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 4.81/4.99 tff(4304,plain,
% 4.81/4.99 (hskp47),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[4303, 197, 4226, 4227, 4260, 4259, 1719, 3215, 4297])).
% 4.81/4.99 tff(4305,plain,
% 4.81/4.99 (~c0_1(a1644)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1732, 4304])).
% 4.81/4.99 tff(4306,plain,
% 4.81/4.99 (~c1_1(a1644)),
% 4.81/4.99 inference(unit_resolution,[status(thm)],[1738, 4304])).
% 4.81/4.99 tff(4307,plain,
% 4.81/4.99 (^[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))))),
% 4.81/4.99 inference(bind,[status(th)],[])).
% 4.81/4.99 tff(4308,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(quant_intro,[status(thm)],[4307])).
% 4.81/4.99 tff(4309,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(rewrite,[status(thm)],[])).
% 4.81/4.99 tff(4310,plain,
% 4.81/4.99 (^[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)))))),
% 4.81/4.99 inference(bind,[status(th)],[])).
% 4.81/4.99 tff(4311,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(quant_intro,[status(thm)],[4310])).
% 4.81/4.99 tff(4312,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')).
% 4.81/4.99 tff(4313,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 4.81/4.99 tff(4314,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4313, 4309])).
% 4.81/4.99 tff(4315,plain,(
% 4.81/4.99 ![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)))),
% 4.81/4.99 inference(skolemize,[status(sab)],[4314])).
% 4.81/4.99 tff(4316,plain,
% 4.81/4.99 (![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)))),
% 4.81/4.99 inference(modus_ponens,[status(thm)],[4315, 4308])).
% 4.81/4.99 tff(4317,plain,
% 4.81/4.99 (((~![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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4318,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4319,plain,
% 4.81/5.00 (((~![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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4318])).
% 4.81/5.00 tff(4320,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4319, 4317])).
% 4.81/5.00 tff(4321,plain,
% 4.81/5.00 ((~![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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4322,plain,
% 4.81/5.00 ((~![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))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 4.81/5.00 tff(4323,plain,
% 4.81/5.00 (hskp34 | (~c2_1(a1667))),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4322, 197, 4226, 4227, 4237, 1213, 4235, 4316])).
% 4.81/5.00 tff(4324,plain,
% 4.81/5.00 (hskp34),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4323, 4250])).
% 4.81/5.00 tff(4325,plain,
% 4.81/5.00 (((~hskp34) | (~c1_1(a1705))) <=> ((~hskp34) | (~c1_1(a1705)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4326,plain,
% 4.81/5.00 (((~c1_1(a1705)) | (~hskp34)) <=> ((~hskp34) | (~c1_1(a1705)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4327,axiom,((~c1_1(a1705)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 4.81/5.00 tff(4328,plain,
% 4.81/5.00 ((~hskp34) | (~c1_1(a1705))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 4.81/5.00 tff(4329,plain,
% 4.81/5.00 ((~hskp34) | (~c1_1(a1705))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4328, 4325])).
% 4.81/5.00 tff(4330,plain,
% 4.81/5.00 (~c1_1(a1705)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4329, 4324])).
% 4.81/5.00 tff(4331,plain,
% 4.81/5.00 (((~hskp34) | (~c3_1(a1705))) <=> ((~hskp34) | (~c3_1(a1705)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4332,plain,
% 4.81/5.00 (((~c3_1(a1705)) | (~hskp34)) <=> ((~hskp34) | (~c3_1(a1705)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4333,axiom,((~c3_1(a1705)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause240')).
% 4.81/5.00 tff(4334,plain,
% 4.81/5.00 ((~hskp34) | (~c3_1(a1705))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4333, 4332])).
% 4.81/5.00 tff(4335,plain,
% 4.81/5.00 ((~hskp34) | (~c3_1(a1705))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4334, 4331])).
% 4.81/5.00 tff(4336,plain,
% 4.81/5.00 (~c3_1(a1705)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4335, 4324])).
% 4.81/5.00 tff(4337,plain,
% 4.81/5.00 (((~hskp34) | c2_1(a1705)) <=> ((~hskp34) | c2_1(a1705))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4338,axiom,((~hskp34) | c2_1(a1705)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 4.81/5.00 tff(4339,plain,
% 4.81/5.00 ((~hskp34) | c2_1(a1705)),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 4.81/5.00 tff(4340,plain,
% 4.81/5.00 ((~hskp34) | c2_1(a1705)),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4339, 4337])).
% 4.81/5.00 tff(4341,plain,
% 4.81/5.00 ((~hskp34) | c2_1(a1705)),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4340, 4337])).
% 4.81/5.00 tff(4342,plain,
% 4.81/5.00 ((~hskp34) | c2_1(a1705)),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4341, 4337])).
% 4.81/5.00 tff(4343,plain,
% 4.81/5.00 ((~hskp34) | c2_1(a1705)),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4342, 4337])).
% 4.81/5.00 tff(4344,plain,
% 4.81/5.00 (c2_1(a1705)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4343, 4324])).
% 4.81/5.00 tff(4345,plain,
% 4.81/5.00 (((~![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(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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4346,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4347,plain,
% 4.81/5.00 (((~![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(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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4346])).
% 4.81/5.00 tff(4348,plain,
% 4.81/5.00 (((~![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(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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4347, 4345])).
% 4.81/5.00 tff(4349,plain,
% 4.81/5.00 ((~![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(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c3_1(a1705) | c1_1(a1705) | (~c2_1(a1705)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4350,plain,
% 4.81/5.00 ((~![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(a1705) | c1_1(a1705) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1705))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4349, 4348])).
% 4.81/5.00 tff(4351,plain,
% 4.81/5.00 (hskp57),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4350, 197, 4344, 4336, 4330, 4260, 4259, 1504, 4297])).
% 4.81/5.00 tff(4352,plain,
% 4.81/5.00 (~c1_1(a1665)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[59, 4351])).
% 4.81/5.00 tff(4353,plain,
% 4.81/5.00 (c3_1(a1644)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1748, 4304])).
% 4.81/5.00 tff(4354,plain,
% 4.81/5.00 (c3_1(a1665)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[67, 4351])).
% 4.81/5.00 tff(4355,plain,
% 4.81/5.00 (c0_1(a1665)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[78, 4351])).
% 4.81/5.00 tff(4356,plain,
% 4.81/5.00 (((~![V: $i, 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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4357,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4358,plain,
% 4.81/5.00 (((~![V: $i, 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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4357])).
% 4.81/5.00 tff(4359,plain,
% 4.81/5.00 (((~![V: $i, 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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4358, 4356])).
% 4.81/5.00 tff(4360,plain,
% 4.81/5.00 ((~![V: $i, 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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4361,plain,
% 4.81/5.00 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1644)) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4360, 4359])).
% 4.81/5.00 tff(4362,plain,
% 4.81/5.00 ($false),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4361, 197, 126, 4355, 4354, 4353, 4352, 4306, 4305, 125])).
% 4.81/5.00 tff(4363,plain,(c2_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.00 tff(4364,plain,
% 4.81/5.00 (c2_1(a1715)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4363, 1539, 126])).
% 4.81/5.00 tff(4365,plain,
% 4.81/5.00 (~hskp72),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[502, 4364])).
% 4.81/5.00 tff(4366,plain,
% 4.81/5.00 (c3_1(a1715)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1202, 334, 126])).
% 4.81/5.00 tff(4367,plain,
% 4.81/5.00 (((~![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)) | 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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4368,plain,
% 4.81/5.00 (((~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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4369,plain,
% 4.81/5.00 (((~![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)) | 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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4368])).
% 4.81/5.00 tff(4370,plain,
% 4.81/5.00 (((~![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)) | 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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4369, 4367])).
% 4.81/5.00 tff(4371,plain,
% 4.81/5.00 ((~![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)) | 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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4372,plain,
% 4.81/5.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | (~c3_1(a1715))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 4.81/5.00 tff(4373,plain,
% 4.81/5.00 ($false),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4372, 197, 335, 1959, 69, 71, 334, 112, 106, 70, 346, 336])).
% 4.81/5.00 tff(4374,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,[]))).
% 4.81/5.00 tff(4375,plain,
% 4.81/5.00 (~hskp16),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4374, 206, 4366, 335, 205, 334, 207, 144, 150, 158])).
% 4.81/5.00 tff(4376,plain,
% 4.81/5.00 (hskp17),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[304, 4375, 206, 205, 207])).
% 4.81/5.00 tff(4377,plain,
% 4.81/5.00 (~c2_1(a1678)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[236, 4376])).
% 4.81/5.00 tff(4378,plain,
% 4.81/5.00 (~c1_1(a1678)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[217, 4376])).
% 4.81/5.00 tff(4379,plain,
% 4.81/5.00 (~c0_1(a1678)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[223, 4376])).
% 4.81/5.00 tff(4380,plain,
% 4.81/5.00 (c1_1(a1655)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[245, 4376, 144, 150, 126, 206, 205, 158])).
% 4.81/5.00 tff(4381,plain,
% 4.81/5.00 (hskp13),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[456, 4380])).
% 4.81/5.00 tff(4382,plain,
% 4.81/5.00 (c0_1(a1715)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[3153, 4381, 126, 4366, 335])).
% 4.81/5.00 tff(4383,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4384,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4385,plain,
% 4.81/5.00 (((~![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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4384])).
% 4.81/5.00 tff(4386,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4385, 4383])).
% 4.81/5.00 tff(4387,plain,
% 4.81/5.00 ((~![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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4388,plain,
% 4.81/5.00 ((~![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))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4387, 4386])).
% 4.81/5.00 tff(4389,plain,
% 4.81/5.00 (hskp26 | (~c0_1(a1715))),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4388, 197, 335, 4366, 334, 20])).
% 4.81/5.00 tff(4390,plain,
% 4.81/5.00 (hskp26),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4389, 4382])).
% 4.81/5.00 tff(4391,plain,
% 4.81/5.00 (~c2_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[612, 4390])).
% 4.81/5.00 tff(4392,plain,
% 4.81/5.00 (~c1_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[618, 4390])).
% 4.81/5.00 tff(4393,plain,
% 4.81/5.00 (~c3_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[632, 4390])).
% 4.81/5.00 tff(4394,plain,
% 4.81/5.00 (((~![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))) | (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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4395,plain,
% 4.81/5.00 (((~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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4396,plain,
% 4.81/5.00 (((~![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(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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4395])).
% 4.81/5.00 tff(4397,plain,
% 4.81/5.00 (((~![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(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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4396, 4394])).
% 4.81/5.00 tff(4398,plain,
% 4.81/5.00 ((~![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(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))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4399,plain,
% 4.81/5.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1656) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1656)) | (~c0_1(a1656))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4398, 4397])).
% 4.81/5.00 tff(4400,plain,
% 4.81/5.00 ($false),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4399, 197, 158, 144, 150, 4393, 4392, 4391, 4379, 4378, 4377, 30])).
% 4.81/5.00 tff(4401,plain,(hskp52 | c1_1(a1715) | (~c2_1(a1715)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.81/5.00 tff(4402,plain,
% 4.81/5.00 (hskp52),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4401, 335, 4364, 126])).
% 4.81/5.00 tff(4403,plain,
% 4.81/5.00 (c3_1(a1654)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[488, 4402])).
% 4.81/5.00 tff(4404,plain,
% 4.81/5.00 (c2_1(a1654)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[496, 4402])).
% 4.81/5.00 tff(4405,plain,
% 4.81/5.00 (c0_1(a1654)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[480, 4402])).
% 4.81/5.00 tff(4406,plain,
% 4.81/5.00 (c3_1(a1715)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1202, 4364, 126])).
% 4.81/5.00 tff(4407,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4408,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4409,plain,
% 4.81/5.00 (((~![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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4408])).
% 4.81/5.00 tff(4410,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4409, 4407])).
% 4.81/5.00 tff(4411,plain,
% 4.81/5.00 ((~![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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4412,plain,
% 4.81/5.00 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1715) | (~c2_1(a1715)) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4411, 4410])).
% 4.81/5.00 tff(4413,plain,
% 4.81/5.00 (hskp26),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4412, 197, 335, 4406, 4405, 4404, 4403, 4364, 20])).
% 4.81/5.00 tff(4414,plain,
% 4.81/5.00 (~c2_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[612, 4413])).
% 4.81/5.00 tff(4415,plain,
% 4.81/5.00 (~c3_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[632, 4413])).
% 4.81/5.00 tff(4416,assumption,(~c0_1(a1691)), introduced(assumption)).
% 4.81/5.00 tff(4417,plain,
% 4.81/5.00 (hskp37 | c0_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[639, 197, 527, 893, 895, 526])).
% 4.81/5.00 tff(4418,plain,
% 4.81/5.00 (hskp37),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4417, 4416])).
% 4.81/5.00 tff(4419,plain,
% 4.81/5.00 (~c1_1(a1714)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[540, 4418])).
% 4.81/5.00 tff(4420,plain,
% 4.81/5.00 (c0_1(a1714)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[548, 4418])).
% 4.81/5.00 tff(4421,plain,
% 4.81/5.00 (c2_1(a1714)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[556, 4418])).
% 4.81/5.00 tff(4422,plain,
% 4.81/5.00 ($false),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[650, 197, 560, 559, 558, 4421, 4420, 4419, 893, 895, 514, 4416])).
% 4.81/5.00 tff(4423,plain,(c0_1(a1691) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654)) | c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.81/5.00 tff(4424,plain,
% 4.81/5.00 (c0_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4423, 4405, 4404, 4403, 4415, 4414, 4365])).
% 4.81/5.00 tff(4425,plain,
% 4.81/5.00 (~c1_1(a1691)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[618, 4413])).
% 4.81/5.00 tff(4426,plain,
% 4.81/5.00 (hskp67),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1885, 197, 4405, 4404, 4403, 1409, 570])).
% 4.81/5.00 tff(4427,plain,
% 4.81/5.00 (c3_1(a1702)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1423, 4426])).
% 4.81/5.00 tff(4428,plain,
% 4.81/5.00 (c2_1(a1702)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1894, 4426])).
% 4.81/5.00 tff(4429,plain,
% 4.81/5.00 (c1_1(a1702)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1431, 4426])).
% 4.81/5.00 tff(4430,plain,
% 4.81/5.00 (hskp63),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1902, 197, 4429, 4428, 4427, 4405, 4403, 1879, 570])).
% 4.81/5.00 tff(4431,plain,
% 4.81/5.00 (~c0_1(a1676)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1908, 4430])).
% 4.81/5.00 tff(4432,plain,
% 4.81/5.00 (c3_1(a1676)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1916, 4430])).
% 4.81/5.00 tff(4433,plain,
% 4.81/5.00 (c1_1(a1676)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4041, 197, 126, 4432, 4405, 4403, 4431, 125, 570])).
% 4.81/5.00 tff(4434,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4435,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4436,plain,
% 4.81/5.00 (((~![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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4435])).
% 4.81/5.00 tff(4437,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4436, 4434])).
% 4.81/5.00 tff(4438,plain,
% 4.81/5.00 ((~![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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4439,plain,
% 4.81/5.00 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1676) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1676)) | (~c1_1(a1676))),
% 4.81/5.00 inference(modus_ponens,[status(thm)],[4438, 4437])).
% 4.81/5.00 tff(4440,plain,
% 4.81/5.00 (hskp73 | (~c1_1(a1676))),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4439, 197, 335, 4406, 4432, 4364, 4431, 1449])).
% 4.81/5.00 tff(4441,plain,
% 4.81/5.00 (hskp73),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4440, 4433])).
% 4.81/5.00 tff(4442,plain,
% 4.81/5.00 (c2_1(a1716)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1477, 4441])).
% 4.81/5.00 tff(4443,plain,
% 4.81/5.00 (c0_1(a1716)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[1492, 4441])).
% 4.81/5.00 tff(4444,plain,
% 4.81/5.00 (~hskp17),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[2993, 4443, 1539, 4442, 4425, 4415, 4414])).
% 4.81/5.00 tff(4445,plain,
% 4.81/5.00 (hskp17 | hskp16 | c1_1(a1654)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[659, 197, 4405, 4403, 10])).
% 4.81/5.00 tff(4446,plain,
% 4.81/5.00 (hskp16),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4445, 4444, 570])).
% 4.81/5.00 tff(4447,plain,
% 4.81/5.00 (~c0_1(a1677)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[111, 4446])).
% 4.81/5.00 tff(4448,plain,
% 4.81/5.00 (~c1_1(a1677)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[99, 4446])).
% 4.81/5.00 tff(4449,plain,
% 4.81/5.00 (~c2_1(a1677)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[105, 4446])).
% 4.81/5.00 tff(4450,plain,
% 4.81/5.00 (c3_1(a1677)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[735, 4449, 4365, 4403, 4404, 4447, 4405])).
% 4.81/5.00 tff(4451,plain,
% 4.81/5.00 ($false),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[745, 4450, 4448, 126, 4403, 4405, 570, 4447])).
% 4.81/5.00 tff(4452,plain,(c1_1(a1654) | hskp29 | c3_1(a1716) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.00 tff(4453,plain,
% 4.81/5.00 (c1_1(a1654)),
% 4.81/5.00 inference(unit_resolution,[status(thm)],[4452, 335, 1539, 126])).
% 4.81/5.00 tff(4454,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4455,plain,
% 4.81/5.00 ((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)))),
% 4.81/5.00 inference(rewrite,[status(thm)],[])).
% 4.81/5.00 tff(4456,plain,
% 4.81/5.00 (((~![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))))),
% 4.81/5.00 inference(monotonicity,[status(thm)],[4455])).
% 4.81/5.00 tff(4457,plain,
% 4.81/5.00 (((~![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)))),
% 4.81/5.00 inference(transitivity,[status(thm)],[4456, 4454])).
% 4.81/5.00 tff(4458,plain,
% 4.81/5.00 ((~![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)))),
% 4.81/5.00 inference(quant_inst,[status(thm)],[])).
% 4.81/5.00 tff(4459,plain,
% 4.81/5.01 ((~![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))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4458, 4457])).
% 4.81/5.01 tff(4460,plain,
% 4.81/5.01 (hskp47 | (~c0_1(a1691)) | (~c1_1(a1654))),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4459, 197, 4405, 4403, 4415, 4414, 1719])).
% 4.81/5.01 tff(4461,plain,
% 4.81/5.01 (hskp47),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4460, 4424, 4453])).
% 4.81/5.01 tff(4462,plain,
% 4.81/5.01 (~c0_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1732, 4461])).
% 4.81/5.01 tff(4463,plain,
% 4.81/5.01 (~c1_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1738, 4461])).
% 4.81/5.01 tff(4464,plain,
% 4.81/5.01 (c3_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1748, 4461])).
% 4.81/5.01 tff(4465,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4466,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4467,plain,
% 4.81/5.01 (((~![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(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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4466])).
% 4.81/5.01 tff(4468,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4467, 4465])).
% 4.81/5.01 tff(4469,plain,
% 4.81/5.01 ((~![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(a1715) | (~c3_1(a1715)) | (~c0_1(a1715)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4470,plain,
% 4.81/5.01 ((~![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(a1715) | c1_1(a1644) | c0_1(a1644) | (~ndr1_0) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c3_1(a1644))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 4.81/5.01 tff(4471,plain,
% 4.81/5.01 (~c0_1(a1715)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4470, 197, 126, 335, 4406, 4464, 4463, 4462, 125])).
% 4.81/5.01 tff(4472,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4473,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4474,plain,
% 4.81/5.01 (((~![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(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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4473])).
% 4.81/5.01 tff(4475,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4474, 4472])).
% 4.81/5.01 tff(4476,plain,
% 4.81/5.01 ((~![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(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4477,plain,
% 4.81/5.01 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1715) | c1_1(a1665) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4476, 4475])).
% 4.81/5.01 tff(4478,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4477, 197, 126, 335, 1959, 79, 68, 60, 125, 1204])).
% 4.81/5.01 tff(4479,plain,((~hskp57) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4480,plain,
% 4.81/5.01 (~hskp57),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4479, 4471, 126, 4406, 335])).
% 4.81/5.01 tff(4481,plain,
% 4.81/5.01 (~hskp13),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[3153, 4471, 126, 4406, 335])).
% 4.81/5.01 tff(4482,plain,
% 4.81/5.01 (~hskp61),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1123, 4424, 4403, 4425, 4414, 4453, 4405])).
% 4.81/5.01 tff(4483,plain,
% 4.81/5.01 (~c3_1(a1637)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1144, 2372, 820, 2371, 2370])).
% 4.81/5.01 tff(4484,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1165, 4483, 2372, 1157, 2371, 2370])).
% 4.81/5.01 tff(4485,plain,((~hskp0) | hskp61 | hskp13), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4486,plain,
% 4.81/5.01 (~hskp0),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4485, 4482, 4481])).
% 4.81/5.01 tff(4487,plain,
% 4.81/5.01 (hskp42),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1003, 972, 894])).
% 4.81/5.01 tff(4488,plain,
% 4.81/5.01 (~c3_1(a1638)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1009, 4487])).
% 4.81/5.01 tff(4489,plain,
% 4.81/5.01 (c0_1(a1638)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1017, 4487])).
% 4.81/5.01 tff(4490,plain,
% 4.81/5.01 (c1_1(a1638)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1025, 4487])).
% 4.81/5.01 tff(4491,plain,
% 4.81/5.01 (hskp2),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1032, 197, 4490, 4489, 4488, 893, 892, 891, 871])).
% 4.81/5.01 tff(4492,plain,
% 4.81/5.01 (~c0_1(a1645)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1038, 4491])).
% 4.81/5.01 tff(4493,plain,
% 4.81/5.01 (~c1_1(a1645)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1044, 4491])).
% 4.81/5.01 tff(4494,plain,
% 4.81/5.01 (c2_1(a1645)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1054, 197, 994, 986, 978, 893, 892, 895, 4493, 4492, 30])).
% 4.81/5.01 tff(4495,plain,
% 4.81/5.01 (~c3_1(a1645)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1060, 4491])).
% 4.81/5.01 tff(4496,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4497,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4498,plain,
% 4.81/5.01 (((~![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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4497])).
% 4.81/5.01 tff(4499,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4498, 4496])).
% 4.81/5.01 tff(4500,plain,
% 4.81/5.01 ((~![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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4501,plain,
% 4.81/5.01 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp57 | c3_1(a1691) | c2_1(a1691) | c1_1(a1645) | c3_1(a1645) | (~ndr1_0) | (~c2_1(a1645)) | (~c0_1(a1691))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 4.81/5.01 tff(4502,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4501, 197, 1505, 893, 895, 4493, 4495, 1504, 871, 4494])).
% 4.81/5.01 tff(4503,plain,((~hskp74) | hskp57 | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c1_1(a1691) | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4504,plain,
% 4.81/5.01 (~hskp74),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4503, 4486, 4415, 4414, 4424, 4425, 4480])).
% 4.81/5.01 tff(4505,plain,
% 4.81/5.01 (hskp38),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[960, 4504, 4402])).
% 4.81/5.01 tff(4506,plain,
% 4.81/5.01 (~c2_1(a1718)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[901, 4505])).
% 4.81/5.01 tff(4507,plain,
% 4.81/5.01 (c3_1(a1718)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[909, 4505])).
% 4.81/5.01 tff(4508,plain,
% 4.81/5.01 (~c1_1(a1718)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[916, 197, 4486, 4405, 4404, 4507, 4506, 881, 4453])).
% 4.81/5.01 tff(4509,plain,
% 4.81/5.01 (((~![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)))) | (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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4510,plain,
% 4.81/5.01 (((~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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4511,plain,
% 4.81/5.01 (((~![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(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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4510])).
% 4.81/5.01 tff(4512,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4511, 4509])).
% 4.81/5.01 tff(4513,plain,
% 4.81/5.01 ((~![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(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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4514,plain,
% 4.81/5.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | c1_1(a1718) | (~c3_1(a1718)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4513, 4512])).
% 4.81/5.01 tff(4515,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4514, 197, 4405, 4403, 4507, 4506, 4425, 4414, 590, 4453, 4508, 4424])).
% 4.81/5.01 tff(4516,plain,(c1_1(a1715) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4517,plain,
% 4.81/5.01 (c1_1(a1715)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4516, 1539, 126])).
% 4.81/5.01 tff(4518,plain,
% 4.81/5.01 (c1_1(a1655)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[327, 206, 126, 205, 158, 150, 144, 207])).
% 4.81/5.01 tff(4519,plain,
% 4.81/5.01 (hskp13),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[456, 4518])).
% 4.81/5.01 tff(4520,plain,
% 4.81/5.01 (~c1_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[279, 4519])).
% 4.81/5.01 tff(4521,plain,
% 4.81/5.01 (c3_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[287, 4519])).
% 4.81/5.01 tff(4522,plain,
% 4.81/5.01 (c0_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[295, 4519])).
% 4.81/5.01 tff(4523,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4524,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4525,plain,
% 4.81/5.01 (((~![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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4524])).
% 4.81/5.01 tff(4526,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4525, 4523])).
% 4.81/5.01 tff(4527,plain,
% 4.81/5.01 ((~![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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4528,plain,
% 4.81/5.01 ((~![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))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4527, 4526])).
% 4.81/5.01 tff(4529,plain,
% 4.81/5.01 (hskp63),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4528, 197, 771, 4366, 4522, 4521, 334, 4520, 1879])).
% 4.81/5.01 tff(4530,plain,
% 4.81/5.01 (~c0_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1908, 4529])).
% 4.81/5.01 tff(4531,plain,
% 4.81/5.01 (c3_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1916, 4529])).
% 4.81/5.01 tff(4532,plain,
% 4.81/5.01 (c2_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[3905, 4529])).
% 4.81/5.01 tff(4533,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4534,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4535,plain,
% 4.81/5.01 (((~![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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4534])).
% 4.81/5.01 tff(4536,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4535, 4533])).
% 4.81/5.01 tff(4537,plain,
% 4.81/5.01 ((~![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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4538,plain,
% 4.81/5.01 ((~![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))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 4.81/5.01 tff(4539,plain,
% 4.81/5.01 (hskp39),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4538, 197, 4532, 4531, 206, 205, 4530, 207, 1380])).
% 4.81/5.01 tff(4540,plain,
% 4.81/5.01 (~c0_1(a1721)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1392, 4539])).
% 4.81/5.01 tff(4541,plain,
% 4.81/5.01 (~c1_1(a1721)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1398, 4539])).
% 4.81/5.01 tff(4542,plain,
% 4.81/5.01 (c3_1(a1721)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1469, 4539])).
% 4.81/5.01 tff(4543,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4544,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4545,plain,
% 4.81/5.01 (((~![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(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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4544])).
% 4.81/5.01 tff(4546,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4545, 4543])).
% 4.81/5.01 tff(4547,plain,
% 4.81/5.01 ((~![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(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1721) | c1_1(a1721) | (~c3_1(a1721)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4548,plain,
% 4.81/5.01 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1721) | c0_1(a1721) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1721))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4547, 4546])).
% 4.81/5.01 tff(4549,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4548, 197, 126, 4542, 4522, 4521, 4541, 4540, 4520, 125])).
% 4.81/5.01 tff(4550,plain,(hskp52 | hskp29 | (~c1_1(a1715)) | (~c2_1(a1715))), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4551,plain,
% 4.81/5.01 (hskp52),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4550, 4517, 126, 4364])).
% 4.81/5.01 tff(4552,plain,
% 4.81/5.01 (c2_1(a1654)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[496, 4551])).
% 4.81/5.01 tff(4553,plain,
% 4.81/5.01 (c3_1(a1654)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[488, 4551])).
% 4.81/5.01 tff(4554,plain,
% 4.81/5.01 (c0_1(a1654)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[480, 4551])).
% 4.81/5.01 tff(4555,plain,
% 4.81/5.01 (hskp26),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[3592, 197, 4554, 4552, 4553, 20, 570])).
% 4.81/5.01 tff(4556,plain,
% 4.81/5.01 (~c2_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[612, 4555])).
% 4.81/5.01 tff(4557,plain,
% 4.81/5.01 (~c3_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[632, 4555])).
% 4.81/5.01 tff(4558,plain,
% 4.81/5.01 (~c1_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[618, 4555])).
% 4.81/5.01 tff(4559,plain,
% 4.81/5.01 (((~![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))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4560,plain,
% 4.81/5.01 ((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))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4561,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4560])).
% 4.81/5.01 tff(4562,plain,
% 4.81/5.01 (((~![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))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4561, 4559])).
% 4.81/5.01 tff(4563,plain,
% 4.81/5.01 ((~![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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4564,plain,
% 4.81/5.01 ((~![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)),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 4.81/5.01 tff(4565,plain,
% 4.81/5.01 (hskp63),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4564, 197, 4517, 4406, 4554, 4553, 4364, 1879, 570])).
% 4.81/5.01 tff(4566,plain,
% 4.81/5.01 (~c0_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1908, 4565])).
% 4.81/5.01 tff(4567,plain,
% 4.81/5.01 (c3_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1916, 4565])).
% 4.81/5.01 tff(4568,plain,
% 4.81/5.01 (c1_1(a1676)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4041, 197, 126, 4567, 4554, 4553, 4566, 125, 570])).
% 4.81/5.01 tff(4569,plain,
% 4.81/5.01 (hskp73 | (~c1_1(a1676))),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4048, 197, 4567, 4552, 4553, 4566, 1449, 570])).
% 4.81/5.01 tff(4570,plain,
% 4.81/5.01 (hskp73),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4569, 4568])).
% 4.81/5.01 tff(4571,plain,
% 4.81/5.01 (c2_1(a1716)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1477, 4570])).
% 4.81/5.01 tff(4572,plain,
% 4.81/5.01 (c0_1(a1716)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1492, 4570])).
% 4.81/5.01 tff(4573,plain,
% 4.81/5.01 (~hskp17),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[2993, 4572, 1539, 4571, 4558, 4557, 4556])).
% 4.81/5.01 tff(4574,plain,
% 4.81/5.01 (hskp17 | hskp16 | c1_1(a1654)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[659, 197, 4554, 4553, 10])).
% 4.81/5.01 tff(4575,plain,
% 4.81/5.01 (hskp16),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4574, 4573, 570])).
% 4.81/5.01 tff(4576,plain,
% 4.81/5.01 (~c0_1(a1677)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[111, 4575])).
% 4.81/5.01 tff(4577,plain,
% 4.81/5.01 (~c1_1(a1677)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[99, 4575])).
% 4.81/5.01 tff(4578,plain,
% 4.81/5.01 (~c2_1(a1677)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[105, 4575])).
% 4.81/5.01 tff(4579,plain,
% 4.81/5.01 (c3_1(a1677)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[735, 4578, 4365, 4553, 4552, 4576, 4554])).
% 4.81/5.01 tff(4580,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[745, 4579, 4577, 126, 4553, 4554, 570, 4576])).
% 4.81/5.01 tff(4581,plain,(c1_1(a1654) | hskp29 | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4582,plain,
% 4.81/5.01 (c1_1(a1654)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4581, 1539, 126])).
% 4.81/5.01 tff(4583,assumption,(~hskp26), introduced(assumption)).
% 4.81/5.01 tff(4584,assumption,(hskp12), introduced(assumption)).
% 4.81/5.01 tff(4585,plain,
% 4.81/5.01 (~c1_1(a1666)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[842, 4584])).
% 4.81/5.01 tff(4586,plain,
% 4.81/5.01 (c3_1(a1666)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[850, 4584])).
% 4.81/5.01 tff(4587,plain,
% 4.81/5.01 (c2_1(a1666)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[858, 4584])).
% 4.81/5.01 tff(4588,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[866, 197, 4583, 560, 559, 558, 4587, 4586, 4585, 20])).
% 4.81/5.01 tff(4589,plain,((~hskp12) | hskp26 | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c3_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 4.81/5.01 tff(4590,plain,
% 4.81/5.01 (~hskp12),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4589, 4583, 560, 559, 558])).
% 4.81/5.01 tff(4591,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4592,plain,
% 4.81/5.01 ((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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4593,plain,
% 4.81/5.01 (((~![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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4592])).
% 4.81/5.01 tff(4594,plain,
% 4.81/5.01 (((~![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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4593, 4591])).
% 4.81/5.01 tff(4595,plain,
% 4.81/5.01 ((~![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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4596,plain,
% 4.81/5.01 ((~![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))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 4.81/5.01 tff(4597,plain,
% 4.81/5.01 (hskp13 | hskp12 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4596, 197, 334, 830])).
% 4.81/5.01 tff(4598,plain,
% 4.81/5.01 (hskp13),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4597, 4590, 1959, 771])).
% 4.81/5.01 tff(4599,plain,
% 4.81/5.01 (~c1_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[279, 4598])).
% 4.81/5.01 tff(4600,plain,
% 4.81/5.01 (c3_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[287, 4598])).
% 4.81/5.01 tff(4601,plain,
% 4.81/5.01 (c0_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[295, 4598])).
% 4.81/5.01 tff(4602,plain,
% 4.81/5.01 (~c2_1(a1667)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4256, 197, 4583, 4601, 4600, 4599, 20])).
% 4.81/5.01 tff(4603,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4604,plain,
% 4.81/5.01 (((~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)))),
% 4.81/5.01 inference(rewrite,[status(thm)],[])).
% 4.81/5.01 tff(4605,plain,
% 4.81/5.01 (((~![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(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))))),
% 4.81/5.01 inference(monotonicity,[status(thm)],[4604])).
% 4.81/5.01 tff(4606,plain,
% 4.81/5.01 (((~![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(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)))),
% 4.81/5.01 inference(transitivity,[status(thm)],[4605, 4603])).
% 4.81/5.01 tff(4607,plain,
% 4.81/5.01 ((~![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(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)))),
% 4.81/5.01 inference(quant_inst,[status(thm)],[])).
% 4.81/5.01 tff(4608,plain,
% 4.81/5.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.81/5.01 inference(modus_ponens,[status(thm)],[4607, 4606])).
% 4.81/5.01 tff(4609,plain,
% 4.81/5.01 ($false),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4608, 197, 560, 558, 4601, 4600, 4599, 590, 819, 4602])).
% 4.81/5.01 tff(4610,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,[]))).
% 4.81/5.01 tff(4611,plain,
% 4.81/5.01 (hskp26),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4610, 4554, 4553, 4582, 4406, 4517, 4364, 4552])).
% 4.81/5.01 tff(4612,plain,
% 4.81/5.01 (~c3_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[632, 4611])).
% 4.81/5.01 tff(4613,plain,
% 4.81/5.01 (~c2_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[612, 4611])).
% 4.81/5.01 tff(4614,plain,
% 4.81/5.01 (c0_1(a1691)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4423, 893, 4552, 4553, 4554, 895, 4365])).
% 4.81/5.01 tff(4615,plain,
% 4.81/5.01 (hskp47),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[4459, 197, 4554, 4553, 893, 895, 1719, 4582, 4614])).
% 4.81/5.01 tff(4616,plain,
% 4.81/5.01 (~c0_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1732, 4615])).
% 4.81/5.01 tff(4617,plain,
% 4.81/5.01 (~c1_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1738, 4615])).
% 4.81/5.01 tff(4618,plain,
% 4.81/5.01 (c3_1(a1644)),
% 4.81/5.01 inference(unit_resolution,[status(thm)],[1748, 4615])).
% 4.81/5.01 tff(4619,assumption,(~c0_1(a1644)), introduced(assumption)).
% 4.81/5.01 tff(4620,assumption,(~c1_1(a1644)), introduced(assumption)).
% 4.81/5.01 tff(4621,assumption,(c3_1(a1644)), introduced(assumption)).
% 4.81/5.02 tff(4622,plain,
% 4.81/5.02 ($false),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1755, 197, 126, 4621, 3145, 3144, 4620, 4619, 3143, 125])).
% 4.81/5.02 tff(4623,plain,((~hskp13) | hskp29 | (~c3_1(a1644)) | c1_1(a1644) | c0_1(a1644)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.02 tff(4624,plain,
% 4.81/5.02 (~hskp13),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4623, 4618, 126, 4617, 4616])).
% 4.81/5.02 tff(4625,plain,
% 4.81/5.02 (hskp13 | hskp12 | (~c3_1(a1715)) | (~c1_1(a1715))),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4596, 197, 4364, 830])).
% 4.81/5.02 tff(4626,plain,
% 4.81/5.02 (hskp12),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4625, 4624, 4406, 4517])).
% 4.81/5.02 tff(4627,plain,
% 4.81/5.02 (~c1_1(a1666)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[842, 4626])).
% 4.81/5.02 tff(4628,plain,
% 4.81/5.02 (c3_1(a1666)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[850, 4626])).
% 4.81/5.02 tff(4629,plain,
% 4.81/5.02 (((~![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(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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4630,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4631,plain,
% 4.81/5.02 (((~![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(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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4630])).
% 4.81/5.02 tff(4632,plain,
% 4.81/5.02 (((~![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(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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4631, 4629])).
% 4.81/5.02 tff(4633,plain,
% 4.81/5.02 ((~![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(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1644) | c1_1(a1644) | (~c3_1(a1644)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4634,plain,
% 4.81/5.02 ((~![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(a1644) | c0_1(a1644) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | (~c3_1(a1644))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4633, 4632])).
% 4.81/5.02 tff(4635,plain,
% 4.81/5.02 (~c0_1(a1666)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4634, 197, 126, 4618, 4628, 4617, 4616, 4627, 125])).
% 4.81/5.02 tff(4636,plain,
% 4.81/5.02 (c2_1(a1666)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[858, 4626])).
% 4.81/5.02 tff(4637,plain,
% 4.81/5.02 (hskp26),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[866, 197, 4554, 4552, 4553, 4636, 4628, 4627, 20])).
% 4.81/5.02 tff(4638,plain,
% 4.81/5.02 (~c1_1(a1691)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[618, 4637])).
% 4.81/5.02 tff(4639,plain,
% 4.81/5.02 (~hskp61),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1123, 4638, 4553, 4582, 895, 4614, 4554])).
% 4.81/5.02 tff(4640,plain,
% 4.81/5.02 (~hskp0),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4485, 4639, 4624])).
% 4.81/5.02 tff(4641,plain,
% 4.81/5.02 (c0_1(a1691)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4423, 893, 832, 831, 860, 895, 503])).
% 4.81/5.02 tff(4642,plain,
% 4.81/5.02 (~hskp74),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4503, 894, 893, 895, 4641, 892, 1505])).
% 4.81/5.02 tff(4643,plain,
% 4.81/5.02 (~hskp61),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1123, 892, 558, 819, 895, 871, 560])).
% 4.81/5.02 tff(4644,plain,
% 4.81/5.02 (hskp62 | hskp61 | c0_1(a1715) | (~c1_1(a1715))),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[2075, 197, 1959, 2069])).
% 4.81/5.02 tff(4645,plain,
% 4.81/5.02 (hskp62),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4644, 1204, 771, 4643])).
% 4.81/5.02 tff(4646,plain,
% 4.81/5.02 (c0_1(a1675)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[2084, 4645])).
% 4.81/5.02 tff(4647,plain,
% 4.81/5.02 (~c3_1(a1675)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[2098, 4645])).
% 4.81/5.02 tff(4648,plain,
% 4.81/5.02 (c1_1(a1675)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[2092, 4645])).
% 4.81/5.02 tff(4649,plain,
% 4.81/5.02 (c2_1(a1675)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[2111, 4648, 4647, 4646, 4643])).
% 4.81/5.02 tff(4650,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4651,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4652,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4651])).
% 4.81/5.02 tff(4653,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4652, 4650])).
% 4.81/5.02 tff(4654,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4655,plain,
% 4.81/5.02 ((~![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))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4654, 4653])).
% 4.81/5.02 tff(4656,plain,
% 4.81/5.02 (hskp2),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4655, 197, 4648, 4646, 4647, 893, 892, 891, 871])).
% 4.81/5.02 tff(4657,plain,
% 4.81/5.02 (~c0_1(a1645)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1038, 4656])).
% 4.81/5.02 tff(4658,plain,
% 4.81/5.02 (~c1_1(a1645)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1044, 4656])).
% 4.81/5.02 tff(4659,plain,
% 4.81/5.02 (hskp47),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4459, 197, 560, 558, 893, 895, 1719, 819, 871])).
% 4.81/5.02 tff(4660,plain,
% 4.81/5.02 (~c1_1(a1644)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1738, 4659])).
% 4.81/5.02 tff(4661,plain,
% 4.81/5.02 (c3_1(a1644)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1748, 4659])).
% 4.81/5.02 tff(4662,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4663,plain,
% 4.81/5.02 (((~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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4664,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4663])).
% 4.81/5.02 tff(4665,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4664, 4662])).
% 4.81/5.02 tff(4666,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4667,plain,
% 4.81/5.02 ((~![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))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 4.81/5.02 tff(4668,plain,
% 4.81/5.02 (c1_1(a1691) | c2_1(a1644)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4667, 197, 560, 558, 4661, 4660, 895, 590, 819, 871])).
% 4.81/5.02 tff(4669,plain,
% 4.81/5.02 (c2_1(a1644)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4668, 892])).
% 4.81/5.02 tff(4670,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4671,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4672,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4671])).
% 4.81/5.02 tff(4673,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4672, 4670])).
% 4.81/5.02 tff(4674,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4675,plain,
% 4.81/5.02 ((~![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))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 4.81/5.02 tff(4676,plain,
% 4.81/5.02 (hskp73),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4675, 197, 771, 1959, 4661, 4660, 1449, 1204, 4669])).
% 4.81/5.02 tff(4677,plain,
% 4.81/5.02 (c0_1(a1716)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1492, 4676])).
% 4.81/5.02 tff(4678,plain,
% 4.81/5.02 (c2_1(a1716)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1477, 4676])).
% 4.81/5.02 tff(4679,plain,
% 4.81/5.02 (((~![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))) | (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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4680,plain,
% 4.81/5.02 (((~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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4681,plain,
% 4.81/5.02 (((~![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(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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4680])).
% 4.81/5.02 tff(4682,plain,
% 4.81/5.02 (((~![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(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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4681, 4679])).
% 4.81/5.02 tff(4683,plain,
% 4.81/5.02 ((~![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(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))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4684,plain,
% 4.81/5.02 ((~![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))) | 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))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4683, 4682])).
% 4.81/5.02 tff(4685,plain,
% 4.81/5.02 (c2_1(a1645)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4684, 197, 4678, 4677, 1539, 893, 892, 895, 4658, 4657, 30])).
% 4.81/5.02 tff(4686,plain,
% 4.81/5.02 (~c3_1(a1645)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1060, 4656])).
% 4.81/5.02 tff(4687,plain,
% 4.81/5.02 (hskp40),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[1067, 197, 560, 558, 4658, 4686, 671, 819, 4685])).
% 4.81/5.02 tff(4688,plain,
% 4.81/5.02 (~c2_1(a1725)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[684, 4687])).
% 4.81/5.02 tff(4689,plain,
% 4.81/5.02 (c3_1(a1725)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[692, 4687])).
% 4.81/5.02 tff(4690,plain,
% 4.81/5.02 (c1_1(a1725)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[700, 4687])).
% 4.81/5.02 tff(4691,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4692,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4693,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4692])).
% 4.81/5.02 tff(4694,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4693, 4691])).
% 4.81/5.02 tff(4695,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4696,plain,
% 4.81/5.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1725) | (~ndr1_0) | (~c3_1(a1725)) | (~c1_1(a1725)) | (~c2_1(a1675)) | (~c1_1(a1675)) | (~c0_1(a1675))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 4.81/5.02 tff(4697,plain,
% 4.81/5.02 ($false),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4696, 197, 894, 4648, 4646, 4690, 4689, 4688, 881, 4649])).
% 4.81/5.02 tff(4698,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,[]))).
% 4.81/5.02 tff(4699,plain,
% 4.81/5.02 (c0_1(a1715)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4698, 894, 860, 831, 819, 1539, 893, 892, 895, 4641, 771, 1959])).
% 4.81/5.02 tff(4700,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4701,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4702,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4701])).
% 4.81/5.02 tff(4703,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4702, 4700])).
% 4.81/5.02 tff(4704,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4705,plain,
% 4.81/5.02 ((~![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))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4704, 4703])).
% 4.81/5.02 tff(4706,plain,
% 4.81/5.02 (~c1_1(a1718)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4705, 197, 894, 771, 910, 334, 902, 881, 1706])).
% 4.81/5.02 tff(4707,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4708,plain,
% 4.81/5.02 (((~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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4709,plain,
% 4.81/5.02 (((~![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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4708])).
% 4.81/5.02 tff(4710,plain,
% 4.81/5.02 (((~![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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4709, 4707])).
% 4.81/5.02 tff(4711,plain,
% 4.81/5.02 ((~![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)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4712,plain,
% 4.81/5.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1718) | c1_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c3_1(a1715)) | (~c0_1(a1715)) | (~c1_1(a1715)) | c1_1(a1718) | (~c3_1(a1718))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 4.81/5.02 tff(4713,plain,
% 4.81/5.02 ($false),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4712, 197, 771, 1959, 910, 902, 892, 895, 590, 1706, 4706, 871])).
% 4.81/5.02 tff(4714,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,[]))).
% 4.81/5.02 tff(4715,plain,
% 4.81/5.02 (~hskp38),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4714, 4699, 1959, 892, 895, 771, 4641, 894, 334])).
% 4.81/5.02 tff(4716,plain,
% 4.81/5.02 ($false),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[960, 4715, 4642, 818])).
% 4.81/5.02 tff(4717,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,[]))).
% 4.81/5.02 tff(4718,plain,
% 4.81/5.02 (hskp57),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[4717, 4640, 4406, 4638, 895, 4517, 4364, 893, 4551, 4582, 1539])).
% 4.81/5.02 tff(4719,plain,
% 4.81/5.02 (~c1_1(a1665)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[59, 4718])).
% 4.81/5.02 tff(4720,plain,
% 4.81/5.02 (c3_1(a1665)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[67, 4718])).
% 4.81/5.02 tff(4721,plain,
% 4.81/5.02 (c0_1(a1665)),
% 4.81/5.02 inference(unit_resolution,[status(thm)],[78, 4718])).
% 4.81/5.02 tff(4722,plain,
% 4.81/5.02 (((~![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) | 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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4723,plain,
% 4.81/5.02 ((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)))),
% 4.81/5.02 inference(rewrite,[status(thm)],[])).
% 4.81/5.02 tff(4724,plain,
% 4.81/5.02 (((~![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(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))))),
% 4.81/5.02 inference(monotonicity,[status(thm)],[4723])).
% 4.81/5.02 tff(4725,plain,
% 4.81/5.02 (((~![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(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)))),
% 4.81/5.02 inference(transitivity,[status(thm)],[4724, 4722])).
% 4.81/5.02 tff(4726,plain,
% 4.81/5.02 ((~![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(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c0_1(a1666) | c1_1(a1666) | (~c3_1(a1666)))),
% 4.81/5.02 inference(quant_inst,[status(thm)],[])).
% 4.81/5.02 tff(4727,plain,
% 4.81/5.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1665) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | c0_1(a1666) | (~c3_1(a1665)) | (~c0_1(a1665))),
% 4.81/5.02 inference(modus_ponens,[status(thm)],[4726, 4725])).
% 4.81/5.02 tff(4728,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4727, 197, 126, 4721, 4720, 4628, 4719, 4627, 125, 4635])).
% 4.81/5.03 tff(4729,plain,(c3_1(a1691) | hskp29 | c2_1(a1691) | c3_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4730,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4729, 4613, 4612, 126, 1539])).
% 4.81/5.03 tff(4731,plain,(c3_1(a1716) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4732,plain,
% 4.81/5.03 (c3_1(a1716)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4731, 126])).
% 4.81/5.03 tff(4733,plain,
% 4.81/5.03 (~hskp73),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1461, 4732])).
% 4.81/5.03 tff(4734,plain,
% 4.81/5.03 (~c1_1(a1676)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4048, 197, 4733, 1917, 559, 558, 1909, 1449, 570])).
% 4.81/5.03 tff(4735,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4041, 197, 126, 1917, 560, 558, 1909, 125, 4734, 570])).
% 4.81/5.03 tff(4736,plain,(c1_1(a1654) | hskp29 | (~c0_1(a1654)) | (~c3_1(a1654)) | (~c2_1(a1654))), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4737,plain,
% 4.81/5.03 (c1_1(a1654)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4736, 1869, 126, 1868, 1867])).
% 4.81/5.03 tff(4738,plain,
% 4.81/5.03 (hskp0),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3585, 4737, 333, 1866, 1768, 1203, 126, 1705])).
% 4.81/5.03 tff(4739,plain,
% 4.81/5.03 (~hskp61),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3223, 4737, 1866, 1203, 1868, 1705, 1869])).
% 4.81/5.03 tff(4740,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3401, 4739, 4738, 333, 1203, 1705])).
% 4.81/5.03 tff(4741,plain,(c3_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4742,plain,
% 4.81/5.03 (c3_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4741, 126])).
% 4.81/5.03 tff(4743,plain,
% 4.81/5.03 (~c2_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4401, 335, 127, 126])).
% 4.81/5.03 tff(4744,plain,
% 4.81/5.03 (c0_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3153, 335, 126, 4742, 329])).
% 4.81/5.03 tff(4745,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3988, 4744, 4743, 4742, 335, 136])).
% 4.81/5.03 tff(4746,plain,(c1_1(a1715) | hskp29 | hskp52), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4747,plain,
% 4.81/5.03 (c1_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4746, 127, 126])).
% 4.81/5.03 tff(4748,plain,
% 4.81/5.03 (~c2_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4550, 4747, 126, 127])).
% 4.81/5.03 tff(4749,plain,
% 4.81/5.03 (~c0_1(a1715)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4285, 4748, 126, 4742, 136, 332, 331, 330])).
% 4.81/5.03 tff(4750,plain,
% 4.81/5.03 (((~![W: $i, 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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4751,plain,
% 4.81/5.03 (((~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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4752,plain,
% 4.81/5.03 (((~![W: $i, 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))))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4751])).
% 4.81/5.03 tff(4753,plain,
% 4.81/5.03 (((~![W: $i, 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)))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4752, 4750])).
% 4.81/5.03 tff(4754,plain,
% 4.81/5.03 ((~![W: $i, 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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4755,plain,
% 4.81/5.03 ((~![W: $i, 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))),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4754, 4753])).
% 4.81/5.03 tff(4756,plain,
% 4.81/5.03 (c1_1(a1656)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4755, 197, 4742, 144, 206, 205, 4748, 150, 207, 380, 4749])).
% 4.81/5.03 tff(4757,plain,
% 4.81/5.03 (hskp61),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[2757, 4749, 4748, 4747])).
% 4.81/5.03 tff(4758,plain,
% 4.81/5.03 (~c2_1(a1674)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1100, 4757])).
% 4.81/5.03 tff(4759,plain,
% 4.81/5.03 (~c1_1(a1674)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1106, 4757])).
% 4.81/5.03 tff(4760,plain,
% 4.81/5.03 (c3_1(a1674)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1114, 4757])).
% 4.81/5.03 tff(4761,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4762,plain,
% 4.81/5.03 (((~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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4763,plain,
% 4.81/5.03 (((~![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))))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4762])).
% 4.81/5.03 tff(4764,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4763, 4761])).
% 4.81/5.03 tff(4765,plain,
% 4.81/5.03 ((~![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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4766,plain,
% 4.81/5.03 ((~![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))),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4765, 4764])).
% 4.81/5.03 tff(4767,plain,
% 4.81/5.03 (~c0_1(a1674)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4766, 197, 4760, 206, 205, 4759, 4758, 590, 328])).
% 4.81/5.03 tff(4768,plain,
% 4.81/5.03 (((~![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(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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4769,plain,
% 4.81/5.03 (((~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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4770,plain,
% 4.81/5.03 (((~![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(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)))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4769])).
% 4.81/5.03 tff(4771,plain,
% 4.81/5.03 (((~![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(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))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4770, 4768])).
% 4.81/5.03 tff(4772,plain,
% 4.81/5.03 ((~![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(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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4773,plain,
% 4.81/5.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1674) | c3_1(a1656) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1656)) | (~c1_1(a1656)) | (~c3_1(a1674)) | c0_1(a1674)),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4772, 4771])).
% 4.81/5.03 tff(4774,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4773, 197, 4760, 158, 332, 331, 4759, 150, 330, 90, 4767, 4756])).
% 4.81/5.03 tff(4775,plain,(hskp52 | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.81/5.03 tff(4776,plain,
% 4.81/5.03 (hskp52),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4775, 126])).
% 4.81/5.03 tff(4777,plain,
% 4.81/5.03 (c0_1(a1654)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[480, 4776])).
% 4.81/5.03 tff(4778,plain,
% 4.81/5.03 (c2_1(a1654)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[496, 4776])).
% 4.81/5.03 tff(4779,plain,
% 4.81/5.03 (c3_1(a1716)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3214, 1213, 1204])).
% 4.81/5.03 tff(4780,plain,
% 4.81/5.03 (~hskp13),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3153, 126, 335, 1952, 1204])).
% 4.81/5.03 tff(4781,assumption,(c3_1(a1716)), introduced(assumption)).
% 4.81/5.03 tff(4782,plain,
% 4.81/5.03 (~hskp73),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1461, 4781])).
% 4.81/5.03 tff(4783,plain,
% 4.81/5.03 (c1_1(a1654)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[3678, 2863, 4782, 2853, 3072, 3071, 2854, 126])).
% 4.81/5.03 tff(4784,plain,
% 4.81/5.03 (hskp12 | (~c1_1(a1654))),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[835, 197, 820, 2863, 2853, 830])).
% 4.81/5.03 tff(4785,plain,
% 4.81/5.03 (hskp12),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4784, 819])).
% 4.81/5.03 tff(4786,plain,
% 4.81/5.03 (~c1_1(a1666)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[842, 4785])).
% 4.81/5.03 tff(4787,plain,
% 4.81/5.03 (c3_1(a1666)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[850, 4785])).
% 4.81/5.03 tff(4788,plain,
% 4.81/5.03 (c2_1(a1666)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[858, 4785])).
% 4.81/5.03 tff(4789,plain,
% 4.81/5.03 (hskp26),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[866, 197, 2854, 2863, 2853, 4788, 4787, 4786, 20])).
% 4.81/5.03 tff(4790,plain,
% 4.81/5.03 (~c2_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[612, 4789])).
% 4.81/5.03 tff(4791,plain,
% 4.81/5.03 (~c1_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[618, 4789])).
% 4.81/5.03 tff(4792,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4793,plain,
% 4.81/5.03 (((~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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4794,plain,
% 4.81/5.03 (((~![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))))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4793])).
% 4.81/5.03 tff(4795,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4794, 4792])).
% 4.81/5.03 tff(4796,plain,
% 4.81/5.03 ((~![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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4797,plain,
% 4.81/5.03 ((~![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))),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4796, 4795])).
% 4.81/5.03 tff(4798,plain,
% 4.81/5.03 (~c0_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4797, 197, 335, 1959, 2854, 2853, 1213, 4791, 4790, 590, 819])).
% 4.81/5.03 tff(4799,plain,
% 4.81/5.03 (((~![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 | 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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4800,plain,
% 4.81/5.03 ((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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4801,plain,
% 4.81/5.03 (((~![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(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)))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4800])).
% 4.81/5.03 tff(4802,plain,
% 4.81/5.03 (((~![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(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))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4801, 4799])).
% 4.81/5.03 tff(4803,plain,
% 4.81/5.03 ((~![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(a1666) | (~c3_1(a1666)) | (~c0_1(a1666)) | c0_1(a1716) | c1_1(a1716) | (~c3_1(a1716)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4804,plain,
% 4.81/5.03 ((~![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 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c0_1(a1666)) | c1_1(a1716)),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 4.81/5.03 tff(4805,plain,
% 4.81/5.03 (~c0_1(a1666)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4804, 197, 126, 1953, 4787, 4781, 4786, 125, 1494])).
% 4.81/5.03 tff(4806,plain,
% 4.81/5.03 (~c3_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[632, 4789])).
% 4.81/5.03 tff(4807,plain,
% 4.81/5.03 (((~![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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4808,plain,
% 4.81/5.03 ((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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4809,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4808])).
% 4.81/5.03 tff(4810,plain,
% 4.81/5.03 (((~![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))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4809, 4807])).
% 4.81/5.03 tff(4811,plain,
% 4.81/5.03 ((~![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))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4812,plain,
% 4.81/5.03 ((~![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)),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4811, 4810])).
% 4.81/5.03 tff(4813,plain,
% 4.81/5.03 (hskp70 | c0_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4812, 197, 4788, 4806, 4790, 4786, 1987, 4805])).
% 4.81/5.03 tff(4814,plain,
% 4.81/5.03 (hskp70),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4813, 4798])).
% 4.81/5.03 tff(4815,plain,
% 4.81/5.03 (~c3_1(a1710)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[2037, 4814])).
% 4.81/5.03 tff(4816,plain,
% 4.81/5.03 (~c0_1(a1710)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[2043, 4814])).
% 4.81/5.03 tff(4817,plain,
% 4.81/5.03 (c1_1(a1710)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[2051, 4814])).
% 4.81/5.03 tff(4818,plain,
% 4.81/5.03 (c2_1(a1710)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[2058, 197, 1249, 4817, 4816, 4815, 1261])).
% 4.81/5.03 tff(4819,plain,
% 4.81/5.03 (hskp37 | c0_1(a1691)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[639, 197, 2241, 4806, 4790, 526])).
% 4.81/5.03 tff(4820,plain,
% 4.81/5.03 (hskp37),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4819, 4798])).
% 4.81/5.03 tff(4821,plain,
% 4.81/5.03 (c0_1(a1714)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[548, 4820])).
% 4.81/5.03 tff(4822,plain,
% 4.81/5.03 (c2_1(a1714)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[556, 4820])).
% 4.81/5.03 tff(4823,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4824,plain,
% 4.81/5.03 ((~![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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4825,plain,
% 4.81/5.03 ((~![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))),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4824, 4823])).
% 4.81/5.03 tff(4826,plain,
% 4.81/5.03 (c3_1(a1714)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4825, 197, 995, 894, 4822, 4821, 971])).
% 4.81/5.03 tff(4827,plain,
% 4.81/5.03 (~c1_1(a1714)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[540, 4820])).
% 4.81/5.03 tff(4828,plain,
% 4.81/5.03 (((~![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)))) | (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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4829,plain,
% 4.81/5.03 (((~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))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4830,plain,
% 4.81/5.03 (((~![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(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)))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4829])).
% 4.81/5.03 tff(4831,plain,
% 4.81/5.03 (((~![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(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))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4830, 4828])).
% 4.81/5.03 tff(4832,plain,
% 4.81/5.03 ((~![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(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)))),
% 4.81/5.03 inference(quant_inst,[status(thm)],[])).
% 4.81/5.03 tff(4833,plain,
% 4.81/5.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c3_1(a1714)) | (~c0_1(a1714)) | (~c2_1(a1710)) | (~c1_1(a1710)) | c1_1(a1716)),
% 4.81/5.03 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 4.81/5.03 tff(4834,plain,
% 4.81/5.03 ($false),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4833, 197, 1953, 4817, 4821, 4781, 4815, 4827, 90, 4826, 4818, 1494])).
% 4.81/5.03 tff(4835,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,[]))).
% 4.81/5.03 tff(4836,plain,
% 4.81/5.03 (hskp21),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[4835, 4783, 4781, 1494, 1953, 995, 894, 335, 1959, 1213, 126, 820])).
% 4.81/5.03 tff(4837,plain,
% 4.81/5.03 (~c1_1(a1683)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1315, 4836])).
% 4.81/5.03 tff(4838,plain,
% 4.81/5.03 (c2_1(a1683)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1284, 4836])).
% 4.81/5.03 tff(4839,plain,
% 4.81/5.03 (c3_1(a1683)),
% 4.81/5.03 inference(unit_resolution,[status(thm)],[1292, 4836])).
% 4.81/5.03 tff(4840,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4841,plain,
% 4.81/5.03 ((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)))),
% 4.81/5.03 inference(rewrite,[status(thm)],[])).
% 4.81/5.03 tff(4842,plain,
% 4.81/5.03 (((~![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))))),
% 4.81/5.03 inference(monotonicity,[status(thm)],[4841])).
% 4.81/5.03 tff(4843,plain,
% 4.81/5.03 (((~![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)))),
% 4.81/5.03 inference(transitivity,[status(thm)],[4842, 4840])).
% 4.81/5.03 tff(4844,plain,
% 4.81/5.03 ((~![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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4845,plain,
% 4.81/5.04 ((~![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))),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 4.81/5.04 tff(4846,plain,
% 4.81/5.04 (hskp26),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4845, 197, 2854, 2863, 2853, 4839, 4838, 4837, 20])).
% 4.81/5.04 tff(4847,plain,
% 4.81/5.04 (~c2_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[612, 4846])).
% 4.81/5.04 tff(4848,plain,
% 4.81/5.04 (~c1_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[618, 4846])).
% 4.81/5.04 tff(4849,plain,
% 4.81/5.04 (~c0_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4797, 197, 335, 1959, 2854, 2853, 1213, 4848, 4847, 590, 4783])).
% 4.81/5.04 tff(4850,plain,
% 4.81/5.04 (~c3_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[632, 4846])).
% 4.81/5.04 tff(4851,plain,
% 4.81/5.04 (hskp37 | c0_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[639, 197, 2241, 4850, 4847, 526])).
% 4.81/5.04 tff(4852,plain,
% 4.81/5.04 (hskp37),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4851, 4849])).
% 4.81/5.04 tff(4853,plain,
% 4.81/5.04 (c0_1(a1714)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[548, 4852])).
% 4.81/5.04 tff(4854,plain,
% 4.81/5.04 (c2_1(a1714)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[556, 4852])).
% 4.81/5.04 tff(4855,plain,
% 4.81/5.04 (c3_1(a1714)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4825, 197, 995, 894, 4854, 4853, 971])).
% 4.81/5.04 tff(4856,plain,
% 4.81/5.04 (~c1_1(a1714)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[540, 4852])).
% 4.81/5.04 tff(4857,plain,
% 4.81/5.04 (((~![V: $i, 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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4858,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4859,plain,
% 4.81/5.04 (((~![V: $i, 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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4858])).
% 4.81/5.04 tff(4860,plain,
% 4.81/5.04 (((~![V: $i, 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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4859, 4857])).
% 4.81/5.04 tff(4861,plain,
% 4.81/5.04 ((~![V: $i, 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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4862,plain,
% 4.81/5.04 ((~![V: $i, 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)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4861, 4860])).
% 4.81/5.04 tff(4863,plain,
% 4.81/5.04 (~c0_1(a1683)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4862, 197, 126, 1953, 4839, 4781, 4837, 125, 1494])).
% 4.81/5.04 tff(4864,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4865,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4866,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4865])).
% 4.81/5.04 tff(4867,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4866, 4864])).
% 4.81/5.04 tff(4868,plain,
% 4.81/5.04 ((~![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))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4869,plain,
% 4.81/5.04 ((~![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)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4868, 4867])).
% 4.81/5.04 tff(4870,plain,
% 4.81/5.04 (hskp70 | c0_1(a1691)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4869, 197, 4838, 4850, 4847, 4837, 1987, 4863])).
% 4.81/5.04 tff(4871,plain,
% 4.81/5.04 (hskp70),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4870, 4849])).
% 4.81/5.04 tff(4872,plain,
% 4.81/5.04 (~c3_1(a1710)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[2037, 4871])).
% 4.81/5.04 tff(4873,plain,
% 4.81/5.04 (c1_1(a1710)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[2051, 4871])).
% 4.81/5.04 tff(4874,plain,
% 4.81/5.04 (~c2_1(a1710)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4833, 197, 1953, 4873, 4853, 4781, 4872, 4856, 90, 4855, 1494])).
% 4.81/5.04 tff(4875,plain,
% 4.81/5.04 (~c0_1(a1710)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[2043, 4871])).
% 4.81/5.04 tff(4876,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4877,plain,
% 4.81/5.04 (((~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)))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4878,plain,
% 4.81/5.04 (((~![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))))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4877])).
% 4.81/5.04 tff(4879,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4878, 4876])).
% 4.81/5.04 tff(4880,plain,
% 4.81/5.04 ((~![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))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4881,plain,
% 4.81/5.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1710) | c3_1(a1710) | c1_1(a1714) | (~ndr1_0) | (~c0_1(a1714)) | (~c2_1(a1714)) | c2_1(a1710) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4880, 4879])).
% 4.81/5.04 tff(4882,plain,
% 4.81/5.04 ($false),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4881, 197, 2854, 2863, 2853, 4854, 4853, 4875, 4872, 4856, 514, 4874])).
% 4.81/5.04 tff(4883,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,[]))).
% 4.81/5.04 tff(4884,plain,
% 4.81/5.04 (hskp42),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4883, 126, 4779, 1494, 894, 335, 1952, 1213, 1953, 4780])).
% 4.81/5.04 tff(4885,plain,
% 4.81/5.04 (~c3_1(a1638)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1009, 4884])).
% 4.81/5.04 tff(4886,plain,
% 4.81/5.04 (c1_1(a1638)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1025, 4884])).
% 4.81/5.04 tff(4887,assumption,(hskp75), introduced(assumption)).
% 4.81/5.04 tff(4888,plain,
% 4.81/5.04 (~c2_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[411, 4887])).
% 4.81/5.04 tff(4889,plain,
% 4.81/5.04 (c0_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[443, 4887])).
% 4.81/5.04 tff(4890,plain,
% 4.81/5.04 (c3_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[435, 4887])).
% 4.81/5.04 tff(4891,plain,
% 4.81/5.04 ($false),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[3163, 4890, 4889, 335, 126, 1959, 1204, 4888])).
% 4.81/5.04 tff(4892,plain,((~hskp75) | c1_1(a1715) | hskp29 | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.81/5.04 tff(4893,plain,
% 4.81/5.04 (~hskp75),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4892, 126, 335, 1952, 1204])).
% 4.81/5.04 tff(4894,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4895,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4896,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4895])).
% 4.81/5.04 tff(4897,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4896, 4894])).
% 4.81/5.04 tff(4898,plain,
% 4.81/5.04 ((~![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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4899,plain,
% 4.81/5.04 ((~![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)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 4.81/5.04 tff(4900,plain,
% 4.81/5.04 (~c2_1(a1638)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4899, 4893, 197, 1919, 4886, 4779, 4885, 398, 1494])).
% 4.81/5.04 tff(4901,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4902,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4903,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4902])).
% 4.81/5.04 tff(4904,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4903, 4901])).
% 4.81/5.04 tff(4905,plain,
% 4.81/5.04 ((~![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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4906,plain,
% 4.81/5.04 ((~![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)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4905, 4904])).
% 4.81/5.04 tff(4907,plain,
% 4.81/5.04 (hskp69),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4906, 197, 1953, 4886, 4779, 4885, 1310, 4900, 1494])).
% 4.81/5.04 tff(4908,plain,
% 4.81/5.04 (~c1_1(a1709)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1329, 4907])).
% 4.81/5.04 tff(4909,plain,
% 4.81/5.04 (c3_1(a1709)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1337, 4907])).
% 4.81/5.04 tff(4910,plain,
% 4.81/5.04 (c0_1(a1709)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1345, 4907])).
% 4.81/5.04 tff(4911,plain,
% 4.81/5.04 (((~![V: $i, 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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4912,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4913,plain,
% 4.81/5.04 (((~![V: $i, 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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4912])).
% 4.81/5.04 tff(4914,plain,
% 4.81/5.04 (((~![V: $i, 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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4913, 4911])).
% 4.81/5.04 tff(4915,plain,
% 4.81/5.04 ((~![V: $i, 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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4916,plain,
% 4.81/5.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1709) | (~ndr1_0) | (~c3_1(a1709)) | (~c0_1(a1709)) | c1_1(a1716)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4915, 4914])).
% 4.81/5.04 tff(4917,plain,
% 4.81/5.04 ($false),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4916, 197, 126, 1953, 4910, 4909, 4779, 4908, 125, 1494])).
% 4.81/5.04 tff(4918,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,[]))).
% 4.81/5.04 tff(4919,plain,
% 4.81/5.04 (hskp29),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4918, 894, 1494, 1919, 1953, 335, 1213, 1204])).
% 4.81/5.04 tff(4920,plain,
% 4.81/5.04 (hskp42),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[2410, 4919, 894])).
% 4.81/5.04 tff(4921,plain,
% 4.81/5.04 (c0_1(a1695)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1933, 4919])).
% 4.81/5.04 tff(4922,plain,
% 4.81/5.04 (~c3_1(a1695)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1925, 4919])).
% 4.81/5.04 tff(4923,plain,
% 4.81/5.04 (c2_1(a1695)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[1941, 4919])).
% 4.81/5.04 tff(4924,assumption,(c1_1(a1695)), introduced(assumption)).
% 4.81/5.04 tff(4925,assumption,(~c3_1(a1695)), introduced(assumption)).
% 4.81/5.04 tff(4926,assumption,(c2_1(a1695)), introduced(assumption)).
% 4.81/5.04 tff(4927,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4928,plain,
% 4.81/5.04 ((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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4929,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4928])).
% 4.81/5.04 tff(4930,plain,
% 4.81/5.04 (((~![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))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4929, 4927])).
% 4.81/5.04 tff(4931,plain,
% 4.81/5.04 ((~![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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4932,plain,
% 4.81/5.04 ((~![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)),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4931, 4930])).
% 4.81/5.04 tff(4933,plain,
% 4.81/5.04 (hskp75 | (~c1_1(a1695))),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4932, 197, 1919, 4926, 4781, 4925, 398, 1494])).
% 4.81/5.04 tff(4934,plain,
% 4.81/5.04 (hskp75),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4933, 4924])).
% 4.81/5.04 tff(4935,plain,
% 4.81/5.04 (~c2_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[411, 4934])).
% 4.81/5.04 tff(4936,assumption,(c0_1(a1695)), introduced(assumption)).
% 4.81/5.04 tff(4937,plain,
% 4.81/5.04 (c3_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[435, 4934])).
% 4.81/5.04 tff(4938,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4939,plain,
% 4.81/5.04 ((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)))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4940,plain,
% 4.81/5.04 (((~![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))))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4939])).
% 4.81/5.04 tff(4941,plain,
% 4.81/5.04 (((~![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)))),
% 4.81/5.04 inference(transitivity,[status(thm)],[4940, 4938])).
% 4.81/5.04 tff(4942,plain,
% 4.81/5.04 ((~![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)))),
% 4.81/5.04 inference(quant_inst,[status(thm)],[])).
% 4.81/5.04 tff(4943,plain,
% 4.81/5.04 ((~![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))),
% 4.81/5.04 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 4.81/5.04 tff(4944,plain,
% 4.81/5.04 (~c1_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[4943, 197, 894, 4937, 4926, 4936, 4935, 881, 4924])).
% 4.81/5.04 tff(4945,plain,
% 4.81/5.04 (c0_1(a1724)),
% 4.81/5.04 inference(unit_resolution,[status(thm)],[443, 4934])).
% 4.81/5.04 tff(4946,plain,
% 4.81/5.04 (((~![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)))) | (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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4947,plain,
% 4.81/5.04 (((~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))),
% 4.81/5.04 inference(rewrite,[status(thm)],[])).
% 4.81/5.04 tff(4948,plain,
% 4.81/5.04 (((~![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(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)))),
% 4.81/5.04 inference(monotonicity,[status(thm)],[4947])).
% 4.81/5.04 tff(4949,plain,
% 4.81/5.04 (((~![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(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))),
% 4.81/5.05 inference(transitivity,[status(thm)],[4948, 4946])).
% 4.81/5.05 tff(4950,plain,
% 4.81/5.05 ((~![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)))),
% 4.81/5.05 inference(quant_inst,[status(thm)],[])).
% 4.81/5.05 tff(4951,plain,
% 4.81/5.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724)) | c1_1(a1724)),
% 4.81/5.05 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 4.81/5.05 tff(4952,plain,
% 4.81/5.05 ($false),
% 4.81/5.05 inference(unit_resolution,[status(thm)],[4951, 197, 4945, 4937, 1953, 4926, 4781, 4925, 90, 4944, 1494, 4924])).
% 4.81/5.05 tff(4953,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,[]))).
% 4.81/5.05 tff(4954,plain,
% 4.81/5.05 (~c1_1(a1695)),
% 4.81/5.05 inference(unit_resolution,[status(thm)],[4953, 4923, 1953, 4779, 4922, 1494, 894, 4921, 1919])).
% 4.81/5.05 tff(4955,plain,
% 4.81/5.05 (((~![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))),
% 4.81/5.05 inference(rewrite,[status(thm)],[])).
% 4.81/5.05 tff(4956,plain,
% 4.81/5.05 ((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))),
% 4.81/5.05 inference(rewrite,[status(thm)],[])).
% 4.81/5.05 tff(4957,plain,
% 4.81/5.05 (((~![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)))),
% 4.81/5.05 inference(monotonicity,[status(thm)],[4956])).
% 4.81/5.05 tff(4958,plain,
% 4.81/5.05 (((~![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))),
% 4.81/5.05 inference(transitivity,[status(thm)],[4957, 4955])).
% 4.81/5.05 tff(4959,plain,
% 4.81/5.05 ((~![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)))),
% 4.81/5.05 inference(quant_inst,[status(thm)],[])).
% 4.81/5.05 tff(4960,plain,
% 4.81/5.05 ((~![V: $i, U: $i] : (hskp60 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp60 | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | c1_1(a1695) | c1_1(a1716)),
% 4.81/5.05 inference(modus_ponens,[status(thm)],[4959, 4958])).
% 4.81/5.05 tff(4961,plain,
% 4.81/5.05 (hskp60 | c1_1(a1695)),
% 4.81/5.05 inference(unit_resolution,[status(thm)],[4960, 197, 1953, 4923, 4779, 4922, 356, 1494])).
% 4.88/5.05 tff(4962,plain,
% 4.88/5.05 (hskp60),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4961, 4954])).
% 4.88/5.05 tff(4963,plain,
% 4.88/5.05 (~c1_1(a1673)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[369, 4962])).
% 4.88/5.05 tff(4964,plain,
% 4.88/5.05 (c3_1(a1673)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[427, 4962])).
% 4.88/5.05 tff(4965,plain,
% 4.88/5.05 (~hskp73),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1461, 4779])).
% 4.88/5.05 tff(4966,plain,
% 4.88/5.05 (c2_1(a1673)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[419, 4962])).
% 4.88/5.05 tff(4967,plain,
% 4.88/5.05 (~hskp30),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2357, 4966, 4965, 4964, 4963])).
% 4.88/5.05 tff(4968,plain,
% 4.88/5.05 (hskp75),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2401, 4967, 335, 1204, 4920, 1213])).
% 4.88/5.05 tff(4969,plain,
% 4.88/5.05 (~c2_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[411, 4968])).
% 4.88/5.05 tff(4970,plain,
% 4.88/5.05 (c0_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[443, 4968])).
% 4.88/5.05 tff(4971,plain,
% 4.88/5.05 (c3_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[435, 4968])).
% 4.88/5.05 tff(4972,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2723, 4971, 4970, 4962, 4969, 1213, 1204])).
% 4.88/5.05 tff(4973,plain,(hskp0 | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c0_1(a1716) | c1_1(a1716) | c2_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.05 tff(4974,plain,
% 4.88/5.05 (hskp0),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4973, 1953, 1204, 335, 1213, 1494, 1919])).
% 4.88/5.05 tff(4975,plain,
% 4.88/5.05 (c0_1(a1637)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1093, 4974])).
% 4.88/5.05 tff(4976,plain,
% 4.88/5.05 (~c2_1(a1637)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1085, 4974])).
% 4.88/5.05 tff(4977,plain,
% 4.88/5.05 (c1_1(a1637)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1131, 4974])).
% 4.88/5.05 tff(4978,plain,
% 4.88/5.05 (~c3_1(a1637)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1144, 4780, 1136, 1135, 1134])).
% 4.88/5.05 tff(4979,plain,
% 4.88/5.05 (hskp61),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1165, 4978, 1136, 1135, 1134])).
% 4.88/5.05 tff(4980,plain,
% 4.88/5.05 (~c1_1(a1674)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1106, 4979])).
% 4.88/5.05 tff(4981,plain,
% 4.88/5.05 (~c2_1(a1674)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1100, 4979])).
% 4.88/5.05 tff(4982,plain,
% 4.88/5.05 (c3_1(a1674)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1114, 4979])).
% 4.88/5.05 tff(4983,plain,
% 4.88/5.05 (~c0_1(a1674)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2629, 4982, 126, 4981, 4980, 1213, 1204, 4893])).
% 4.88/5.05 tff(4984,plain,
% 4.88/5.05 (((~![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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(4985,plain,
% 4.88/5.05 ((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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(4986,plain,
% 4.88/5.05 (((~![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)))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[4985])).
% 4.88/5.05 tff(4987,plain,
% 4.88/5.05 (((~![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))),
% 4.88/5.05 inference(transitivity,[status(thm)],[4986, 4984])).
% 4.88/5.05 tff(4988,plain,
% 4.88/5.05 ((~![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)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(4989,plain,
% 4.88/5.05 ((~![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)),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 4.88/5.05 tff(4990,plain,
% 4.88/5.05 (hskp69),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4989, 197, 1953, 1136, 4779, 1134, 1310, 4978, 1494])).
% 4.88/5.05 tff(4991,plain,
% 4.88/5.05 (~c1_1(a1709)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1329, 4990])).
% 4.88/5.05 tff(4992,plain,
% 4.88/5.05 (c3_1(a1709)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1337, 4990])).
% 4.88/5.05 tff(4993,plain,
% 4.88/5.05 (c0_1(a1709)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1345, 4990])).
% 4.88/5.05 tff(4994,plain,
% 4.88/5.05 (((~![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 | 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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(4995,plain,
% 4.88/5.05 ((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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(4996,plain,
% 4.88/5.05 (((~![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(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))))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[4995])).
% 4.88/5.05 tff(4997,plain,
% 4.88/5.05 (((~![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(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)))),
% 4.88/5.05 inference(transitivity,[status(thm)],[4996, 4994])).
% 4.88/5.05 tff(4998,plain,
% 4.88/5.05 ((~![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(a1709) | (~c3_1(a1709)) | (~c0_1(a1709)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(4999,plain,
% 4.88/5.05 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1709) | c1_1(a1674) | (~ndr1_0) | (~c3_1(a1674)) | c0_1(a1674) | (~c3_1(a1709)) | (~c0_1(a1709))),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 4.88/5.05 tff(5000,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4999, 197, 126, 4993, 4992, 4982, 4991, 4980, 125, 4983])).
% 4.88/5.05 tff(5001,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,[]))).
% 4.88/5.05 tff(5002,plain,
% 4.88/5.05 (hskp29),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5001, 1953, 4977, 4976, 1494, 1213, 1204, 4975, 335])).
% 4.88/5.05 tff(5003,plain,
% 4.88/5.05 (~c3_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1925, 5002])).
% 4.88/5.05 tff(5004,plain,
% 4.88/5.05 (c2_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1941, 5002])).
% 4.88/5.05 tff(5005,plain,
% 4.88/5.05 (hskp30),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2381, 4974, 335, 1952, 1204])).
% 4.88/5.05 tff(5006,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2357, 2714, 2715, 1960, 2327, 2713])).
% 4.88/5.05 tff(5007,plain,((~hskp60) | hskp73 | (~hskp30)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.05 tff(5008,plain,
% 4.88/5.05 (~hskp60),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5007, 5005, 4965])).
% 4.88/5.05 tff(5009,plain,
% 4.88/5.05 (c1_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4960, 197, 5008, 1953, 5004, 4779, 5003, 356, 1494])).
% 4.88/5.05 tff(5010,plain,
% 4.88/5.05 (hskp75 | (~c1_1(a1695))),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4932, 197, 1919, 5004, 4779, 5003, 398, 1494])).
% 4.88/5.05 tff(5011,plain,
% 4.88/5.05 (hskp75),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5010, 5009])).
% 4.88/5.05 tff(5012,plain,
% 4.88/5.05 (c3_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[435, 5011])).
% 4.88/5.05 tff(5013,plain,
% 4.88/5.05 (c0_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[443, 5011])).
% 4.88/5.05 tff(5014,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[4951, 197, 2137, 2142, 1953, 4926, 4781, 4925, 90, 2143, 1494, 4924])).
% 4.88/5.05 tff(5015,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,[]))).
% 4.88/5.05 tff(5016,plain,
% 4.88/5.05 (c1_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5015, 5013, 5012, 1953, 5004, 4779, 5003, 1494, 5009])).
% 4.88/5.05 tff(5017,plain,
% 4.88/5.05 (~c2_1(a1724)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[411, 5011])).
% 4.88/5.05 tff(5018,plain,
% 4.88/5.05 (hskp13 | (~c1_1(a1724))),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2159, 197, 5013, 5012, 5017, 266])).
% 4.88/5.05 tff(5019,plain,
% 4.88/5.05 (hskp13),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5018, 5016])).
% 4.88/5.05 tff(5020,plain,
% 4.88/5.05 (~c1_1(a1667)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[279, 5019])).
% 4.88/5.05 tff(5021,plain,
% 4.88/5.05 (c3_1(a1667)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[287, 5019])).
% 4.88/5.05 tff(5022,plain,
% 4.88/5.05 (c0_1(a1667)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[295, 5019])).
% 4.88/5.05 tff(5023,plain,
% 4.88/5.05 (((~![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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5024,plain,
% 4.88/5.05 (((~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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5025,plain,
% 4.88/5.05 (((~![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)))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5024])).
% 4.88/5.05 tff(5026,plain,
% 4.88/5.05 (((~![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))),
% 4.88/5.05 inference(transitivity,[status(thm)],[5025, 5023])).
% 4.88/5.05 tff(5027,plain,
% 4.88/5.05 ((~![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)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(5028,plain,
% 4.88/5.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1716) | (~c3_1(a1716)) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | c1_1(a1716)),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[5027, 5026])).
% 4.88/5.05 tff(5029,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5028, 197, 1953, 5004, 5022, 5021, 4779, 5003, 5020, 90, 1494, 5009])).
% 4.88/5.05 tff(5030,plain,(c0_1(a1716) | c1_1(a1716) | c2_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.05 tff(5031,plain,
% 4.88/5.05 (c0_1(a1716)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5030, 1919, 1494, 1213, 1204, 335])).
% 4.88/5.05 tff(5032,plain,
% 4.88/5.05 (((~![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 | 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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5033,plain,
% 4.88/5.05 ((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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5034,plain,
% 4.88/5.05 (((~![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(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))))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5033])).
% 4.88/5.05 tff(5035,plain,
% 4.88/5.05 (((~![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(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)))),
% 4.88/5.05 inference(transitivity,[status(thm)],[5034, 5032])).
% 4.88/5.05 tff(5036,plain,
% 4.88/5.05 ((~![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(a1716) | (~c3_1(a1716)) | (~c0_1(a1716)) | c0_1(a1715) | c1_1(a1715) | (~c3_1(a1715)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(5037,plain,
% 4.88/5.05 ((~![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 | c1_1(a1715) | (~c3_1(a1716)) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | c1_1(a1716) | (~c0_1(a1716))),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 4.88/5.05 tff(5038,plain,
% 4.88/5.05 (hskp29 | (~c0_1(a1716))),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5037, 197, 335, 1952, 4779, 125, 1204, 1494])).
% 4.88/5.05 tff(5039,plain,
% 4.88/5.05 (hskp29),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5038, 5031])).
% 4.88/5.05 tff(5040,plain,
% 4.88/5.05 (~c3_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1925, 5039])).
% 4.88/5.05 tff(5041,plain,
% 4.88/5.05 (c2_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1941, 5039])).
% 4.88/5.05 tff(5042,plain,
% 4.88/5.05 (((~![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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5043,plain,
% 4.88/5.05 (((~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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5044,plain,
% 4.88/5.05 (((~![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))))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5043])).
% 4.88/5.05 tff(5045,plain,
% 4.88/5.05 (((~![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)))),
% 4.88/5.05 inference(transitivity,[status(thm)],[5044, 5042])).
% 4.88/5.05 tff(5046,plain,
% 4.88/5.05 ((~![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)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(5047,plain,
% 4.88/5.05 ((~![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))),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[5046, 5045])).
% 4.88/5.05 tff(5048,plain,
% 4.88/5.05 (~c1_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5047, 197, 5031, 335, 1952, 5041, 4779, 5040, 90, 1204, 1494])).
% 4.88/5.05 tff(5049,plain,
% 4.88/5.05 (c0_1(a1695)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[1933, 5039])).
% 4.88/5.05 tff(5050,plain,
% 4.88/5.05 (((~![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)))) | (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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5051,plain,
% 4.88/5.05 (((~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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5052,plain,
% 4.88/5.05 (((~![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(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))))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5051])).
% 4.88/5.05 tff(5053,plain,
% 4.88/5.05 (((~![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(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)))),
% 4.88/5.05 inference(transitivity,[status(thm)],[5052, 5050])).
% 4.88/5.05 tff(5054,plain,
% 4.88/5.05 ((~![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(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)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(5055,plain,
% 4.88/5.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1716) | (~c3_1(a1716)) | c2_1(a1715) | c3_1(a1695) | (~ndr1_0) | c1_1(a1695) | (~c0_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715) | (~c0_1(a1716))),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 4.88/5.05 tff(5056,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5055, 197, 1919, 5031, 1952, 5049, 4779, 1213, 5040, 380, 1204, 5048])).
% 4.88/5.05 tff(5057,plain,(c2_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.05 tff(5058,plain,
% 4.88/5.05 (c2_1(a1716)),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5057, 1494, 1204, 335, 1213])).
% 4.88/5.05 tff(5059,plain,
% 4.88/5.05 (((~![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 | (~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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5060,plain,
% 4.88/5.05 ((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))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5061,plain,
% 4.88/5.05 (((~![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(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)))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5060])).
% 4.88/5.05 tff(5062,plain,
% 4.88/5.05 (((~![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(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))),
% 4.88/5.05 inference(transitivity,[status(thm)],[5061, 5059])).
% 4.88/5.05 tff(5063,plain,
% 4.88/5.05 ((~![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(a1716) | (~c3_1(a1716)) | (~c2_1(a1716)) | c0_1(a1698) | (~c3_1(a1698)) | (~c1_1(a1698)))),
% 4.88/5.05 inference(quant_inst,[status(thm)],[])).
% 4.88/5.05 tff(5064,plain,
% 4.88/5.05 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | (~c3_1(a1716)) | c0_1(a1698) | (~ndr1_0) | (~c3_1(a1698)) | (~c1_1(a1698)) | (~c2_1(a1716)) | c1_1(a1716)),
% 4.88/5.05 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 4.88/5.05 tff(5065,plain,
% 4.88/5.05 ($false),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5064, 197, 4782, 1540, 2349, 2341, 4781, 2333, 1449, 1494])).
% 4.88/5.05 tff(5066,plain,((~hskp30) | (~c2_1(a1716)) | (~c3_1(a1716)) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.05 tff(5067,plain,
% 4.88/5.05 (~hskp30),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[5066, 5058, 4779, 1494])).
% 4.88/5.05 tff(5068,plain,
% 4.88/5.05 (~hskp0),
% 4.88/5.05 inference(unit_resolution,[status(thm)],[2381, 5067, 335, 1952, 1204])).
% 4.88/5.05 tff(5069,plain,
% 4.88/5.05 (((~![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)) | 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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5070,plain,
% 4.88/5.05 (((~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)))),
% 4.88/5.05 inference(rewrite,[status(thm)],[])).
% 4.88/5.05 tff(5071,plain,
% 4.88/5.05 (((~![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)) | 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))))),
% 4.88/5.05 inference(monotonicity,[status(thm)],[5070])).
% 4.88/5.05 tff(5072,plain,
% 4.88/5.05 (((~![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)) | 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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5071, 5069])).
% 4.88/5.06 tff(5073,plain,
% 4.88/5.06 ((~![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)) | 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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5074,plain,
% 4.88/5.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1724) | (~c3_1(a1716)) | c2_1(a1715) | (~ndr1_0) | (~c3_1(a1715)) | c0_1(a1715) | (~c2_1(a1716)) | c1_1(a1716) | (~c3_1(a1724)) | (~c0_1(a1724))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5073, 5072])).
% 4.88/5.06 tff(5075,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5074, 197, 4889, 4890, 1540, 1952, 4888, 4779, 1213, 346, 1204, 1494])).
% 4.88/5.06 tff(5076,plain,((~hskp75) | (~c2_1(a1716)) | c2_1(a1715) | c0_1(a1715) | c1_1(a1716)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5077,plain,
% 4.88/5.06 (~hskp75),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5076, 5058, 1213, 1204, 1494])).
% 4.88/5.06 tff(5078,plain,
% 4.88/5.06 (~hskp42),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2401, 5077, 335, 1204, 5067, 1213])).
% 4.88/5.06 tff(5079,plain,
% 4.88/5.06 (~hskp29),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2410, 5078, 5068])).
% 4.88/5.06 tff(5080,plain,
% 4.88/5.06 (~hskp13),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[3153, 5079, 335, 1952, 1204])).
% 4.88/5.06 tff(5081,plain,
% 4.88/5.06 (~c0_1(a1716)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5038, 5079])).
% 4.88/5.06 tff(5082,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[4883, 5081, 5079, 4779, 1494, 5068, 335, 1952, 1213, 5078, 5080])).
% 4.88/5.06 tff(5083,plain,(c1_1(a1716) | c1_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5084,plain,
% 4.88/5.06 (c1_1(a1716)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5083, 335, 1213, 1204])).
% 4.88/5.06 tff(5085,assumption,(~hskp12), introduced(assumption)).
% 4.88/5.06 tff(5086,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5087,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5088,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5087])).
% 4.88/5.06 tff(5089,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5088, 5086])).
% 4.88/5.06 tff(5090,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5091,plain,
% 4.88/5.06 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5090, 5089])).
% 4.88/5.06 tff(5092,plain,
% 4.88/5.06 (hskp13 | hskp12 | (~c2_1(a1716)) | (~c1_1(a1716))),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5091, 197, 4779, 830])).
% 4.88/5.06 tff(5093,plain,
% 4.88/5.06 (~c2_1(a1716)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5092, 4780, 5084, 5085])).
% 4.88/5.06 tff(5094,assumption,(hskp69), introduced(assumption)).
% 4.88/5.06 tff(5095,plain,
% 4.88/5.06 (~c1_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1329, 5094])).
% 4.88/5.06 tff(5096,plain,
% 4.88/5.06 (c3_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1337, 5094])).
% 4.88/5.06 tff(5097,plain,
% 4.88/5.06 (c0_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1345, 5094])).
% 4.88/5.06 tff(5098,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2287, 197, 126, 335, 1959, 5097, 5096, 5095, 125, 1204])).
% 4.88/5.06 tff(5099,plain,((~hskp69) | hskp29 | c1_1(a1715) | (~c3_1(a1715)) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5100,plain,
% 4.88/5.06 (~hskp69),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5099, 126, 335, 1952, 1204])).
% 4.88/5.06 tff(5101,plain,
% 4.88/5.06 (hskp61),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1165, 4483, 2372, 2371, 2370])).
% 4.88/5.06 tff(5102,plain,
% 4.88/5.06 (~c1_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1106, 5101])).
% 4.88/5.06 tff(5103,plain,
% 4.88/5.06 (~c2_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1100, 5101])).
% 4.88/5.06 tff(5104,plain,
% 4.88/5.06 (c3_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1114, 5101])).
% 4.88/5.06 tff(5105,plain,
% 4.88/5.06 (~c0_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2629, 5104, 126, 5103, 5102, 1213, 1204, 1918])).
% 4.88/5.06 tff(5106,plain,
% 4.88/5.06 (((~![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))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5107,plain,
% 4.88/5.06 ((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))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5108,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5107])).
% 4.88/5.06 tff(5109,plain,
% 4.88/5.06 (((~![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))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5108, 5106])).
% 4.88/5.06 tff(5110,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5111,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp69 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp69 | c1_1(a1674) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1674)) | c0_1(a1674)),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5110, 5109])).
% 4.88/5.06 tff(5112,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5111, 197, 2225, 5104, 2372, 5102, 2370, 1310, 4483, 5105])).
% 4.88/5.06 tff(5113,plain,((~hskp0) | hskp69 | hskp29 | c2_1(a1715) | c0_1(a1715) | hskp75 | hskp13), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5114,plain,
% 4.88/5.06 (~hskp0),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5113, 5100, 126, 1213, 1204, 4893, 4780])).
% 4.88/5.06 tff(5115,plain,
% 4.88/5.06 (c1_1(a1654)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[3678, 3071, 4782, 2853, 2863, 3072, 2854, 126])).
% 4.88/5.06 tff(5116,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5117,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5118,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5117])).
% 4.88/5.06 tff(5119,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5118, 5116])).
% 4.88/5.06 tff(5120,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5121,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c1_1(a1716)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5120, 5119])).
% 4.88/5.06 tff(5122,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5121, 197, 820, 1919, 2854, 2853, 4781, 266, 2725, 5115])).
% 4.88/5.06 tff(5123,plain,(hskp42 | hskp13 | c2_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716)) | hskp29 | hskp0), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5124,plain,
% 4.88/5.06 (hskp42),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5123, 894, 1919, 4779, 5084, 126, 4780])).
% 4.88/5.06 tff(5125,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5126,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5127,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5126])).
% 4.88/5.06 tff(5128,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5127, 5125])).
% 4.88/5.06 tff(5129,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5130,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp61 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp61 | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c0_1(a1638))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5129, 5128])).
% 4.88/5.06 tff(5131,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5130, 197, 1157, 2385, 2393, 2384, 1156, 2997])).
% 4.88/5.06 tff(5132,plain,((~hskp42) | hskp61 | hskp75 | c1_1(a1715) | (~c3_1(a1715)) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5133,plain,
% 4.88/5.06 (hskp61),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5132, 5124, 4893, 335, 1952, 1213])).
% 4.88/5.06 tff(5134,plain,
% 4.88/5.06 (~c1_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1106, 5133])).
% 4.88/5.06 tff(5135,plain,
% 4.88/5.06 (~c2_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1100, 5133])).
% 4.88/5.06 tff(5136,plain,
% 4.88/5.06 (c3_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1114, 5133])).
% 4.88/5.06 tff(5137,plain,
% 4.88/5.06 (~c0_1(a1674)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2629, 5136, 126, 5135, 5134, 1213, 1204, 4893])).
% 4.88/5.06 tff(5138,plain,
% 4.88/5.06 (c0_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1017, 5124])).
% 4.88/5.06 tff(5139,plain,
% 4.88/5.06 (c1_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1025, 5124])).
% 4.88/5.06 tff(5140,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5141,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5142,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5141])).
% 4.88/5.06 tff(5143,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5142, 5140])).
% 4.88/5.06 tff(5144,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5145,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a1716) | (~c3_1(a1716)) | (~ndr1_0) | (~c2_1(a1638)) | (~c1_1(a1638)) | (~c0_1(a1638)) | (~c1_1(a1716))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 4.88/5.06 tff(5146,plain,
% 4.88/5.06 (~c2_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5145, 197, 894, 1919, 5139, 5138, 4779, 881, 5084])).
% 4.88/5.06 tff(5147,plain,
% 4.88/5.06 (~c3_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1009, 5124])).
% 4.88/5.06 tff(5148,plain,
% 4.88/5.06 (hskp69),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2889, 197, 335, 1952, 5139, 5147, 1310, 1204, 5146])).
% 4.88/5.06 tff(5149,plain,
% 4.88/5.06 (~c1_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1329, 5148])).
% 4.88/5.06 tff(5150,plain,
% 4.88/5.06 (c3_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1337, 5148])).
% 4.88/5.06 tff(5151,plain,
% 4.88/5.06 (c0_1(a1709)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1345, 5148])).
% 4.88/5.06 tff(5152,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[4999, 197, 126, 5151, 5150, 5136, 5149, 5134, 125, 5137])).
% 4.88/5.06 tff(5153,plain,(hskp0 | hskp29 | c1_1(a1715) | c0_1(a1715) | c2_1(a1716) | c2_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5154,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5153, 5114, 5093, 335, 1204, 126, 1213])).
% 4.88/5.06 tff(5155,plain,(hskp29 | c1_1(a1715) | c0_1(a1715) | c2_1(a1715) | hskp12), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5156,plain,
% 4.88/5.06 (hskp12),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5155, 126, 1204, 1213, 335])).
% 4.88/5.06 tff(5157,plain,
% 4.88/5.06 (~c1_1(a1666)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[842, 5156])).
% 4.88/5.06 tff(5158,plain,
% 4.88/5.06 (c3_1(a1666)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[850, 5156])).
% 4.88/5.06 tff(5159,plain,
% 4.88/5.06 (c2_1(a1666)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[858, 5156])).
% 4.88/5.06 tff(5160,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5161,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5162,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5161])).
% 4.88/5.06 tff(5163,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5162, 5160])).
% 4.88/5.06 tff(5164,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5165,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1666) | (~ndr1_0) | (~c3_1(a1666)) | (~c2_1(a1666)) | (~c1_1(a1716))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 4.88/5.06 tff(5166,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5165, 197, 4782, 1953, 4587, 4586, 4781, 4585, 1449, 2725])).
% 4.88/5.06 tff(5167,plain,((~hskp12) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5168,plain,
% 4.88/5.06 (~hskp12),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5167, 1953, 4779, 5084])).
% 4.88/5.06 tff(5169,plain,
% 4.88/5.06 (hskp29),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5155, 5168, 1204, 1213, 335])).
% 4.88/5.06 tff(5170,plain,
% 4.88/5.06 (hskp42),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2410, 894, 1920])).
% 4.88/5.06 tff(5171,plain,
% 4.88/5.06 (c0_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1017, 5170])).
% 4.88/5.06 tff(5172,plain,
% 4.88/5.06 (c1_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1025, 5170])).
% 4.88/5.06 tff(5173,plain,
% 4.88/5.06 (~c2_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5145, 197, 894, 1919, 5172, 5171, 4781, 881, 2725])).
% 4.88/5.06 tff(5174,plain,
% 4.88/5.06 (~c3_1(a1638)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1009, 5170])).
% 4.88/5.06 tff(5175,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5176,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5177,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5176])).
% 4.88/5.06 tff(5178,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5177, 5175])).
% 4.88/5.06 tff(5179,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5180,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c0_1(a1716) | (~c3_1(a1716)) | c1_1(a1683) | (~ndr1_0) | (~c3_1(a1683)) | (~c2_1(a1683)) | (~c1_1(a1716))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 4.88/5.06 tff(5181,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5180, 197, 4782, 1953, 1958, 1957, 4781, 1956, 1449, 2725])).
% 4.88/5.06 tff(5182,plain,((~hskp21) | c0_1(a1716) | (~c3_1(a1716)) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5183,plain,
% 4.88/5.06 (~hskp21),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5182, 1953, 4781, 2725])).
% 4.88/5.06 tff(5184,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5185,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5186,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5185])).
% 4.88/5.06 tff(5187,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5186, 5184])).
% 4.88/5.06 tff(5188,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5189,plain,
% 4.88/5.06 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c1_1(a1638)) | (~c1_1(a1716))),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5188, 5187])).
% 4.88/5.06 tff(5190,plain,
% 4.88/5.06 ($false),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5189, 197, 5183, 1919, 1953, 5172, 5174, 1261, 5173, 2725])).
% 4.88/5.06 tff(5191,plain,(hskp0 | c2_1(a1716) | c0_1(a1716) | (~c1_1(a1716)) | (~c3_1(a1716)) | (~hskp29)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.06 tff(5192,plain,
% 4.88/5.06 (hskp0),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5191, 1919, 1953, 2725, 4781, 1920])).
% 4.88/5.06 tff(5193,plain,
% 4.88/5.06 (hskp30),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[2381, 5192, 335, 1959, 1204])).
% 4.88/5.06 tff(5194,plain,
% 4.88/5.06 (~hskp60),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5007, 5193, 4782])).
% 4.88/5.06 tff(5195,plain,
% 4.88/5.06 (((~![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))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5196,plain,
% 4.88/5.06 ((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))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5197,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(monotonicity,[status(thm)],[5196])).
% 4.88/5.06 tff(5198,plain,
% 4.88/5.06 (((~![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))),
% 4.88/5.06 inference(transitivity,[status(thm)],[5197, 5195])).
% 4.88/5.06 tff(5199,plain,
% 4.88/5.06 ((~![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)))),
% 4.88/5.06 inference(quant_inst,[status(thm)],[])).
% 4.88/5.06 tff(5200,plain,
% 4.88/5.06 ((~![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)),
% 4.88/5.06 inference(modus_ponens,[status(thm)],[5199, 5198])).
% 4.88/5.06 tff(5201,plain,
% 4.88/5.06 (hskp60 | c1_1(a1695)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5200, 197, 335, 1959, 1942, 1926, 356, 1204])).
% 4.88/5.06 tff(5202,plain,
% 4.88/5.06 (c1_1(a1695)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[5201, 5194])).
% 4.88/5.06 tff(5203,plain,
% 4.88/5.06 (~c2_1(a1637)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1085, 5192])).
% 4.88/5.06 tff(5204,plain,
% 4.88/5.06 (c0_1(a1637)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1093, 5192])).
% 4.88/5.06 tff(5205,plain,
% 4.88/5.06 (c1_1(a1637)),
% 4.88/5.06 inference(unit_resolution,[status(thm)],[1131, 5192])).
% 4.88/5.06 tff(5206,plain,
% 4.88/5.06 (((~![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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5207,plain,
% 4.88/5.06 ((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)))),
% 4.88/5.06 inference(rewrite,[status(thm)],[])).
% 4.88/5.06 tff(5208,plain,
% 4.88/5.06 (((~![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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5207])).
% 4.88/5.07 tff(5209,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5208, 5206])).
% 4.88/5.07 tff(5210,plain,
% 4.88/5.07 ((~![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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5211,plain,
% 4.88/5.07 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a1716) | c0_1(a1716) | c2_1(a1637) | (~ndr1_0) | c3_1(a1637) | (~c1_1(a1637)) | (~c1_1(a1716))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 4.88/5.07 tff(5212,plain,
% 4.88/5.07 ($false),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5211, 197, 1249, 1919, 1953, 1136, 1134, 1261, 1146, 2725])).
% 4.88/5.07 tff(5213,plain,(c3_1(a1637) | hskp21 | c2_1(a1716) | c0_1(a1716) | (~c1_1(a1637)) | c2_1(a1637) | (~c1_1(a1716))), inference(lemma,lemma(discharge,[]))).
% 4.88/5.07 tff(5214,plain,
% 4.88/5.07 (c3_1(a1637)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5213, 1919, 5183, 1953, 5205, 5203, 2725])).
% 4.88/5.07 tff(5215,plain,
% 4.88/5.07 (hskp13),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1144, 5214, 5205, 5204, 5203])).
% 4.88/5.07 tff(5216,plain,
% 4.88/5.07 (~c1_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[279, 5215])).
% 4.88/5.07 tff(5217,plain,
% 4.88/5.07 (c3_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[287, 5215])).
% 4.88/5.07 tff(5218,plain,
% 4.88/5.07 (c0_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[295, 5215])).
% 4.88/5.07 tff(5219,plain,
% 4.88/5.07 (((~![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))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5220,plain,
% 4.88/5.07 (((~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))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5221,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5220])).
% 4.88/5.07 tff(5222,plain,
% 4.88/5.07 (((~![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))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5221, 5219])).
% 4.88/5.07 tff(5223,plain,
% 4.88/5.07 ((~![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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5224,plain,
% 4.88/5.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1715) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1715)) | c0_1(a1715)),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 4.88/5.07 tff(5225,plain,
% 4.88/5.07 ($false),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5224, 197, 335, 1959, 1942, 5218, 5217, 1926, 5216, 90, 1204, 5202])).
% 4.88/5.07 tff(5226,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,[]))).
% 4.88/5.07 tff(5227,plain,
% 4.88/5.07 (c2_1(a1716)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5226, 1953, 1952, 1204, 335, 5084, 4779, 5169])).
% 4.88/5.07 tff(5228,plain,
% 4.88/5.07 (hskp13),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5092, 5227, 5084, 5168])).
% 4.88/5.07 tff(5229,plain,
% 4.88/5.07 (~c1_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[279, 5228])).
% 4.88/5.07 tff(5230,plain,
% 4.88/5.07 (~c3_1(a1695)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1925, 5169])).
% 4.88/5.07 tff(5231,plain,
% 4.88/5.07 (c3_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[287, 5228])).
% 4.88/5.07 tff(5232,plain,
% 4.88/5.07 (c0_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[295, 5228])).
% 4.88/5.07 tff(5233,plain,
% 4.88/5.07 (c2_1(a1695)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1941, 5169])).
% 4.88/5.07 tff(5234,plain,
% 4.88/5.07 (~c1_1(a1695)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5224, 197, 335, 1952, 5233, 5232, 5231, 5230, 5229, 90, 1204])).
% 4.88/5.07 tff(5235,plain,
% 4.88/5.07 (hskp60 | c1_1(a1695)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5200, 197, 335, 1952, 5233, 5230, 356, 1204])).
% 4.88/5.07 tff(5236,plain,
% 4.88/5.07 (hskp60),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5235, 5234])).
% 4.88/5.07 tff(5237,plain,
% 4.88/5.07 (~hskp30),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5007, 5236, 4965])).
% 4.88/5.07 tff(5238,plain,
% 4.88/5.07 (~hskp0),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2381, 5237, 335, 1952, 1204])).
% 4.88/5.07 tff(5239,plain,
% 4.88/5.07 (hskp42),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2410, 5238, 5169])).
% 4.88/5.07 tff(5240,plain,
% 4.88/5.07 (hskp75),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2401, 5239, 335, 1204, 5237, 1213])).
% 4.88/5.07 tff(5241,plain,
% 4.88/5.07 (~c2_1(a1724)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[411, 5240])).
% 4.88/5.07 tff(5242,plain,
% 4.88/5.07 (c0_1(a1724)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[443, 5240])).
% 4.88/5.07 tff(5243,plain,
% 4.88/5.07 (c3_1(a1724)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[435, 5240])).
% 4.88/5.07 tff(5244,plain,
% 4.88/5.07 ($false),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2723, 5243, 5242, 5236, 5241, 1213, 1204])).
% 4.88/5.07 tff(5245,plain,(c0_1(a1716) | c2_1(a1715) | c0_1(a1715) | c1_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.07 tff(5246,plain,
% 4.88/5.07 (c0_1(a1716)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5245, 335, 1204, 1213])).
% 4.88/5.07 tff(5247,plain,
% 4.88/5.07 (c2_1(a1716)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5153, 5114, 335, 1204, 126, 1213])).
% 4.88/5.07 tff(5248,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5249,plain,
% 4.88/5.07 ((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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5250,plain,
% 4.88/5.07 (((~![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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5249])).
% 4.88/5.07 tff(5251,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5250, 5248])).
% 4.88/5.07 tff(5252,plain,
% 4.88/5.07 ((~![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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5253,plain,
% 4.88/5.07 ((~![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))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5252, 5251])).
% 4.88/5.07 tff(5254,plain,
% 4.88/5.07 (hskp26),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5253, 197, 5247, 5246, 5159, 5158, 4779, 5157, 20])).
% 4.88/5.07 tff(5255,plain,
% 4.88/5.07 (~c2_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[612, 5254])).
% 4.88/5.07 tff(5256,plain,
% 4.88/5.07 (~c1_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[618, 5254])).
% 4.88/5.07 tff(5257,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5258,plain,
% 4.88/5.07 (((~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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5259,plain,
% 4.88/5.07 (((~![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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5258])).
% 4.88/5.07 tff(5260,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5259, 5257])).
% 4.88/5.07 tff(5261,plain,
% 4.88/5.07 ((~![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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5262,plain,
% 4.88/5.07 ((~![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))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 4.88/5.07 tff(5263,plain,
% 4.88/5.07 (~c0_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5262, 197, 5246, 335, 1952, 4779, 1213, 5256, 5255, 590, 5084])).
% 4.88/5.07 tff(5264,plain,
% 4.88/5.07 (~c3_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[632, 5254])).
% 4.88/5.07 tff(5265,plain,
% 4.88/5.07 (hskp37 | c0_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[639, 197, 2241, 5264, 5255, 526])).
% 4.88/5.07 tff(5266,plain,
% 4.88/5.07 (hskp37),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5265, 5263])).
% 4.88/5.07 tff(5267,plain,
% 4.88/5.07 (~c1_1(a1714)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[540, 5266])).
% 4.88/5.07 tff(5268,plain,
% 4.88/5.07 (c0_1(a1714)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[548, 5266])).
% 4.88/5.07 tff(5269,plain,
% 4.88/5.07 (c2_1(a1714)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[556, 5266])).
% 4.88/5.07 tff(5270,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5271,plain,
% 4.88/5.07 (((~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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5272,plain,
% 4.88/5.07 (((~![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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5271])).
% 4.88/5.07 tff(5273,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5272, 5270])).
% 4.88/5.07 tff(5274,plain,
% 4.88/5.07 ((~![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))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5275,plain,
% 4.88/5.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c3_1(a1716)) | c1_1(a1714) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | c0_1(a1691) | (~c0_1(a1714)) | (~c2_1(a1714)) | (~c2_1(a1716)) | (~c0_1(a1716))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5274, 5273])).
% 4.88/5.07 tff(5276,plain,
% 4.88/5.07 ($false),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5275, 197, 5247, 5246, 5269, 5268, 4779, 5267, 5264, 5255, 514, 5263])).
% 4.88/5.07 tff(5277,plain,(hskp29 | c1_1(a1715) | c2_1(a1715) | c0_1(a1715)), inference(lemma,lemma(discharge,[]))).
% 4.88/5.07 tff(5278,plain,
% 4.88/5.07 (c0_1(a1715)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5277, 1213, 126, 335])).
% 4.88/5.07 tff(5279,plain,
% 4.88/5.07 (c3_1(a1654)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[488, 4776])).
% 4.88/5.07 tff(5280,plain,
% 4.88/5.07 (c1_1(a1654)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4736, 4777, 126, 5279, 4778])).
% 4.88/5.07 tff(5281,plain,
% 4.88/5.07 (~hskp61),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[3223, 1213, 5280, 335, 5279, 5278, 4777])).
% 4.88/5.07 tff(5282,plain,
% 4.88/5.07 (hskp0),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4128, 5278, 126, 4742, 335, 5281, 1213])).
% 4.88/5.07 tff(5283,plain,
% 4.88/5.07 (hskp13),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4485, 5281, 5282])).
% 4.88/5.07 tff(5284,plain,
% 4.88/5.07 (~c1_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[279, 5283])).
% 4.88/5.07 tff(5285,plain,
% 4.88/5.07 (hskp61 | hskp33 | c2_1(a1715) | (~c0_1(a1715))),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4097, 197, 4742, 2486])).
% 4.88/5.07 tff(5286,plain,
% 4.88/5.07 (hskp33),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5285, 5281, 1213, 5278])).
% 4.88/5.07 tff(5287,plain,
% 4.88/5.07 (~c2_1(a1704)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2499, 5286])).
% 4.88/5.07 tff(5288,plain,
% 4.88/5.07 (~c0_1(a1704)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2505, 5286])).
% 4.88/5.07 tff(5289,plain,
% 4.88/5.07 (c3_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[287, 5283])).
% 4.88/5.07 tff(5290,plain,
% 4.88/5.07 (c3_1(a1704)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2514, 5286])).
% 4.88/5.07 tff(5291,plain,
% 4.88/5.07 (((~![W: $i, 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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5292,plain,
% 4.88/5.07 (((~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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5293,plain,
% 4.88/5.07 (((~![W: $i, 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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5292])).
% 4.88/5.07 tff(5294,plain,
% 4.88/5.07 (((~![W: $i, 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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5293, 5291])).
% 4.88/5.07 tff(5295,plain,
% 4.88/5.07 ((~![W: $i, 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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5296,plain,
% 4.88/5.07 ((~![W: $i, 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))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 4.88/5.07 tff(5297,plain,
% 4.88/5.07 (~c2_1(a1667)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5296, 197, 4742, 5290, 5289, 1213, 5288, 5287, 5284, 346, 5278])).
% 4.88/5.07 tff(5298,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5299,plain,
% 4.88/5.07 (((~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)))),
% 4.88/5.07 inference(rewrite,[status(thm)],[])).
% 4.88/5.07 tff(5300,plain,
% 4.88/5.07 (((~![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))))),
% 4.88/5.07 inference(monotonicity,[status(thm)],[5299])).
% 4.88/5.07 tff(5301,plain,
% 4.88/5.07 (((~![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)))),
% 4.88/5.07 inference(transitivity,[status(thm)],[5300, 5298])).
% 4.88/5.07 tff(5302,plain,
% 4.88/5.07 ((~![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)))),
% 4.88/5.07 inference(quant_inst,[status(thm)],[])).
% 4.88/5.07 tff(5303,plain,
% 4.88/5.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1715) | c2_1(a1715) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | c2_1(a1667) | (~c0_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.88/5.07 inference(modus_ponens,[status(thm)],[5302, 5301])).
% 4.88/5.07 tff(5304,plain,
% 4.88/5.07 ($false),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5303, 197, 335, 4777, 5279, 5289, 1213, 5284, 590, 5278, 5280, 5297])).
% 4.88/5.07 tff(5305,plain,(c2_1(a1715) | c1_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.88/5.07 tff(5306,plain,
% 4.88/5.07 (c2_1(a1715)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5305, 335, 126])).
% 4.88/5.07 tff(5307,plain,
% 4.88/5.07 (hskp26 | (~c2_1(a1715))),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4412, 197, 335, 4742, 4777, 4778, 5279, 20])).
% 4.88/5.07 tff(5308,plain,
% 4.88/5.07 (hskp26),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[5307, 5306])).
% 4.88/5.07 tff(5309,plain,
% 4.88/5.07 (~c2_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[612, 5308])).
% 4.88/5.07 tff(5310,plain,
% 4.88/5.07 (~c3_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[632, 5308])).
% 4.88/5.07 tff(5311,plain,
% 4.88/5.07 (c0_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4423, 5310, 2241, 5279, 4778, 5309, 4777])).
% 4.88/5.07 tff(5312,plain,
% 4.88/5.07 (~c1_1(a1691)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[618, 5308])).
% 4.88/5.07 tff(5313,plain,
% 4.88/5.07 (~hskp61),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1123, 5312, 5279, 5280, 5309, 5311, 4777])).
% 4.88/5.07 tff(5314,plain,
% 4.88/5.07 (hskp47),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4459, 197, 4777, 5279, 5310, 5309, 1719, 5280, 5311])).
% 4.88/5.07 tff(5315,plain,
% 4.88/5.07 (~c0_1(a1644)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1732, 5314])).
% 4.88/5.07 tff(5316,plain,
% 4.88/5.07 (c3_1(a1644)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1748, 5314])).
% 4.88/5.07 tff(5317,plain,
% 4.88/5.07 (~c1_1(a1644)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[1738, 5314])).
% 4.88/5.07 tff(5318,plain,
% 4.88/5.07 (~hskp13),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4623, 5317, 126, 5316, 5315])).
% 4.88/5.07 tff(5319,plain,
% 4.88/5.07 (~hskp0),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4485, 5318, 5313])).
% 4.88/5.07 tff(5320,plain,
% 4.88/5.07 (~c0_1(a1715)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4470, 197, 126, 335, 4742, 5316, 5317, 5315, 125])).
% 4.88/5.07 tff(5321,plain,
% 4.88/5.07 (~hskp57),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4479, 5320, 126, 4742, 335])).
% 4.88/5.07 tff(5322,plain,
% 4.88/5.07 (~hskp74),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[4503, 5321, 5310, 5309, 5311, 5312, 5319])).
% 4.88/5.07 tff(5323,plain,
% 4.88/5.07 (hskp38),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[960, 5322, 4776])).
% 4.88/5.07 tff(5324,plain,
% 4.88/5.07 (~c0_1(a1718)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[2418, 5323])).
% 4.88/5.07 tff(5325,plain,
% 4.88/5.07 (c3_1(a1718)),
% 4.88/5.07 inference(unit_resolution,[status(thm)],[909, 5323])).
% 4.88/5.07 tff(5326,plain,
% 4.88/5.07 (((~![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 | 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)))),
% 4.91/5.07 inference(rewrite,[status(thm)],[])).
% 4.91/5.07 tff(5327,plain,
% 4.91/5.07 ((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)))),
% 4.91/5.07 inference(rewrite,[status(thm)],[])).
% 4.91/5.07 tff(5328,plain,
% 4.91/5.07 (((~![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(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))))),
% 4.91/5.07 inference(monotonicity,[status(thm)],[5327])).
% 4.91/5.07 tff(5329,plain,
% 4.91/5.07 (((~![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(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)))),
% 4.91/5.07 inference(transitivity,[status(thm)],[5328, 5326])).
% 4.91/5.07 tff(5330,plain,
% 4.91/5.07 ((~![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(a1715) | (~c3_1(a1715)) | (~c2_1(a1715)) | c0_1(a1718) | (~c3_1(a1718)) | (~c1_1(a1718)))),
% 4.91/5.07 inference(quant_inst,[status(thm)],[])).
% 4.91/5.07 tff(5331,plain,
% 4.91/5.07 ((~![V: $i, U: $i] : (hskp73 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp73 | c1_1(a1715) | (~c2_1(a1715)) | c0_1(a1718) | (~ndr1_0) | (~c3_1(a1715)) | (~c3_1(a1718)) | (~c1_1(a1718))),
% 4.91/5.07 inference(modus_ponens,[status(thm)],[5330, 5329])).
% 4.91/5.07 tff(5332,plain,
% 4.91/5.07 (~c1_1(a1718)),
% 4.91/5.07 inference(unit_resolution,[status(thm)],[5331, 197, 4733, 335, 4742, 5325, 5306, 5324, 1449])).
% 4.91/5.07 tff(5333,plain,
% 4.91/5.07 (~c2_1(a1718)),
% 4.91/5.07 inference(unit_resolution,[status(thm)],[901, 5323])).
% 4.91/5.07 tff(5334,plain,
% 4.91/5.07 ($false),
% 4.91/5.07 inference(unit_resolution,[status(thm)],[4514, 197, 4777, 5279, 5325, 5333, 5312, 5309, 590, 5280, 5332, 5311])).
% 4.91/5.07 tff(5335,plain,(c1_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.91/5.07 tff(5336,plain,
% 4.91/5.07 (c1_1(a1715)),
% 4.91/5.07 inference(unit_resolution,[status(thm)],[5335, 126])).
% 4.91/5.07 tff(5337,plain,
% 4.91/5.07 (((~![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)))),
% 4.91/5.07 inference(rewrite,[status(thm)],[])).
% 4.91/5.07 tff(5338,plain,
% 4.91/5.07 ((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)))),
% 4.91/5.07 inference(rewrite,[status(thm)],[])).
% 4.91/5.07 tff(5339,plain,
% 4.91/5.07 (((~![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))))),
% 4.91/5.07 inference(monotonicity,[status(thm)],[5338])).
% 4.91/5.08 tff(5340,plain,
% 4.91/5.08 (((~![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(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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5339, 5337])).
% 4.91/5.08 tff(5341,plain,
% 4.91/5.08 ((~![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(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c1_1(a1654)) | (~c2_1(a1654)) | (~c0_1(a1654)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5342,plain,
% 4.91/5.08 ((~![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(a1715) | (~ndr1_0) | (~c3_1(a1715)) | (~c1_1(a1715)) | (~c0_1(a1654)) | (~c2_1(a1654)) | (~c1_1(a1654))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5341, 5340])).
% 4.91/5.08 tff(5343,plain,
% 4.91/5.08 (hskp0),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5342, 197, 5336, 4742, 4777, 4778, 1213, 881, 5280])).
% 4.91/5.08 tff(5344,plain,
% 4.91/5.08 (c1_1(a1637)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1131, 5343])).
% 4.91/5.08 tff(5345,plain,
% 4.91/5.08 (c0_1(a1637)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1093, 5343])).
% 4.91/5.08 tff(5346,plain,
% 4.91/5.08 (~c2_1(a1637)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1085, 5343])).
% 4.91/5.08 tff(5347,plain,
% 4.91/5.08 (hskp61),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[2531, 5346, 4742, 5336, 1213, 5345, 5344])).
% 4.91/5.08 tff(5348,plain,
% 4.91/5.08 (~c2_1(a1674)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1100, 5347])).
% 4.91/5.08 tff(5349,plain,
% 4.91/5.08 (~c1_1(a1674)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1106, 5347])).
% 4.91/5.08 tff(5350,plain,
% 4.91/5.08 (c3_1(a1674)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1114, 5347])).
% 4.91/5.08 tff(5351,plain,
% 4.91/5.08 (~c0_1(a1674)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[2616, 197, 5350, 4777, 5279, 5349, 5348, 590, 5280])).
% 4.91/5.08 tff(5352,plain,
% 4.91/5.08 (((~![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)) | (~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5353,plain,
% 4.91/5.08 ((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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5354,plain,
% 4.91/5.08 (((~![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(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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5353])).
% 4.91/5.08 tff(5355,plain,
% 4.91/5.08 (((~![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(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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5354, 5352])).
% 4.91/5.08 tff(5356,plain,
% 4.91/5.08 ((~![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(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654)) | c2_1(a1715) | (~c3_1(a1715)) | (~c1_1(a1715)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5357,plain,
% 4.91/5.08 ((~![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)) | (~c1_1(a1715)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5356, 5355])).
% 4.91/5.08 tff(5358,plain,
% 4.91/5.08 (hskp13),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5357, 197, 5336, 4742, 4777, 5279, 1213, 266, 5280])).
% 4.91/5.08 tff(5359,plain,
% 4.91/5.08 (~c1_1(a1667)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[279, 5358])).
% 4.91/5.08 tff(5360,plain,
% 4.91/5.08 (c3_1(a1667)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[287, 5358])).
% 4.91/5.08 tff(5361,plain,
% 4.91/5.08 (c0_1(a1667)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[295, 5358])).
% 4.91/5.08 tff(5362,plain,
% 4.91/5.08 (((~![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(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))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5363,plain,
% 4.91/5.08 ((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))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5364,plain,
% 4.91/5.08 (((~![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(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)))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5363])).
% 4.91/5.08 tff(5365,plain,
% 4.91/5.08 (((~![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(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))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5364, 5362])).
% 4.91/5.08 tff(5366,plain,
% 4.91/5.08 ((~![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(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1674) | c1_1(a1674) | (~c3_1(a1674)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5367,plain,
% 4.91/5.08 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a1674) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c3_1(a1674)) | c0_1(a1674)),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5366, 5365])).
% 4.91/5.08 tff(5368,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5367, 197, 126, 5350, 5361, 5360, 5349, 5359, 125, 5351])).
% 4.91/5.08 tff(5369,plain,(c2_1(a1715) | hskp29), inference(lemma,lemma(discharge,[]))).
% 4.91/5.08 tff(5370,plain,
% 4.91/5.08 (c2_1(a1715)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5369, 126])).
% 4.91/5.08 tff(5371,plain,
% 4.91/5.08 (hskp26),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4610, 5370, 4742, 4777, 5280, 5279, 5336, 4778])).
% 4.91/5.08 tff(5372,plain,
% 4.91/5.08 (~c2_1(a1691)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[612, 5371])).
% 4.91/5.08 tff(5373,plain,
% 4.91/5.08 (~hskp72),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[502, 5370])).
% 4.91/5.08 tff(5374,plain,
% 4.91/5.08 (~c3_1(a1691)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[632, 5371])).
% 4.91/5.08 tff(5375,plain,
% 4.91/5.08 (c0_1(a1691)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4423, 5374, 5373, 5279, 4778, 5372, 4777])).
% 4.91/5.08 tff(5376,plain,
% 4.91/5.08 (hskp47),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4459, 197, 4777, 5279, 5374, 5372, 1719, 5280, 5375])).
% 4.91/5.08 tff(5377,plain,
% 4.91/5.08 (~c0_1(a1644)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1732, 5376])).
% 4.91/5.08 tff(5378,plain,
% 4.91/5.08 (~c1_1(a1644)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1738, 5376])).
% 4.91/5.08 tff(5379,plain,
% 4.91/5.08 (~c1_1(a1691)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[618, 5371])).
% 4.91/5.08 tff(5380,plain,
% 4.91/5.08 (~hskp61),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1123, 5372, 5279, 5280, 5379, 5375, 4777])).
% 4.91/5.08 tff(5381,plain,
% 4.91/5.08 (c3_1(a1644)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1748, 5376])).
% 4.91/5.08 tff(5382,plain,
% 4.91/5.08 (~hskp13),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4623, 5378, 126, 5381, 5377])).
% 4.91/5.08 tff(5383,plain,
% 4.91/5.08 (~hskp0),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4485, 5382, 5380])).
% 4.91/5.08 tff(5384,plain,
% 4.91/5.08 (c2_1(a1644)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4667, 197, 4777, 5279, 5381, 5378, 5379, 5372, 590, 5280, 5375])).
% 4.91/5.08 tff(5385,assumption,(c2_1(a1644)), introduced(assumption)).
% 4.91/5.08 tff(5386,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4675, 197, 1960, 771, 1959, 4621, 4620, 1449, 1204, 5385])).
% 4.91/5.08 tff(5387,plain,(c0_1(a1715) | hskp73 | (~c1_1(a1715)) | (~c3_1(a1715)) | (~c3_1(a1644)) | c1_1(a1644) | (~c2_1(a1644))), inference(lemma,lemma(discharge,[]))).
% 4.91/5.08 tff(5388,plain,
% 4.91/5.08 (c0_1(a1715)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5387, 4733, 5336, 4742, 5381, 5378, 5384])).
% 4.91/5.08 tff(5389,plain,
% 4.91/5.08 (~hskp38),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4714, 5388, 4742, 5370, 5372, 5379, 5375, 5383, 5336])).
% 4.91/5.08 tff(5390,plain,
% 4.91/5.08 (hskp74),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[960, 5389, 4776])).
% 4.91/5.08 tff(5391,plain,
% 4.91/5.08 (hskp57),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4503, 5390, 5374, 5372, 5375, 5379, 5383])).
% 4.91/5.08 tff(5392,plain,
% 4.91/5.08 (~c1_1(a1665)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[59, 5391])).
% 4.91/5.08 tff(5393,plain,
% 4.91/5.08 (c3_1(a1665)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[67, 5391])).
% 4.91/5.08 tff(5394,plain,
% 4.91/5.08 (c0_1(a1665)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[78, 5391])).
% 4.91/5.08 tff(5395,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[4361, 197, 126, 5394, 5393, 5381, 5392, 5378, 5377, 125])).
% 4.91/5.08 tff(5396,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 4.91/5.08 tff(5397,plain,
% 4.91/5.08 (~c3_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1925, 5396])).
% 4.91/5.08 tff(5398,plain,
% 4.91/5.08 (c2_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1941, 5396])).
% 4.91/5.08 tff(5399,plain,
% 4.91/5.08 (((~![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)))) | (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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5400,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5401,plain,
% 4.91/5.08 (((~![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(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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5400])).
% 4.91/5.08 tff(5402,plain,
% 4.91/5.08 (((~![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(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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5401, 5399])).
% 4.91/5.08 tff(5403,plain,
% 4.91/5.08 ((~![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(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)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5404,plain,
% 4.91/5.08 ((~![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)))) | 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))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5403, 5402])).
% 4.91/5.08 tff(5405,plain,
% 4.91/5.08 ((~c3_1(a1677)) | (~c1_1(a1695))),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5404, 197, 93, 92, 5398, 91, 5397, 115, 114, 90])).
% 4.91/5.08 tff(5406,plain,
% 4.91/5.08 (~c1_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5405, 113])).
% 4.91/5.08 tff(5407,plain,
% 4.91/5.08 (c0_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[1933, 5396])).
% 4.91/5.08 tff(5408,plain,
% 4.91/5.08 (((~![W: $i, 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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5409,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5410,plain,
% 4.91/5.08 (((~![W: $i, 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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5409])).
% 4.91/5.08 tff(5411,plain,
% 4.91/5.08 (((~![W: $i, 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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5410, 5408])).
% 4.91/5.08 tff(5412,plain,
% 4.91/5.08 ((~![W: $i, 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)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5413,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1677)) | c1_1(a1695) | (~c0_1(a1695))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5412, 5411])).
% 4.91/5.08 tff(5414,plain,
% 4.91/5.08 ((~c3_1(a1677)) | c1_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5413, 197, 5407, 69, 71, 5397, 115, 310, 70, 380])).
% 4.91/5.08 tff(5415,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5414, 5406, 113])).
% 4.91/5.08 tff(5416,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,[]))).
% 4.91/5.08 tff(5417,plain,
% 4.91/5.08 (~c3_1(a1677)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5416, 112, 71, 69, 106, 70, 93, 92, 91, 100])).
% 4.91/5.08 tff(5418,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5419,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5420,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5419])).
% 4.91/5.08 tff(5421,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5420, 5418])).
% 4.91/5.08 tff(5422,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5423,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | c3_1(a1677) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5422, 5421])).
% 4.91/5.08 tff(5424,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5423, 197, 5398, 5407, 5397, 112, 106, 100, 30, 5417])).
% 4.91/5.08 tff(5425,plain,((~hskp16) | (~c0_1(a1655)) | (~c3_1(a1655)) | c2_1(a1655) | (~c0_1(a1665)) | (~c3_1(a1665)) | c1_1(a1665)), inference(lemma,lemma(discharge,[]))).
% 4.91/5.08 tff(5426,plain,
% 4.91/5.08 (~hskp16),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5425, 93, 69, 70, 71, 92, 91])).
% 4.91/5.08 tff(5427,plain,
% 4.91/5.08 (hskp17),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[304, 5426, 69, 71, 70])).
% 4.91/5.08 tff(5428,plain,
% 4.91/5.08 (~c1_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[217, 5427])).
% 4.91/5.08 tff(5429,plain,
% 4.91/5.08 (~c0_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[223, 5427])).
% 4.91/5.08 tff(5430,plain,
% 4.91/5.08 (((~![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)))) | (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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5431,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5432,plain,
% 4.91/5.08 (((~![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(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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5431])).
% 4.91/5.08 tff(5433,plain,
% 4.91/5.08 (((~![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(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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5432, 5430])).
% 4.91/5.08 tff(5434,plain,
% 4.91/5.08 ((~![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(a1665) | (~c3_1(a1665)) | (~c0_1(a1665)) | c3_1(a1695) | (~c2_1(a1695)) | (~c1_1(a1695)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5435,plain,
% 4.91/5.08 ((~![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)))) | 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))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5434, 5433])).
% 4.91/5.08 tff(5436,plain,
% 4.91/5.08 ((~c3_1(a1678)) | (~c1_1(a1695))),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5435, 197, 93, 92, 5398, 91, 5397, 5429, 5428, 90])).
% 4.91/5.08 tff(5437,plain,
% 4.91/5.08 (~c1_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5436, 80])).
% 4.91/5.08 tff(5438,plain,
% 4.91/5.08 (~c2_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[236, 5427])).
% 4.91/5.08 tff(5439,plain,
% 4.91/5.08 (((~![W: $i, 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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5440,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5441,plain,
% 4.91/5.08 (((~![W: $i, 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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5440])).
% 4.91/5.08 tff(5442,plain,
% 4.91/5.08 (((~![W: $i, 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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5441, 5439])).
% 4.91/5.08 tff(5443,plain,
% 4.91/5.08 ((~![W: $i, 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)))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5444,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1695) | c0_1(a1678) | c2_1(a1678) | c2_1(a1655) | (~ndr1_0) | (~c3_1(a1655)) | (~c0_1(a1655)) | (~c3_1(a1678)) | c1_1(a1695) | (~c0_1(a1695))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5443, 5442])).
% 4.91/5.08 tff(5445,plain,
% 4.91/5.08 ((~c3_1(a1678)) | c1_1(a1695)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5444, 197, 5407, 69, 71, 5397, 5429, 5438, 70, 380])).
% 4.91/5.08 tff(5446,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5445, 5437, 80])).
% 4.91/5.08 tff(5447,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,[]))).
% 4.91/5.08 tff(5448,plain,
% 4.91/5.08 (~c3_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5447, 79, 71, 70, 69, 68, 60])).
% 4.91/5.08 tff(5449,plain,
% 4.91/5.08 (~hskp16),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5425, 79, 69, 70, 71, 68, 60])).
% 4.91/5.08 tff(5450,plain,
% 4.91/5.08 (hskp17),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[304, 5449, 69, 71, 70])).
% 4.91/5.08 tff(5451,plain,
% 4.91/5.08 (~c2_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[236, 5450])).
% 4.91/5.08 tff(5452,plain,
% 4.91/5.08 (~c1_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[217, 5450])).
% 4.91/5.08 tff(5453,plain,
% 4.91/5.08 (~c0_1(a1678)),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[223, 5450])).
% 4.91/5.08 tff(5454,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5455,plain,
% 4.91/5.08 (((~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)))),
% 4.91/5.08 inference(rewrite,[status(thm)],[])).
% 4.91/5.08 tff(5456,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.08 inference(monotonicity,[status(thm)],[5455])).
% 4.91/5.08 tff(5457,plain,
% 4.91/5.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.08 inference(transitivity,[status(thm)],[5456, 5454])).
% 4.91/5.08 tff(5458,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.08 inference(quant_inst,[status(thm)],[])).
% 4.91/5.08 tff(5459,plain,
% 4.91/5.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | c3_1(a1678) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.08 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 4.91/5.08 tff(5460,plain,
% 4.91/5.08 ($false),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5459, 197, 5398, 5407, 5397, 5453, 5452, 5451, 30, 5448])).
% 4.91/5.08 tff(5461,plain,((~hskp57) | (~c0_1(a1655)) | c2_1(a1655) | (~c3_1(a1655))), inference(lemma,lemma(discharge,[]))).
% 4.91/5.08 tff(5462,plain,
% 4.91/5.08 (~hskp57),
% 4.91/5.08 inference(unit_resolution,[status(thm)],[5461, 53, 45, 39])).
% 4.91/5.08 tff(5463,plain,
% 4.91/5.08 (((~![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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5464,plain,
% 4.91/5.09 ((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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5465,plain,
% 4.91/5.09 (((~![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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5464])).
% 4.91/5.09 tff(5466,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5465, 5463])).
% 4.91/5.09 tff(5467,plain,
% 4.91/5.09 ((~![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)))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5468,plain,
% 4.91/5.09 ((~![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))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 4.91/5.09 tff(5469,plain,
% 4.91/5.09 (hskp57 | hskp11),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5468, 197, 39, 53, 45, 1516])).
% 4.91/5.09 tff(5470,plain,
% 4.91/5.09 (hskp11),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5469, 5462])).
% 4.91/5.09 tff(5471,plain,
% 4.91/5.09 (~c1_1(a1664)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1552, 5470])).
% 4.91/5.09 tff(5472,plain,
% 4.91/5.09 (~c2_1(a1664)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1531, 5470])).
% 4.91/5.09 tff(5473,plain,
% 4.91/5.09 (~c3_1(a1664)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1537, 5470])).
% 4.91/5.09 tff(5474,assumption,(~c1_1(a1664)), introduced(assumption)).
% 4.91/5.09 tff(5475,assumption,(~c2_1(a1664)), introduced(assumption)).
% 4.91/5.09 tff(5476,assumption,(~c3_1(a1664)), introduced(assumption)).
% 4.91/5.09 tff(5477,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5478,plain,
% 4.91/5.09 (((~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5479,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5478])).
% 4.91/5.09 tff(5480,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5479, 5477])).
% 4.91/5.09 tff(5481,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5482,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5481, 5480])).
% 4.91/5.09 tff(5483,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5482, 197, 5398, 5407, 5397, 224, 218, 237, 5476, 5475, 5474, 30])).
% 4.91/5.09 tff(5484,plain,((~hskp17) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664)), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5485,plain,
% 4.91/5.09 (~hskp17),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5484, 5473, 5472, 5471])).
% 4.91/5.09 tff(5486,plain,
% 4.91/5.09 (hskp16),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[304, 5485, 39, 53, 45])).
% 4.91/5.09 tff(5487,plain,
% 4.91/5.09 (~c1_1(a1677)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[99, 5486])).
% 4.91/5.09 tff(5488,plain,
% 4.91/5.09 (~c2_1(a1677)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[105, 5486])).
% 4.91/5.09 tff(5489,plain,
% 4.91/5.09 (~c0_1(a1677)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[111, 5486])).
% 4.91/5.09 tff(5490,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5491,plain,
% 4.91/5.09 (((~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5492,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5491])).
% 4.91/5.09 tff(5493,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5492, 5490])).
% 4.91/5.09 tff(5494,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5495,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | c3_1(a1664) | c2_1(a1664) | c1_1(a1664) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 4.91/5.09 tff(5496,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5495, 197, 5398, 5407, 5397, 5489, 5488, 5487, 5473, 5472, 5471, 30])).
% 4.91/5.09 tff(5497,plain,(~hskp7), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5498,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5499,plain,
% 4.91/5.09 ((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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5500,plain,
% 4.91/5.09 (((~![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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5499])).
% 4.91/5.09 tff(5501,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5500, 5498])).
% 4.91/5.09 tff(5502,plain,
% 4.91/5.09 ((~![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)))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5503,plain,
% 4.91/5.09 ((~![U: $i] : (hskp52 | hskp7 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp52 | hskp7 | c3_1(a1695) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 4.91/5.09 tff(5504,plain,
% 4.91/5.09 (hskp52 | hskp7),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5503, 197, 5398, 5407, 5397, 168])).
% 4.91/5.09 tff(5505,plain,
% 4.91/5.09 (hskp52),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5504, 5497])).
% 4.91/5.09 tff(5506,plain,
% 4.91/5.09 (c3_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[488, 5505])).
% 4.91/5.09 tff(5507,plain,
% 4.91/5.09 (c2_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[496, 5505])).
% 4.91/5.09 tff(5508,plain,
% 4.91/5.09 (c0_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[480, 5505])).
% 4.91/5.09 tff(5509,plain,
% 4.91/5.09 (~hskp12),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[4589, 4583, 5508, 5507, 5506])).
% 4.91/5.09 tff(5510,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[3592, 197, 4583, 5508, 5507, 5506, 20, 570])).
% 4.91/5.09 tff(5511,plain,(c1_1(a1654) | hskp26), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5512,plain,
% 4.91/5.09 (c1_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5511, 4583])).
% 4.91/5.09 tff(5513,plain,
% 4.91/5.09 (hskp13 | hskp12 | (~c1_1(a1654))),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[835, 197, 5507, 5506, 830])).
% 4.91/5.09 tff(5514,plain,
% 4.91/5.09 (hskp13),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5513, 5512, 5509])).
% 4.91/5.09 tff(5515,plain,
% 4.91/5.09 (~c1_1(a1667)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[279, 5514])).
% 4.91/5.09 tff(5516,plain,
% 4.91/5.09 (c3_1(a1667)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[287, 5514])).
% 4.91/5.09 tff(5517,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5518,plain,
% 4.91/5.09 ((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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5519,plain,
% 4.91/5.09 (((~![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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5518])).
% 4.91/5.09 tff(5520,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5519, 5517])).
% 4.91/5.09 tff(5521,plain,
% 4.91/5.09 ((~![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)))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5522,plain,
% 4.91/5.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp26 | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c2_1(a1667)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c2_1(a1654))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5521, 5520])).
% 4.91/5.09 tff(5523,plain,
% 4.91/5.09 (~c2_1(a1667)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5522, 197, 4583, 5508, 5507, 5506, 5516, 5515, 20])).
% 4.91/5.09 tff(5524,plain,
% 4.91/5.09 (c0_1(a1667)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[295, 5514])).
% 4.91/5.09 tff(5525,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[4608, 197, 5508, 5506, 5524, 5516, 5515, 590, 5512, 5523])).
% 4.91/5.09 tff(5526,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5527,plain,
% 4.91/5.09 (~c2_1(a1691)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[612, 5526])).
% 4.91/5.09 tff(5528,plain,
% 4.91/5.09 (~c1_1(a1691)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[618, 5526])).
% 4.91/5.09 tff(5529,plain,
% 4.91/5.09 (~c3_1(a1691)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[632, 5526])).
% 4.91/5.09 tff(5530,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5531,plain,
% 4.91/5.09 (((~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5532,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5531])).
% 4.91/5.09 tff(5533,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5532, 5530])).
% 4.91/5.09 tff(5534,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5535,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1678) | c1_1(a1678) | c2_1(a1678) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5534, 5533])).
% 4.91/5.09 tff(5536,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5535, 197, 5398, 5407, 5397, 893, 892, 895, 224, 218, 237, 30])).
% 4.91/5.09 tff(5537,plain,((~hskp17) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5538,plain,
% 4.91/5.09 (~hskp17),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5537, 5529, 5528, 5527])).
% 4.91/5.09 tff(5539,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5540,plain,
% 4.91/5.09 (((~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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5541,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5540])).
% 4.91/5.09 tff(5542,plain,
% 4.91/5.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5541, 5539])).
% 4.91/5.09 tff(5543,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~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))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5544,plain,
% 4.91/5.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c3_1(a1691) | c1_1(a1691) | c2_1(a1691) | c0_1(a1677) | c2_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 4.91/5.09 tff(5545,plain,
% 4.91/5.09 ($false),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5544, 197, 5398, 5407, 5397, 5529, 5528, 5527, 112, 106, 100, 30])).
% 4.91/5.09 tff(5546,plain,(~hskp16), inference(lemma,lemma(discharge,[]))).
% 4.91/5.09 tff(5547,plain,
% 4.91/5.09 (hskp17 | hskp16 | c1_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[659, 197, 5508, 5506, 10])).
% 4.91/5.09 tff(5548,plain,
% 4.91/5.09 (c1_1(a1654)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5547, 5546, 5538])).
% 4.91/5.09 tff(5549,assumption,(c1_1(a1691)), introduced(assumption)).
% 4.91/5.09 tff(5550,plain,
% 4.91/5.09 (c0_1(a1691)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[4423, 893, 5507, 5506, 527, 895, 5508])).
% 4.91/5.09 tff(5551,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5552,plain,
% 4.91/5.09 ((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)))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5553,plain,
% 4.91/5.09 (((~![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))))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5552])).
% 4.91/5.09 tff(5554,plain,
% 4.91/5.09 (((~![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)))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5553, 5551])).
% 4.91/5.09 tff(5555,plain,
% 4.91/5.09 ((~![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)))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5556,plain,
% 4.91/5.09 ((~![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))),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5555, 5554])).
% 4.91/5.09 tff(5557,plain,
% 4.91/5.09 (hskp61 | (~c1_1(a1691))),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5556, 197, 893, 895, 1156, 5550])).
% 4.91/5.09 tff(5558,plain,
% 4.91/5.09 (hskp61),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5557, 5549])).
% 4.91/5.09 tff(5559,plain,
% 4.91/5.09 (~c2_1(a1674)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1100, 5558])).
% 4.91/5.09 tff(5560,plain,
% 4.91/5.09 (~c1_1(a1674)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1106, 5558])).
% 4.91/5.09 tff(5561,plain,
% 4.91/5.09 (c3_1(a1674)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[1114, 5558])).
% 4.91/5.09 tff(5562,plain,
% 4.91/5.09 (~hskp26),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[618, 5549])).
% 4.91/5.09 tff(5563,plain,
% 4.91/5.09 (~hskp12),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[4589, 5562, 5508, 5507, 5506])).
% 4.91/5.09 tff(5564,plain,
% 4.91/5.09 (((~![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(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))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5565,plain,
% 4.91/5.09 ((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))),
% 4.91/5.09 inference(rewrite,[status(thm)],[])).
% 4.91/5.09 tff(5566,plain,
% 4.91/5.09 (((~![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(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)))),
% 4.91/5.09 inference(monotonicity,[status(thm)],[5565])).
% 4.91/5.09 tff(5567,plain,
% 4.91/5.09 (((~![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(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))),
% 4.91/5.09 inference(transitivity,[status(thm)],[5566, 5564])).
% 4.91/5.09 tff(5568,plain,
% 4.91/5.09 ((~![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(a1695) | c1_1(a1695) | (~c2_1(a1695)))),
% 4.91/5.09 inference(quant_inst,[status(thm)],[])).
% 4.91/5.09 tff(5569,plain,
% 4.91/5.09 ((~![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(a1695) | c3_1(a1691) | c2_1(a1691) | (~ndr1_0) | (~c0_1(a1691)) | (~c2_1(a1695)) | c1_1(a1695)),
% 4.91/5.09 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 4.91/5.09 tff(5570,plain,
% 4.91/5.09 (hskp57 | c1_1(a1695)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5569, 197, 5398, 5397, 893, 895, 1504, 5550])).
% 4.91/5.09 tff(5571,plain,
% 4.91/5.09 (c1_1(a1695)),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5570, 1505])).
% 4.91/5.09 tff(5572,plain,
% 4.91/5.09 (hskp75 | (~c1_1(a1695))),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[2646, 197, 2140, 5398, 2138, 2182, 5397, 398])).
% 4.91/5.09 tff(5573,plain,
% 4.91/5.09 (hskp75),
% 4.91/5.09 inference(unit_resolution,[status(thm)],[5572, 5571])).
% 4.91/5.10 tff(5574,plain,
% 4.91/5.10 (~c2_1(a1724)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[411, 5573])).
% 4.91/5.10 tff(5575,plain,
% 4.91/5.10 (c3_1(a1724)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[435, 5573])).
% 4.91/5.10 tff(5576,plain,
% 4.91/5.10 (c0_1(a1724)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[443, 5573])).
% 4.91/5.10 tff(5577,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5578,plain,
% 4.91/5.10 ((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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5579,plain,
% 4.91/5.10 (((~![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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5578])).
% 4.91/5.10 tff(5580,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5579, 5577])).
% 4.91/5.10 tff(5581,plain,
% 4.91/5.10 ((~![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)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5582,plain,
% 4.91/5.10 ((~![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))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 4.91/5.10 tff(5583,plain,
% 4.91/5.10 (hskp11),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5582, 197, 1505, 5576, 5575, 5574, 1516])).
% 4.91/5.10 tff(5584,plain,
% 4.91/5.10 (~c1_1(a1664)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1552, 5583])).
% 4.91/5.10 tff(5585,plain,
% 4.91/5.10 (~c2_1(a1664)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1531, 5583])).
% 4.91/5.10 tff(5586,plain,
% 4.91/5.10 (~c3_1(a1664)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1537, 5583])).
% 4.91/5.10 tff(5587,plain,
% 4.91/5.10 (~hskp17),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5484, 5586, 5585, 5584])).
% 4.91/5.10 tff(5588,plain,
% 4.91/5.10 (hskp16),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5547, 570, 247])).
% 4.91/5.10 tff(5589,plain,
% 4.91/5.10 (~c2_1(a1677)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[105, 5588])).
% 4.91/5.10 tff(5590,plain,
% 4.91/5.10 (~c0_1(a1677)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[111, 5588])).
% 4.91/5.10 tff(5591,plain,
% 4.91/5.10 (c3_1(a1677)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[735, 5590, 5507, 5506, 527, 5589, 5508])).
% 4.91/5.10 tff(5592,plain,
% 4.91/5.10 (~c1_1(a1677)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[99, 5588])).
% 4.91/5.10 tff(5593,plain,
% 4.91/5.10 (((~![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))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5594,plain,
% 4.91/5.10 (((~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))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5595,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5594])).
% 4.91/5.10 tff(5596,plain,
% 4.91/5.10 (((~![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))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5595, 5593])).
% 4.91/5.10 tff(5597,plain,
% 4.91/5.10 ((~![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)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5598,plain,
% 4.91/5.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1695) | c0_1(a1677) | c1_1(a1677) | (~ndr1_0) | (~c3_1(a1677)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1654)) | (~c0_1(a1654)) | c1_1(a1654)),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 4.91/5.10 tff(5599,plain,
% 4.91/5.10 ($false),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5598, 197, 5508, 5506, 5398, 5397, 5590, 5592, 90, 570, 4924, 5591])).
% 4.91/5.10 tff(5600,plain,(c1_1(a1654) | (~c1_1(a1695)) | hskp72 | hskp17), inference(lemma,lemma(discharge,[]))).
% 4.91/5.10 tff(5601,plain,
% 4.91/5.10 (c1_1(a1654)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5600, 5571, 527, 5587])).
% 4.91/5.10 tff(5602,plain,
% 4.91/5.10 (hskp13),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5513, 5601, 5085])).
% 4.91/5.10 tff(5603,plain,
% 4.91/5.10 (~c1_1(a1667)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[279, 5602])).
% 4.91/5.10 tff(5604,plain,
% 4.91/5.10 (hskp47 | (~c1_1(a1654))),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[4459, 197, 5508, 5506, 893, 895, 1719, 5550])).
% 4.91/5.10 tff(5605,plain,
% 4.91/5.10 (hskp47),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5604, 5601])).
% 4.91/5.10 tff(5606,plain,
% 4.91/5.10 (~c0_1(a1644)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1732, 5605])).
% 4.91/5.10 tff(5607,plain,
% 4.91/5.10 (~c1_1(a1644)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1738, 5605])).
% 4.91/5.10 tff(5608,plain,
% 4.91/5.10 (c3_1(a1667)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[287, 5602])).
% 4.91/5.10 tff(5609,plain,
% 4.91/5.10 (c0_1(a1667)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[295, 5602])).
% 4.91/5.10 tff(5610,plain,
% 4.91/5.10 (c3_1(a1644)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1748, 5605])).
% 4.91/5.10 tff(5611,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5612,plain,
% 4.91/5.10 (((~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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5613,plain,
% 4.91/5.10 (((~![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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5612])).
% 4.91/5.10 tff(5614,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5613, 5611])).
% 4.91/5.10 tff(5615,plain,
% 4.91/5.10 ((~![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)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5616,plain,
% 4.91/5.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1644) | c0_1(a1644) | c3_1(a1695) | c1_1(a1667) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1695)) | (~c1_1(a1695)) | (~c3_1(a1644))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 4.91/5.10 tff(5617,plain,
% 4.91/5.10 ($false),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5616, 197, 5610, 5398, 5609, 5608, 5607, 5606, 5397, 5603, 90, 5571])).
% 4.91/5.10 tff(5618,plain,(hskp57 | hskp12 | c3_1(a1691) | c2_1(a1691) | hskp72 | (~c3_1(a1674)) | c1_1(a1674) | c2_1(a1674)), inference(lemma,lemma(discharge,[]))).
% 4.91/5.10 tff(5619,plain,
% 4.91/5.10 (hskp57),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5618, 5563, 893, 895, 527, 5561, 5560, 5559])).
% 4.91/5.10 tff(5620,plain,
% 4.91/5.10 (~c1_1(a1665)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[59, 5619])).
% 4.91/5.10 tff(5621,plain,
% 4.91/5.10 (c3_1(a1665)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[67, 5619])).
% 4.91/5.10 tff(5622,plain,
% 4.91/5.10 (c0_1(a1665)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[78, 5619])).
% 4.91/5.10 tff(5623,plain,
% 4.91/5.10 (((~![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(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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5624,plain,
% 4.91/5.10 ((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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5625,plain,
% 4.91/5.10 (((~![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(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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5624])).
% 4.91/5.10 tff(5626,plain,
% 4.91/5.10 (((~![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(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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5625, 5623])).
% 4.91/5.10 tff(5627,plain,
% 4.91/5.10 ((~![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(a1665) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c3_1(a1665)) | (~c2_1(a1665)) | (~c0_1(a1665)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5628,plain,
% 4.91/5.10 ((~![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(a1665) | (~ndr1_0) | (~c3_1(a1665)) | (~c0_1(a1665)) | (~c2_1(a1665))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5627, 5626])).
% 4.91/5.10 tff(5629,plain,
% 4.91/5.10 (~c2_1(a1665)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5628, 197, 5562, 5622, 5621, 5620, 20])).
% 4.91/5.10 tff(5630,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5631,plain,
% 4.91/5.10 (((~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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5632,plain,
% 4.91/5.10 (((~![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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5631])).
% 4.91/5.10 tff(5633,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5632, 5630])).
% 4.91/5.10 tff(5634,plain,
% 4.91/5.10 ((~![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)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5635,plain,
% 4.91/5.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1674) | c2_1(a1674) | c1_1(a1665) | (~ndr1_0) | (~c0_1(a1665)) | c2_1(a1665) | (~c3_1(a1674)) | (~c3_1(a1654)) | (~c0_1(a1654)) | (~c1_1(a1654))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5634, 5633])).
% 4.91/5.10 tff(5636,plain,
% 4.91/5.10 (~c1_1(a1654)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5635, 197, 5561, 5622, 5508, 5506, 5560, 5559, 5620, 590, 5629])).
% 4.91/5.10 tff(5637,plain,
% 4.91/5.10 ($false),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[3592, 197, 5562, 5508, 5507, 5506, 20, 5636])).
% 4.91/5.10 tff(5638,plain,((~c1_1(a1691)) | c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.91/5.10 tff(5639,plain,
% 4.91/5.10 (~c1_1(a1691)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5638, 893, 895, 527])).
% 4.91/5.10 tff(5640,plain,
% 4.91/5.10 (~hskp17),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5537, 5639, 893, 895])).
% 4.91/5.10 tff(5641,plain,
% 4.91/5.10 (hskp57 | c1_1(a1695)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5569, 197, 5398, 5397, 893, 895, 1504, 871])).
% 4.91/5.10 tff(5642,plain,
% 4.91/5.10 (c1_1(a1695)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5641, 1505])).
% 4.91/5.10 tff(5643,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5644,plain,
% 4.91/5.10 ((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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5645,plain,
% 4.91/5.10 (((~![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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5644])).
% 4.91/5.10 tff(5646,plain,
% 4.91/5.10 (((~![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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5645, 5643])).
% 4.91/5.10 tff(5647,plain,
% 4.91/5.10 ((~![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)))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5648,plain,
% 4.91/5.10 ((~![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))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5647, 5646])).
% 4.91/5.10 tff(5649,plain,
% 4.91/5.10 (hskp2 | c1_1(a1691) | (~c1_1(a1695))),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5648, 197, 5407, 5397, 893, 891, 871])).
% 4.91/5.10 tff(5650,plain,
% 4.91/5.10 (hskp2),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5649, 5642, 892])).
% 4.91/5.10 tff(5651,plain,
% 4.91/5.10 (~c3_1(a1645)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1060, 5650])).
% 4.91/5.10 tff(5652,plain,
% 4.91/5.10 (~c0_1(a1645)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1038, 5650])).
% 4.91/5.10 tff(5653,plain,
% 4.91/5.10 (~c1_1(a1645)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[1044, 5650])).
% 4.91/5.10 tff(5654,plain,
% 4.91/5.10 (((~![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(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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5655,plain,
% 4.91/5.10 (((~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)))),
% 4.91/5.10 inference(rewrite,[status(thm)],[])).
% 4.91/5.10 tff(5656,plain,
% 4.91/5.10 (((~![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(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))))),
% 4.91/5.10 inference(monotonicity,[status(thm)],[5655])).
% 4.91/5.10 tff(5657,plain,
% 4.91/5.10 (((~![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(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)))),
% 4.91/5.10 inference(transitivity,[status(thm)],[5656, 5654])).
% 4.91/5.10 tff(5658,plain,
% 4.91/5.10 ((~![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(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))),
% 4.91/5.10 inference(quant_inst,[status(thm)],[])).
% 4.91/5.10 tff(5659,plain,
% 4.91/5.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1695) | c1_1(a1645) | c0_1(a1645) | c3_1(a1645) | (~ndr1_0) | c2_1(a1645) | (~c2_1(a1695)) | (~c0_1(a1695))),
% 4.91/5.10 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 4.91/5.10 tff(5660,plain,
% 4.91/5.10 (c2_1(a1645)),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5659, 197, 5398, 5407, 5397, 5653, 5652, 5651, 30])).
% 4.91/5.10 tff(5661,plain,
% 4.91/5.10 ($false),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[4501, 197, 1505, 893, 895, 5653, 5651, 1504, 871, 5660])).
% 4.91/5.10 tff(5662,plain,(hskp57 | c3_1(a1691) | c2_1(a1691) | (~c0_1(a1691)) | c1_1(a1691)), inference(lemma,lemma(discharge,[]))).
% 4.91/5.10 tff(5663,plain,
% 4.91/5.10 (hskp57),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5662, 893, 895, 5550, 5639])).
% 4.91/5.10 tff(5664,plain,
% 4.91/5.10 ($false),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[3041, 197, 247, 248, 79, 68, 60, 10])).
% 4.91/5.10 tff(5665,plain,((~hskp57) | hskp17 | hskp16), inference(lemma,lemma(discharge,[]))).
% 4.91/5.10 tff(5666,plain,
% 4.91/5.10 (hskp16),
% 4.91/5.10 inference(unit_resolution,[status(thm)],[5665, 5663, 5640])).
% 4.91/5.12 tff(5667,plain,
% 4.91/5.12 (~c1_1(a1677)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[99, 5666])).
% 4.91/5.12 tff(5668,plain,
% 4.91/5.12 (~c2_1(a1677)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[105, 5666])).
% 4.91/5.12 tff(5669,plain,
% 4.91/5.12 (~c0_1(a1677)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[111, 5666])).
% 4.91/5.12 tff(5670,plain,
% 4.91/5.12 ($false),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[5544, 197, 5398, 5407, 5397, 893, 5639, 895, 5669, 5668, 5667, 30])).
% 4.91/5.12 tff(5671,plain,(c3_1(a1691) | c2_1(a1691) | hskp72), inference(lemma,lemma(discharge,[]))).
% 4.91/5.12 tff(5672,plain,
% 4.91/5.12 (hskp72),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[5671, 5527, 5529])).
% 4.91/5.12 tff(5673,plain,
% 4.91/5.12 (~c2_1(a1715)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[502, 5672])).
% 4.91/5.12 tff(5674,plain,
% 4.91/5.12 (c3_1(a1715)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[1211, 5672])).
% 4.91/5.12 tff(5675,plain,
% 4.91/5.12 (c1_1(a1715)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[2240, 5672])).
% 4.91/5.12 tff(5676,plain,
% 4.91/5.12 (hskp13 | (~c1_1(a1654))),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[5357, 197, 5675, 5674, 5508, 5506, 5673, 266])).
% 4.91/5.12 tff(5677,plain,
% 4.91/5.12 (hskp13),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[5676, 5548])).
% 4.91/5.12 tff(5678,plain,
% 4.91/5.12 (~c1_1(a1667)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[279, 5677])).
% 4.91/5.12 tff(5679,plain,
% 4.91/5.12 (c3_1(a1667)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[287, 5677])).
% 4.91/5.12 tff(5680,plain,
% 4.91/5.12 (c0_1(a1667)),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[295, 5677])).
% 4.91/5.12 tff(5681,plain,
% 4.91/5.12 ($false),
% 4.91/5.12 inference(unit_resolution,[status(thm)],[302, 197, 5538, 5546, 5680, 5679, 5678, 10])).
% 4.91/5.12 % SZS output end Proof
% 4.91/5.12 % E exiting
%------------------------------------------------------------------------------