%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN478-1 : 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 05:39:16 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.85s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN478-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % 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 12:35:40 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.62/0.85 % SZS status Unsatisfiable
% 0.62/0.85 % SZS output start Proof
% 0.62/0.85 tff(c3_1_type, type, (
% 0.62/0.85 c3_1: $i > $o)).
% 0.62/0.85 tff(a1307_type, type, (
% 0.62/0.85 a1307: $i)).
% 0.62/0.85 tff(c0_1_type, type, (
% 0.62/0.85 c0_1: $i > $o)).
% 0.62/0.85 tff(a1338_type, type, (
% 0.62/0.85 a1338: $i)).
% 0.62/0.85 tff(c2_1_type, type, (
% 0.62/0.85 c2_1: $i > $o)).
% 0.62/0.85 tff(hskp29_type, type, (
% 0.62/0.85 hskp29: $o)).
% 0.62/0.85 tff(a1315_type, type, (
% 0.62/0.85 a1315: $i)).
% 0.62/0.85 tff(c1_1_type, type, (
% 0.62/0.85 c1_1: $i > $o)).
% 0.62/0.85 tff(ndr1_0_type, type, (
% 0.62/0.85 ndr1_0: $o)).
% 0.62/0.85 tff(hskp6_type, type, (
% 0.62/0.85 hskp6: $o)).
% 0.62/0.85 tff(a1326_type, type, (
% 0.62/0.85 a1326: $i)).
% 0.62/0.85 tff(hskp18_type, type, (
% 0.62/0.85 hskp18: $o)).
% 0.62/0.85 tff(hskp13_type, type, (
% 0.62/0.85 hskp13: $o)).
% 0.62/0.85 tff(hskp27_type, type, (
% 0.62/0.85 hskp27: $o)).
% 0.62/0.85 tff(a1339_type, type, (
% 0.62/0.85 a1339: $i)).
% 0.62/0.85 tff(a1319_type, type, (
% 0.62/0.85 a1319: $i)).
% 0.62/0.85 tff(hskp8_type, type, (
% 0.62/0.85 hskp8: $o)).
% 0.62/0.85 tff(a1320_type, type, (
% 0.62/0.85 a1320: $i)).
% 0.62/0.85 tff(hskp9_type, type, (
% 0.62/0.85 hskp9: $o)).
% 0.62/0.85 tff(a1324_type, type, (
% 0.62/0.85 a1324: $i)).
% 0.62/0.85 tff(hskp11_type, type, (
% 0.62/0.85 hskp11: $o)).
% 0.62/0.85 tff(a1356_type, type, (
% 0.62/0.85 a1356: $i)).
% 0.62/0.85 tff(hskp22_type, type, (
% 0.62/0.85 hskp22: $o)).
% 0.62/0.85 tff(a1348_type, type, (
% 0.62/0.85 a1348: $i)).
% 0.62/0.85 tff(hskp28_type, type, (
% 0.62/0.85 hskp28: $o)).
% 0.62/0.85 tff(hskp20_type, type, (
% 0.62/0.85 hskp20: $o)).
% 0.62/0.85 tff(a1308_type, type, (
% 0.62/0.85 a1308: $i)).
% 0.62/0.85 tff(a1330_type, type, (
% 0.62/0.85 a1330: $i)).
% 0.62/0.85 tff(hskp14_type, type, (
% 0.62/0.85 hskp14: $o)).
% 0.62/0.85 tff(hskp1_type, type, (
% 0.62/0.85 hskp1: $o)).
% 0.62/0.85 tff(a1328_type, type, (
% 0.62/0.85 a1328: $i)).
% 0.62/0.85 tff(hskp7_type, type, (
% 0.62/0.85 hskp7: $o)).
% 0.62/0.85 tff(a1316_type, type, (
% 0.62/0.85 a1316: $i)).
% 0.62/0.85 tff(hskp3_type, type, (
% 0.62/0.85 hskp3: $o)).
% 0.62/0.85 tff(a1311_type, type, (
% 0.62/0.85 a1311: $i)).
% 0.62/0.85 tff(a1325_type, type, (
% 0.62/0.85 a1325: $i)).
% 0.62/0.85 tff(a1333_type, type, (
% 0.62/0.85 a1333: $i)).
% 0.62/0.85 tff(a1309_type, type, (
% 0.62/0.85 a1309: $i)).
% 0.62/0.85 tff(hskp2_type, type, (
% 0.62/0.85 hskp2: $o)).
% 0.62/0.85 tff(hskp16_type, type, (
% 0.62/0.85 hskp16: $o)).
% 0.62/0.85 tff(a1312_type, type, (
% 0.62/0.85 a1312: $i)).
% 0.62/0.85 tff(hskp4_type, type, (
% 0.62/0.85 hskp4: $o)).
% 0.62/0.85 tff(a1314_type, type, (
% 0.62/0.85 a1314: $i)).
% 0.62/0.85 tff(hskp5_type, type, (
% 0.62/0.85 hskp5: $o)).
% 0.62/0.85 tff(a1334_type, type, (
% 0.62/0.85 a1334: $i)).
% 0.62/0.85 tff(hskp17_type, type, (
% 0.62/0.85 hskp17: $o)).
% 0.62/0.85 tff(a1331_type, type, (
% 0.62/0.85 a1331: $i)).
% 0.62/0.85 tff(hskp15_type, type, (
% 0.62/0.85 hskp15: $o)).
% 0.62/0.85 tff(hskp12_type, type, (
% 0.62/0.85 hskp12: $o)).
% 0.62/0.85 tff(a1352_type, type, (
% 0.62/0.85 a1352: $i)).
% 0.62/0.85 tff(hskp21_type, type, (
% 0.62/0.85 hskp21: $o)).
% 0.62/0.85 tff(a1372_type, type, (
% 0.62/0.85 a1372: $i)).
% 0.62/0.85 tff(hskp30_type, type, (
% 0.62/0.85 hskp30: $o)).
% 0.62/0.85 tff(a1394_type, type, (
% 0.62/0.85 a1394: $i)).
% 0.62/0.85 tff(hskp25_type, type, (
% 0.62/0.85 hskp25: $o)).
% 0.62/0.85 tff(1,plain,
% 0.62/0.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(2,plain,
% 0.62/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.85 tff(3,plain,
% 0.62/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(4,plain,
% 0.62/0.85 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(5,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[4])).
% 0.69/0.85 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 0.69/0.85 tff(7,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.69/0.85 tff(8,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.69/0.85 tff(9,plain,(
% 0.69/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[8])).
% 0.69/0.85 tff(10,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.69/0.85 tff(11,assumption,(~hskp29), introduced(assumption)).
% 0.69/0.85 tff(12,plain,
% 0.69/0.85 (^[U: $i] : refl((hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(13,plain,
% 0.69/0.85 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[12])).
% 0.69/0.85 tff(14,plain,
% 0.69/0.85 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(15,plain,
% 0.69/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(16,plain,
% 0.69/0.85 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18) <=> ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[15])).
% 0.69/0.85 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.69/0.85 tff(18,plain,
% 0.69/0.85 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.69/0.85 tff(19,plain,
% 0.69/0.85 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.69/0.85 tff(20,plain,(
% 0.69/0.85 ![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[19])).
% 0.69/0.85 tff(21,plain,
% 0.69/0.85 (![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.69/0.85 tff(22,assumption,(~hskp27), introduced(assumption)).
% 0.69/0.85 tff(23,assumption,(~c2_1(a1339)), introduced(assumption)).
% 0.69/0.85 tff(24,assumption,(~c0_1(a1339)), introduced(assumption)).
% 0.69/0.85 tff(25,assumption,(c3_1(a1339)), introduced(assumption)).
% 0.69/0.85 tff(26,plain,
% 0.69/0.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(27,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[26])).
% 0.69/0.85 tff(28,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(29,plain,
% 0.69/0.85 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(30,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[29])).
% 0.69/0.85 tff(31,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 0.69/0.85 tff(32,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.69/0.85 tff(33,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.69/0.85 tff(34,plain,(
% 0.69/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[33])).
% 0.69/0.85 tff(35,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.69/0.85 tff(36,plain,
% 0.69/0.85 (^[U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(37,plain,
% 0.69/0.85 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[36])).
% 0.69/0.85 tff(38,plain,
% 0.69/0.85 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(39,plain,
% 0.69/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(40,plain,
% 0.69/0.86 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[39])).
% 0.69/0.86 tff(41,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.69/0.86 tff(42,plain,
% 0.69/0.86 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.69/0.86 tff(43,plain,
% 0.69/0.86 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.69/0.86 tff(44,plain,(
% 0.69/0.86 ![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[43])).
% 0.69/0.86 tff(45,plain,
% 0.69/0.86 (![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.69/0.86 tff(46,assumption,(~hskp11), introduced(assumption)).
% 0.69/0.86 tff(47,assumption,(~hskp20), introduced(assumption)).
% 0.69/0.86 tff(48,plain,
% 0.69/0.86 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(49,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[48])).
% 0.69/0.86 tff(50,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(51,plain,
% 0.69/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(52,plain,
% 0.69/0.86 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[51])).
% 0.69/0.86 tff(53,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.69/0.86 tff(54,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.69/0.86 tff(55,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.69/0.86 tff(56,plain,(
% 0.69/0.86 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(skolemize,[status(sab)],[55])).
% 0.69/0.86 tff(57,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.69/0.86 tff(58,plain,
% 0.69/0.86 ((hskp20 | hskp18) <=> (hskp20 | hskp18)),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(59,axiom,(hskp20 | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.69/0.86 tff(60,plain,
% 0.69/0.86 (hskp20 | hskp18),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.69/0.86 tff(61,plain,
% 0.69/0.86 (hskp20 | hskp18),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.69/0.86 tff(62,plain,
% 0.69/0.86 (hskp20 | hskp18),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.69/0.86 tff(63,plain,
% 0.69/0.86 (hskp20 | hskp18),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.69/0.86 tff(64,plain,
% 0.69/0.86 (hskp20 | hskp18),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.69/0.86 tff(65,plain,
% 0.69/0.86 (hskp18),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[64, 47])).
% 0.69/0.86 tff(66,plain,
% 0.69/0.86 (((~hskp18) | (~c2_1(a1339))) <=> ((~hskp18) | (~c2_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(67,plain,
% 0.69/0.86 (((~c2_1(a1339)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(68,axiom,((~c2_1(a1339)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.69/0.86 tff(69,plain,
% 0.69/0.86 ((~hskp18) | (~c2_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.69/0.86 tff(70,plain,
% 0.69/0.86 ((~hskp18) | (~c2_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.69/0.86 tff(71,plain,
% 0.69/0.86 (~c2_1(a1339)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.69/0.86 tff(72,plain,
% 0.69/0.86 (((~hskp18) | (~c0_1(a1339))) <=> ((~hskp18) | (~c0_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(73,plain,
% 0.69/0.86 (((~c0_1(a1339)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(74,axiom,((~c0_1(a1339)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.69/0.86 tff(75,plain,
% 0.69/0.86 ((~hskp18) | (~c0_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.69/0.86 tff(76,plain,
% 0.69/0.86 ((~hskp18) | (~c0_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.69/0.86 tff(77,plain,
% 0.69/0.86 (~c0_1(a1339)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[76, 65])).
% 0.69/0.86 tff(78,plain,
% 0.69/0.86 (((~hskp18) | c1_1(a1339)) <=> ((~hskp18) | c1_1(a1339))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(79,axiom,((~hskp18) | c1_1(a1339)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.69/0.86 tff(80,plain,
% 0.69/0.86 ((~hskp18) | c1_1(a1339)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.69/0.86 tff(81,plain,
% 0.69/0.86 ((~hskp18) | c1_1(a1339)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.69/0.86 tff(82,plain,
% 0.69/0.86 ((~hskp18) | c1_1(a1339)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.69/0.86 tff(83,plain,
% 0.69/0.86 ((~hskp18) | c1_1(a1339)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.69/0.86 tff(84,plain,
% 0.69/0.86 ((~hskp18) | c1_1(a1339)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.69/0.86 tff(85,plain,
% 0.69/0.86 (c1_1(a1339)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[84, 65])).
% 0.69/0.86 tff(86,assumption,(hskp11), introduced(assumption)).
% 0.69/0.86 tff(87,plain,
% 0.69/0.86 (((~hskp11) | (~c1_1(a1324))) <=> ((~hskp11) | (~c1_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(88,plain,
% 0.69/0.86 (((~c1_1(a1324)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(89,axiom,((~c1_1(a1324)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.69/0.86 tff(90,plain,
% 0.69/0.86 ((~hskp11) | (~c1_1(a1324))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.69/0.86 tff(91,plain,
% 0.69/0.86 ((~hskp11) | (~c1_1(a1324))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.69/0.86 tff(92,plain,
% 0.69/0.86 (~c1_1(a1324)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[91, 86])).
% 0.69/0.86 tff(93,plain,
% 0.69/0.86 (((~hskp11) | c0_1(a1324)) <=> ((~hskp11) | c0_1(a1324))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(94,axiom,((~hskp11) | c0_1(a1324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.69/0.86 tff(95,plain,
% 0.69/0.86 ((~hskp11) | c0_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.69/0.86 tff(96,plain,
% 0.69/0.86 ((~hskp11) | c0_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[95, 93])).
% 0.69/0.86 tff(97,plain,
% 0.69/0.86 ((~hskp11) | c0_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.69/0.86 tff(98,plain,
% 0.69/0.86 ((~hskp11) | c0_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.69/0.86 tff(99,plain,
% 0.69/0.86 ((~hskp11) | c0_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.69/0.86 tff(100,plain,
% 0.69/0.86 (c0_1(a1324)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[99, 86])).
% 0.69/0.86 tff(101,plain,
% 0.69/0.86 (((~hskp11) | c3_1(a1324)) <=> ((~hskp11) | c3_1(a1324))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(102,axiom,((~hskp11) | c3_1(a1324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.69/0.86 tff(103,plain,
% 0.69/0.86 ((~hskp11) | c3_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.69/0.86 tff(104,plain,
% 0.69/0.86 ((~hskp11) | c3_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[103, 101])).
% 0.69/0.86 tff(105,plain,
% 0.69/0.86 ((~hskp11) | c3_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.69/0.86 tff(106,plain,
% 0.69/0.86 ((~hskp11) | c3_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.69/0.86 tff(107,plain,
% 0.69/0.86 ((~hskp11) | c3_1(a1324)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[106, 101])).
% 0.69/0.86 tff(108,plain,
% 0.69/0.86 (c3_1(a1324)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[107, 86])).
% 0.69/0.86 tff(109,assumption,(~c1_1(a1324)), introduced(assumption)).
% 0.69/0.86 tff(110,plain,
% 0.69/0.86 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(111,plain,
% 0.69/0.86 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(112,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause15')).
% 0.69/0.86 tff(113,plain,
% 0.69/0.86 (ndr1_0 | (~hskp18)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.69/0.86 tff(114,plain,
% 0.69/0.86 (ndr1_0 | (~hskp18)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.69/0.86 tff(115,plain,
% 0.69/0.86 (ndr1_0),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[114, 65])).
% 0.69/0.86 tff(116,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(117,plain,
% 0.69/0.86 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(118,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.69/0.86 tff(119,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[118, 116])).
% 0.69/0.86 tff(120,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(121,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.69/0.86 tff(122,plain,
% 0.69/0.86 ((~c3_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[121, 115, 85, 77, 71, 109, 35])).
% 0.69/0.86 tff(123,plain,
% 0.69/0.86 (~c3_1(a1339)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[122, 108, 100])).
% 0.69/0.86 tff(124,plain,
% 0.69/0.86 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(125,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[124])).
% 0.69/0.86 tff(126,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(127,plain,
% 0.69/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(128,plain,
% 0.69/0.86 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[127])).
% 0.69/0.86 tff(129,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.69/0.86 tff(130,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.69/0.86 tff(131,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.69/0.86 tff(132,plain,(
% 0.69/0.86 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[131])).
% 0.69/0.86 tff(133,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.69/0.86 tff(134,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(135,plain,
% 0.69/0.86 ((hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324))) <=> (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(136,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[135])).
% 0.69/0.86 tff(137,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[136, 134])).
% 0.69/0.86 tff(138,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c0_1(a1324)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(139,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.69/0.86 tff(140,plain,
% 0.69/0.86 (c3_1(a1339) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[139, 47, 115, 85, 71, 109, 133])).
% 0.69/0.86 tff(141,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[140, 123, 108, 100])).
% 0.69/0.86 tff(142,plain,((~hskp11) | hskp20 | c1_1(a1324)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(143,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[142, 92, 86, 47])).
% 0.69/0.86 tff(144,plain,((~hskp11) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(145,plain,
% 0.69/0.86 (~hskp11),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[144, 47])).
% 0.69/0.86 tff(146,assumption,(hskp13), introduced(assumption)).
% 0.69/0.86 tff(147,plain,
% 0.69/0.86 (((~hskp13) | (~c3_1(a1326))) <=> ((~hskp13) | (~c3_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(148,plain,
% 0.69/0.86 (((~c3_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(149,axiom,((~c3_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.69/0.86 tff(150,plain,
% 0.69/0.86 ((~hskp13) | (~c3_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.69/0.86 tff(151,plain,
% 0.69/0.86 ((~hskp13) | (~c3_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.69/0.86 tff(152,plain,
% 0.69/0.86 (~c3_1(a1326)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[151, 146])).
% 0.69/0.86 tff(153,plain,
% 0.69/0.86 (((~hskp13) | (~c2_1(a1326))) <=> ((~hskp13) | (~c2_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(154,plain,
% 0.69/0.86 (((~c2_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(155,axiom,((~c2_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.69/0.86 tff(156,plain,
% 0.69/0.86 ((~hskp13) | (~c2_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.69/0.86 tff(157,plain,
% 0.69/0.86 ((~hskp13) | (~c2_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.69/0.86 tff(158,plain,
% 0.69/0.86 (~c2_1(a1326)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[157, 146])).
% 0.69/0.86 tff(159,plain,
% 0.69/0.86 (((~hskp13) | (~c1_1(a1326))) <=> ((~hskp13) | (~c1_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(160,plain,
% 0.69/0.86 (((~c1_1(a1326)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1326)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(161,axiom,((~c1_1(a1326)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.69/0.86 tff(162,plain,
% 0.69/0.86 ((~hskp13) | (~c1_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.69/0.86 tff(163,plain,
% 0.69/0.86 ((~hskp13) | (~c1_1(a1326))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.69/0.86 tff(164,plain,
% 0.69/0.86 (~c1_1(a1326)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[163, 146])).
% 0.69/0.86 tff(165,assumption,(c1_1(a1339)), introduced(assumption)).
% 0.69/0.86 tff(166,assumption,(ndr1_0), introduced(assumption)).
% 0.69/0.86 tff(167,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(168,plain,
% 0.69/0.86 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(169,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[168])).
% 0.69/0.86 tff(170,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[169, 167])).
% 0.69/0.86 tff(171,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(172,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.69/0.86 tff(173,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[172, 166, 46, 165, 24, 23, 164, 158, 152, 57])).
% 0.69/0.86 tff(174,plain,((~hskp13) | (~ndr1_0) | hskp11 | (~c1_1(a1339)) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(175,plain,
% 0.69/0.86 (~hskp13),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[174, 115, 145, 85, 77, 71])).
% 0.69/0.86 tff(176,assumption,(~c3_1(a1339)), introduced(assumption)).
% 0.69/0.86 tff(177,plain,
% 0.69/0.86 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(178,plain,
% 0.69/0.86 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[177])).
% 0.69/0.86 tff(179,plain,
% 0.69/0.86 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(180,plain,
% 0.69/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(181,plain,
% 0.69/0.86 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[180])).
% 0.69/0.86 tff(182,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.69/0.86 tff(183,plain,
% 0.69/0.86 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.69/0.86 tff(184,plain,
% 0.69/0.86 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.69/0.86 tff(185,plain,(
% 0.69/0.86 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[184])).
% 0.69/0.86 tff(186,plain,
% 0.69/0.86 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.69/0.86 tff(187,plain,
% 0.69/0.86 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(188,plain,
% 0.69/0.86 ((hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339))) <=> (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(189,plain,
% 0.69/0.86 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[188])).
% 0.69/0.86 tff(190,plain,
% 0.69/0.86 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[189, 187])).
% 0.69/0.86 tff(191,plain,
% 0.69/0.86 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(192,plain,
% 0.69/0.86 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.69/0.86 tff(193,plain,
% 0.69/0.86 (hskp14 | hskp13 | c3_1(a1339)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[192, 115, 85, 71, 186])).
% 0.69/0.86 tff(194,plain,
% 0.69/0.86 (hskp14),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[193, 176, 175])).
% 0.69/0.86 tff(195,plain,
% 0.69/0.86 (((~hskp14) | (~c2_1(a1330))) <=> ((~hskp14) | (~c2_1(a1330)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(196,plain,
% 0.69/0.86 (((~c2_1(a1330)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1330)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(197,axiom,((~c2_1(a1330)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.69/0.86 tff(198,plain,
% 0.69/0.86 ((~hskp14) | (~c2_1(a1330))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.69/0.86 tff(199,plain,
% 0.69/0.86 ((~hskp14) | (~c2_1(a1330))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[198, 195])).
% 0.69/0.86 tff(200,plain,
% 0.69/0.86 (~c2_1(a1330)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[199, 194])).
% 0.69/0.86 tff(201,plain,
% 0.69/0.86 (((~hskp14) | (~c1_1(a1330))) <=> ((~hskp14) | (~c1_1(a1330)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(202,plain,
% 0.69/0.86 (((~c1_1(a1330)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1330)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(203,axiom,((~c1_1(a1330)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.69/0.86 tff(204,plain,
% 0.69/0.86 ((~hskp14) | (~c1_1(a1330))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.69/0.86 tff(205,plain,
% 0.69/0.86 ((~hskp14) | (~c1_1(a1330))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.69/0.86 tff(206,plain,
% 0.69/0.86 (~c1_1(a1330)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[205, 194])).
% 0.69/0.86 tff(207,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(208,plain,
% 0.69/0.87 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(209,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[208])).
% 0.69/0.87 tff(210,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330))),
% 0.69/0.87 inference(transitivity,[status(thm)],[209, 207])).
% 0.69/0.87 tff(211,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1330) | c1_1(a1330) | c3_1(a1330))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(212,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | c3_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.69/0.87 tff(213,plain,
% 0.69/0.87 (c3_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[212, 115, 145, 85, 77, 71, 206, 200, 57])).
% 0.69/0.87 tff(214,plain,
% 0.69/0.87 (((~hskp14) | c0_1(a1330)) <=> ((~hskp14) | c0_1(a1330))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(215,axiom,((~hskp14) | c0_1(a1330)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.69/0.87 tff(216,plain,
% 0.69/0.87 ((~hskp14) | c0_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.69/0.87 tff(217,plain,
% 0.69/0.87 ((~hskp14) | c0_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[216, 214])).
% 0.69/0.87 tff(218,plain,
% 0.69/0.87 ((~hskp14) | c0_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.69/0.87 tff(219,plain,
% 0.69/0.87 ((~hskp14) | c0_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.69/0.87 tff(220,plain,
% 0.69/0.87 ((~hskp14) | c0_1(a1330)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[219, 214])).
% 0.69/0.87 tff(221,plain,
% 0.69/0.87 (c0_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[220, 194])).
% 0.69/0.87 tff(222,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(223,plain,
% 0.69/0.87 ((hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330))) <=> (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(224,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[223])).
% 0.69/0.87 tff(225,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[224, 222])).
% 0.69/0.87 tff(226,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c1_1(a1330) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(227,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.69/0.87 tff(228,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[227, 47, 115, 85, 221, 71, 206, 133, 176, 213])).
% 0.69/0.87 tff(229,plain,(c3_1(a1339) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(230,plain,
% 0.69/0.87 (c3_1(a1339)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[229, 47])).
% 0.69/0.87 tff(231,assumption,(hskp28), introduced(assumption)).
% 0.69/0.87 tff(232,plain,
% 0.69/0.87 (((~hskp28) | c2_1(a1328)) <=> ((~hskp28) | c2_1(a1328))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(233,axiom,((~hskp28) | c2_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.69/0.87 tff(234,plain,
% 0.69/0.87 ((~hskp28) | c2_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.69/0.87 tff(235,plain,
% 0.69/0.87 ((~hskp28) | c2_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[234, 232])).
% 0.69/0.87 tff(236,plain,
% 0.69/0.87 ((~hskp28) | c2_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.69/0.87 tff(237,plain,
% 0.69/0.87 ((~hskp28) | c2_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.69/0.87 tff(238,plain,
% 0.69/0.87 ((~hskp28) | c2_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[237, 232])).
% 0.69/0.87 tff(239,plain,
% 0.69/0.87 (c2_1(a1328)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[238, 231])).
% 0.69/0.87 tff(240,plain,
% 0.69/0.87 (((~hskp28) | c0_1(a1328)) <=> ((~hskp28) | c0_1(a1328))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(241,axiom,((~hskp28) | c0_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.69/0.87 tff(242,plain,
% 0.69/0.87 ((~hskp28) | c0_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.69/0.87 tff(243,plain,
% 0.69/0.87 ((~hskp28) | c0_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[242, 240])).
% 0.69/0.87 tff(244,plain,
% 0.69/0.87 ((~hskp28) | c0_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.69/0.87 tff(245,plain,
% 0.69/0.87 ((~hskp28) | c0_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.69/0.87 tff(246,plain,
% 0.69/0.87 ((~hskp28) | c0_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[245, 240])).
% 0.69/0.87 tff(247,plain,
% 0.69/0.87 (c0_1(a1328)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[246, 231])).
% 0.69/0.87 tff(248,assumption,(~hskp13), introduced(assumption)).
% 0.69/0.87 tff(249,plain,
% 0.69/0.87 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(250,plain,
% 0.69/0.87 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(251,plain,
% 0.69/0.87 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1328)) | (~c2_1(a1328)) | (~c0_1(a1328))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.69/0.87 tff(252,plain,
% 0.69/0.87 (~c1_1(a1328)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[251, 166, 248, 247, 239, 45])).
% 0.69/0.87 tff(253,plain,
% 0.69/0.87 (((~hskp28) | c3_1(a1328)) <=> ((~hskp28) | c3_1(a1328))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(254,axiom,((~hskp28) | c3_1(a1328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.69/0.87 tff(255,plain,
% 0.69/0.87 ((~hskp28) | c3_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.69/0.87 tff(256,plain,
% 0.69/0.87 ((~hskp28) | c3_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[255, 253])).
% 0.69/0.87 tff(257,plain,
% 0.69/0.87 ((~hskp28) | c3_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[256, 253])).
% 0.69/0.87 tff(258,plain,
% 0.69/0.87 ((~hskp28) | c3_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.69/0.87 tff(259,plain,
% 0.69/0.87 ((~hskp28) | c3_1(a1328)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[258, 253])).
% 0.69/0.87 tff(260,plain,
% 0.69/0.87 (c3_1(a1328)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[259, 231])).
% 0.69/0.87 tff(261,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(262,plain,
% 0.69/0.87 (((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(263,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[262])).
% 0.69/0.87 tff(264,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[263, 261])).
% 0.69/0.87 tff(265,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1328) | (~c0_1(a1328)) | (~c3_1(a1328)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(266,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c0_1(a1328)) | c1_1(a1328) | (~c3_1(a1328))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.69/0.87 tff(267,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[266, 166, 247, 260, 165, 24, 23, 35, 25, 252])).
% 0.69/0.87 tff(268,plain,((~hskp28) | (~ndr1_0) | (~c1_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(269,plain,
% 0.69/0.87 (~hskp28),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[268, 115, 85, 77, 71, 230, 175])).
% 0.69/0.87 tff(270,assumption,(hskp7), introduced(assumption)).
% 0.69/0.87 tff(271,plain,
% 0.69/0.87 (((~hskp7) | (~c2_1(a1316))) <=> ((~hskp7) | (~c2_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(272,plain,
% 0.69/0.87 (((~c2_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(273,axiom,((~c2_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.69/0.87 tff(274,plain,
% 0.69/0.87 ((~hskp7) | (~c2_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.69/0.87 tff(275,plain,
% 0.69/0.87 ((~hskp7) | (~c2_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[274, 271])).
% 0.69/0.87 tff(276,plain,
% 0.69/0.87 (~c2_1(a1316)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[275, 270])).
% 0.69/0.87 tff(277,plain,
% 0.69/0.87 (((~hskp7) | (~c3_1(a1316))) <=> ((~hskp7) | (~c3_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(278,plain,
% 0.69/0.87 (((~c3_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(279,axiom,((~c3_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.69/0.87 tff(280,plain,
% 0.69/0.87 ((~hskp7) | (~c3_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.69/0.87 tff(281,plain,
% 0.69/0.87 ((~hskp7) | (~c3_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[280, 277])).
% 0.69/0.87 tff(282,plain,
% 0.69/0.87 (~c3_1(a1316)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[281, 270])).
% 0.69/0.87 tff(283,assumption,(~c3_1(a1316)), introduced(assumption)).
% 0.69/0.87 tff(284,assumption,(~c2_1(a1316)), introduced(assumption)).
% 0.69/0.87 tff(285,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(286,plain,
% 0.69/0.87 ((hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316)) <=> (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(287,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[286])).
% 0.69/0.87 tff(288,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316))),
% 0.69/0.87 inference(transitivity,[status(thm)],[287, 285])).
% 0.69/0.87 tff(289,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)) | c2_1(a1316) | c1_1(a1316) | c3_1(a1316))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(290,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | c1_1(a1316)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.69/0.87 tff(291,plain,
% 0.69/0.87 (c3_1(a1316) | c1_1(a1316)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[290, 115, 145, 85, 77, 71, 284, 57])).
% 0.69/0.87 tff(292,plain,
% 0.69/0.87 (c1_1(a1316)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[291, 283])).
% 0.69/0.87 tff(293,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(294,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[293])).
% 0.69/0.87 tff(295,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(296,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(297,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[296])).
% 0.69/0.87 tff(298,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.69/0.87 tff(299,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.69/0.87 tff(300,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.69/0.87 tff(301,plain,(
% 0.69/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[300])).
% 0.69/0.87 tff(302,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[301, 294])).
% 0.69/0.87 tff(303,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(304,plain,
% 0.69/0.87 (((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(305,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[304])).
% 0.69/0.87 tff(306,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[305, 303])).
% 0.69/0.87 tff(307,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(308,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.69/0.87 tff(309,plain,
% 0.69/0.87 (c3_1(a1316) | (~c3_1(a1339)) | (~c1_1(a1316))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[308, 115, 85, 77, 71, 284, 302])).
% 0.69/0.87 tff(310,plain,
% 0.69/0.87 (~c3_1(a1339)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[309, 292, 283])).
% 0.69/0.87 tff(311,plain,
% 0.69/0.87 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(312,plain,
% 0.69/0.87 ((hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316))) <=> (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(313,plain,
% 0.69/0.87 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[312])).
% 0.69/0.87 tff(314,plain,
% 0.69/0.87 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[313, 311])).
% 0.69/0.87 tff(315,plain,
% 0.69/0.87 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(316,plain,
% 0.69/0.87 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp13 | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.69/0.87 tff(317,plain,
% 0.69/0.87 (hskp14 | c3_1(a1316) | (~c1_1(a1316))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[316, 115, 175, 284, 186])).
% 0.69/0.87 tff(318,plain,
% 0.69/0.87 (hskp14),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[317, 283, 292])).
% 0.69/0.87 tff(319,plain,
% 0.69/0.87 (~c1_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[205, 318])).
% 0.69/0.87 tff(320,plain,
% 0.69/0.87 (c0_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[220, 318])).
% 0.69/0.87 tff(321,plain,
% 0.69/0.87 (~c3_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[227, 47, 115, 85, 320, 71, 319, 133, 310])).
% 0.69/0.87 tff(322,plain,
% 0.69/0.87 (~c2_1(a1330)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[199, 318])).
% 0.69/0.87 tff(323,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[212, 115, 145, 85, 77, 71, 319, 322, 57, 321])).
% 0.69/0.87 tff(324,plain,(c3_1(a1316) | hskp20 | c2_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(325,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[324, 282, 276, 47])).
% 0.69/0.87 tff(326,plain,((~hskp7) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(327,plain,
% 0.69/0.87 (~hskp7),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[326, 47])).
% 0.69/0.87 tff(328,plain,
% 0.69/0.87 ((hskp28 | hskp7 | hskp1) <=> (hskp28 | hskp7 | hskp1)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(329,plain,
% 0.69/0.87 (((hskp28 | hskp1) | hskp7) <=> (hskp28 | hskp7 | hskp1)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(330,plain,
% 0.69/0.87 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(331,plain,
% 0.69/0.87 (((hskp28 | hskp1) | hskp7) <=> ((hskp28 | hskp1) | hskp7)),
% 0.69/0.87 inference(monotonicity,[status(thm)],[330])).
% 0.69/0.87 tff(332,plain,
% 0.69/0.87 (((hskp28 | hskp1) | hskp7) <=> (hskp28 | hskp7 | hskp1)),
% 0.69/0.87 inference(transitivity,[status(thm)],[331, 329])).
% 0.69/0.87 tff(333,axiom,((hskp28 | hskp1) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.69/0.87 tff(334,plain,
% 0.69/0.87 (hskp28 | hskp7 | hskp1),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.69/0.87 tff(335,plain,
% 0.69/0.87 (hskp28 | hskp7 | hskp1),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[334, 328])).
% 0.69/0.87 tff(336,plain,
% 0.69/0.87 (hskp28 | hskp7 | hskp1),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[335, 328])).
% 0.69/0.87 tff(337,plain,
% 0.69/0.87 (hskp28 | hskp7 | hskp1),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[336, 328])).
% 0.69/0.87 tff(338,plain,
% 0.69/0.87 (hskp28 | hskp7 | hskp1),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[337, 328])).
% 0.69/0.87 tff(339,plain,
% 0.69/0.87 (hskp1),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[338, 327, 269])).
% 0.69/0.87 tff(340,plain,
% 0.69/0.87 (((~hskp1) | (~c1_1(a1308))) <=> ((~hskp1) | (~c1_1(a1308)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(341,plain,
% 0.69/0.87 (((~c1_1(a1308)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1308)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(342,axiom,((~c1_1(a1308)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.69/0.87 tff(343,plain,
% 0.69/0.87 ((~hskp1) | (~c1_1(a1308))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.69/0.87 tff(344,plain,
% 0.69/0.87 ((~hskp1) | (~c1_1(a1308))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[343, 340])).
% 0.69/0.87 tff(345,plain,
% 0.69/0.87 (~c1_1(a1308)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[344, 339])).
% 0.69/0.87 tff(346,plain,
% 0.69/0.87 (((~hskp1) | c3_1(a1308)) <=> ((~hskp1) | c3_1(a1308))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(347,axiom,((~hskp1) | c3_1(a1308)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.69/0.87 tff(348,plain,
% 0.69/0.87 ((~hskp1) | c3_1(a1308)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.69/0.87 tff(349,plain,
% 0.69/0.87 ((~hskp1) | c3_1(a1308)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[348, 346])).
% 0.69/0.87 tff(350,plain,
% 0.69/0.87 ((~hskp1) | c3_1(a1308)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[349, 346])).
% 0.69/0.87 tff(351,plain,
% 0.69/0.87 ((~hskp1) | c3_1(a1308)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.69/0.87 tff(352,plain,
% 0.69/0.87 ((~hskp1) | c3_1(a1308)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[351, 346])).
% 0.69/0.87 tff(353,plain,
% 0.69/0.87 (c3_1(a1308)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[352, 339])).
% 0.69/0.87 tff(354,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(355,plain,
% 0.69/0.87 (((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(356,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[355])).
% 0.69/0.87 tff(357,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[356, 354])).
% 0.69/0.88 tff(358,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(359,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1308)) | (~c0_1(a1308))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.69/0.88 tff(360,plain,
% 0.69/0.88 (~c0_1(a1308)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[359, 115, 85, 353, 77, 71, 345, 35, 230])).
% 0.69/0.88 tff(361,plain,
% 0.69/0.88 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(362,plain,
% 0.69/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[361])).
% 0.69/0.88 tff(363,plain,
% 0.69/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(364,plain,
% 0.69/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(365,plain,
% 0.69/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[364])).
% 0.69/0.88 tff(366,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.69/0.88 tff(367,plain,
% 0.69/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.69/0.88 tff(368,plain,
% 0.69/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[367, 363])).
% 0.69/0.88 tff(369,plain,(
% 0.69/0.88 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(skolemize,[status(sab)],[368])).
% 0.69/0.88 tff(370,plain,
% 0.69/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[369, 362])).
% 0.69/0.88 tff(371,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(372,plain,
% 0.69/0.88 ((hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308))) <=> (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(373,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[372])).
% 0.69/0.88 tff(374,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[373, 371])).
% 0.69/0.88 tff(375,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1308) | c0_1(a1308) | (~c3_1(a1308)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(376,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c1_1(a1308) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1308) | (~c3_1(a1308))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.69/0.88 tff(377,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[376, 115, 327, 85, 353, 71, 345, 370, 230, 360])).
% 0.69/0.88 tff(378,plain,(hskp20), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(379,plain,
% 0.69/0.88 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(380,plain,
% 0.69/0.88 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(381,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause13')).
% 0.69/0.88 tff(382,plain,
% 0.69/0.88 (ndr1_0 | (~hskp20)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.69/0.88 tff(383,plain,
% 0.69/0.88 (ndr1_0 | (~hskp20)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[382, 379])).
% 0.69/0.88 tff(384,plain,
% 0.69/0.88 (ndr1_0),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[383, 378])).
% 0.69/0.88 tff(385,assumption,(~c1_1(a1339)), introduced(assumption)).
% 0.69/0.88 tff(386,plain,
% 0.69/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(387,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[386])).
% 0.69/0.88 tff(388,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(389,plain,
% 0.69/0.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(390,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[389])).
% 0.69/0.88 tff(391,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 0.69/0.88 tff(392,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.69/0.88 tff(393,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.69/0.88 tff(394,plain,(
% 0.69/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(skolemize,[status(sab)],[393])).
% 0.69/0.88 tff(395,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[394, 387])).
% 0.69/0.88 tff(396,plain,
% 0.69/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(397,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[396])).
% 0.69/0.88 tff(398,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(399,plain,
% 0.69/0.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(400,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[399])).
% 0.69/0.88 tff(401,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 0.69/0.88 tff(402,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.69/0.88 tff(403,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.69/0.88 tff(404,plain,(
% 0.69/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(skolemize,[status(sab)],[403])).
% 0.69/0.88 tff(405,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.69/0.88 tff(406,plain,
% 0.69/0.88 (^[U: $i] : refl((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(407,plain,
% 0.69/0.88 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[406])).
% 0.69/0.88 tff(408,plain,
% 0.69/0.88 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(409,plain,
% 0.69/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite(((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(410,plain,
% 0.69/0.88 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[409])).
% 0.69/0.88 tff(411,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.69/0.88 tff(412,plain,
% 0.69/0.88 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.69/0.88 tff(413,plain,
% 0.69/0.88 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.69/0.88 tff(414,plain,(
% 0.69/0.88 ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(skolemize,[status(sab)],[413])).
% 0.69/0.88 tff(415,plain,
% 0.69/0.88 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[414, 407])).
% 0.69/0.88 tff(416,plain,
% 0.69/0.88 (~hskp18),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[84, 385])).
% 0.69/0.88 tff(417,assumption,(hskp27), introduced(assumption)).
% 0.69/0.88 tff(418,plain,
% 0.69/0.88 (((~hskp27) | c2_1(a1307)) <=> ((~hskp27) | c2_1(a1307))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(419,axiom,((~hskp27) | c2_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.69/0.88 tff(420,plain,
% 0.69/0.88 ((~hskp27) | c2_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.69/0.88 tff(421,plain,
% 0.69/0.88 ((~hskp27) | c2_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[420, 418])).
% 0.69/0.88 tff(422,plain,
% 0.69/0.88 ((~hskp27) | c2_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[421, 418])).
% 0.69/0.88 tff(423,plain,
% 0.69/0.88 ((~hskp27) | c2_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.69/0.88 tff(424,plain,
% 0.69/0.88 ((~hskp27) | c2_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[423, 418])).
% 0.69/0.88 tff(425,plain,
% 0.69/0.88 (c2_1(a1307)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[424, 417])).
% 0.69/0.88 tff(426,plain,
% 0.69/0.88 (((~hskp27) | c1_1(a1307)) <=> ((~hskp27) | c1_1(a1307))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(427,axiom,((~hskp27) | c1_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.69/0.88 tff(428,plain,
% 0.69/0.88 ((~hskp27) | c1_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.69/0.88 tff(429,plain,
% 0.69/0.88 ((~hskp27) | c1_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[428, 426])).
% 0.69/0.88 tff(430,plain,
% 0.69/0.88 ((~hskp27) | c1_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[429, 426])).
% 0.69/0.88 tff(431,plain,
% 0.69/0.88 ((~hskp27) | c1_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[430, 426])).
% 0.69/0.88 tff(432,plain,
% 0.69/0.88 ((~hskp27) | c1_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[431, 426])).
% 0.69/0.88 tff(433,plain,
% 0.69/0.88 (c1_1(a1307)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[432, 417])).
% 0.69/0.88 tff(434,plain,
% 0.69/0.88 (((~hskp27) | c0_1(a1307)) <=> ((~hskp27) | c0_1(a1307))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(435,axiom,((~hskp27) | c0_1(a1307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.69/0.88 tff(436,plain,
% 0.69/0.88 ((~hskp27) | c0_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.69/0.88 tff(437,plain,
% 0.69/0.88 ((~hskp27) | c0_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[436, 434])).
% 0.69/0.88 tff(438,plain,
% 0.69/0.88 ((~hskp27) | c0_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.69/0.88 tff(439,plain,
% 0.69/0.88 ((~hskp27) | c0_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.69/0.88 tff(440,plain,
% 0.69/0.88 ((~hskp27) | c0_1(a1307)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[439, 434])).
% 0.69/0.88 tff(441,plain,
% 0.69/0.88 (c0_1(a1307)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[440, 417])).
% 0.69/0.88 tff(442,plain,
% 0.69/0.88 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(443,plain,
% 0.69/0.88 ((hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307))) <=> (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(444,plain,
% 0.69/0.88 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[443])).
% 0.69/0.88 tff(445,plain,
% 0.69/0.88 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[444, 442])).
% 0.69/0.88 tff(446,plain,
% 0.69/0.88 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(447,plain,
% 0.69/0.88 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.69/0.88 tff(448,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[447, 384, 248, 441, 433, 425, 45])).
% 0.69/0.88 tff(449,plain,((~hskp27) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(450,plain,
% 0.69/0.88 (~hskp27),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[449, 248])).
% 0.69/0.88 tff(451,plain,
% 0.69/0.88 ((hskp18 | hskp27 | hskp14) <=> (hskp18 | hskp27 | hskp14)),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(452,plain,
% 0.69/0.88 (((hskp27 | hskp14) | hskp18) <=> (hskp18 | hskp27 | hskp14)),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(453,plain,
% 0.69/0.88 ((hskp27 | hskp14) <=> (hskp27 | hskp14)),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(454,plain,
% 0.69/0.88 (((hskp27 | hskp14) | hskp18) <=> ((hskp27 | hskp14) | hskp18)),
% 0.69/0.88 inference(monotonicity,[status(thm)],[453])).
% 0.69/0.88 tff(455,plain,
% 0.69/0.88 (((hskp27 | hskp14) | hskp18) <=> (hskp18 | hskp27 | hskp14)),
% 0.69/0.88 inference(transitivity,[status(thm)],[454, 452])).
% 0.69/0.88 tff(456,axiom,((hskp27 | hskp14) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.69/0.88 tff(457,plain,
% 0.69/0.88 (hskp18 | hskp27 | hskp14),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.69/0.88 tff(458,plain,
% 0.69/0.88 (hskp18 | hskp27 | hskp14),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[457, 451])).
% 0.69/0.88 tff(459,plain,
% 0.69/0.88 (hskp18 | hskp27 | hskp14),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[458, 451])).
% 0.69/0.88 tff(460,plain,
% 0.69/0.88 (hskp18 | hskp27 | hskp14),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[459, 451])).
% 0.69/0.88 tff(461,plain,
% 0.69/0.88 (hskp18 | hskp27 | hskp14),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[460, 451])).
% 0.69/0.88 tff(462,plain,
% 0.69/0.88 (hskp14),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[461, 450, 416])).
% 0.69/0.88 tff(463,plain,
% 0.69/0.88 (~c2_1(a1330)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[199, 462])).
% 0.69/0.88 tff(464,plain,
% 0.69/0.88 (~c1_1(a1330)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[205, 462])).
% 0.69/0.88 tff(465,plain,
% 0.69/0.88 (c0_1(a1330)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[220, 462])).
% 0.69/0.88 tff(466,plain,
% 0.69/0.88 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(467,plain,
% 0.69/0.88 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(468,plain,
% 0.69/0.88 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[467])).
% 0.69/0.88 tff(469,plain,
% 0.69/0.88 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[468, 466])).
% 0.69/0.88 tff(470,plain,
% 0.69/0.88 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(471,plain,
% 0.69/0.88 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.69/0.88 tff(472,plain,
% 0.69/0.88 (hskp29),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[471, 416, 384, 465, 464, 463, 21])).
% 0.69/0.88 tff(473,plain,
% 0.69/0.88 (((~hskp29) | c3_1(a1338)) <=> ((~hskp29) | c3_1(a1338))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(474,axiom,((~hskp29) | c3_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.69/0.88 tff(475,plain,
% 0.69/0.88 ((~hskp29) | c3_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.69/0.88 tff(476,plain,
% 0.69/0.88 ((~hskp29) | c3_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[475, 473])).
% 0.69/0.88 tff(477,plain,
% 0.69/0.88 ((~hskp29) | c3_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.69/0.88 tff(478,plain,
% 0.69/0.88 ((~hskp29) | c3_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.69/0.88 tff(479,plain,
% 0.69/0.88 ((~hskp29) | c3_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[478, 473])).
% 0.69/0.88 tff(480,plain,
% 0.69/0.88 (c3_1(a1338)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[479, 472])).
% 0.69/0.88 tff(481,plain,
% 0.69/0.88 (((~hskp29) | c2_1(a1338)) <=> ((~hskp29) | c2_1(a1338))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(482,axiom,((~hskp29) | c2_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.69/0.88 tff(483,plain,
% 0.69/0.88 ((~hskp29) | c2_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.69/0.88 tff(484,plain,
% 0.69/0.88 ((~hskp29) | c2_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[483, 481])).
% 0.69/0.88 tff(485,plain,
% 0.69/0.88 ((~hskp29) | c2_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[484, 481])).
% 0.69/0.88 tff(486,plain,
% 0.69/0.88 ((~hskp29) | c2_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[485, 481])).
% 0.69/0.88 tff(487,plain,
% 0.69/0.88 ((~hskp29) | c2_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[486, 481])).
% 0.69/0.88 tff(488,plain,
% 0.69/0.88 (c2_1(a1338)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[487, 472])).
% 0.69/0.88 tff(489,plain,
% 0.69/0.88 (((~hskp29) | c1_1(a1338)) <=> ((~hskp29) | c1_1(a1338))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(490,axiom,((~hskp29) | c1_1(a1338)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.69/0.88 tff(491,plain,
% 0.69/0.88 ((~hskp29) | c1_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.69/0.88 tff(492,plain,
% 0.69/0.88 ((~hskp29) | c1_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[491, 489])).
% 0.69/0.88 tff(493,plain,
% 0.69/0.88 ((~hskp29) | c1_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[492, 489])).
% 0.69/0.88 tff(494,plain,
% 0.69/0.88 ((~hskp29) | c1_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[493, 489])).
% 0.69/0.88 tff(495,plain,
% 0.69/0.88 ((~hskp29) | c1_1(a1338)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[494, 489])).
% 0.69/0.88 tff(496,plain,
% 0.69/0.88 (c1_1(a1338)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[495, 472])).
% 0.69/0.88 tff(497,plain,
% 0.69/0.88 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(498,plain,
% 0.69/0.88 ((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(499,plain,
% 0.69/0.88 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[498])).
% 0.69/0.88 tff(500,plain,
% 0.69/0.88 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[499, 497])).
% 0.69/0.88 tff(501,plain,
% 0.69/0.88 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(502,plain,
% 0.69/0.88 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.69/0.88 tff(503,plain,
% 0.69/0.88 (hskp22),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[502, 384, 46, 496, 488, 480, 415])).
% 0.69/0.88 tff(504,plain,
% 0.69/0.88 (((~hskp22) | c1_1(a1356)) <=> ((~hskp22) | c1_1(a1356))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(505,axiom,((~hskp22) | c1_1(a1356)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.69/0.88 tff(506,plain,
% 0.69/0.88 ((~hskp22) | c1_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.69/0.88 tff(507,plain,
% 0.69/0.88 ((~hskp22) | c1_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[506, 504])).
% 0.69/0.88 tff(508,plain,
% 0.69/0.88 ((~hskp22) | c1_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.69/0.88 tff(509,plain,
% 0.69/0.88 ((~hskp22) | c1_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.69/0.88 tff(510,plain,
% 0.69/0.88 ((~hskp22) | c1_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[509, 504])).
% 0.69/0.88 tff(511,plain,
% 0.69/0.88 (c1_1(a1356)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[510, 503])).
% 0.69/0.88 tff(512,plain,
% 0.69/0.88 (((~hskp22) | c0_1(a1356)) <=> ((~hskp22) | c0_1(a1356))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(513,axiom,((~hskp22) | c0_1(a1356)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.69/0.88 tff(514,plain,
% 0.69/0.88 ((~hskp22) | c0_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.69/0.88 tff(515,plain,
% 0.69/0.88 ((~hskp22) | c0_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[514, 512])).
% 0.69/0.88 tff(516,plain,
% 0.69/0.88 ((~hskp22) | c0_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[515, 512])).
% 0.69/0.88 tff(517,plain,
% 0.69/0.88 ((~hskp22) | c0_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[516, 512])).
% 0.69/0.88 tff(518,plain,
% 0.69/0.88 ((~hskp22) | c0_1(a1356)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[517, 512])).
% 0.69/0.88 tff(519,plain,
% 0.69/0.88 (c0_1(a1356)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[518, 503])).
% 0.69/0.88 tff(520,plain,
% 0.69/0.88 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(521,plain,
% 0.69/0.88 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(522,plain,
% 0.69/0.88 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.69/0.88 tff(523,plain,
% 0.69/0.88 (~c2_1(a1356)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[522, 384, 248, 519, 511, 45])).
% 0.69/0.88 tff(524,plain,
% 0.69/0.88 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(525,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[524])).
% 0.69/0.89 tff(526,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(527,plain,
% 0.69/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(528,plain,
% 0.69/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[527])).
% 0.69/0.89 tff(529,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.69/0.89 tff(530,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.69/0.89 tff(531,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[530, 526])).
% 0.69/0.89 tff(532,plain,(
% 0.69/0.89 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[531])).
% 0.69/0.89 tff(533,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[532, 525])).
% 0.69/0.89 tff(534,plain,
% 0.69/0.89 (((~hskp22) | (~c3_1(a1356))) <=> ((~hskp22) | (~c3_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(535,plain,
% 0.69/0.89 (((~c3_1(a1356)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(536,axiom,((~c3_1(a1356)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.69/0.89 tff(537,plain,
% 0.69/0.89 ((~hskp22) | (~c3_1(a1356))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.69/0.89 tff(538,plain,
% 0.69/0.89 ((~hskp22) | (~c3_1(a1356))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[537, 534])).
% 0.69/0.89 tff(539,plain,
% 0.69/0.89 (~c3_1(a1356)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[538, 503])).
% 0.69/0.89 tff(540,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(541,plain,
% 0.69/0.89 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330))) <=> (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(542,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[541])).
% 0.69/0.89 tff(543,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[542, 540])).
% 0.69/0.89 tff(544,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(545,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | c2_1(a1330) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.69/0.89 tff(546,plain,
% 0.69/0.89 (c3_1(a1330)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[545, 384, 450, 519, 511, 465, 539, 463, 533])).
% 0.69/0.89 tff(547,plain,
% 0.69/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(548,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[547])).
% 0.69/0.89 tff(549,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(550,plain,
% 0.69/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(551,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[550])).
% 0.69/0.89 tff(552,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 0.69/0.89 tff(553,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.69/0.89 tff(554,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[553, 549])).
% 0.69/0.89 tff(555,plain,(
% 0.69/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[554])).
% 0.69/0.89 tff(556,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[555, 548])).
% 0.69/0.89 tff(557,plain,
% 0.69/0.89 (((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(558,plain,
% 0.69/0.89 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(559,plain,
% 0.69/0.89 ((~![U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.69/0.89 tff(560,plain,
% 0.69/0.89 (~c0_1(a1338)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[559, 384, 248, 496, 488, 45])).
% 0.69/0.89 tff(561,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(562,plain,
% 0.69/0.89 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(563,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[562])).
% 0.69/0.89 tff(564,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[563, 561])).
% 0.69/0.89 tff(565,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(566,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.69/0.89 tff(567,plain,
% 0.69/0.89 ((~c3_1(a1339)) | (~c3_1(a1330))),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[566, 384, 496, 480, 465, 24, 23, 464, 35, 560])).
% 0.69/0.89 tff(568,plain,
% 0.69/0.89 (~c3_1(a1339)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[567, 546])).
% 0.69/0.89 tff(569,plain,
% 0.69/0.89 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(570,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[569])).
% 0.69/0.89 tff(571,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(572,plain,
% 0.69/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(573,plain,
% 0.69/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[572])).
% 0.69/0.89 tff(574,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.69/0.89 tff(575,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.69/0.89 tff(576,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[575, 571])).
% 0.69/0.89 tff(577,plain,(
% 0.69/0.89 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(skolemize,[status(sab)],[576])).
% 0.69/0.89 tff(578,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[577, 570])).
% 0.69/0.89 tff(579,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(580,plain,
% 0.69/0.89 ((hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(581,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[580])).
% 0.69/0.89 tff(582,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[581, 579])).
% 0.69/0.89 tff(583,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(584,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1330) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.69/0.89 tff(585,plain,
% 0.69/0.89 (hskp3 | c3_1(a1339) | (~c3_1(a1330))),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[584, 384, 385, 465, 24, 463, 578])).
% 0.69/0.89 tff(586,plain,
% 0.69/0.89 (hskp3),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[585, 568, 546])).
% 0.69/0.89 tff(587,plain,
% 0.69/0.89 (((~hskp3) | (~c1_1(a1311))) <=> ((~hskp3) | (~c1_1(a1311)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(588,plain,
% 0.69/0.89 (((~c1_1(a1311)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a1311)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(589,axiom,((~c1_1(a1311)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.69/0.89 tff(590,plain,
% 0.69/0.89 ((~hskp3) | (~c1_1(a1311))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.69/0.89 tff(591,plain,
% 0.69/0.89 ((~hskp3) | (~c1_1(a1311))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[590, 587])).
% 0.69/0.89 tff(592,plain,
% 0.69/0.89 (~c1_1(a1311)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[591, 586])).
% 0.69/0.89 tff(593,plain,
% 0.69/0.89 (((~hskp3) | c2_1(a1311)) <=> ((~hskp3) | c2_1(a1311))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(594,axiom,((~hskp3) | c2_1(a1311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.69/0.89 tff(595,plain,
% 0.69/0.89 ((~hskp3) | c2_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.69/0.89 tff(596,plain,
% 0.69/0.89 ((~hskp3) | c2_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[595, 593])).
% 0.69/0.89 tff(597,plain,
% 0.69/0.89 ((~hskp3) | c2_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[596, 593])).
% 0.69/0.89 tff(598,plain,
% 0.69/0.89 ((~hskp3) | c2_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[597, 593])).
% 0.69/0.89 tff(599,plain,
% 0.69/0.89 ((~hskp3) | c2_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[598, 593])).
% 0.69/0.89 tff(600,plain,
% 0.69/0.89 (c2_1(a1311)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[599, 586])).
% 0.69/0.89 tff(601,plain,
% 0.69/0.89 (((~hskp3) | c0_1(a1311)) <=> ((~hskp3) | c0_1(a1311))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(602,axiom,((~hskp3) | c0_1(a1311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.69/0.89 tff(603,plain,
% 0.69/0.89 ((~hskp3) | c0_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.69/0.89 tff(604,plain,
% 0.69/0.89 ((~hskp3) | c0_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[603, 601])).
% 0.69/0.89 tff(605,plain,
% 0.69/0.89 ((~hskp3) | c0_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.69/0.89 tff(606,plain,
% 0.69/0.89 ((~hskp3) | c0_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[605, 601])).
% 0.69/0.89 tff(607,plain,
% 0.69/0.89 ((~hskp3) | c0_1(a1311)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[606, 601])).
% 0.69/0.89 tff(608,plain,
% 0.69/0.89 (c0_1(a1311)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[607, 586])).
% 0.69/0.89 tff(609,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(610,plain,
% 0.69/0.89 (((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(611,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[610])).
% 0.69/0.89 tff(612,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[611, 609])).
% 0.69/0.89 tff(613,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(614,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1356) | (~c0_1(a1356))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.69/0.89 tff(615,plain,
% 0.69/0.89 ($false),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[614, 384, 519, 608, 600, 539, 464, 463, 592, 556, 546, 523])).
% 0.69/0.89 tff(616,plain,(hskp13 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.69/0.89 tff(617,plain,
% 0.69/0.89 (hskp13),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[616, 46, 24, 23, 385])).
% 0.69/0.89 tff(618,plain,
% 0.69/0.89 (~c3_1(a1326)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[151, 617])).
% 0.69/0.89 tff(619,plain,
% 0.69/0.89 (~c2_1(a1326)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[157, 617])).
% 0.69/0.89 tff(620,plain,
% 0.69/0.89 (~c1_1(a1326)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[163, 617])).
% 0.69/0.89 tff(621,plain,
% 0.69/0.89 (((~hskp20) | (~c0_1(a1348))) <=> ((~hskp20) | (~c0_1(a1348)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(622,plain,
% 0.69/0.89 (((~c0_1(a1348)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1348)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(623,axiom,((~c0_1(a1348)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.69/0.89 tff(624,plain,
% 0.69/0.89 ((~hskp20) | (~c0_1(a1348))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.69/0.89 tff(625,plain,
% 0.69/0.89 ((~hskp20) | (~c0_1(a1348))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[624, 621])).
% 0.69/0.89 tff(626,plain,
% 0.69/0.89 (~c0_1(a1348)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[625, 378])).
% 0.69/0.89 tff(627,plain,
% 0.69/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(628,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[627])).
% 0.69/0.89 tff(629,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(630,plain,
% 0.69/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(631,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[630])).
% 0.69/0.90 tff(632,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.69/0.90 tff(633,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.69/0.90 tff(634,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[633, 629])).
% 0.69/0.90 tff(635,plain,(
% 0.69/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.90 inference(skolemize,[status(sab)],[634])).
% 0.69/0.90 tff(636,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[635, 628])).
% 0.69/0.90 tff(637,assumption,(~hskp14), introduced(assumption)).
% 0.69/0.90 tff(638,plain,
% 0.69/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(639,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[638])).
% 0.69/0.90 tff(640,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(641,plain,
% 0.69/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(642,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[641])).
% 0.69/0.90 tff(643,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 0.69/0.90 tff(644,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.69/0.90 tff(645,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[644, 640])).
% 0.69/0.90 tff(646,plain,(
% 0.69/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(skolemize,[status(sab)],[645])).
% 0.69/0.90 tff(647,plain,
% 0.69/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[646, 639])).
% 0.69/0.90 tff(648,assumption,(~hskp1), introduced(assumption)).
% 0.69/0.90 tff(649,plain,
% 0.69/0.90 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(650,plain,
% 0.69/0.90 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[649])).
% 0.69/0.90 tff(651,plain,
% 0.69/0.90 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(652,plain,
% 0.69/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(653,plain,
% 0.69/0.90 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[652])).
% 0.69/0.90 tff(654,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.69/0.90 tff(655,plain,
% 0.69/0.90 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.69/0.90 tff(656,plain,
% 0.69/0.90 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[655, 651])).
% 0.69/0.90 tff(657,plain,(
% 0.69/0.90 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(skolemize,[status(sab)],[656])).
% 0.69/0.90 tff(658,plain,
% 0.69/0.90 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[657, 650])).
% 0.69/0.90 tff(659,plain,
% 0.69/0.90 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(660,plain,
% 0.69/0.90 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(661,plain,
% 0.69/0.90 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[660])).
% 0.69/0.90 tff(662,plain,
% 0.69/0.90 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.69/0.90 inference(transitivity,[status(thm)],[661, 659])).
% 0.69/0.90 tff(663,plain,
% 0.69/0.90 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(664,plain,
% 0.69/0.90 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.69/0.90 tff(665,plain,
% 0.69/0.90 (hskp2 | hskp1 | c1_1(a1339) | c0_1(a1339)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[664, 384, 23, 658])).
% 0.69/0.90 tff(666,plain,
% 0.69/0.90 (hskp2),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[665, 648, 385, 24])).
% 0.69/0.90 tff(667,plain,
% 0.69/0.90 (((~hskp2) | (~c2_1(a1309))) <=> ((~hskp2) | (~c2_1(a1309)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(668,plain,
% 0.69/0.90 (((~c2_1(a1309)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1309)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(669,axiom,((~c2_1(a1309)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.69/0.90 tff(670,plain,
% 0.69/0.90 ((~hskp2) | (~c2_1(a1309))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.69/0.90 tff(671,plain,
% 0.69/0.90 ((~hskp2) | (~c2_1(a1309))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[670, 667])).
% 0.69/0.90 tff(672,plain,
% 0.69/0.90 (~c2_1(a1309)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[671, 666])).
% 0.69/0.90 tff(673,plain,
% 0.69/0.90 ((hskp14 | hskp4 | hskp1) <=> (hskp14 | hskp4 | hskp1)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(674,plain,
% 0.69/0.90 (((hskp14 | hskp4) | hskp1) <=> (hskp14 | hskp4 | hskp1)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(675,axiom,((hskp14 | hskp4) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.69/0.90 tff(676,plain,
% 0.69/0.90 (hskp14 | hskp4 | hskp1),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.69/0.90 tff(677,plain,
% 0.69/0.90 (hskp14 | hskp4 | hskp1),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[676, 673])).
% 0.69/0.90 tff(678,plain,
% 0.69/0.90 (hskp14 | hskp4 | hskp1),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[677, 673])).
% 0.69/0.90 tff(679,plain,
% 0.69/0.90 (hskp14 | hskp4 | hskp1),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[678, 673])).
% 0.69/0.90 tff(680,plain,
% 0.69/0.90 (hskp14 | hskp4 | hskp1),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[679, 673])).
% 0.69/0.90 tff(681,plain,
% 0.69/0.90 (hskp4),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[680, 648, 637])).
% 0.69/0.90 tff(682,plain,
% 0.69/0.90 (((~hskp4) | (~c1_1(a1312))) <=> ((~hskp4) | (~c1_1(a1312)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(683,plain,
% 0.69/0.90 (((~c1_1(a1312)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1312)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(684,axiom,((~c1_1(a1312)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.69/0.90 tff(685,plain,
% 0.69/0.90 ((~hskp4) | (~c1_1(a1312))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.69/0.90 tff(686,plain,
% 0.69/0.90 ((~hskp4) | (~c1_1(a1312))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[685, 682])).
% 0.69/0.90 tff(687,plain,
% 0.69/0.90 (~c1_1(a1312)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[686, 681])).
% 0.69/0.90 tff(688,plain,
% 0.69/0.90 (((~hskp4) | c0_1(a1312)) <=> ((~hskp4) | c0_1(a1312))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(689,axiom,((~hskp4) | c0_1(a1312)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.69/0.90 tff(690,plain,
% 0.69/0.90 ((~hskp4) | c0_1(a1312)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.69/0.90 tff(691,plain,
% 0.69/0.90 ((~hskp4) | c0_1(a1312)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[690, 688])).
% 0.69/0.90 tff(692,plain,
% 0.69/0.90 ((~hskp4) | c0_1(a1312)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[691, 688])).
% 0.69/0.90 tff(693,plain,
% 0.69/0.90 ((~hskp4) | c0_1(a1312)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.69/0.90 tff(694,plain,
% 0.69/0.90 ((~hskp4) | c0_1(a1312)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[693, 688])).
% 0.69/0.90 tff(695,plain,
% 0.69/0.90 (c0_1(a1312)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[694, 681])).
% 0.69/0.90 tff(696,plain,
% 0.69/0.90 (^[U: $i] : refl((hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(697,plain,
% 0.69/0.90 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[696])).
% 0.69/0.90 tff(698,plain,
% 0.69/0.90 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(699,plain,
% 0.69/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(700,plain,
% 0.69/0.90 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16) <=> ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[699])).
% 0.69/0.90 tff(701,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.69/0.90 tff(702,plain,
% 0.69/0.90 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.69/0.90 tff(703,plain,
% 0.69/0.90 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[702, 698])).
% 0.69/0.90 tff(704,plain,(
% 0.69/0.90 ![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(skolemize,[status(sab)],[703])).
% 0.69/0.90 tff(705,plain,
% 0.69/0.90 (![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[704, 697])).
% 0.69/0.90 tff(706,assumption,(~hskp18), introduced(assumption)).
% 0.69/0.90 tff(707,assumption,(~hskp16), introduced(assumption)).
% 0.69/0.90 tff(708,plain,
% 0.69/0.90 ((hskp18 | hskp16 | hskp5) <=> (hskp18 | hskp16 | hskp5)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(709,plain,
% 0.69/0.90 (((hskp18 | hskp5) | hskp16) <=> (hskp18 | hskp16 | hskp5)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(710,axiom,((hskp18 | hskp5) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.69/0.90 tff(711,plain,
% 0.69/0.90 (hskp18 | hskp16 | hskp5),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.69/0.90 tff(712,plain,
% 0.69/0.90 (hskp18 | hskp16 | hskp5),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[711, 708])).
% 0.69/0.90 tff(713,plain,
% 0.69/0.90 (hskp18 | hskp16 | hskp5),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[712, 708])).
% 0.69/0.90 tff(714,plain,
% 0.69/0.90 (hskp18 | hskp16 | hskp5),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[713, 708])).
% 0.69/0.90 tff(715,plain,
% 0.69/0.90 (hskp18 | hskp16 | hskp5),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[714, 708])).
% 0.69/0.90 tff(716,plain,
% 0.69/0.90 (hskp5),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[715, 707, 706])).
% 0.69/0.90 tff(717,plain,
% 0.69/0.90 (((~hskp5) | (~c3_1(a1314))) <=> ((~hskp5) | (~c3_1(a1314)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(718,plain,
% 0.69/0.90 (((~c3_1(a1314)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1314)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(719,axiom,((~c3_1(a1314)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.69/0.90 tff(720,plain,
% 0.69/0.90 ((~hskp5) | (~c3_1(a1314))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.69/0.90 tff(721,plain,
% 0.69/0.90 ((~hskp5) | (~c3_1(a1314))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[720, 717])).
% 0.69/0.90 tff(722,plain,
% 0.69/0.90 (~c3_1(a1314)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[721, 716])).
% 0.69/0.90 tff(723,plain,
% 0.69/0.90 (((~hskp5) | c1_1(a1314)) <=> ((~hskp5) | c1_1(a1314))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(724,axiom,((~hskp5) | c1_1(a1314)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.69/0.90 tff(725,plain,
% 0.69/0.90 ((~hskp5) | c1_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.69/0.90 tff(726,plain,
% 0.69/0.90 ((~hskp5) | c1_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[725, 723])).
% 0.69/0.90 tff(727,plain,
% 0.69/0.90 ((~hskp5) | c1_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[726, 723])).
% 0.69/0.90 tff(728,plain,
% 0.69/0.90 ((~hskp5) | c1_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[727, 723])).
% 0.69/0.90 tff(729,plain,
% 0.69/0.90 ((~hskp5) | c1_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[728, 723])).
% 0.69/0.90 tff(730,plain,
% 0.69/0.90 (c1_1(a1314)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[729, 716])).
% 0.69/0.90 tff(731,plain,
% 0.69/0.90 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(732,plain,
% 0.69/0.90 ((hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314))) <=> (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(733,plain,
% 0.69/0.90 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314)))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[732])).
% 0.69/0.90 tff(734,plain,
% 0.69/0.90 (((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))) <=> ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314))),
% 0.69/0.90 inference(transitivity,[status(thm)],[733, 731])).
% 0.69/0.90 tff(735,plain,
% 0.69/0.90 ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp14 | (~ndr1_0) | c2_1(a1314) | c3_1(a1314) | (~c1_1(a1314)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(736,plain,
% 0.69/0.90 ((~![U: $i] : (hskp16 | hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp14 | c3_1(a1314) | (~ndr1_0) | (~c1_1(a1314)) | c2_1(a1314)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.69/0.90 tff(737,plain,
% 0.69/0.90 (c2_1(a1314)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[736, 384, 707, 637, 730, 722, 705])).
% 0.74/0.90 tff(738,assumption,(~c1_1(a1312)), introduced(assumption)).
% 0.74/0.90 tff(739,plain,
% 0.74/0.90 (((~hskp5) | (~c0_1(a1314))) <=> ((~hskp5) | (~c0_1(a1314)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(740,plain,
% 0.74/0.90 (((~c0_1(a1314)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1314)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(741,axiom,((~c0_1(a1314)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.74/0.90 tff(742,plain,
% 0.74/0.90 ((~hskp5) | (~c0_1(a1314))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.74/0.90 tff(743,plain,
% 0.74/0.90 ((~hskp5) | (~c0_1(a1314))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[742, 739])).
% 0.74/0.90 tff(744,plain,
% 0.74/0.90 (~c0_1(a1314)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[743, 716])).
% 0.74/0.90 tff(745,plain,
% 0.74/0.90 (^[U: $i] : refl((hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 0.74/0.90 inference(bind,[status(th)],[])).
% 0.74/0.90 tff(746,plain,
% 0.74/0.90 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(quant_intro,[status(thm)],[745])).
% 0.74/0.90 tff(747,plain,
% 0.74/0.90 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(748,plain,
% 0.74/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.74/0.90 inference(bind,[status(th)],[])).
% 0.74/0.90 tff(749,plain,
% 0.74/0.90 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(quant_intro,[status(thm)],[748])).
% 0.74/0.90 tff(750,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.74/0.90 tff(751,plain,
% 0.74/0.90 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.74/0.90 tff(752,plain,
% 0.74/0.90 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[751, 747])).
% 0.74/0.90 tff(753,plain,(
% 0.74/0.90 ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(skolemize,[status(sab)],[752])).
% 0.74/0.90 tff(754,plain,
% 0.74/0.90 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[753, 746])).
% 0.74/0.90 tff(755,plain,
% 0.74/0.90 (((~hskp20) | c2_1(a1348)) <=> ((~hskp20) | c2_1(a1348))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(756,axiom,((~hskp20) | c2_1(a1348)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.74/0.90 tff(757,plain,
% 0.74/0.90 ((~hskp20) | c2_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.74/0.90 tff(758,plain,
% 0.74/0.90 ((~hskp20) | c2_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[757, 755])).
% 0.74/0.90 tff(759,plain,
% 0.74/0.90 ((~hskp20) | c2_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[758, 755])).
% 0.74/0.90 tff(760,plain,
% 0.74/0.90 ((~hskp20) | c2_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[759, 755])).
% 0.74/0.90 tff(761,plain,
% 0.74/0.90 ((~hskp20) | c2_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[760, 755])).
% 0.74/0.90 tff(762,plain,
% 0.74/0.90 (c2_1(a1348)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[761, 378])).
% 0.74/0.90 tff(763,plain,
% 0.74/0.90 (((~hskp20) | c1_1(a1348)) <=> ((~hskp20) | c1_1(a1348))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(764,axiom,((~hskp20) | c1_1(a1348)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.74/0.90 tff(765,plain,
% 0.74/0.90 ((~hskp20) | c1_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.74/0.90 tff(766,plain,
% 0.74/0.90 ((~hskp20) | c1_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[765, 763])).
% 0.74/0.90 tff(767,plain,
% 0.74/0.90 ((~hskp20) | c1_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[766, 763])).
% 0.74/0.90 tff(768,plain,
% 0.74/0.90 ((~hskp20) | c1_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[767, 763])).
% 0.74/0.90 tff(769,plain,
% 0.74/0.90 ((~hskp20) | c1_1(a1348)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[768, 763])).
% 0.74/0.90 tff(770,plain,
% 0.74/0.90 (c1_1(a1348)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[769, 378])).
% 0.74/0.90 tff(771,plain,
% 0.74/0.90 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(772,plain,
% 0.74/0.90 ((hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348))) <=> (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(773,plain,
% 0.74/0.90 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[772])).
% 0.74/0.90 tff(774,plain,
% 0.74/0.90 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.90 inference(transitivity,[status(thm)],[773, 771])).
% 0.74/0.90 tff(775,plain,
% 0.74/0.90 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(776,plain,
% 0.74/0.90 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp16 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.74/0.91 tff(777,plain,
% 0.74/0.91 (hskp17 | hskp16),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[776, 384, 770, 762, 626, 754])).
% 0.74/0.91 tff(778,plain,
% 0.74/0.91 (hskp17),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[777, 707])).
% 0.74/0.91 tff(779,plain,
% 0.74/0.91 (((~hskp17) | (~c0_1(a1334))) <=> ((~hskp17) | (~c0_1(a1334)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(780,plain,
% 0.74/0.91 (((~c0_1(a1334)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1334)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(781,axiom,((~c0_1(a1334)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.74/0.91 tff(782,plain,
% 0.74/0.91 ((~hskp17) | (~c0_1(a1334))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.74/0.91 tff(783,plain,
% 0.74/0.91 ((~hskp17) | (~c0_1(a1334))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.74/0.91 tff(784,plain,
% 0.74/0.91 (~c0_1(a1334)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[783, 778])).
% 0.74/0.91 tff(785,assumption,(c0_1(a1312)), introduced(assumption)).
% 0.74/0.91 tff(786,plain,
% 0.74/0.91 (((~hskp17) | c3_1(a1334)) <=> ((~hskp17) | c3_1(a1334))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(787,axiom,((~hskp17) | c3_1(a1334)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.74/0.91 tff(788,plain,
% 0.74/0.91 ((~hskp17) | c3_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.74/0.91 tff(789,plain,
% 0.74/0.91 ((~hskp17) | c3_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[788, 786])).
% 0.74/0.91 tff(790,plain,
% 0.74/0.91 ((~hskp17) | c3_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[789, 786])).
% 0.74/0.91 tff(791,plain,
% 0.74/0.91 ((~hskp17) | c3_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[790, 786])).
% 0.74/0.91 tff(792,plain,
% 0.74/0.91 ((~hskp17) | c3_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[791, 786])).
% 0.74/0.91 tff(793,plain,
% 0.74/0.91 (c3_1(a1334)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[792, 778])).
% 0.74/0.91 tff(794,plain,
% 0.74/0.91 (((~hskp17) | c2_1(a1334)) <=> ((~hskp17) | c2_1(a1334))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(795,axiom,((~hskp17) | c2_1(a1334)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.74/0.91 tff(796,plain,
% 0.74/0.91 ((~hskp17) | c2_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.74/0.91 tff(797,plain,
% 0.74/0.91 ((~hskp17) | c2_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[796, 794])).
% 0.74/0.91 tff(798,plain,
% 0.74/0.91 ((~hskp17) | c2_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[797, 794])).
% 0.74/0.91 tff(799,plain,
% 0.74/0.91 ((~hskp17) | c2_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.74/0.91 tff(800,plain,
% 0.74/0.91 ((~hskp17) | c2_1(a1334)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[799, 794])).
% 0.74/0.91 tff(801,plain,
% 0.74/0.91 (c2_1(a1334)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[800, 778])).
% 0.74/0.91 tff(802,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(803,plain,
% 0.74/0.91 (((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314))) <=> (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(804,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[803])).
% 0.74/0.91 tff(805,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[804, 802])).
% 0.74/0.91 tff(806,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(807,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1314))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.74/0.91 tff(808,plain,
% 0.74/0.91 (~c2_1(a1312)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[807, 384, 801, 793, 785, 784, 744, 722, 738, 395, 737])).
% 0.74/0.91 tff(809,plain,
% 0.74/0.91 (hskp27),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[461, 637, 706])).
% 0.74/0.91 tff(810,plain,
% 0.74/0.91 (c1_1(a1307)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[432, 809])).
% 0.74/0.91 tff(811,plain,
% 0.74/0.91 (c0_1(a1307)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[440, 809])).
% 0.74/0.91 tff(812,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(813,plain,
% 0.74/0.91 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314))) <=> (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(814,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[813])).
% 0.74/0.91 tff(815,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[814, 812])).
% 0.74/0.91 tff(816,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1314) | c0_1(a1314) | (~c2_1(a1314)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(817,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1314) | c3_1(a1314) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1314))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.74/0.91 tff(818,plain,
% 0.74/0.91 (~c3_1(a1307)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[817, 384, 811, 810, 801, 793, 784, 744, 722, 10, 737])).
% 0.74/0.91 tff(819,plain,
% 0.74/0.91 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(820,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[819])).
% 0.74/0.91 tff(821,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(822,plain,
% 0.74/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(823,plain,
% 0.74/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[822])).
% 0.74/0.91 tff(824,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.74/0.91 tff(825,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.74/0.91 tff(826,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.74/0.91 tff(827,plain,(
% 0.74/0.91 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[826])).
% 0.74/0.91 tff(828,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[827, 820])).
% 0.74/0.91 tff(829,plain,
% 0.74/0.91 (c2_1(a1307)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[424, 809])).
% 0.74/0.91 tff(830,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(831,plain,
% 0.74/0.91 ((hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312))) <=> (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(832,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[831])).
% 0.74/0.91 tff(833,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[832, 830])).
% 0.74/0.91 tff(834,plain,
% 0.74/0.91 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(835,plain,
% 0.74/0.91 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1312) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1312) | (~c0_1(a1312))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.74/0.91 tff(836,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[835, 384, 637, 811, 829, 785, 738, 828, 818, 808])).
% 0.74/0.91 tff(837,plain,(hskp16 | hskp14 | (~c0_1(a1312)) | c1_1(a1312) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(838,plain,
% 0.74/0.91 (hskp16),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[837, 695, 637, 687, 416])).
% 0.74/0.91 tff(839,plain,
% 0.74/0.91 (((~hskp16) | (~c3_1(a1333))) <=> ((~hskp16) | (~c3_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(840,plain,
% 0.74/0.91 (((~c3_1(a1333)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(841,axiom,((~c3_1(a1333)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.74/0.91 tff(842,plain,
% 0.74/0.91 ((~hskp16) | (~c3_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.74/0.91 tff(843,plain,
% 0.74/0.91 ((~hskp16) | (~c3_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[842, 839])).
% 0.74/0.91 tff(844,plain,
% 0.74/0.91 (~c3_1(a1333)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[843, 838])).
% 0.74/0.91 tff(845,plain,
% 0.74/0.91 (((~hskp2) | c3_1(a1309)) <=> ((~hskp2) | c3_1(a1309))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(846,axiom,((~hskp2) | c3_1(a1309)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.74/0.91 tff(847,plain,
% 0.74/0.91 ((~hskp2) | c3_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.74/0.91 tff(848,plain,
% 0.74/0.91 ((~hskp2) | c3_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[847, 845])).
% 0.74/0.91 tff(849,plain,
% 0.74/0.91 ((~hskp2) | c3_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[848, 845])).
% 0.74/0.91 tff(850,plain,
% 0.74/0.91 ((~hskp2) | c3_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[849, 845])).
% 0.74/0.91 tff(851,plain,
% 0.74/0.91 ((~hskp2) | c3_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[850, 845])).
% 0.74/0.91 tff(852,plain,
% 0.74/0.91 (c3_1(a1309)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[851, 666])).
% 0.74/0.91 tff(853,plain,
% 0.74/0.91 (((~hskp2) | c1_1(a1309)) <=> ((~hskp2) | c1_1(a1309))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(854,axiom,((~hskp2) | c1_1(a1309)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.74/0.91 tff(855,plain,
% 0.74/0.91 ((~hskp2) | c1_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.74/0.91 tff(856,plain,
% 0.74/0.91 ((~hskp2) | c1_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[855, 853])).
% 0.74/0.91 tff(857,plain,
% 0.74/0.91 ((~hskp2) | c1_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[856, 853])).
% 0.74/0.91 tff(858,plain,
% 0.74/0.91 ((~hskp2) | c1_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[857, 853])).
% 0.74/0.91 tff(859,plain,
% 0.74/0.91 ((~hskp2) | c1_1(a1309)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[858, 853])).
% 0.74/0.91 tff(860,plain,
% 0.74/0.91 (c1_1(a1309)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[859, 666])).
% 0.74/0.91 tff(861,plain,
% 0.74/0.91 (((~hskp16) | c1_1(a1333)) <=> ((~hskp16) | c1_1(a1333))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(862,axiom,((~hskp16) | c1_1(a1333)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.74/0.91 tff(863,plain,
% 0.74/0.91 ((~hskp16) | c1_1(a1333)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.74/0.91 tff(864,plain,
% 0.74/0.91 ((~hskp16) | c1_1(a1333)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[863, 861])).
% 0.74/0.91 tff(865,plain,
% 0.74/0.91 ((~hskp16) | c1_1(a1333)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[864, 861])).
% 0.74/0.91 tff(866,plain,
% 0.74/0.91 ((~hskp16) | c1_1(a1333)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[865, 861])).
% 0.74/0.91 tff(867,plain,
% 0.74/0.91 ((~hskp16) | c1_1(a1333)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[866, 861])).
% 0.74/0.91 tff(868,plain,
% 0.74/0.91 (c1_1(a1333)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[867, 838])).
% 0.74/0.91 tff(869,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(870,plain,
% 0.74/0.91 (((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)) <=> (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(871,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[870])).
% 0.74/0.91 tff(872,plain,
% 0.74/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[871, 869])).
% 0.74/0.91 tff(873,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(874,plain,
% 0.74/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.74/0.91 tff(875,plain,
% 0.74/0.91 (~c0_1(a1333)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[874, 384, 385, 868, 860, 852, 24, 23, 844, 672, 647])).
% 0.74/0.91 tff(876,plain,
% 0.74/0.91 (((~hskp16) | (~c2_1(a1333))) <=> ((~hskp16) | (~c2_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(877,plain,
% 0.74/0.91 (((~c2_1(a1333)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(878,axiom,((~c2_1(a1333)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.74/0.91 tff(879,plain,
% 0.74/0.91 ((~hskp16) | (~c2_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.74/0.91 tff(880,plain,
% 0.74/0.91 ((~hskp16) | (~c2_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[879, 876])).
% 0.74/0.91 tff(881,plain,
% 0.74/0.91 (~c2_1(a1333)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[880, 838])).
% 0.74/0.91 tff(882,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(883,plain,
% 0.74/0.91 ((hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326)) <=> (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(884,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[883])).
% 0.74/0.91 tff(885,plain,
% 0.74/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[884, 882])).
% 0.74/0.91 tff(886,plain,
% 0.74/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1326) | c1_1(a1326) | c3_1(a1326))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(887,plain,
% 0.74/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c2_1(a1333) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.74/0.91 tff(888,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[887, 384, 46, 868, 881, 620, 619, 618, 57, 875])).
% 0.74/0.91 tff(889,plain,(hskp1 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(890,plain,
% 0.74/0.91 (hskp1),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[889, 637, 385, 24, 23, 46])).
% 0.74/0.91 tff(891,plain,
% 0.74/0.91 (((~hskp1) | (~c2_1(a1308))) <=> ((~hskp1) | (~c2_1(a1308)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(892,plain,
% 0.74/0.91 (((~c2_1(a1308)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a1308)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(893,axiom,((~c2_1(a1308)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.74/0.91 tff(894,plain,
% 0.74/0.91 ((~hskp1) | (~c2_1(a1308))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.74/0.91 tff(895,plain,
% 0.74/0.91 ((~hskp1) | (~c2_1(a1308))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[894, 891])).
% 0.74/0.91 tff(896,plain,
% 0.74/0.91 (~c2_1(a1308)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[895, 890])).
% 0.74/0.91 tff(897,plain,
% 0.74/0.91 (~c1_1(a1308)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[344, 890])).
% 0.74/0.91 tff(898,plain,
% 0.74/0.91 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(899,plain,
% 0.74/0.91 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[898])).
% 0.74/0.91 tff(900,plain,
% 0.74/0.91 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(901,plain,
% 0.74/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(902,plain,
% 0.74/0.91 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[901])).
% 0.74/0.91 tff(903,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.74/0.91 tff(904,plain,
% 0.74/0.91 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.74/0.91 tff(905,plain,
% 0.74/0.91 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[904, 900])).
% 0.74/0.91 tff(906,plain,(
% 0.74/0.91 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[905])).
% 0.74/0.91 tff(907,plain,
% 0.74/0.91 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[906, 899])).
% 0.74/0.91 tff(908,plain,
% 0.74/0.91 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(909,plain,
% 0.74/0.91 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[908])).
% 0.74/0.91 tff(910,plain,
% 0.74/0.91 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(911,plain,
% 0.74/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(912,plain,
% 0.74/0.91 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[911])).
% 0.74/0.91 tff(913,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.74/0.91 tff(914,plain,
% 0.74/0.91 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.74/0.91 tff(915,plain,
% 0.74/0.91 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[914, 910])).
% 0.74/0.91 tff(916,plain,(
% 0.74/0.91 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[915])).
% 0.74/0.91 tff(917,plain,
% 0.74/0.91 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[916, 909])).
% 0.74/0.91 tff(918,assumption,(~hskp7), introduced(assumption)).
% 0.74/0.91 tff(919,plain,
% 0.74/0.91 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(920,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[919])).
% 0.74/0.92 tff(921,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(922,plain,
% 0.74/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(923,plain,
% 0.74/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[922])).
% 0.74/0.92 tff(924,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.74/0.92 tff(925,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.74/0.92 tff(926,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[925, 921])).
% 0.74/0.92 tff(927,plain,(
% 0.74/0.92 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(skolemize,[status(sab)],[926])).
% 0.74/0.92 tff(928,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[927, 920])).
% 0.74/0.92 tff(929,plain,
% 0.74/0.92 (hskp27),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[461, 637, 416])).
% 0.74/0.92 tff(930,plain,
% 0.74/0.92 (c2_1(a1307)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[424, 929])).
% 0.74/0.92 tff(931,plain,
% 0.74/0.92 (c1_1(a1307)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[432, 929])).
% 0.74/0.92 tff(932,plain,
% 0.74/0.92 (c0_1(a1307)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[440, 929])).
% 0.74/0.92 tff(933,assumption,(~hskp8), introduced(assumption)).
% 0.74/0.92 tff(934,plain,
% 0.74/0.92 (^[U: $i] : refl((hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(935,plain,
% 0.74/0.92 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[934])).
% 0.74/0.92 tff(936,plain,
% 0.74/0.92 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(937,plain,
% 0.74/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(938,plain,
% 0.74/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[937])).
% 0.74/0.92 tff(939,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.74/0.92 tff(940,plain,
% 0.74/0.92 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.74/0.92 tff(941,plain,
% 0.74/0.92 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[940, 936])).
% 0.74/0.92 tff(942,plain,(
% 0.74/0.92 ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(skolemize,[status(sab)],[941])).
% 0.74/0.92 tff(943,plain,
% 0.74/0.92 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[942, 935])).
% 0.74/0.92 tff(944,assumption,(c1_1(a1307)), introduced(assumption)).
% 0.74/0.92 tff(945,assumption,(c0_1(a1307)), introduced(assumption)).
% 0.74/0.92 tff(946,plain,
% 0.74/0.92 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(947,plain,
% 0.74/0.92 ((hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307))) <=> (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(948,plain,
% 0.74/0.92 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[947])).
% 0.74/0.92 tff(949,plain,
% 0.74/0.92 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.74/0.92 inference(transitivity,[status(thm)],[948, 946])).
% 0.74/0.92 tff(950,plain,
% 0.74/0.92 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(951,plain,
% 0.74/0.92 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.74/0.92 tff(952,plain,
% 0.74/0.92 (hskp8 | c3_1(a1307)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[951, 384, 637, 945, 944, 943])).
% 0.74/0.92 tff(953,plain,
% 0.74/0.92 (c3_1(a1307)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[952, 933])).
% 0.74/0.92 tff(954,assumption,(~c2_1(a1326)), introduced(assumption)).
% 0.74/0.92 tff(955,assumption,(~c1_1(a1326)), introduced(assumption)).
% 0.74/0.92 tff(956,plain,
% 0.74/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(957,plain,
% 0.74/0.92 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326))) <=> (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(958,plain,
% 0.74/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[957])).
% 0.74/0.92 tff(959,plain,
% 0.74/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[958, 956])).
% 0.74/0.92 tff(960,plain,
% 0.74/0.92 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(961,plain,
% 0.74/0.92 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.74/0.92 tff(962,plain,
% 0.74/0.92 (hskp8 | hskp7 | (~c0_1(a1326))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[961, 384, 955, 954, 917])).
% 0.74/0.92 tff(963,plain,
% 0.74/0.92 (~c0_1(a1326)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[962, 933, 918])).
% 0.74/0.92 tff(964,plain,
% 0.74/0.92 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(965,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[964])).
% 0.74/0.92 tff(966,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(967,plain,
% 0.74/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(968,plain,
% 0.74/0.92 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[967])).
% 0.74/0.92 tff(969,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.74/0.92 tff(970,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.74/0.92 tff(971,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[970, 966])).
% 0.74/0.92 tff(972,plain,(
% 0.74/0.92 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(skolemize,[status(sab)],[971])).
% 0.74/0.92 tff(973,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[972, 965])).
% 0.74/0.92 tff(974,assumption,(~c3_1(a1326)), introduced(assumption)).
% 0.74/0.92 tff(975,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(976,plain,
% 0.74/0.92 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(977,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[976])).
% 0.74/0.92 tff(978,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.74/0.92 inference(transitivity,[status(thm)],[977, 975])).
% 0.74/0.92 tff(979,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(980,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.74/0.92 tff(981,plain,
% 0.74/0.92 (hskp8 | (~c3_1(a1348)) | c0_1(a1326)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[980, 384, 762, 626, 954, 974, 973])).
% 0.74/0.92 tff(982,plain,
% 0.74/0.92 (~c3_1(a1348)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[981, 963, 933])).
% 0.74/0.92 tff(983,plain,
% 0.74/0.92 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(984,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[983])).
% 0.74/0.92 tff(985,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(986,plain,
% 0.74/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(987,plain,
% 0.74/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[986])).
% 0.74/0.92 tff(988,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.74/0.92 tff(989,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.74/0.92 tff(990,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.74/0.92 tff(991,plain,(
% 0.74/0.92 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(skolemize,[status(sab)],[990])).
% 0.74/0.92 tff(992,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[991, 984])).
% 0.74/0.92 tff(993,assumption,(c2_1(a1307)), introduced(assumption)).
% 0.74/0.92 tff(994,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(995,plain,
% 0.74/0.92 ((hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(996,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.92 tff(997,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[996, 994])).
% 0.74/0.92 tff(998,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(999,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.74/0.92 tff(1000,plain,
% 0.74/0.92 (hskp17 | (~c3_1(a1307))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[999, 384, 945, 944, 993, 992])).
% 0.74/0.92 tff(1001,plain,
% 0.74/0.92 (hskp17),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1000, 953])).
% 0.74/0.92 tff(1002,plain,
% 0.74/0.92 (~c0_1(a1334)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[783, 1001])).
% 0.74/0.92 tff(1003,plain,
% 0.74/0.92 (c3_1(a1334)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[792, 1001])).
% 0.74/0.92 tff(1004,plain,
% 0.74/0.92 (c2_1(a1334)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[800, 1001])).
% 0.74/0.92 tff(1005,plain,
% 0.74/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1006,plain,
% 0.74/0.92 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1007,plain,
% 0.74/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1006])).
% 0.74/0.92 tff(1008,plain,
% 0.74/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.74/0.92 tff(1009,plain,
% 0.74/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1010,plain,
% 0.74/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1334) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.74/0.92 tff(1011,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1010, 384, 945, 944, 762, 1004, 1003, 626, 1002, 10, 982, 953])).
% 0.74/0.92 tff(1012,plain,(hskp8 | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | c2_1(a1326) | c3_1(a1326) | hskp14 | hskp7 | c1_1(a1326)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1013,plain,
% 0.74/0.93 (hskp8),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1012, 932, 931, 930, 619, 618, 637, 918, 620])).
% 0.74/0.93 tff(1014,plain,
% 0.74/0.93 (((~hskp8) | (~c3_1(a1319))) <=> ((~hskp8) | (~c3_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1015,plain,
% 0.74/0.93 (((~c3_1(a1319)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1016,axiom,((~c3_1(a1319)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.74/0.93 tff(1017,plain,
% 0.74/0.93 ((~hskp8) | (~c3_1(a1319))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.74/0.93 tff(1018,plain,
% 0.74/0.93 ((~hskp8) | (~c3_1(a1319))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1017, 1014])).
% 0.74/0.93 tff(1019,plain,
% 0.74/0.93 (~c3_1(a1319)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1018, 1013])).
% 0.74/0.93 tff(1020,plain,
% 0.74/0.93 (((~hskp8) | (~c0_1(a1319))) <=> ((~hskp8) | (~c0_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1021,plain,
% 0.74/0.93 (((~c0_1(a1319)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1022,axiom,((~c0_1(a1319)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.74/0.93 tff(1023,plain,
% 0.74/0.93 ((~hskp8) | (~c0_1(a1319))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.74/0.93 tff(1024,plain,
% 0.74/0.93 ((~hskp8) | (~c0_1(a1319))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1023, 1020])).
% 0.74/0.93 tff(1025,plain,
% 0.74/0.93 (~c0_1(a1319)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1024, 1013])).
% 0.74/0.93 tff(1026,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1027,plain,
% 0.74/0.93 ((hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339))) <=> (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1028,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1027])).
% 0.74/0.93 tff(1029,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1028, 1026])).
% 0.74/0.93 tff(1030,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | (~c3_1(a1339)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1031,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1309)) | (~c1_1(a1309))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.74/0.93 tff(1032,plain,
% 0.74/0.93 (~c3_1(a1339)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1031, 384, 918, 385, 860, 852, 24, 672, 370])).
% 0.74/0.93 tff(1033,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1034,plain,
% 0.74/0.93 ((hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339)) <=> (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1035,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1034])).
% 0.74/0.93 tff(1036,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.74/0.93 tff(1037,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1309) | c0_1(a1309) | (~c1_1(a1309)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1038,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | c0_1(a1309) | (~c1_1(a1309))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.74/0.93 tff(1039,plain,
% 0.74/0.93 (c0_1(a1309)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1038, 384, 46, 385, 860, 23, 672, 57, 1032])).
% 0.74/0.93 tff(1040,plain,
% 0.74/0.93 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(1041,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[1040])).
% 0.74/0.93 tff(1042,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1043,plain,
% 0.74/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(1044,plain,
% 0.74/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[1043])).
% 0.74/0.93 tff(1045,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.74/0.93 tff(1046,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.74/0.93 tff(1047,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1046, 1042])).
% 0.74/0.93 tff(1048,plain,(
% 0.74/0.93 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(skolemize,[status(sab)],[1047])).
% 0.74/0.93 tff(1049,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1048, 1041])).
% 0.74/0.93 tff(1050,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1051,plain,
% 0.74/0.93 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1052,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1051])).
% 0.74/0.93 tff(1053,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1052, 1050])).
% 0.74/0.93 tff(1054,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1055,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.74/0.93 tff(1056,plain,
% 0.74/0.93 (hskp6 | c0_1(a1339) | c3_1(a1339)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1055, 384, 770, 762, 626, 23, 1049])).
% 0.74/0.93 tff(1057,plain,
% 0.74/0.93 (hskp6),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1056, 1032, 24])).
% 0.74/0.93 tff(1058,plain,
% 0.74/0.93 (((~hskp6) | (~c0_1(a1315))) <=> ((~hskp6) | (~c0_1(a1315)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1059,plain,
% 0.74/0.93 (((~c0_1(a1315)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a1315)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1060,axiom,((~c0_1(a1315)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.74/0.93 tff(1061,plain,
% 0.74/0.93 ((~hskp6) | (~c0_1(a1315))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.74/0.93 tff(1062,plain,
% 0.74/0.93 ((~hskp6) | (~c0_1(a1315))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1061, 1058])).
% 0.74/0.93 tff(1063,plain,
% 0.74/0.93 (~c0_1(a1315)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1062, 1057])).
% 0.74/0.93 tff(1064,plain,
% 0.74/0.93 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(1065,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[1064])).
% 0.74/0.93 tff(1066,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1067,plain,
% 0.74/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(1068,plain,
% 0.74/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[1067])).
% 0.74/0.93 tff(1069,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 0.74/0.93 tff(1070,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.74/0.93 tff(1071,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 0.74/0.93 tff(1072,plain,(
% 0.74/0.93 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(skolemize,[status(sab)],[1071])).
% 0.74/0.93 tff(1073,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1072, 1065])).
% 0.74/0.93 tff(1074,plain,
% 0.74/0.93 (((~hskp4) | (~c3_1(a1312))) <=> ((~hskp4) | (~c3_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1075,plain,
% 0.74/0.93 (((~c3_1(a1312)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1076,axiom,((~c3_1(a1312)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.74/0.93 tff(1077,plain,
% 0.74/0.93 ((~hskp4) | (~c3_1(a1312))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.74/0.93 tff(1078,plain,
% 0.74/0.93 ((~hskp4) | (~c3_1(a1312))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1077, 1074])).
% 0.74/0.93 tff(1079,plain,
% 0.74/0.93 (~c3_1(a1312)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1078, 681])).
% 0.74/0.93 tff(1080,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1081,plain,
% 0.74/0.93 ((hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312))) <=> (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1082,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1081])).
% 0.74/0.93 tff(1083,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1082, 1080])).
% 0.74/0.93 tff(1084,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c3_1(a1312) | (~c0_1(a1312)) | (~c2_1(a1312)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1085,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a1312) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1312)) | (~c0_1(a1312))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.74/0.93 tff(1086,plain,
% 0.74/0.93 ((~c0_1(a1309)) | (~c2_1(a1312))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1085, 384, 46, 695, 860, 852, 1079, 1073])).
% 0.74/0.93 tff(1087,plain,
% 0.74/0.93 (~c2_1(a1312)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1086, 1039])).
% 0.74/0.93 tff(1088,plain,
% 0.74/0.93 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1089,plain,
% 0.74/0.93 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312))) <=> (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1090,plain,
% 0.74/0.93 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1089])).
% 0.74/0.93 tff(1091,plain,
% 0.74/0.93 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.74/0.93 tff(1092,plain,
% 0.74/0.93 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1312) | c1_1(a1312) | (~c0_1(a1312)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1093,plain,
% 0.74/0.93 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1312) | (~ndr1_0) | c2_1(a1312) | (~c0_1(a1312))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.74/0.93 tff(1094,plain,
% 0.74/0.93 (hskp8 | c2_1(a1312)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1093, 384, 918, 695, 687, 917])).
% 0.74/0.93 tff(1095,plain,
% 0.74/0.93 (hskp8),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1094, 1087])).
% 0.74/0.93 tff(1096,plain,
% 0.74/0.93 (~c3_1(a1319)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1018, 1095])).
% 0.74/0.93 tff(1097,plain,
% 0.74/0.93 (~c0_1(a1319)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1024, 1095])).
% 0.74/0.93 tff(1098,plain,
% 0.74/0.93 (((~hskp6) | c3_1(a1315)) <=> ((~hskp6) | c3_1(a1315))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1099,axiom,((~hskp6) | c3_1(a1315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.74/0.93 tff(1100,plain,
% 0.74/0.93 ((~hskp6) | c3_1(a1315)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.74/0.93 tff(1101,plain,
% 0.74/0.93 ((~hskp6) | c3_1(a1315)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1100, 1098])).
% 0.74/0.93 tff(1102,plain,
% 0.74/0.93 ((~hskp6) | c3_1(a1315)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1101, 1098])).
% 0.74/0.93 tff(1103,plain,
% 0.74/0.93 ((~hskp6) | c3_1(a1315)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1102, 1098])).
% 0.74/0.93 tff(1104,plain,
% 0.74/0.93 ((~hskp6) | c3_1(a1315)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1103, 1098])).
% 0.74/0.93 tff(1105,plain,
% 0.74/0.93 (c3_1(a1315)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1104, 1057])).
% 0.74/0.93 tff(1106,plain,
% 0.74/0.93 (((~hskp8) | c2_1(a1319)) <=> ((~hskp8) | c2_1(a1319))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1107,axiom,((~hskp8) | c2_1(a1319)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.74/0.93 tff(1108,plain,
% 0.74/0.93 ((~hskp8) | c2_1(a1319)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.74/0.93 tff(1109,plain,
% 0.74/0.93 ((~hskp8) | c2_1(a1319)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1108, 1106])).
% 0.74/0.93 tff(1110,plain,
% 0.74/0.93 ((~hskp8) | c2_1(a1319)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1109, 1106])).
% 0.74/0.93 tff(1111,plain,
% 0.74/0.93 ((~hskp8) | c2_1(a1319)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 0.74/0.93 tff(1112,plain,
% 0.74/0.93 ((~hskp8) | c2_1(a1319)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1111, 1106])).
% 0.74/0.93 tff(1113,plain,
% 0.74/0.93 (c2_1(a1319)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1112, 1095])).
% 0.74/0.93 tff(1114,plain,
% 0.74/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1115,plain,
% 0.74/0.93 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1116,plain,
% 0.74/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1115])).
% 0.74/0.93 tff(1117,plain,
% 0.74/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1116, 1114])).
% 0.74/0.93 tff(1118,plain,
% 0.74/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1119,plain,
% 0.74/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.74/0.93 tff(1120,plain,
% 0.74/0.93 (~c2_1(a1315)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1119, 384, 1113, 1105, 860, 852, 1097, 1096, 1063, 10, 1039])).
% 0.74/0.93 tff(1121,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1122,plain,
% 0.74/0.93 ((hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1123,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1122])).
% 0.74/0.93 tff(1124,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1123, 1121])).
% 0.74/0.93 tff(1125,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1309) | (~c0_1(a1309)) | (~c3_1(a1309)) | c1_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1126,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a1339) | c0_1(a1339) | c2_1(a1309) | (~ndr1_0) | c3_1(a1339) | (~c3_1(a1309)) | (~c0_1(a1309))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 0.74/0.93 tff(1127,plain,
% 0.74/0.93 (hskp3 | (~c0_1(a1309))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1126, 384, 385, 852, 24, 672, 578, 1032])).
% 0.74/0.93 tff(1128,plain,
% 0.74/0.93 (hskp3),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1127, 1039])).
% 0.74/0.93 tff(1129,plain,
% 0.74/0.93 (~c1_1(a1311)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[591, 1128])).
% 0.74/0.93 tff(1130,plain,
% 0.74/0.93 (((~hskp6) | (~c1_1(a1315))) <=> ((~hskp6) | (~c1_1(a1315)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1131,plain,
% 0.74/0.93 (((~c1_1(a1315)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a1315)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1132,axiom,((~c1_1(a1315)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.74/0.93 tff(1133,plain,
% 0.74/0.93 ((~hskp6) | (~c1_1(a1315))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.74/0.93 tff(1134,plain,
% 0.74/0.93 ((~hskp6) | (~c1_1(a1315))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1133, 1130])).
% 0.74/0.93 tff(1135,plain,
% 0.74/0.93 (~c1_1(a1315)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1134, 1057])).
% 0.74/0.93 tff(1136,plain,
% 0.74/0.93 (c2_1(a1311)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[599, 1128])).
% 0.74/0.94 tff(1137,plain,
% 0.74/0.94 (c0_1(a1311)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[607, 1128])).
% 0.74/0.94 tff(1138,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1139,plain,
% 0.74/0.94 (((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1140,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315)))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1139])).
% 0.74/0.94 tff(1141,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1140, 1138])).
% 0.74/0.94 tff(1142,plain,
% 0.74/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1143,plain,
% 0.74/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1315) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | (~c3_1(a1315)) | c2_1(a1315)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.74/0.94 tff(1144,plain,
% 0.74/0.94 ($false),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1143, 384, 1105, 695, 1137, 1136, 1135, 1079, 1129, 556, 1087, 1120])).
% 0.74/0.94 tff(1145,plain,(hskp1 | hskp7 | c1_1(a1339) | c0_1(a1339) | hskp11 | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(1146,plain,
% 0.74/0.94 (hskp1),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1145, 637, 385, 24, 46, 23, 918])).
% 0.74/0.94 tff(1147,plain,
% 0.74/0.94 (~c2_1(a1308)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[895, 1146])).
% 0.74/0.94 tff(1148,plain,
% 0.74/0.94 (~c1_1(a1308)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[344, 1146])).
% 0.74/0.94 tff(1149,plain,
% 0.74/0.94 (c2_1(a1319)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1112, 1013])).
% 0.74/0.94 tff(1150,plain,
% 0.74/0.94 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1151,plain,
% 0.74/0.94 ((hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1152,plain,
% 0.74/0.94 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1151])).
% 0.74/0.94 tff(1153,plain,
% 0.74/0.94 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1152, 1150])).
% 0.74/0.94 tff(1154,plain,
% 0.74/0.94 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1155,plain,
% 0.74/0.94 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp15 | hskp14 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.74/0.94 tff(1156,plain,
% 0.74/0.94 (hskp15),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1155, 384, 637, 1149, 1025, 1019, 907])).
% 0.74/0.94 tff(1157,plain,
% 0.74/0.94 (((~hskp15) | (~c3_1(a1331))) <=> ((~hskp15) | (~c3_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1158,plain,
% 0.74/0.94 (((~c3_1(a1331)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1159,axiom,((~c3_1(a1331)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.74/0.94 tff(1160,plain,
% 0.74/0.94 ((~hskp15) | (~c3_1(a1331))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.74/0.94 tff(1161,plain,
% 0.74/0.94 ((~hskp15) | (~c3_1(a1331))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1160, 1157])).
% 0.74/0.94 tff(1162,plain,
% 0.74/0.94 (~c3_1(a1331)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1161, 1156])).
% 0.74/0.94 tff(1163,plain,
% 0.74/0.94 (c3_1(a1308)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[352, 1146])).
% 0.74/0.94 tff(1164,plain,
% 0.74/0.94 (((~hskp15) | c2_1(a1331)) <=> ((~hskp15) | c2_1(a1331))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1165,axiom,((~hskp15) | c2_1(a1331)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.74/0.94 tff(1166,plain,
% 0.74/0.94 ((~hskp15) | c2_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.74/0.94 tff(1167,plain,
% 0.74/0.94 ((~hskp15) | c2_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1166, 1164])).
% 0.74/0.94 tff(1168,plain,
% 0.74/0.94 ((~hskp15) | c2_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1167, 1164])).
% 0.74/0.94 tff(1169,plain,
% 0.74/0.94 ((~hskp15) | c2_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1168, 1164])).
% 0.74/0.94 tff(1170,plain,
% 0.74/0.94 ((~hskp15) | c2_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1169, 1164])).
% 0.74/0.94 tff(1171,plain,
% 0.74/0.94 (c2_1(a1331)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1170, 1156])).
% 0.74/0.94 tff(1172,plain,
% 0.74/0.94 (((~hskp15) | c1_1(a1331)) <=> ((~hskp15) | c1_1(a1331))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1173,axiom,((~hskp15) | c1_1(a1331)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.74/0.94 tff(1174,plain,
% 0.74/0.94 ((~hskp15) | c1_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.74/0.94 tff(1175,plain,
% 0.74/0.94 ((~hskp15) | c1_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1174, 1172])).
% 0.74/0.94 tff(1176,plain,
% 0.74/0.94 ((~hskp15) | c1_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1175, 1172])).
% 0.74/0.94 tff(1177,plain,
% 0.74/0.94 ((~hskp15) | c1_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1176, 1172])).
% 0.74/0.94 tff(1178,plain,
% 0.74/0.94 ((~hskp15) | c1_1(a1331)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1177, 1172])).
% 0.74/0.94 tff(1179,plain,
% 0.74/0.94 (c1_1(a1331)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1178, 1156])).
% 0.74/0.94 tff(1180,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1181,plain,
% 0.74/0.94 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1182,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1181])).
% 0.74/0.94 tff(1183,plain,
% 0.74/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1182, 1180])).
% 0.74/0.94 tff(1184,plain,
% 0.74/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1185,plain,
% 0.74/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.74/0.94 tff(1186,plain,
% 0.74/0.94 (~c0_1(a1331)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1185, 384, 1179, 1171, 1163, 1162, 1148, 1147, 636])).
% 0.74/0.94 tff(1187,plain,
% 0.74/0.94 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.74/0.94 inference(bind,[status(th)],[])).
% 0.74/0.94 tff(1188,plain,
% 0.74/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(quant_intro,[status(thm)],[1187])).
% 0.74/0.94 tff(1189,plain,
% 0.74/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1190,plain,
% 0.74/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.74/0.94 inference(bind,[status(th)],[])).
% 0.74/0.94 tff(1191,plain,
% 0.74/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(quant_intro,[status(thm)],[1190])).
% 0.74/0.94 tff(1192,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.74/0.94 tff(1193,plain,
% 0.74/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.74/0.94 tff(1194,plain,
% 0.74/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1193, 1189])).
% 0.74/0.94 tff(1195,plain,(
% 0.74/0.94 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(skolemize,[status(sab)],[1194])).
% 0.74/0.94 tff(1196,plain,
% 0.74/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1195, 1188])).
% 0.74/0.94 tff(1197,plain,
% 0.74/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1198,plain,
% 0.74/0.94 ((hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331))) <=> (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1199,plain,
% 0.74/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1198])).
% 0.74/0.94 tff(1200,plain,
% 0.74/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331)))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1199, 1197])).
% 0.74/0.94 tff(1201,plain,
% 0.74/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1202,plain,
% 0.74/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c0_1(a1331) | (~c1_1(a1331))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.74/0.94 tff(1203,plain,
% 0.74/0.94 (hskp12),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1202, 384, 932, 931, 930, 1179, 1162, 1196, 1186])).
% 0.74/0.94 tff(1204,plain,
% 0.74/0.94 (((~hskp12) | (~c0_1(a1325))) <=> ((~hskp12) | (~c0_1(a1325)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1205,plain,
% 0.74/0.94 (((~c0_1(a1325)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1325)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1206,axiom,((~c0_1(a1325)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.74/0.94 tff(1207,plain,
% 0.74/0.94 ((~hskp12) | (~c0_1(a1325))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 0.78/0.94 tff(1208,plain,
% 0.78/0.94 ((~hskp12) | (~c0_1(a1325))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1207, 1204])).
% 0.78/0.94 tff(1209,plain,
% 0.78/0.94 (~c0_1(a1325)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1208, 1203])).
% 0.78/0.94 tff(1210,plain,
% 0.78/0.94 (((~hskp12) | c3_1(a1325)) <=> ((~hskp12) | c3_1(a1325))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1211,axiom,((~hskp12) | c3_1(a1325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.78/0.94 tff(1212,plain,
% 0.78/0.94 ((~hskp12) | c3_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.78/0.94 tff(1213,plain,
% 0.78/0.94 ((~hskp12) | c3_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1212, 1210])).
% 0.78/0.94 tff(1214,plain,
% 0.78/0.94 ((~hskp12) | c3_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1213, 1210])).
% 0.78/0.94 tff(1215,plain,
% 0.78/0.94 ((~hskp12) | c3_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 0.78/0.94 tff(1216,plain,
% 0.78/0.94 ((~hskp12) | c3_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1215, 1210])).
% 0.78/0.94 tff(1217,plain,
% 0.78/0.94 (c3_1(a1325)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1216, 1203])).
% 0.78/0.94 tff(1218,plain,
% 0.78/0.94 (((~hskp12) | c1_1(a1325)) <=> ((~hskp12) | c1_1(a1325))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1219,axiom,((~hskp12) | c1_1(a1325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.78/0.94 tff(1220,plain,
% 0.78/0.94 ((~hskp12) | c1_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.78/0.94 tff(1221,plain,
% 0.78/0.94 ((~hskp12) | c1_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1220, 1218])).
% 0.78/0.94 tff(1222,plain,
% 0.78/0.94 ((~hskp12) | c1_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1221, 1218])).
% 0.78/0.94 tff(1223,plain,
% 0.78/0.94 ((~hskp12) | c1_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1222, 1218])).
% 0.78/0.94 tff(1224,plain,
% 0.78/0.94 ((~hskp12) | c1_1(a1325)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1223, 1218])).
% 0.78/0.94 tff(1225,plain,
% 0.78/0.94 (c1_1(a1325)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1224, 1203])).
% 0.78/0.94 tff(1226,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1227,plain,
% 0.78/0.94 ((hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1228,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1227])).
% 0.78/0.94 tff(1229,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1228, 1226])).
% 0.78/0.94 tff(1230,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1231,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1325) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 0.78/0.94 tff(1232,plain,
% 0.78/0.94 (hskp4),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1231, 384, 1225, 1217, 1149, 1209, 1025, 1019, 928])).
% 0.78/0.94 tff(1233,plain,
% 0.78/0.94 (~c1_1(a1312)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[686, 1232])).
% 0.78/0.94 tff(1234,plain,
% 0.78/0.94 (c0_1(a1312)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[694, 1232])).
% 0.78/0.94 tff(1235,plain,
% 0.78/0.94 (hskp16),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[837, 637, 1234, 1233, 416])).
% 0.78/0.94 tff(1236,plain,
% 0.78/0.94 (~c2_1(a1333)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[880, 1235])).
% 0.78/0.94 tff(1237,plain,
% 0.78/0.94 (c1_1(a1333)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[867, 1235])).
% 0.78/0.94 tff(1238,plain,
% 0.78/0.94 (c0_1(a1333)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[887, 384, 46, 1237, 1236, 620, 619, 618, 57])).
% 0.78/0.94 tff(1239,plain,
% 0.78/0.94 (~c3_1(a1333)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[843, 1235])).
% 0.78/0.94 tff(1240,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1241,plain,
% 0.78/0.94 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1242,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1241])).
% 0.78/0.94 tff(1243,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1242, 1240])).
% 0.78/0.94 tff(1244,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1245,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1333) | c3_1(a1331) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.78/0.94 tff(1246,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1245, 384, 1237, 1179, 1171, 1163, 1239, 1162, 1148, 1147, 636, 1238])).
% 0.78/0.94 tff(1247,plain,(hskp14 | hskp11 | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1248,plain,
% 0.78/0.94 (hskp14),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1247, 918, 46, 385, 24, 23])).
% 0.78/0.94 tff(1249,plain,
% 0.78/0.94 (~c2_1(a1330)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[199, 1248])).
% 0.78/0.94 tff(1250,plain,
% 0.78/0.94 (~c1_1(a1330)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[205, 1248])).
% 0.78/0.94 tff(1251,plain,
% 0.78/0.94 (c0_1(a1330)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[220, 1248])).
% 0.78/0.94 tff(1252,plain,
% 0.78/0.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1253,plain,
% 0.78/0.94 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1254,plain,
% 0.78/0.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1253])).
% 0.78/0.94 tff(1255,plain,
% 0.78/0.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.78/0.94 tff(1256,plain,
% 0.78/0.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1257,plain,
% 0.78/0.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c0_1(a1330))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.78/0.94 tff(1258,plain,
% 0.78/0.94 (hskp8),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1257, 384, 918, 1251, 1250, 1249, 917])).
% 0.78/0.94 tff(1259,plain,
% 0.78/0.94 (~c3_1(a1319)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1018, 1258])).
% 0.78/0.94 tff(1260,plain,
% 0.78/0.94 (~c0_1(a1319)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1024, 1258])).
% 0.78/0.94 tff(1261,plain,
% 0.78/0.94 (hskp29),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[471, 416, 384, 1251, 1250, 1249, 21])).
% 0.78/0.94 tff(1262,plain,
% 0.78/0.94 (c3_1(a1338)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[479, 1261])).
% 0.78/0.94 tff(1263,plain,
% 0.78/0.94 (c2_1(a1338)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[487, 1261])).
% 0.78/0.94 tff(1264,plain,
% 0.78/0.94 (c1_1(a1338)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[495, 1261])).
% 0.78/0.94 tff(1265,plain,
% 0.78/0.94 (hskp22),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[502, 384, 46, 1264, 1263, 1262, 415])).
% 0.78/0.94 tff(1266,plain,
% 0.78/0.94 (~c3_1(a1356)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[538, 1265])).
% 0.78/0.94 tff(1267,plain,
% 0.78/0.94 (c1_1(a1356)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[510, 1265])).
% 0.78/0.94 tff(1268,plain,
% 0.78/0.94 (c0_1(a1356)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[518, 1265])).
% 0.78/0.94 tff(1269,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1270,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1271,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1270])).
% 0.78/0.95 tff(1272,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.78/0.95 tff(1273,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1274,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1356)) | (~c0_1(a1356)) | (~c1_1(a1319))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.78/0.95 tff(1275,plain,
% 0.78/0.95 (~c1_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1274, 384, 1268, 1267, 1266, 620, 619, 618, 1260, 1259, 405])).
% 0.78/0.95 tff(1276,plain,
% 0.78/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1277,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1276])).
% 0.78/0.95 tff(1278,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1279,plain,
% 0.78/0.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1280,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1279])).
% 0.78/0.95 tff(1281,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.78/0.95 tff(1282,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.78/0.95 tff(1283,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.78/0.95 tff(1284,plain,(
% 0.78/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1283])).
% 0.78/0.95 tff(1285,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 0.78/0.95 tff(1286,plain,
% 0.78/0.95 (c2_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1112, 1258])).
% 0.78/0.95 tff(1287,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1288,plain,
% 0.78/0.95 (((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319)) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1289,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1288])).
% 0.78/0.95 tff(1290,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.78/0.95 tff(1291,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1292,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1319))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.78/0.95 tff(1293,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1292, 384, 1286, 1260, 1259, 1285, 1275])).
% 0.78/0.95 tff(1294,plain,(hskp7 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1295,plain,
% 0.78/0.95 (hskp7),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1294, 46, 385, 24, 23])).
% 0.78/0.95 tff(1296,plain,
% 0.78/0.95 (~c3_1(a1316)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[281, 1295])).
% 0.78/0.95 tff(1297,plain,
% 0.78/0.95 (~c2_1(a1316)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[275, 1295])).
% 0.78/0.95 tff(1298,plain,
% 0.78/0.95 (((~hskp7) | (~c0_1(a1316))) <=> ((~hskp7) | (~c0_1(a1316)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1299,plain,
% 0.78/0.95 (((~c0_1(a1316)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a1316)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1300,axiom,((~c0_1(a1316)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.78/0.95 tff(1301,plain,
% 0.78/0.95 ((~hskp7) | (~c0_1(a1316))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.78/0.95 tff(1302,plain,
% 0.78/0.95 ((~hskp7) | (~c0_1(a1316))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1301, 1298])).
% 0.78/0.95 tff(1303,plain,
% 0.78/0.95 (~c0_1(a1316)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1302, 1295])).
% 0.78/0.95 tff(1304,assumption,(~c0_1(a1316)), introduced(assumption)).
% 0.78/0.95 tff(1305,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1306,plain,
% 0.78/0.95 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1307,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1306])).
% 0.78/0.95 tff(1308,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1307, 1305])).
% 0.78/0.95 tff(1309,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1310,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 0.78/0.95 tff(1311,plain,
% 0.78/0.95 (hskp8 | (~c3_1(a1348))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1310, 384, 762, 626, 1304, 284, 283, 973])).
% 0.78/0.95 tff(1312,plain,
% 0.78/0.95 (~c3_1(a1348)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1311, 933])).
% 0.78/0.95 tff(1313,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1010, 384, 945, 944, 762, 1004, 1003, 626, 1002, 10, 1312, 953])).
% 0.78/0.95 tff(1314,plain,(hskp8 | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | hskp14 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1315,plain,
% 0.78/0.95 (hskp8),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1314, 932, 931, 930, 637, 1303, 1297, 1296])).
% 0.78/0.95 tff(1316,plain,
% 0.78/0.95 (~c3_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1018, 1315])).
% 0.78/0.95 tff(1317,plain,
% 0.78/0.95 (~c0_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1024, 1315])).
% 0.78/0.95 tff(1318,plain,
% 0.78/0.95 (c2_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1112, 1315])).
% 0.78/0.95 tff(1319,plain,
% 0.78/0.95 (hskp15),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1155, 384, 637, 1318, 1317, 1316, 907])).
% 0.78/0.95 tff(1320,plain,
% 0.78/0.95 (~c3_1(a1331)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1161, 1319])).
% 0.78/0.95 tff(1321,plain,
% 0.78/0.95 (c3_1(a1308)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[352, 890])).
% 0.78/0.95 tff(1322,plain,
% 0.78/0.95 (c2_1(a1331)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1170, 1319])).
% 0.78/0.95 tff(1323,plain,
% 0.78/0.95 (c1_1(a1331)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1178, 1319])).
% 0.78/0.95 tff(1324,plain,
% 0.78/0.95 (~c0_1(a1331)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1185, 384, 1323, 1322, 1321, 1320, 897, 896, 636])).
% 0.78/0.95 tff(1325,plain,
% 0.78/0.95 (hskp12),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1202, 384, 932, 931, 930, 1323, 1320, 1196, 1324])).
% 0.78/0.95 tff(1326,plain,
% 0.78/0.95 (~c0_1(a1325)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1208, 1325])).
% 0.78/0.95 tff(1327,plain,
% 0.78/0.95 (c3_1(a1325)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1216, 1325])).
% 0.78/0.95 tff(1328,plain,
% 0.78/0.95 (c1_1(a1325)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1224, 1325])).
% 0.78/0.95 tff(1329,plain,
% 0.78/0.95 (hskp4),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1231, 384, 1328, 1327, 1318, 1326, 1317, 1316, 928])).
% 0.78/0.95 tff(1330,plain,
% 0.78/0.95 (~c1_1(a1312)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[686, 1329])).
% 0.78/0.95 tff(1331,plain,
% 0.78/0.95 (c0_1(a1312)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[694, 1329])).
% 0.78/0.95 tff(1332,plain,
% 0.78/0.95 (hskp16),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[837, 1331, 637, 1330, 416])).
% 0.78/0.95 tff(1333,plain,
% 0.78/0.95 (~c3_1(a1333)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[843, 1332])).
% 0.78/0.95 tff(1334,plain,
% 0.78/0.95 (c1_1(a1333)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[867, 1332])).
% 0.78/0.95 tff(1335,plain,
% 0.78/0.95 (~c0_1(a1333)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1245, 384, 1334, 1323, 1322, 1321, 1333, 1320, 897, 896, 636])).
% 0.78/0.95 tff(1336,plain,
% 0.78/0.95 (~c2_1(a1333)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[880, 1332])).
% 0.78/0.95 tff(1337,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[887, 384, 46, 1334, 1336, 620, 619, 618, 57, 1335])).
% 0.78/0.95 tff(1338,plain,(hskp14 | hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1339,plain,
% 0.78/0.95 (hskp14),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1338, 46, 385, 24, 23])).
% 0.78/0.95 tff(1340,plain,
% 0.78/0.95 (~c2_1(a1330)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[199, 1339])).
% 0.78/0.95 tff(1341,plain,
% 0.78/0.95 (~c1_1(a1330)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[205, 1339])).
% 0.78/0.95 tff(1342,plain,
% 0.78/0.95 (c0_1(a1330)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[220, 1339])).
% 0.78/0.95 tff(1343,plain,
% 0.78/0.95 (hskp29),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[471, 416, 384, 1342, 1341, 1340, 21])).
% 0.78/0.95 tff(1344,plain,
% 0.78/0.95 (c3_1(a1338)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[479, 1343])).
% 0.78/0.95 tff(1345,plain,
% 0.78/0.95 (c2_1(a1338)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[487, 1343])).
% 0.78/0.95 tff(1346,plain,
% 0.78/0.95 (c1_1(a1338)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[495, 1343])).
% 0.78/0.95 tff(1347,plain,
% 0.78/0.95 (hskp22),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[502, 384, 46, 1346, 1345, 1344, 415])).
% 0.78/0.95 tff(1348,plain,
% 0.78/0.95 (~c3_1(a1356)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[538, 1347])).
% 0.78/0.95 tff(1349,plain,
% 0.78/0.95 (c1_1(a1356)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[510, 1347])).
% 0.78/0.95 tff(1350,plain,
% 0.78/0.95 (c0_1(a1356)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[518, 1347])).
% 0.78/0.95 tff(1351,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1352,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1353,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1352])).
% 0.78/0.95 tff(1354,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1353, 1351])).
% 0.78/0.95 tff(1355,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1356,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.78/0.95 tff(1357,plain,
% 0.78/0.95 (c3_1(a1348)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1356, 384, 1350, 1349, 770, 1348, 626, 620, 619, 618, 405])).
% 0.78/0.95 tff(1358,plain,
% 0.78/0.95 (hskp8 | (~c3_1(a1348))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1310, 384, 762, 626, 1303, 1297, 1296, 973])).
% 0.78/0.95 tff(1359,plain,
% 0.78/0.95 (hskp8),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1358, 1357])).
% 0.78/0.95 tff(1360,plain,
% 0.78/0.95 (~c3_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1018, 1359])).
% 0.78/0.95 tff(1361,plain,
% 0.78/0.95 (~c0_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1024, 1359])).
% 0.78/0.95 tff(1362,plain,
% 0.78/0.95 (~c1_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1274, 384, 1350, 1349, 1348, 620, 619, 618, 1361, 1360, 405])).
% 0.78/0.95 tff(1363,plain,
% 0.78/0.95 (c2_1(a1319)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1112, 1359])).
% 0.78/0.95 tff(1364,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1292, 384, 1363, 1361, 1360, 1285, 1362])).
% 0.78/0.95 tff(1365,plain,(hskp11 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1366,plain,
% 0.78/0.95 (hskp11),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1365, 24, 385, 23])).
% 0.78/0.95 tff(1367,plain,
% 0.78/0.95 (~c1_1(a1324)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[91, 1366])).
% 0.78/0.95 tff(1368,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1369,plain,
% 0.78/0.95 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1370,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1369])).
% 0.78/0.95 tff(1371,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1370, 1368])).
% 0.78/0.95 tff(1372,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1373,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1339) | c2_1(a1339) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1333) | (~c1_1(a1333))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.78/0.95 tff(1374,plain,
% 0.78/0.95 (~c3_1(a1339)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1373, 384, 868, 24, 23, 881, 844, 302, 875])).
% 0.78/0.95 tff(1375,plain,
% 0.78/0.95 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1376,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1375])).
% 0.78/0.95 tff(1377,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1378,plain,
% 0.78/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1379,plain,
% 0.78/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1378])).
% 0.78/0.95 tff(1380,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.78/0.95 tff(1381,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 0.78/0.95 tff(1382,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1381, 1377])).
% 0.78/0.95 tff(1383,plain,(
% 0.78/0.95 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1382])).
% 0.78/0.95 tff(1384,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1383, 1376])).
% 0.78/0.95 tff(1385,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1386,plain,
% 0.78/0.95 ((hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333))) <=> (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1387,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1386])).
% 0.78/0.96 tff(1388,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1387, 1385])).
% 0.78/0.96 tff(1389,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1390,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c1_1(a1333))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.78/0.96 tff(1391,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1390, 384, 868, 881, 844, 1384, 875])).
% 0.78/0.96 tff(1392,plain,
% 0.78/0.96 (((~hskp9) | (~c1_1(a1320))) <=> ((~hskp9) | (~c1_1(a1320)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1393,plain,
% 0.78/0.96 (((~c1_1(a1320)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1320)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1394,axiom,((~c1_1(a1320)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.78/0.96 tff(1395,plain,
% 0.78/0.96 ((~hskp9) | (~c1_1(a1320))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 0.78/0.96 tff(1396,plain,
% 0.78/0.96 ((~hskp9) | (~c1_1(a1320))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1395, 1392])).
% 0.78/0.96 tff(1397,plain,
% 0.78/0.96 (~c1_1(a1320)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1396, 1391])).
% 0.78/0.96 tff(1398,plain,
% 0.78/0.96 (((~hskp9) | (~c0_1(a1320))) <=> ((~hskp9) | (~c0_1(a1320)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1399,plain,
% 0.78/0.96 (((~c0_1(a1320)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1320)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1400,axiom,((~c0_1(a1320)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.78/0.96 tff(1401,plain,
% 0.78/0.96 ((~hskp9) | (~c0_1(a1320))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 0.78/0.96 tff(1402,plain,
% 0.78/0.96 ((~hskp9) | (~c0_1(a1320))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1401, 1398])).
% 0.78/0.96 tff(1403,plain,
% 0.78/0.96 (~c0_1(a1320)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1402, 1391])).
% 0.78/0.96 tff(1404,plain,
% 0.78/0.96 (((~hskp9) | c2_1(a1320)) <=> ((~hskp9) | c2_1(a1320))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1405,axiom,((~hskp9) | c2_1(a1320)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.78/0.96 tff(1406,plain,
% 0.78/0.96 ((~hskp9) | c2_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 0.78/0.96 tff(1407,plain,
% 0.78/0.96 ((~hskp9) | c2_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1406, 1404])).
% 0.78/0.96 tff(1408,plain,
% 0.78/0.96 ((~hskp9) | c2_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1407, 1404])).
% 0.78/0.96 tff(1409,plain,
% 0.78/0.96 ((~hskp9) | c2_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1408, 1404])).
% 0.78/0.96 tff(1410,plain,
% 0.78/0.96 ((~hskp9) | c2_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1409, 1404])).
% 0.78/0.96 tff(1411,plain,
% 0.78/0.96 (c2_1(a1320)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1410, 1391])).
% 0.78/0.96 tff(1412,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1413,plain,
% 0.78/0.96 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1414,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1413])).
% 0.78/0.96 tff(1415,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1414, 1412])).
% 0.78/0.96 tff(1416,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1417,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1339) | c0_1(a1339) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | c3_1(a1320)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.78/0.96 tff(1418,plain,
% 0.78/0.96 (c3_1(a1320)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1417, 384, 385, 1411, 24, 1403, 1397, 1285, 1374])).
% 0.78/0.96 tff(1419,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1420,plain,
% 0.78/0.96 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1421,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1420])).
% 0.78/0.96 tff(1422,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1421, 1419])).
% 0.78/0.96 tff(1423,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1309) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1424,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1309) | (~ndr1_0) | c0_1(a1309) | (~c3_1(a1309)) | c0_1(a1333) | (~c1_1(a1333))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 0.78/0.96 tff(1425,plain,
% 0.78/0.96 (c0_1(a1309)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1424, 384, 868, 852, 881, 844, 672, 302, 875])).
% 0.78/0.96 tff(1426,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1427,plain,
% 0.78/0.96 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333)) <=> (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1428,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1427])).
% 0.78/0.96 tff(1429,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1428, 1426])).
% 0.78/0.96 tff(1430,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1431,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1333)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 0.78/0.96 tff(1432,plain,
% 0.78/0.96 (hskp6),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1431, 384, 770, 762, 626, 881, 844, 1049, 875])).
% 0.78/0.96 tff(1433,plain,
% 0.78/0.96 (~c1_1(a1315)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1134, 1432])).
% 0.78/0.96 tff(1434,plain,
% 0.78/0.96 (~c0_1(a1315)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1062, 1432])).
% 0.78/0.96 tff(1435,plain,
% 0.78/0.96 (c3_1(a1315)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1104, 1432])).
% 0.78/0.96 tff(1436,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1437,plain,
% 0.78/0.96 ((hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315))) <=> (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1438,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1437])).
% 0.78/0.96 tff(1439,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.78/0.96 tff(1440,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1309) | (~c1_1(a1309)) | (~c3_1(a1309)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1441,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1315) | c1_1(a1315) | c2_1(a1309) | (~ndr1_0) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c3_1(a1315))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.78/0.96 tff(1442,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1441, 384, 918, 1435, 860, 852, 1434, 1433, 672, 370])).
% 0.78/0.96 tff(1443,plain,(hskp1 | hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1444,plain,
% 0.78/0.96 (hskp1),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1443, 918, 385, 24, 23, 637])).
% 0.78/0.96 tff(1445,plain,
% 0.78/0.96 (~c2_1(a1308)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[895, 1444])).
% 0.78/0.96 tff(1446,plain,
% 0.78/0.96 (~c1_1(a1308)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[344, 1444])).
% 0.78/0.96 tff(1447,plain,
% 0.78/0.96 (hskp13),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[449, 929])).
% 0.78/0.96 tff(1448,plain,
% 0.78/0.96 (~c1_1(a1326)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[163, 1447])).
% 0.78/0.96 tff(1449,plain,
% 0.78/0.96 (~c3_1(a1326)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[151, 1447])).
% 0.78/0.96 tff(1450,plain,
% 0.78/0.96 (~c2_1(a1326)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[157, 1447])).
% 0.78/0.96 tff(1451,plain,
% 0.78/0.96 (hskp8),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1012, 918, 931, 930, 1450, 1449, 637, 932, 1448])).
% 0.78/0.96 tff(1452,plain,
% 0.78/0.96 (~c3_1(a1319)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1018, 1451])).
% 0.78/0.96 tff(1453,plain,
% 0.78/0.96 (~c0_1(a1319)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1024, 1451])).
% 0.78/0.96 tff(1454,plain,
% 0.78/0.96 (c2_1(a1319)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1112, 1451])).
% 0.78/0.96 tff(1455,plain,
% 0.78/0.96 (hskp15),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1155, 384, 637, 1454, 1453, 1452, 907])).
% 0.78/0.96 tff(1456,plain,
% 0.78/0.96 (~c3_1(a1331)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1161, 1455])).
% 0.78/0.96 tff(1457,plain,
% 0.78/0.96 (c3_1(a1308)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[352, 1444])).
% 0.78/0.96 tff(1458,plain,
% 0.78/0.96 (c2_1(a1331)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1170, 1455])).
% 0.78/0.96 tff(1459,plain,
% 0.78/0.96 (c1_1(a1331)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1178, 1455])).
% 0.78/0.96 tff(1460,plain,
% 0.78/0.96 (~c0_1(a1331)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1185, 384, 1459, 1458, 1457, 1456, 1446, 1445, 636])).
% 0.78/0.96 tff(1461,plain,
% 0.78/0.96 (hskp12),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1202, 384, 932, 931, 930, 1459, 1456, 1196, 1460])).
% 0.78/0.96 tff(1462,plain,
% 0.78/0.96 (~c0_1(a1325)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1208, 1461])).
% 0.78/0.96 tff(1463,plain,
% 0.78/0.96 (c3_1(a1324)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[107, 1366])).
% 0.78/0.96 tff(1464,plain,
% 0.78/0.96 (c0_1(a1324)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[99, 1366])).
% 0.78/0.96 tff(1465,plain,
% 0.78/0.96 (c3_1(a1325)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1216, 1461])).
% 0.78/0.96 tff(1466,plain,
% 0.78/0.96 (c1_1(a1325)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1224, 1461])).
% 0.78/0.96 tff(1467,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1468,plain,
% 0.78/0.96 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325))) <=> (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1469,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1468])).
% 0.78/0.96 tff(1470,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.78/0.96 tff(1471,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1325) | c2_1(a1325) | (~c3_1(a1325)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1472,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | c2_1(a1325) | (~c1_1(a1325))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.78/0.96 tff(1473,plain,
% 0.78/0.96 (c2_1(a1325)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1472, 384, 1466, 1465, 1464, 1463, 1462, 1367, 35])).
% 0.78/0.96 tff(1474,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1475,plain,
% 0.78/0.96 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1476,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1475])).
% 0.78/0.96 tff(1477,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1476, 1474])).
% 0.78/0.96 tff(1478,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1479,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.78/0.96 tff(1480,plain,
% 0.78/0.96 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1479, 384, 932, 931, 1458, 1465, 1456, 1462, 10, 1460])).
% 0.78/0.96 tff(1481,plain,
% 0.78/0.96 (~c3_1(a1307)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1480, 1473])).
% 0.78/0.96 tff(1482,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1483,plain,
% 0.78/0.96 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1484,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1483])).
% 0.78/0.96 tff(1485,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.78/0.96 tff(1486,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1487,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | c0_1(a1325) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1324)) | (~c0_1(a1324)) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.78/0.96 tff(1488,plain,
% 0.78/0.96 ((~c2_1(a1324)) | (~c2_1(a1325))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1487, 384, 1458, 1465, 1464, 1456, 1462, 1367, 395, 1460])).
% 0.78/0.96 tff(1489,plain,
% 0.78/0.96 (~c2_1(a1324)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1488, 1473])).
% 0.78/0.96 tff(1490,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1491,plain,
% 0.78/0.96 ((hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324))) <=> (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1492,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1491])).
% 0.78/0.97 tff(1493,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1492, 1490])).
% 0.78/0.97 tff(1494,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)) | c2_1(a1324) | c1_1(a1324) | (~c0_1(a1324)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1495,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c0_1(a1324))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 0.78/0.97 tff(1496,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1495, 384, 637, 932, 930, 1464, 1367, 828, 1489, 1481])).
% 0.78/0.97 tff(1497,plain,(hskp7 | hskp14 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(1498,plain,
% 0.78/0.97 (hskp7),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1497, 637, 385, 24, 23])).
% 0.78/0.97 tff(1499,plain,
% 0.78/0.97 (~c3_1(a1316)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[281, 1498])).
% 0.78/0.97 tff(1500,plain,
% 0.78/0.97 (~c2_1(a1316)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[275, 1498])).
% 0.78/0.97 tff(1501,plain,
% 0.78/0.97 (~c0_1(a1316)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1302, 1498])).
% 0.78/0.97 tff(1502,plain,
% 0.78/0.97 (hskp8),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1314, 1501, 931, 930, 637, 932, 1500, 1499])).
% 0.78/0.97 tff(1503,plain,
% 0.78/0.97 (~c3_1(a1319)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1018, 1502])).
% 0.78/0.97 tff(1504,plain,
% 0.78/0.97 (~c0_1(a1319)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1024, 1502])).
% 0.78/0.97 tff(1505,plain,
% 0.78/0.97 (c2_1(a1319)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1112, 1502])).
% 0.78/0.97 tff(1506,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1507,plain,
% 0.78/0.97 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1508,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1507])).
% 0.78/0.97 tff(1509,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1508, 1506])).
% 0.78/0.97 tff(1510,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1511,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1319))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.78/0.97 tff(1512,plain,
% 0.78/0.97 ((~c3_1(a1348)) | (~c0_1(a1309))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1511, 384, 762, 1505, 860, 852, 626, 1504, 1503, 10])).
% 0.78/0.97 tff(1513,plain,
% 0.78/0.97 (~c3_1(a1348)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1512, 1425])).
% 0.78/0.97 tff(1514,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1515,plain,
% 0.78/0.97 (((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1516,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1515])).
% 0.78/0.97 tff(1517,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1516, 1514])).
% 0.78/0.97 tff(1518,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c3_1(a1309)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1519,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1320) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1309)) | (~c1_1(a1309)) | (~c0_1(a1309)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 0.78/0.97 tff(1520,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1519, 384, 762, 1411, 860, 852, 626, 1403, 10, 1513, 1425, 1418])).
% 0.78/0.97 tff(1521,plain,(hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(1522,plain,
% 0.78/0.97 (hskp1),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1521, 637, 24, 23, 385])).
% 0.78/0.97 tff(1523,plain,
% 0.78/0.97 (~c2_1(a1308)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[895, 1522])).
% 0.78/0.97 tff(1524,plain,
% 0.78/0.97 (~c1_1(a1308)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[344, 1522])).
% 0.78/0.97 tff(1525,plain,
% 0.78/0.97 (hskp15),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1155, 384, 637, 1505, 1504, 1503, 907])).
% 0.78/0.97 tff(1526,plain,
% 0.78/0.97 (~c3_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1161, 1525])).
% 0.78/0.97 tff(1527,plain,
% 0.78/0.97 (c3_1(a1308)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[352, 1522])).
% 0.78/0.97 tff(1528,plain,
% 0.78/0.97 (c2_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1170, 1525])).
% 0.78/0.97 tff(1529,plain,
% 0.78/0.97 (c1_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1178, 1525])).
% 0.78/0.97 tff(1530,plain,
% 0.78/0.97 (~c0_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1185, 384, 1529, 1528, 1527, 1526, 1524, 1523, 636])).
% 0.78/0.97 tff(1531,plain,
% 0.78/0.97 (hskp12),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1202, 384, 932, 931, 930, 1529, 1526, 1196, 1530])).
% 0.78/0.97 tff(1532,plain,
% 0.78/0.97 (~c0_1(a1325)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1208, 1531])).
% 0.78/0.97 tff(1533,plain,
% 0.78/0.97 (c3_1(a1325)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1216, 1531])).
% 0.78/0.97 tff(1534,plain,
% 0.78/0.97 (c1_1(a1325)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1224, 1531])).
% 0.78/0.97 tff(1535,plain,
% 0.78/0.97 (c2_1(a1325)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1472, 384, 1534, 1533, 1464, 1463, 1532, 1367, 35])).
% 0.78/0.97 tff(1536,plain,
% 0.78/0.97 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1479, 384, 932, 931, 1528, 1533, 1526, 1532, 10, 1530])).
% 0.78/0.97 tff(1537,plain,
% 0.78/0.97 (~c3_1(a1307)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1536, 1535])).
% 0.78/0.97 tff(1538,plain,
% 0.78/0.97 ((~c2_1(a1324)) | (~c2_1(a1325))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1487, 384, 1528, 1533, 1464, 1526, 1532, 1367, 395, 1530])).
% 0.78/0.97 tff(1539,plain,
% 0.78/0.97 (~c2_1(a1324)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1538, 1535])).
% 0.78/0.97 tff(1540,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1495, 384, 637, 932, 930, 1464, 1367, 828, 1539, 1537])).
% 0.78/0.97 tff(1541,plain,(hskp14 | c0_1(a1339) | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(1542,plain,
% 0.78/0.97 (hskp14),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1541, 24, 23, 385])).
% 0.78/0.97 tff(1543,plain,
% 0.78/0.97 (~c2_1(a1330)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[199, 1542])).
% 0.78/0.97 tff(1544,plain,
% 0.78/0.97 (~c1_1(a1330)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[205, 1542])).
% 0.78/0.97 tff(1545,plain,
% 0.78/0.97 (c0_1(a1330)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[220, 1542])).
% 0.78/0.97 tff(1546,plain,
% 0.78/0.97 (hskp29),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[471, 416, 384, 1545, 1544, 1543, 21])).
% 0.78/0.97 tff(1547,plain,
% 0.78/0.97 (c1_1(a1338)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[495, 1546])).
% 0.78/0.97 tff(1548,plain,
% 0.78/0.97 (c2_1(a1338)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[487, 1546])).
% 0.78/0.97 tff(1549,plain,
% 0.78/0.97 (c3_1(a1338)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[479, 1546])).
% 0.78/0.97 tff(1550,assumption,(~hskp3), introduced(assumption)).
% 0.78/0.97 tff(1551,plain,
% 0.78/0.97 ((hskp21 | hskp7 | hskp3) <=> (hskp21 | hskp7 | hskp3)),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1552,plain,
% 0.78/0.97 (((hskp21 | hskp3) | hskp7) <=> (hskp21 | hskp7 | hskp3)),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1553,plain,
% 0.78/0.97 ((hskp3 | hskp21) <=> (hskp21 | hskp3)),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1554,plain,
% 0.78/0.97 (((hskp3 | hskp21) | hskp7) <=> ((hskp21 | hskp3) | hskp7)),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1553])).
% 0.78/0.97 tff(1555,plain,
% 0.78/0.97 (((hskp3 | hskp21) | hskp7) <=> (hskp21 | hskp7 | hskp3)),
% 0.78/0.97 inference(transitivity,[status(thm)],[1554, 1552])).
% 0.78/0.97 tff(1556,axiom,((hskp3 | hskp21) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.78/0.97 tff(1557,plain,
% 0.78/0.97 (hskp21 | hskp7 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 0.78/0.97 tff(1558,plain,
% 0.78/0.97 (hskp21 | hskp7 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1557, 1551])).
% 0.78/0.97 tff(1559,plain,
% 0.78/0.97 (hskp21 | hskp7 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1558, 1551])).
% 0.78/0.97 tff(1560,plain,
% 0.78/0.97 (hskp21 | hskp7 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1559, 1551])).
% 0.78/0.97 tff(1561,plain,
% 0.78/0.97 (hskp21 | hskp7 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1560, 1551])).
% 0.78/0.97 tff(1562,plain,
% 0.78/0.97 (hskp21),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1561, 1550, 918])).
% 0.78/0.97 tff(1563,plain,
% 0.78/0.97 (((~hskp21) | (~c2_1(a1352))) <=> ((~hskp21) | (~c2_1(a1352)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1564,plain,
% 0.78/0.97 (((~c2_1(a1352)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a1352)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1565,axiom,((~c2_1(a1352)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.78/0.97 tff(1566,plain,
% 0.78/0.97 ((~hskp21) | (~c2_1(a1352))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 0.78/0.97 tff(1567,plain,
% 0.78/0.97 ((~hskp21) | (~c2_1(a1352))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1566, 1563])).
% 0.78/0.97 tff(1568,plain,
% 0.78/0.97 (~c2_1(a1352)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1567, 1562])).
% 0.78/0.97 tff(1569,plain,
% 0.78/0.97 (((~hskp21) | (~c0_1(a1352))) <=> ((~hskp21) | (~c0_1(a1352)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1570,plain,
% 0.78/0.97 (((~c0_1(a1352)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1352)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1571,axiom,((~c0_1(a1352)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.78/0.97 tff(1572,plain,
% 0.78/0.97 ((~hskp21) | (~c0_1(a1352))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 0.78/0.97 tff(1573,plain,
% 0.78/0.97 ((~hskp21) | (~c0_1(a1352))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1572, 1569])).
% 0.78/0.97 tff(1574,plain,
% 0.78/0.97 (~c0_1(a1352)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1573, 1562])).
% 0.78/0.97 tff(1575,assumption,(c3_1(a1324)), introduced(assumption)).
% 0.78/0.97 tff(1576,assumption,(c0_1(a1324)), introduced(assumption)).
% 0.78/0.97 tff(1577,plain,
% 0.78/0.97 (((~hskp21) | c3_1(a1352)) <=> ((~hskp21) | c3_1(a1352))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1578,axiom,((~hskp21) | c3_1(a1352)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.78/0.97 tff(1579,plain,
% 0.78/0.97 ((~hskp21) | c3_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 0.78/0.97 tff(1580,plain,
% 0.78/0.97 ((~hskp21) | c3_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1579, 1577])).
% 0.78/0.97 tff(1581,plain,
% 0.78/0.97 ((~hskp21) | c3_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1580, 1577])).
% 0.78/0.97 tff(1582,plain,
% 0.78/0.97 ((~hskp21) | c3_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1581, 1577])).
% 0.78/0.97 tff(1583,plain,
% 0.78/0.97 ((~hskp21) | c3_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1582, 1577])).
% 0.78/0.97 tff(1584,plain,
% 0.78/0.97 (c3_1(a1352)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1583, 1562])).
% 0.78/0.97 tff(1585,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1586,plain,
% 0.78/0.97 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1587,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1586])).
% 0.78/0.97 tff(1588,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1587, 1585])).
% 0.78/0.97 tff(1589,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | (~c1_1(a1352)) | (~c3_1(a1352)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1590,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1352)) | (~c1_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 0.78/0.97 tff(1591,plain,
% 0.78/0.97 (~c1_1(a1352)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1590, 384, 1584, 1576, 1575, 1574, 1568, 109, 35])).
% 0.78/0.97 tff(1592,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1593,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1592])).
% 0.78/0.97 tff(1594,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1595,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1596,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1595])).
% 0.78/0.97 tff(1597,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.78/0.97 tff(1598,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 0.78/0.97 tff(1599,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1598, 1594])).
% 0.78/0.97 tff(1600,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[1599])).
% 0.78/0.97 tff(1601,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1600, 1593])).
% 0.78/0.97 tff(1602,plain,
% 0.78/0.97 ((hskp7 | hskp4 | hskp3) <=> (hskp7 | hskp4 | hskp3)),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1603,plain,
% 0.78/0.97 (((hskp3 | hskp4) | hskp7) <=> (hskp7 | hskp4 | hskp3)),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1604,axiom,((hskp3 | hskp4) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.78/0.97 tff(1605,plain,
% 0.78/0.97 (hskp7 | hskp4 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.78/0.97 tff(1606,plain,
% 0.78/0.97 (hskp7 | hskp4 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1605, 1602])).
% 0.78/0.97 tff(1607,plain,
% 0.78/0.97 (hskp7 | hskp4 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1606, 1602])).
% 0.78/0.97 tff(1608,plain,
% 0.78/0.97 (hskp7 | hskp4 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1607, 1602])).
% 0.78/0.97 tff(1609,plain,
% 0.78/0.97 (hskp7 | hskp4 | hskp3),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1608, 1602])).
% 0.78/0.97 tff(1610,plain,
% 0.78/0.97 (hskp4),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1609, 1550, 918])).
% 0.78/0.97 tff(1611,plain,
% 0.78/0.97 (~c3_1(a1312)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1078, 1610])).
% 0.78/0.97 tff(1612,plain,
% 0.78/0.97 (~c1_1(a1312)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[686, 1610])).
% 0.78/0.97 tff(1613,assumption,(~c2_1(a1330)), introduced(assumption)).
% 0.78/0.97 tff(1614,assumption,(~c1_1(a1330)), introduced(assumption)).
% 0.78/0.97 tff(1615,plain,
% 0.78/0.97 (c0_1(a1312)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[694, 1610])).
% 0.78/0.97 tff(1616,assumption,(c0_1(a1330)), introduced(assumption)).
% 0.78/0.97 tff(1617,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1618,plain,
% 0.78/0.97 ((hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1619,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1618])).
% 0.78/0.97 tff(1620,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1619, 1617])).
% 0.78/0.97 tff(1621,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1622,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1312))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 0.78/0.97 tff(1623,plain,
% 0.78/0.97 (hskp15),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1622, 384, 1616, 1615, 1614, 1613, 1612, 1611, 1601])).
% 0.78/0.97 tff(1624,plain,
% 0.78/0.97 (~c3_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1161, 1623])).
% 0.78/0.97 tff(1625,plain,
% 0.78/0.97 (c2_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1170, 1623])).
% 0.78/0.97 tff(1626,plain,
% 0.78/0.97 (c1_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1178, 1623])).
% 0.78/0.97 tff(1627,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1628,plain,
% 0.78/0.97 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1629,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1628])).
% 0.78/0.97 tff(1630,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1629, 1627])).
% 0.78/0.97 tff(1631,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1632,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1352) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)) | (~c3_1(a1352)) | c1_1(a1352)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.78/0.97 tff(1633,plain,
% 0.78/0.97 (~c0_1(a1331)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1632, 384, 1584, 1626, 1625, 1568, 1624, 636, 1591])).
% 0.78/0.97 tff(1634,assumption,(c1_1(a1338)), introduced(assumption)).
% 0.78/0.97 tff(1635,assumption,(c3_1(a1338)), introduced(assumption)).
% 0.78/0.97 tff(1636,assumption,(~c0_1(a1338)), introduced(assumption)).
% 0.78/0.97 tff(1637,assumption,(~c2_1(a1352)), introduced(assumption)).
% 0.78/0.97 tff(1638,assumption,(~c0_1(a1352)), introduced(assumption)).
% 0.78/0.97 tff(1639,assumption,(c3_1(a1352)), introduced(assumption)).
% 0.78/0.97 tff(1640,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1641,plain,
% 0.78/0.98 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1642,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1641])).
% 0.78/0.98 tff(1643,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1642, 1640])).
% 0.78/0.98 tff(1644,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1645,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 0.78/0.98 tff(1646,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1645, 384, 1634, 1635, 1639, 1576, 1575, 1638, 1637, 109, 35, 1636])).
% 0.78/0.98 tff(1647,plain,(c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c3_1(a1352)) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1352) | c2_1(a1352) | c1_1(a1324)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(1648,plain,
% 0.78/0.98 (c0_1(a1338)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1647, 1584, 1635, 1634, 1576, 1575, 1574, 1568, 109])).
% 0.78/0.98 tff(1649,assumption,(c2_1(a1338)), introduced(assumption)).
% 0.78/0.98 tff(1650,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1651,plain,
% 0.78/0.98 ((hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338))) <=> (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1652,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1651])).
% 0.78/0.98 tff(1653,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1652, 1650])).
% 0.78/0.98 tff(1654,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1338)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1655,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1338))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.78/0.98 tff(1656,plain,
% 0.78/0.98 (hskp17 | (~c0_1(a1338))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1655, 384, 1634, 1649, 1635, 992])).
% 0.78/0.98 tff(1657,plain,
% 0.78/0.98 (hskp17),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1656, 1648])).
% 0.78/0.98 tff(1658,plain,
% 0.78/0.98 (~c0_1(a1334)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[783, 1657])).
% 0.78/0.98 tff(1659,plain,
% 0.78/0.98 (c3_1(a1334)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[792, 1657])).
% 0.78/0.98 tff(1660,plain,
% 0.78/0.98 (c2_1(a1334)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[800, 1657])).
% 0.78/0.98 tff(1661,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1662,plain,
% 0.78/0.98 (((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1663,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1662])).
% 0.78/0.98 tff(1664,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1663, 1661])).
% 0.78/0.98 tff(1665,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1666,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.78/0.98 tff(1667,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1666, 384, 1634, 1635, 1660, 1659, 1625, 1658, 1624, 10, 1648, 1633])).
% 0.78/0.98 tff(1668,plain,(hskp3 | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1324) | (~c0_1(a1330)) | c1_1(a1330) | c2_1(a1330) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(1669,plain,
% 0.78/0.98 (hskp3),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1668, 918, 1549, 1548, 1464, 1463, 1367, 1545, 1544, 1543, 1547])).
% 0.78/0.98 tff(1670,plain,
% 0.78/0.98 (~c1_1(a1311)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[591, 1669])).
% 0.78/0.98 tff(1671,assumption,(hskp2), introduced(assumption)).
% 0.78/0.98 tff(1672,plain,
% 0.78/0.98 (~c2_1(a1309)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[671, 1671])).
% 0.78/0.98 tff(1673,plain,
% 0.78/0.98 (c3_1(a1309)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[851, 1671])).
% 0.78/0.98 tff(1674,plain,
% 0.78/0.98 (c1_1(a1309)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[859, 1671])).
% 0.78/0.98 tff(1675,plain,
% 0.78/0.98 (~c3_1(a1339)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1031, 384, 918, 385, 1674, 1673, 24, 1672, 370])).
% 0.78/0.98 tff(1676,plain,
% 0.78/0.98 (hskp6),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1056, 1675, 24])).
% 0.78/0.98 tff(1677,plain,
% 0.78/0.98 (~c1_1(a1315)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1134, 1676])).
% 0.78/0.98 tff(1678,plain,
% 0.78/0.98 (~c0_1(a1315)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1062, 1676])).
% 0.78/0.98 tff(1679,plain,
% 0.78/0.98 (c3_1(a1315)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1104, 1676])).
% 0.78/0.98 tff(1680,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1441, 384, 918, 1679, 1674, 1673, 1678, 1677, 1672, 370])).
% 0.78/0.98 tff(1681,plain,((~hskp2) | hskp7 | c0_1(a1339) | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(1682,plain,
% 0.78/0.98 (~hskp2),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1681, 918, 24, 23, 385])).
% 0.78/0.98 tff(1683,plain,
% 0.78/0.98 (hskp1),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[665, 1682, 385, 24])).
% 0.78/0.98 tff(1684,plain,
% 0.78/0.98 (~c2_1(a1308)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[895, 1683])).
% 0.78/0.98 tff(1685,plain,
% 0.78/0.98 (~c1_1(a1308)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[344, 1683])).
% 0.78/0.98 tff(1686,plain,
% 0.78/0.98 (c3_1(a1308)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[352, 1683])).
% 0.78/0.98 tff(1687,assumption,(~c2_1(a1308)), introduced(assumption)).
% 0.78/0.98 tff(1688,assumption,(~c1_1(a1308)), introduced(assumption)).
% 0.78/0.98 tff(1689,assumption,(hskp3), introduced(assumption)).
% 0.78/0.98 tff(1690,plain,
% 0.78/0.98 (~c1_1(a1311)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[591, 1689])).
% 0.78/0.98 tff(1691,assumption,(c3_1(a1308)), introduced(assumption)).
% 0.78/0.98 tff(1692,plain,
% 0.78/0.98 (c2_1(a1311)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[599, 1689])).
% 0.78/0.98 tff(1693,plain,
% 0.78/0.98 (c0_1(a1311)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[607, 1689])).
% 0.78/0.98 tff(1694,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1695,plain,
% 0.78/0.98 (((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1696,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1695])).
% 0.78/0.98 tff(1697,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1696, 1694])).
% 0.78/0.98 tff(1698,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1699,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.78/0.98 tff(1700,plain,
% 0.78/0.98 (c3_1(a1330)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1699, 384, 1616, 1693, 1692, 1691, 1613, 1690, 1688, 1687, 556])).
% 0.78/0.98 tff(1701,plain,
% 0.78/0.98 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1702,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1701])).
% 0.78/0.98 tff(1703,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1704,plain,
% 0.78/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1705,plain,
% 0.78/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1704])).
% 0.78/0.98 tff(1706,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.78/0.98 tff(1707,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.78/0.98 tff(1708,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1707, 1703])).
% 0.78/0.98 tff(1709,plain,(
% 0.78/0.98 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(skolemize,[status(sab)],[1708])).
% 0.78/0.98 tff(1710,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1709, 1702])).
% 0.78/0.98 tff(1711,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1712,plain,
% 0.78/0.98 ((hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311))) <=> (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1713,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1712])).
% 0.78/0.98 tff(1714,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1713, 1711])).
% 0.78/0.98 tff(1715,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1716,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1311)) | (~c2_1(a1311))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 0.78/0.98 tff(1717,plain,
% 0.78/0.98 (~c3_1(a1311)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1716, 384, 22, 1616, 1692, 1613, 1690, 1710, 1700])).
% 0.78/0.98 tff(1718,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1719,plain,
% 0.78/0.98 ((hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330))) <=> (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1720,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311)))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1719])).
% 0.78/0.98 tff(1721,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1720, 1718])).
% 0.78/0.98 tff(1722,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1311) | c3_1(a1311) | (~c0_1(a1311)) | c2_1(a1330) | c1_1(a1330) | (~c0_1(a1330)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1723,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1330) | c2_1(a1330) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1330)) | (~c0_1(a1311)) | c3_1(a1311)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.78/0.98 tff(1724,plain,
% 0.78/0.98 (hskp15),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1723, 384, 1616, 1693, 1614, 1613, 1690, 1601, 1717])).
% 0.78/0.98 tff(1725,plain,
% 0.78/0.98 (~c3_1(a1331)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1161, 1724])).
% 0.78/0.98 tff(1726,plain,
% 0.78/0.98 (c2_1(a1331)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1170, 1724])).
% 0.78/0.98 tff(1727,plain,
% 0.78/0.98 (c1_1(a1331)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1178, 1724])).
% 0.78/0.98 tff(1728,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1729,plain,
% 0.78/0.98 (((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1730,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1729])).
% 0.78/0.98 tff(1731,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1730, 1728])).
% 0.78/0.98 tff(1732,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c2_1(a1331)) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1733,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1331) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1331)) | (~c2_1(a1331)) | (~c1_1(a1331))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 0.78/0.98 tff(1734,plain,
% 0.78/0.98 (~c0_1(a1331)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1733, 384, 1727, 1726, 1725, 1614, 1613, 636, 1700])).
% 0.78/0.98 tff(1735,plain,
% 0.78/0.98 (^[U: $i] : refl((hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1736,plain,
% 0.78/0.98 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1735])).
% 0.78/0.98 tff(1737,plain,
% 0.78/0.98 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1738,plain,
% 0.78/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1739,plain,
% 0.78/0.98 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1738])).
% 0.78/0.98 tff(1740,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.78/0.98 tff(1741,plain,
% 0.78/0.98 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 0.78/0.98 tff(1742,plain,
% 0.78/0.98 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1741, 1737])).
% 0.78/0.98 tff(1743,plain,(
% 0.78/0.98 ![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(skolemize,[status(sab)],[1742])).
% 0.78/0.98 tff(1744,plain,
% 0.78/0.98 (![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1743, 1736])).
% 0.78/0.99 tff(1745,plain,
% 0.78/0.99 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1746,plain,
% 0.78/0.99 ((hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311))) <=> (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1747,plain,
% 0.78/0.99 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1746])).
% 0.78/0.99 tff(1748,plain,
% 0.78/0.99 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1747, 1745])).
% 0.78/0.99 tff(1749,plain,
% 0.78/0.99 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1750,plain,
% 0.78/0.99 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 0.78/0.99 tff(1751,plain,
% 0.78/0.99 (hskp30),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1750, 706, 384, 1693, 1692, 1744, 1717])).
% 0.78/0.99 tff(1752,plain,
% 0.78/0.99 (((~hskp30) | c3_1(a1372)) <=> ((~hskp30) | c3_1(a1372))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1753,axiom,((~hskp30) | c3_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.78/0.99 tff(1754,plain,
% 0.78/0.99 ((~hskp30) | c3_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 0.78/0.99 tff(1755,plain,
% 0.78/0.99 ((~hskp30) | c3_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1754, 1752])).
% 0.78/0.99 tff(1756,plain,
% 0.78/0.99 ((~hskp30) | c3_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1755, 1752])).
% 0.78/0.99 tff(1757,plain,
% 0.78/0.99 ((~hskp30) | c3_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1756, 1752])).
% 0.78/0.99 tff(1758,plain,
% 0.78/0.99 ((~hskp30) | c3_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1757, 1752])).
% 0.78/0.99 tff(1759,plain,
% 0.78/0.99 (c3_1(a1372)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1758, 1751])).
% 0.78/0.99 tff(1760,plain,
% 0.78/0.99 (((~hskp30) | c1_1(a1372)) <=> ((~hskp30) | c1_1(a1372))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1761,axiom,((~hskp30) | c1_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.78/0.99 tff(1762,plain,
% 0.78/0.99 ((~hskp30) | c1_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.78/0.99 tff(1763,plain,
% 0.78/0.99 ((~hskp30) | c1_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1762, 1760])).
% 0.78/0.99 tff(1764,plain,
% 0.78/0.99 ((~hskp30) | c1_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1763, 1760])).
% 0.78/0.99 tff(1765,plain,
% 0.78/0.99 ((~hskp30) | c1_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1764, 1760])).
% 0.78/0.99 tff(1766,plain,
% 0.78/0.99 ((~hskp30) | c1_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1765, 1760])).
% 0.78/0.99 tff(1767,plain,
% 0.78/0.99 (c1_1(a1372)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1766, 1751])).
% 0.78/0.99 tff(1768,plain,
% 0.78/0.99 (((~hskp30) | c0_1(a1372)) <=> ((~hskp30) | c0_1(a1372))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1769,axiom,((~hskp30) | c0_1(a1372)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.78/0.99 tff(1770,plain,
% 0.78/0.99 ((~hskp30) | c0_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 0.78/0.99 tff(1771,plain,
% 0.78/0.99 ((~hskp30) | c0_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1770, 1768])).
% 0.78/0.99 tff(1772,plain,
% 0.78/0.99 ((~hskp30) | c0_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1771, 1768])).
% 0.78/0.99 tff(1773,plain,
% 0.78/0.99 ((~hskp30) | c0_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1772, 1768])).
% 0.78/0.99 tff(1774,plain,
% 0.78/0.99 ((~hskp30) | c0_1(a1372)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1773, 1768])).
% 0.78/0.99 tff(1775,plain,
% 0.78/0.99 (c0_1(a1372)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1774, 1751])).
% 0.78/0.99 tff(1776,assumption,(~c0_1(a1331)), introduced(assumption)).
% 0.78/0.99 tff(1777,assumption,(~c3_1(a1331)), introduced(assumption)).
% 0.78/0.99 tff(1778,assumption,(hskp17), introduced(assumption)).
% 0.78/0.99 tff(1779,plain,
% 0.78/0.99 (~c0_1(a1334)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[783, 1778])).
% 0.78/0.99 tff(1780,assumption,(c2_1(a1331)), introduced(assumption)).
% 0.78/0.99 tff(1781,plain,
% 0.78/0.99 (c3_1(a1334)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[792, 1778])).
% 0.78/0.99 tff(1782,plain,
% 0.78/0.99 (c2_1(a1334)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[800, 1778])).
% 0.78/0.99 tff(1783,assumption,(c3_1(a1372)), introduced(assumption)).
% 0.78/0.99 tff(1784,assumption,(c1_1(a1372)), introduced(assumption)).
% 0.78/0.99 tff(1785,assumption,(c0_1(a1372)), introduced(assumption)).
% 0.78/0.99 tff(1786,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1787,plain,
% 0.78/0.99 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1788,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1787])).
% 0.78/0.99 tff(1789,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1788, 1786])).
% 0.78/0.99 tff(1790,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1791,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 0.78/0.99 tff(1792,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1791, 384, 1785, 1784, 1783, 1782, 1781, 1780, 1779, 1777, 10, 1776])).
% 0.78/0.99 tff(1793,plain,((~hskp17) | (~c0_1(a1372)) | (~c1_1(a1372)) | (~c3_1(a1372)) | (~c2_1(a1331)) | c3_1(a1331) | c0_1(a1331)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(1794,plain,
% 0.78/0.99 (~hskp17),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1793, 1775, 1767, 1759, 1726, 1725, 1734])).
% 0.78/0.99 tff(1795,plain,
% 0.78/0.99 (hskp29),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[471, 706, 384, 1616, 1614, 1613, 21])).
% 0.78/0.99 tff(1796,plain,
% 0.78/0.99 (c3_1(a1338)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[479, 1795])).
% 0.78/0.99 tff(1797,plain,
% 0.78/0.99 (c2_1(a1338)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[487, 1795])).
% 0.78/0.99 tff(1798,plain,
% 0.78/0.99 (c1_1(a1338)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[495, 1795])).
% 0.78/0.99 tff(1799,plain,
% 0.78/0.99 (hskp17 | (~c0_1(a1338))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1655, 384, 1798, 1797, 1796, 992])).
% 0.78/0.99 tff(1800,plain,
% 0.78/0.99 (~c0_1(a1338)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1799, 1794])).
% 0.78/0.99 tff(1801,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1802,plain,
% 0.78/0.99 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1803,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1802])).
% 0.78/0.99 tff(1804,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.78/0.99 tff(1805,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1806,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1331) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.78/0.99 tff(1807,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1806, 384, 1775, 1767, 1759, 1797, 1796, 1726, 1725, 10, 1800, 1734])).
% 0.78/0.99 tff(1808,plain,((~hskp3) | c1_1(a1330) | c2_1(a1330) | hskp18 | (~c0_1(a1330)) | hskp27 | (~c3_1(a1308)) | c1_1(a1308) | c2_1(a1308)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(1809,plain,
% 0.78/0.99 (hskp27),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1808, 1669, 1543, 416, 1545, 1544, 1686, 1685, 1684])).
% 0.78/0.99 tff(1810,plain,
% 0.78/0.99 (hskp13),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[449, 1809])).
% 0.78/0.99 tff(1811,plain,
% 0.78/0.99 (~c3_1(a1326)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[151, 1810])).
% 0.78/0.99 tff(1812,plain,
% 0.78/0.99 (~c2_1(a1326)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[157, 1810])).
% 0.78/0.99 tff(1813,plain,
% 0.78/0.99 (c2_1(a1311)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[599, 1669])).
% 0.78/0.99 tff(1814,plain,
% 0.78/0.99 (c0_1(a1311)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[607, 1669])).
% 0.78/0.99 tff(1815,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1816,plain,
% 0.78/0.99 (((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308))) <=> (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1817,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1816])).
% 0.78/0.99 tff(1818,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1817, 1815])).
% 0.78/0.99 tff(1819,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1326) | c3_1(a1326) | (~c0_1(a1326)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1308) | c2_1(a1308) | (~c3_1(a1308)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1820,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1326) | c3_1(a1326) | c1_1(a1311) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c0_1(a1326))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 0.78/0.99 tff(1821,plain,
% 0.78/0.99 (~c0_1(a1326)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1820, 384, 1814, 1813, 1686, 1812, 1811, 1670, 1685, 1684, 556])).
% 0.78/0.99 tff(1822,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1823,plain,
% 0.78/0.99 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1824,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1823])).
% 0.78/0.99 tff(1825,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1824, 1822])).
% 0.78/0.99 tff(1826,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1827,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c0_1(a1326)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.78/0.99 tff(1828,plain,
% 0.78/0.99 (hskp6),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1827, 384, 770, 762, 626, 1812, 1811, 1049, 1821])).
% 0.78/0.99 tff(1829,plain,
% 0.78/0.99 (~c0_1(a1315)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1062, 1828])).
% 0.78/0.99 tff(1830,plain,
% 0.78/0.99 (hskp8 | hskp7),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1257, 384, 1545, 1544, 1543, 917])).
% 0.78/0.99 tff(1831,plain,
% 0.78/0.99 (hskp8),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1830, 918])).
% 0.78/0.99 tff(1832,plain,
% 0.78/0.99 (~c3_1(a1319)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1018, 1831])).
% 0.78/0.99 tff(1833,plain,
% 0.78/0.99 (~c0_1(a1319)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1024, 1831])).
% 0.78/0.99 tff(1834,plain,
% 0.78/0.99 (c3_1(a1315)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1104, 1828])).
% 0.78/0.99 tff(1835,plain,
% 0.78/0.99 (c2_1(a1319)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1112, 1831])).
% 0.78/0.99 tff(1836,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1837,plain,
% 0.78/0.99 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1838,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1837])).
% 0.78/0.99 tff(1839,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1838, 1836])).
% 0.78/0.99 tff(1840,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1841,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 0.78/0.99 tff(1842,plain,
% 0.78/0.99 (~c2_1(a1315)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1841, 384, 1835, 1834, 1814, 1813, 1833, 1832, 1829, 1670, 395])).
% 0.78/0.99 tff(1843,plain,
% 0.78/0.99 (c3_1(a1330)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1699, 384, 1545, 1814, 1813, 1686, 1543, 1670, 1685, 1684, 556])).
% 0.78/0.99 tff(1844,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1845,plain,
% 0.78/0.99 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1846,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1845])).
% 0.78/0.99 tff(1847,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1846, 1844])).
% 0.78/0.99 tff(1848,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1849,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 0.78/0.99 tff(1850,plain,
% 0.78/0.99 (~c3_1(a1348)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1849, 384, 762, 1835, 1814, 1813, 626, 1833, 1832, 1670, 395])).
% 0.78/0.99 tff(1851,plain,
% 0.78/0.99 (c2_1(a1307)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[424, 1809])).
% 0.78/0.99 tff(1852,plain,
% 0.78/0.99 (c1_1(a1307)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[432, 1809])).
% 0.78/0.99 tff(1853,plain,
% 0.78/0.99 (c0_1(a1307)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[440, 1809])).
% 0.78/0.99 tff(1854,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1855,plain,
% 0.78/0.99 ((hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348))) <=> (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1856,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1855])).
% 0.78/0.99 tff(1857,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1856, 1854])).
% 0.78/0.99 tff(1858,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1859,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 0.78/1.00 tff(1860,plain,
% 0.78/1.00 (hskp12 | c3_1(a1348)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1859, 384, 1853, 1852, 1851, 770, 626, 1196])).
% 0.78/1.00 tff(1861,plain,
% 0.78/1.00 (hskp12),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1860, 1850])).
% 0.78/1.00 tff(1862,plain,
% 0.78/1.00 (~c0_1(a1325)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1208, 1861])).
% 0.78/1.00 tff(1863,plain,
% 0.78/1.00 (c3_1(a1325)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1216, 1861])).
% 0.78/1.00 tff(1864,plain,
% 0.78/1.00 (c1_1(a1325)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1224, 1861])).
% 0.78/1.00 tff(1865,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1866,plain,
% 0.78/1.00 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1867,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1866])).
% 0.78/1.00 tff(1868,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1867, 1865])).
% 0.78/1.00 tff(1869,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1870,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1330) | c0_1(a1325) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.78/1.00 tff(1871,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1870, 384, 1545, 1864, 1863, 1834, 1544, 1862, 1829, 35, 1843, 1842])).
% 0.78/1.00 tff(1872,plain,(hskp7 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(1873,plain,
% 0.78/1.00 (hskp7),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1872, 24, 385, 23])).
% 0.78/1.00 tff(1874,plain,
% 0.78/1.00 (~c3_1(a1316)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[281, 1873])).
% 0.78/1.00 tff(1875,plain,
% 0.78/1.00 (~c2_1(a1316)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[275, 1873])).
% 0.78/1.00 tff(1876,plain,
% 0.78/1.00 (~c0_1(a1316)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1302, 1873])).
% 0.78/1.00 tff(1877,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1878,plain,
% 0.78/1.00 ((hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1879,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1878])).
% 0.78/1.00 tff(1880,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1879, 1877])).
% 0.78/1.00 tff(1881,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1882,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 0.78/1.00 tff(1883,plain,
% 0.78/1.00 (hskp17),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1882, 384, 1634, 1649, 1635, 441, 433, 425, 992])).
% 0.78/1.00 tff(1884,plain,
% 0.78/1.00 (~c0_1(a1334)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[783, 1883])).
% 0.78/1.00 tff(1885,plain,
% 0.78/1.00 (c3_1(a1334)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[792, 1883])).
% 0.78/1.00 tff(1886,plain,
% 0.78/1.00 (c2_1(a1334)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[800, 1883])).
% 0.78/1.00 tff(1887,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1888,plain,
% 0.78/1.00 ((hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1889,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1888])).
% 0.78/1.00 tff(1890,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1889, 1887])).
% 0.78/1.00 tff(1891,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1892,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.78/1.00 tff(1893,plain,
% 0.78/1.00 (hskp8),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1892, 384, 1886, 1885, 1884, 1304, 284, 283, 973])).
% 0.78/1.00 tff(1894,plain,
% 0.78/1.00 (~c3_1(a1319)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1018, 1893])).
% 0.78/1.00 tff(1895,plain,
% 0.78/1.00 (~c0_1(a1319)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1024, 1893])).
% 0.78/1.00 tff(1896,plain,
% 0.78/1.00 (c2_1(a1319)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1112, 1893])).
% 0.78/1.00 tff(1897,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1898,plain,
% 0.78/1.00 (((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1899,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1898])).
% 0.78/1.00 tff(1900,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1899, 1897])).
% 0.78/1.00 tff(1901,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c3_1(a1338)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1902,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c0_1(a1338)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.78/1.00 tff(1903,plain,
% 0.78/1.00 (~c0_1(a1338)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1902, 384, 1634, 1635, 1886, 1885, 1896, 1884, 1895, 1894, 10])).
% 0.78/1.00 tff(1904,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1905,plain,
% 0.78/1.00 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1906,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1905])).
% 0.78/1.00 tff(1907,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1906, 1904])).
% 0.78/1.00 tff(1908,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1909,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1319))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 0.78/1.00 tff(1910,plain,
% 0.78/1.00 (~c3_1(a1307)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1909, 384, 441, 433, 1886, 1885, 1896, 1884, 1895, 1894, 10])).
% 0.78/1.00 tff(1911,plain,
% 0.78/1.00 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1912,plain,
% 0.78/1.00 ((hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307))) <=> (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1913,plain,
% 0.78/1.00 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307)))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1912])).
% 0.78/1.00 tff(1914,plain,
% 0.78/1.00 (((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))) <=> ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1913, 1911])).
% 0.78/1.00 tff(1915,plain,
% 0.78/1.00 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp30 | (~ndr1_0) | c3_1(a1307) | (~c2_1(a1307)) | (~c0_1(a1307)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1916,plain,
% 0.78/1.00 ((~![U: $i] : (hskp18 | hskp30 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp30 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 0.78/1.00 tff(1917,plain,
% 0.78/1.00 (hskp30 | c3_1(a1307)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1916, 706, 384, 441, 425, 1744])).
% 0.78/1.00 tff(1918,plain,
% 0.78/1.00 (hskp30),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1917, 1910])).
% 0.78/1.00 tff(1919,plain,
% 0.78/1.00 (c3_1(a1372)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1758, 1918])).
% 0.78/1.00 tff(1920,plain,
% 0.78/1.00 (c1_1(a1372)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1766, 1918])).
% 0.78/1.00 tff(1921,plain,
% 0.78/1.00 (c0_1(a1372)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1774, 1918])).
% 0.78/1.00 tff(1922,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1923,plain,
% 0.78/1.00 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1924,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[1923])).
% 0.78/1.00 tff(1925,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[1924, 1922])).
% 0.78/1.00 tff(1926,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(1927,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 0.78/1.00 tff(1928,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1927, 384, 1921, 1920, 1919, 1649, 1635, 1896, 1895, 1894, 10, 1903])).
% 0.78/1.00 tff(1929,plain,((~hskp27) | (~c2_1(a1338)) | (~c3_1(a1338)) | hskp18 | (~c1_1(a1338)) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(1930,plain,
% 0.78/1.00 (~hskp27),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1929, 1548, 1549, 416, 1547, 1876, 1875, 1874])).
% 0.78/1.00 tff(1931,plain,
% 0.78/1.00 (^[U: $i] : refl((hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.78/1.00 inference(bind,[status(th)],[])).
% 0.78/1.00 tff(1932,plain,
% 0.78/1.00 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.00 inference(quant_intro,[status(thm)],[1931])).
% 0.78/1.00 tff(1933,plain,
% 0.78/1.00 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(1934,plain,
% 0.78/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(1935,plain,
% 0.78/1.01 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[1934])).
% 0.78/1.01 tff(1936,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.78/1.01 tff(1937,plain,
% 0.78/1.01 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.78/1.01 tff(1938,plain,
% 0.78/1.01 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1937, 1933])).
% 0.78/1.01 tff(1939,plain,(
% 0.78/1.01 ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.01 inference(skolemize,[status(sab)],[1938])).
% 0.78/1.01 tff(1940,plain,
% 0.78/1.01 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1939, 1932])).
% 0.78/1.01 tff(1941,plain,
% 0.78/1.01 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1942,plain,
% 0.78/1.01 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339)) <=> (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1943,plain,
% 0.78/1.01 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1942])).
% 0.78/1.01 tff(1944,plain,
% 0.78/1.01 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1943, 1941])).
% 0.78/1.01 tff(1945,plain,
% 0.78/1.01 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | c0_1(a1339))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1946,plain,
% 0.78/1.01 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 0.78/1.01 tff(1947,plain,
% 0.78/1.01 (hskp27 | hskp1 | c1_1(a1339) | c0_1(a1339)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1946, 384, 23, 1940])).
% 0.78/1.01 tff(1948,plain,
% 0.78/1.01 (hskp1),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1947, 1930, 385, 24])).
% 0.78/1.01 tff(1949,plain,
% 0.78/1.01 (~c2_1(a1308)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[895, 1948])).
% 0.78/1.01 tff(1950,plain,
% 0.78/1.01 (~c1_1(a1308)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[344, 1948])).
% 0.78/1.01 tff(1951,plain,
% 0.78/1.01 (c3_1(a1308)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[352, 1948])).
% 0.78/1.01 tff(1952,plain,
% 0.78/1.01 (~hskp3),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1808, 1951, 1543, 416, 1545, 1544, 1930, 1950, 1949])).
% 0.78/1.01 tff(1953,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1954,plain,
% 0.78/1.01 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1955,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1954])).
% 0.78/1.01 tff(1956,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1955, 1953])).
% 0.78/1.01 tff(1957,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1958,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a1348) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 0.78/1.01 tff(1959,plain,
% 0.78/1.01 (hskp6),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1958, 384, 770, 762, 626, 1304, 284, 283, 1049])).
% 0.78/1.01 tff(1960,plain,
% 0.78/1.01 (~c0_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1062, 1959])).
% 0.78/1.01 tff(1961,plain,
% 0.78/1.01 (c3_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1104, 1959])).
% 0.78/1.01 tff(1962,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1963,plain,
% 0.78/1.01 ((hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1964,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1963])).
% 0.78/1.01 tff(1965,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1964, 1962])).
% 0.78/1.01 tff(1966,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1967,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 0.78/1.01 tff(1968,plain,
% 0.78/1.01 (hskp8 | (~c2_1(a1315))),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1967, 384, 1961, 1304, 284, 283, 1960, 973])).
% 0.78/1.01 tff(1969,plain,
% 0.78/1.01 (~c2_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1968, 933])).
% 0.78/1.01 tff(1970,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1971,plain,
% 0.78/1.01 (((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316))) <=> (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1972,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1971])).
% 0.78/1.01 tff(1973,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1972, 1970])).
% 0.78/1.01 tff(1974,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1316) | c2_1(a1316) | (~c1_1(a1316)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1975,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1316))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 0.78/1.01 tff(1976,plain,
% 0.78/1.01 (~c1_1(a1316)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1975, 384, 1961, 1304, 284, 283, 1960, 302, 1969])).
% 0.78/1.01 tff(1977,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1978,plain,
% 0.78/1.01 ((hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1979,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316)))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1978])).
% 0.78/1.01 tff(1980,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1979, 1977])).
% 0.78/1.01 tff(1981,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1982,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a1330) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | c1_1(a1316)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.78/1.01 tff(1983,plain,
% 0.78/1.01 (~c3_1(a1330)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1982, 384, 1550, 1616, 1613, 1304, 283, 578, 1976])).
% 0.78/1.01 tff(1984,plain,
% 0.78/1.01 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(1985,plain,
% 0.78/1.01 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[1984])).
% 0.78/1.01 tff(1986,plain,
% 0.78/1.01 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1987,plain,
% 0.78/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(1988,plain,
% 0.78/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[1987])).
% 0.78/1.01 tff(1989,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.78/1.01 tff(1990,plain,
% 0.78/1.01 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 0.78/1.01 tff(1991,plain,
% 0.78/1.01 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1990, 1986])).
% 0.78/1.01 tff(1992,plain,(
% 0.78/1.01 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(skolemize,[status(sab)],[1991])).
% 0.78/1.01 tff(1993,plain,
% 0.78/1.01 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1992, 1985])).
% 0.78/1.01 tff(1994,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1995,plain,
% 0.78/1.01 ((hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(1996,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[1995])).
% 0.78/1.01 tff(1997,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.78/1.01 tff(1998,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(1999,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1330) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.78/1.01 tff(2000,plain,
% 0.78/1.01 (hskp9 | c3_1(a1330)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1999, 384, 1616, 1613, 1304, 284, 283, 1993])).
% 0.78/1.01 tff(2001,plain,
% 0.78/1.01 (hskp9),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[2000, 1983])).
% 0.78/1.01 tff(2002,plain,
% 0.78/1.01 (~c0_1(a1320)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1402, 2001])).
% 0.78/1.01 tff(2003,plain,
% 0.78/1.01 (c2_1(a1320)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1410, 2001])).
% 0.78/1.01 tff(2004,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(2005,plain,
% 0.78/1.01 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(2006,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[2005])).
% 0.78/1.01 tff(2007,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[2006, 2004])).
% 0.78/1.01 tff(2008,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(2009,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1320) | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 0.78/1.01 tff(2010,plain,
% 0.78/1.01 (~c3_1(a1320)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[2009, 384, 933, 2003, 2002, 1304, 284, 283, 973])).
% 0.78/1.01 tff(2011,plain,
% 0.78/1.01 (~c1_1(a1320)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1396, 2001])).
% 0.78/1.01 tff(2012,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(2013,plain,
% 0.78/1.01 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316)) <=> (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(2014,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320)))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[2013])).
% 0.78/1.01 tff(2015,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.78/1.01 inference(transitivity,[status(thm)],[2014, 2012])).
% 0.78/1.01 tff(2016,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(2017,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | (~c2_1(a1320)) | c3_1(a1320)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.78/1.01 tff(2018,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[2017, 384, 2003, 2002, 2011, 1304, 283, 1285, 1976, 2010])).
% 0.78/1.01 tff(2019,plain,(hskp8 | c0_1(a1316) | c3_1(a1316) | c2_1(a1316) | (~c0_1(a1330)) | c2_1(a1330) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(2020,plain,
% 0.78/1.01 (hskp8),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[2019, 1876, 1874, 1875, 1545, 1543, 1952])).
% 0.78/1.01 tff(2021,plain,
% 0.78/1.01 (~c3_1(a1319)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1018, 2020])).
% 0.78/1.01 tff(2022,plain,
% 0.78/1.01 (~c0_1(a1319)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1024, 2020])).
% 0.78/1.01 tff(2023,plain,
% 0.78/1.01 (c2_1(a1319)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1112, 2020])).
% 0.78/1.01 tff(2024,plain,
% 0.78/1.01 (hskp6),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1958, 384, 770, 762, 626, 1876, 1875, 1874, 1049])).
% 0.78/1.01 tff(2025,plain,
% 0.78/1.01 (~c0_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1062, 2024])).
% 0.78/1.01 tff(2026,plain,
% 0.78/1.01 (~c1_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1134, 2024])).
% 0.78/1.01 tff(2027,plain,
% 0.78/1.01 (c3_1(a1315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[1104, 2024])).
% 0.78/1.01 tff(2028,assumption,(~c0_1(a1315)), introduced(assumption)).
% 0.78/1.01 tff(2029,assumption,(c3_1(a1315)), introduced(assumption)).
% 0.78/1.01 tff(2030,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2031,plain,
% 0.78/1.02 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2032,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2031])).
% 0.78/1.02 tff(2033,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2032, 2030])).
% 0.78/1.02 tff(2034,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2035,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 0.78/1.02 tff(2036,plain,
% 0.78/1.02 (c2_1(a1315)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2035, 384, 1634, 1635, 1576, 1575, 2029, 109, 2028, 35, 1636])).
% 0.78/1.02 tff(2037,assumption,(~c3_1(a1319)), introduced(assumption)).
% 0.78/1.02 tff(2038,assumption,(~c0_1(a1319)), introduced(assumption)).
% 0.78/1.02 tff(2039,assumption,(c2_1(a1319)), introduced(assumption)).
% 0.78/1.02 tff(2040,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2041,plain,
% 0.78/1.02 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2042,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2041])).
% 0.78/1.02 tff(2043,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2042, 2040])).
% 0.78/1.02 tff(2044,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2045,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 0.78/1.02 tff(2046,plain,
% 0.78/1.02 (~c2_1(a1324)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2045, 384, 1649, 1635, 1576, 2039, 109, 2038, 2037, 395, 1636])).
% 0.78/1.02 tff(2047,assumption,(~c1_1(a1315)), introduced(assumption)).
% 0.78/1.02 tff(2048,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2049,plain,
% 0.78/1.02 ((hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2050,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2049])).
% 0.78/1.02 tff(2051,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2050, 2048])).
% 0.78/1.02 tff(2052,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2053,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 0.78/1.02 tff(2054,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2053, 384, 22, 1576, 1575, 2029, 2047, 1710, 2046, 2036])).
% 0.78/1.02 tff(2055,plain,(c0_1(a1338) | hskp27 | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1315)) | c1_1(a1315) | (~c1_1(a1338)) | (~c3_1(a1338)) | c1_1(a1324) | c0_1(a1315) | (~c2_1(a1338)) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(2056,plain,
% 0.78/1.02 (c0_1(a1338)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2055, 1930, 1464, 1463, 2027, 2026, 1547, 1549, 1367, 2025, 1548, 2023, 2022, 2021])).
% 0.78/1.02 tff(2057,plain,
% 0.78/1.02 (hskp17 | (~c0_1(a1338))),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1655, 384, 1547, 1548, 1549, 992])).
% 0.78/1.02 tff(2058,plain,
% 0.78/1.02 (hskp17),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2057, 2056])).
% 0.78/1.02 tff(2059,plain,
% 0.78/1.02 (~c0_1(a1334)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[783, 2058])).
% 0.78/1.02 tff(2060,plain,
% 0.78/1.02 (c3_1(a1334)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[792, 2058])).
% 0.78/1.02 tff(2061,plain,
% 0.78/1.02 (c2_1(a1334)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[800, 2058])).
% 0.78/1.02 tff(2062,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1902, 384, 1547, 1549, 2061, 2060, 2023, 2059, 2022, 2021, 10, 2056])).
% 0.78/1.02 tff(2063,plain,(c0_1(a1339) | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(2064,plain,
% 0.78/1.02 (c0_1(a1339)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2063, 385, 23])).
% 0.78/1.02 tff(2065,plain,
% 0.78/1.02 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2066,plain,
% 0.78/1.02 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2067,plain,
% 0.78/1.02 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2066])).
% 0.78/1.02 tff(2068,plain,
% 0.78/1.02 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2067, 2065])).
% 0.78/1.02 tff(2069,plain,
% 0.78/1.02 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2070,plain,
% 0.78/1.02 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 0.78/1.02 tff(2071,plain,
% 0.78/1.02 (hskp8 | hskp7 | c1_1(a1339) | (~c0_1(a1339))),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2070, 384, 23, 917])).
% 0.78/1.02 tff(2072,plain,
% 0.78/1.02 (hskp8),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2071, 918, 385, 2064])).
% 0.78/1.02 tff(2073,plain,
% 0.78/1.02 (~c3_1(a1319)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1018, 2072])).
% 0.78/1.02 tff(2074,plain,
% 0.78/1.02 (~c0_1(a1319)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1024, 2072])).
% 0.78/1.02 tff(2075,plain,
% 0.78/1.02 (c2_1(a1319)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1112, 2072])).
% 0.78/1.02 tff(2076,plain,
% 0.78/1.02 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2077,plain,
% 0.78/1.02 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2078,plain,
% 0.78/1.02 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2077])).
% 0.78/1.02 tff(2079,plain,
% 0.78/1.02 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2078, 2076])).
% 0.78/1.02 tff(2080,plain,
% 0.78/1.02 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2081,plain,
% 0.78/1.02 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 0.78/1.02 tff(2082,plain,
% 0.78/1.02 (hskp18 | hskp29 | c1_1(a1339) | (~c0_1(a1339))),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2081, 384, 23, 21])).
% 0.78/1.02 tff(2083,plain,
% 0.78/1.02 (hskp29),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2082, 2064, 385, 416])).
% 0.78/1.02 tff(2084,plain,
% 0.78/1.02 (c2_1(a1338)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[487, 2083])).
% 0.78/1.02 tff(2085,plain,
% 0.78/1.02 (c3_1(a1338)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[479, 2083])).
% 0.78/1.02 tff(2086,plain,
% 0.78/1.02 (c1_1(a1338)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[495, 2083])).
% 0.78/1.02 tff(2087,plain,
% 0.78/1.02 (~c0_1(a1338)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1902, 384, 2086, 2085, 1782, 1781, 2075, 1779, 2074, 2073, 10])).
% 0.78/1.02 tff(2088,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2089,plain,
% 0.78/1.02 ((hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319))) <=> (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2090,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2089])).
% 0.78/1.02 tff(2091,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2090, 2088])).
% 0.78/1.02 tff(2092,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1319) | c3_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2093,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1319))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 0.78/1.02 tff(2094,plain,
% 0.78/1.02 (hskp4),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2093, 384, 2086, 2085, 2075, 2074, 2073, 928, 2087])).
% 0.78/1.02 tff(2095,plain,
% 0.78/1.02 (~c1_1(a1312)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[686, 2094])).
% 0.78/1.02 tff(2096,plain,
% 0.78/1.02 (c0_1(a1312)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[694, 2094])).
% 0.78/1.02 tff(2097,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2098,plain,
% 0.78/1.02 (((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2099,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2098])).
% 0.78/1.02 tff(2100,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2099, 2097])).
% 0.78/1.02 tff(2101,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1312) | (~c2_1(a1312)) | (~c0_1(a1312)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2102,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | c1_1(a1312) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1312)) | (~c0_1(a1312)) | (~c2_1(a1319))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 0.78/1.02 tff(2103,plain,
% 0.78/1.02 (~c2_1(a1312)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2102, 384, 1782, 1781, 2075, 2096, 1779, 2074, 2073, 2095, 395])).
% 0.78/1.02 tff(2104,plain,
% 0.78/1.02 (~c3_1(a1312)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1078, 2094])).
% 0.78/1.02 tff(2105,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2106,plain,
% 0.78/1.02 ((hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2107,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2106])).
% 0.78/1.02 tff(2108,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2107, 2105])).
% 0.78/1.02 tff(2109,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2110,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1312))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 0.78/1.02 tff(2111,plain,
% 0.78/1.02 (hskp15),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2110, 384, 385, 2096, 2064, 23, 2095, 2104, 1601])).
% 0.78/1.02 tff(2112,plain,
% 0.78/1.02 (~c3_1(a1331)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1161, 2111])).
% 0.78/1.02 tff(2113,plain,
% 0.78/1.02 (c1_1(a1331)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1178, 2111])).
% 0.78/1.02 tff(2114,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2115,plain,
% 0.78/1.02 ((hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312))) <=> (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2116,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2115])).
% 0.78/1.02 tff(2117,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2116, 2114])).
% 0.78/1.02 tff(2118,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1331) | (~c1_1(a1331)) | (~c0_1(a1331)) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2119,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1331) | c3_1(a1312) | (~ndr1_0) | (~c0_1(a1331)) | (~c1_1(a1331)) | c2_1(a1312) | (~c0_1(a1312))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 0.78/1.02 tff(2120,plain,
% 0.78/1.02 (~c0_1(a1331)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2119, 384, 22, 2113, 2096, 2112, 2104, 533, 2103])).
% 0.78/1.02 tff(2121,assumption,(~c2_1(a1312)), introduced(assumption)).
% 0.78/1.02 tff(2122,assumption,(~c3_1(a1312)), introduced(assumption)).
% 0.78/1.02 tff(2123,assumption,(hskp22), introduced(assumption)).
% 0.78/1.02 tff(2124,plain,
% 0.78/1.02 (~c3_1(a1356)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[538, 2123])).
% 0.78/1.02 tff(2125,assumption,(c1_1(a1331)), introduced(assumption)).
% 0.78/1.02 tff(2126,plain,
% 0.78/1.02 (c1_1(a1356)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[510, 2123])).
% 0.78/1.02 tff(2127,plain,
% 0.78/1.02 (c0_1(a1356)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[518, 2123])).
% 0.78/1.02 tff(2128,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2129,plain,
% 0.78/1.02 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312)) <=> (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(2130,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[2129])).
% 0.78/1.02 tff(2131,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[2130, 2128])).
% 0.78/1.02 tff(2132,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c0_1(a1331) | c3_1(a1331) | (~c1_1(a1331)) | c3_1(a1312) | c1_1(a1312) | c2_1(a1312))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(2133,plain,
% 0.78/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1356) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | (~ndr1_0) | c0_1(a1331) | (~c1_1(a1331)) | c2_1(a1312) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 0.78/1.02 tff(2134,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2133, 384, 2127, 2126, 2125, 2124, 1777, 738, 2122, 405, 1776, 2121])).
% 0.78/1.02 tff(2135,plain,((~hskp22) | (~c1_1(a1331)) | c3_1(a1331) | c1_1(a1312) | c3_1(a1312) | c0_1(a1331) | c2_1(a1312)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(2136,plain,
% 0.78/1.02 (~hskp22),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2135, 2113, 2112, 2095, 2104, 2120, 2103])).
% 0.78/1.02 tff(2137,plain,
% 0.78/1.02 (hskp22 | hskp11),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[502, 384, 2086, 2084, 2085, 415])).
% 0.78/1.02 tff(2138,plain,
% 0.78/1.02 (hskp11),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[2137, 2136])).
% 0.78/1.02 tff(2139,plain,
% 0.78/1.02 (~c1_1(a1324)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[91, 2138])).
% 0.78/1.02 tff(2140,plain,
% 0.78/1.02 (c0_1(a1324)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[99, 2138])).
% 0.78/1.02 tff(2141,plain,
% 0.78/1.02 (c2_1(a1331)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[1170, 2111])).
% 0.78/1.02 tff(2142,plain,
% 0.78/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2143,plain,
% 0.78/1.03 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2144,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2143])).
% 0.78/1.03 tff(2145,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2144, 2142])).
% 0.78/1.03 tff(2146,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2147,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | c1_1(a1324) | (~ndr1_0) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 0.78/1.03 tff(2148,plain,
% 0.78/1.03 (~c2_1(a1324)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2147, 384, 1782, 1781, 2141, 2140, 1779, 2112, 2139, 395, 2120])).
% 0.78/1.03 tff(2149,plain,
% 0.78/1.03 (hskp15 | hskp14),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1155, 384, 2039, 2038, 2037, 907])).
% 0.78/1.03 tff(2150,plain,
% 0.78/1.03 (hskp15),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2149, 637])).
% 0.78/1.03 tff(2151,plain,
% 0.78/1.03 (~c3_1(a1331)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1161, 2150])).
% 0.78/1.03 tff(2152,plain,
% 0.78/1.03 (c2_1(a1331)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1170, 2150])).
% 0.78/1.03 tff(2153,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2154,plain,
% 0.78/1.03 ((hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339))) <=> (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2155,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2154])).
% 0.78/1.03 tff(2156,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2155, 2153])).
% 0.78/1.03 tff(2157,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1331) | (~c2_1(a1331)) | (~c0_1(a1331)) | c2_1(a1339) | c1_1(a1339) | (~c0_1(a1339)))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2158,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1339) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1331)) | (~c2_1(a1331))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 0.78/1.03 tff(2159,plain,
% 0.78/1.03 (~c0_1(a1331)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2158, 384, 637, 385, 2152, 2064, 23, 2151, 828])).
% 0.78/1.03 tff(2160,plain,
% 0.78/1.03 (hskp17),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1882, 384, 2086, 2084, 2085, 932, 931, 930, 992])).
% 0.78/1.03 tff(2161,plain,
% 0.78/1.03 (~c0_1(a1334)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[783, 2160])).
% 0.78/1.03 tff(2162,plain,
% 0.78/1.03 (c3_1(a1334)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[792, 2160])).
% 0.78/1.03 tff(2163,plain,
% 0.78/1.03 (c2_1(a1334)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[800, 2160])).
% 0.78/1.03 tff(2164,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2165,plain,
% 0.78/1.03 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331))) <=> (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2166,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2165])).
% 0.78/1.03 tff(2167,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2166, 2164])).
% 0.78/1.03 tff(2168,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1331) | c0_1(a1331) | (~c2_1(a1331)))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2169,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c3_1(a1331) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1331)) | c0_1(a1331) | (~c2_1(a1334)) | (~c3_1(a1334))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 0.78/1.03 tff(2170,plain,
% 0.78/1.03 (~c3_1(a1307)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2169, 384, 932, 931, 2163, 2162, 2152, 2161, 2151, 10, 2159])).
% 0.78/1.03 tff(2171,plain,
% 0.78/1.03 (hskp30 | c3_1(a1307)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1916, 416, 384, 932, 930, 1744])).
% 0.78/1.03 tff(2172,plain,
% 0.78/1.03 (hskp30),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2171, 2170])).
% 0.78/1.03 tff(2173,plain,
% 0.78/1.03 (c0_1(a1372)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1774, 2172])).
% 0.78/1.03 tff(2174,plain,
% 0.78/1.03 (c1_1(a1372)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1766, 2172])).
% 0.78/1.03 tff(2175,plain,
% 0.78/1.03 (c3_1(a1372)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1758, 2172])).
% 0.78/1.03 tff(2176,plain,
% 0.78/1.03 ($false),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1793, 2175, 2174, 2160, 2159, 2152, 2151, 2173])).
% 0.78/1.03 tff(2177,plain,(hskp14 | c1_1(a1339) | c2_1(a1339) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.03 tff(2178,plain,
% 0.78/1.03 (hskp14),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2177, 2075, 23, 385, 2074, 2073])).
% 0.78/1.03 tff(2179,plain,
% 0.78/1.03 (~c2_1(a1330)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[199, 2178])).
% 0.78/1.03 tff(2180,plain,
% 0.78/1.03 (~c1_1(a1330)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[205, 2178])).
% 0.78/1.03 tff(2181,plain,
% 0.78/1.03 (c0_1(a1330)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[220, 2178])).
% 0.78/1.03 tff(2182,plain,
% 0.78/1.03 (c3_1(a1324)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[107, 2138])).
% 0.78/1.03 tff(2183,plain,
% 0.78/1.03 (hskp3),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1668, 2140, 2085, 2084, 918, 2182, 2139, 2181, 2180, 2179, 2086])).
% 0.78/1.03 tff(2184,plain,
% 0.78/1.03 (~c1_1(a1311)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[591, 2183])).
% 0.78/1.03 tff(2185,plain,
% 0.78/1.03 (c2_1(a1311)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[599, 2183])).
% 0.78/1.03 tff(2186,plain,
% 0.78/1.03 (c0_1(a1311)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[607, 2183])).
% 0.78/1.03 tff(2187,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2188,plain,
% 0.78/1.03 (((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2189,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2188])).
% 0.78/1.03 tff(2190,plain,
% 0.78/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2189, 2187])).
% 0.78/1.03 tff(2191,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1312) | c3_1(a1312) | (~c0_1(a1312)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2192,plain,
% 0.78/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | c3_1(a1312) | c1_1(a1311) | (~ndr1_0) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1312) | (~c0_1(a1312)) | c2_1(a1324) | (~c3_1(a1324))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 0.78/1.03 tff(2193,plain,
% 0.78/1.03 ($false),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2192, 384, 2182, 2096, 2186, 2185, 2139, 2104, 2184, 556, 2103, 2148])).
% 0.78/1.03 tff(2194,plain,((~hskp17) | hskp7 | hskp27 | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.03 tff(2195,plain,
% 0.78/1.03 (~hskp17),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2194, 22, 918, 385, 23])).
% 0.78/1.03 tff(2196,plain,
% 0.78/1.03 (hskp16),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[777, 2195])).
% 0.78/1.03 tff(2197,plain,
% 0.78/1.03 (~c3_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[843, 2196])).
% 0.78/1.03 tff(2198,plain,
% 0.78/1.03 (~c2_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[880, 2196])).
% 0.78/1.03 tff(2199,plain,
% 0.78/1.03 (c1_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[867, 2196])).
% 0.78/1.03 tff(2200,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2201,plain,
% 0.78/1.03 ((hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333))) <=> (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2202,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2201])).
% 0.78/1.03 tff(2203,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2202, 2200])).
% 0.78/1.03 tff(2204,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1333) | (~c1_1(a1333)) | (~c0_1(a1333)) | c2_1(a1333) | c3_1(a1333) | (~c0_1(a1333)))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2205,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | (~c0_1(a1333)) | (~c1_1(a1333))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 0.78/1.03 tff(2206,plain,
% 0.78/1.03 (~c0_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2205, 384, 22, 2199, 2198, 2197, 533])).
% 0.78/1.03 tff(2207,plain,
% 0.78/1.03 (hskp17 | (~c0_1(a1338))),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1655, 384, 2086, 2084, 2085, 992])).
% 0.78/1.03 tff(2208,plain,
% 0.78/1.03 (~c0_1(a1338)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2207, 2195])).
% 0.78/1.03 tff(2209,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2210,plain,
% 0.78/1.03 ((hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333)) <=> (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.03 inference(rewrite,[status(thm)],[])).
% 0.78/1.03 tff(2211,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338))))),
% 0.78/1.03 inference(monotonicity,[status(thm)],[2210])).
% 0.78/1.03 tff(2212,plain,
% 0.78/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)))),
% 0.78/1.03 inference(transitivity,[status(thm)],[2211, 2209])).
% 0.78/1.03 tff(2213,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338)) | c2_1(a1333) | c0_1(a1333) | c3_1(a1333))),
% 0.78/1.03 inference(quant_inst,[status(thm)],[])).
% 0.78/1.03 tff(2214,plain,
% 0.78/1.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1333) | c3_1(a1333) | (~ndr1_0) | c0_1(a1333) | c0_1(a1338) | (~c1_1(a1338)) | (~c2_1(a1338))),
% 0.78/1.03 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 0.78/1.03 tff(2215,plain,
% 0.78/1.03 (hskp6),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2214, 384, 2086, 2084, 2198, 2197, 1049, 2208, 2206])).
% 0.78/1.03 tff(2216,plain,
% 0.78/1.03 (~c0_1(a1315)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1062, 2215])).
% 0.78/1.03 tff(2217,assumption,(~hskp17), introduced(assumption)).
% 0.78/1.03 tff(2218,plain,
% 0.78/1.03 (hskp16),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[777, 2217])).
% 0.78/1.03 tff(2219,plain,
% 0.78/1.03 (~c3_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[843, 2218])).
% 0.78/1.03 tff(2220,plain,
% 0.78/1.03 (~c2_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[880, 2218])).
% 0.78/1.03 tff(2221,plain,
% 0.78/1.03 (c1_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[867, 2218])).
% 0.78/1.03 tff(2222,plain,
% 0.78/1.03 (~c0_1(a1333)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[2205, 384, 22, 2221, 2220, 2219, 533])).
% 0.78/1.03 tff(2223,plain,
% 0.78/1.03 (hskp6),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1431, 384, 770, 762, 626, 2220, 2219, 1049, 2222])).
% 0.78/1.03 tff(2224,plain,
% 0.78/1.03 (~c0_1(a1315)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1062, 2223])).
% 0.78/1.03 tff(2225,plain,
% 0.78/1.03 (~c1_1(a1315)),
% 0.78/1.03 inference(unit_resolution,[status(thm)],[1134, 2223])).
% 0.78/1.03 tff(2226,plain,
% 0.78/1.03 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2227,plain,
% 0.87/1.03 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315)) <=> (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2228,plain,
% 0.87/1.03 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315)))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2227])).
% 0.87/1.03 tff(2229,plain,
% 0.87/1.03 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2228, 2226])).
% 0.87/1.03 tff(2230,plain,
% 0.87/1.03 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1315) | c1_1(a1315) | c0_1(a1315))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2231,plain,
% 0.87/1.03 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | c2_1(a1315)),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 0.87/1.03 tff(2232,plain,
% 0.87/1.03 (c2_1(a1315)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2231, 384, 22, 648, 2224, 2225, 1940])).
% 0.87/1.03 tff(2233,plain,
% 0.87/1.03 (c3_1(a1315)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1104, 2223])).
% 0.87/1.03 tff(2234,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2235,plain,
% 0.87/1.03 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2236,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2235])).
% 0.87/1.03 tff(2237,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2236, 2234])).
% 0.87/1.03 tff(2238,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2239,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1315) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.87/1.03 tff(2240,plain,
% 0.87/1.03 (~c3_1(a1339)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2239, 384, 22, 2233, 2064, 23, 2225, 1710, 2232])).
% 0.87/1.03 tff(2241,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2242,plain,
% 0.87/1.03 ((hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339)) <=> (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2243,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2242])).
% 0.87/1.03 tff(2244,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2243, 2241])).
% 0.87/1.03 tff(2245,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)) | c2_1(a1339) | c1_1(a1339) | c3_1(a1339))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2246,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp11 | c1_1(a1339) | c2_1(a1339) | c2_1(a1333) | (~ndr1_0) | c3_1(a1339) | c0_1(a1333) | (~c1_1(a1333))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 0.87/1.03 tff(2247,plain,
% 0.87/1.03 (hskp11 | c3_1(a1339)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2246, 384, 385, 2221, 23, 2220, 57, 2222])).
% 0.87/1.03 tff(2248,plain,
% 0.87/1.03 (hskp11),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2247, 2240])).
% 0.87/1.03 tff(2249,plain,
% 0.87/1.03 (~c1_1(a1324)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[91, 2248])).
% 0.87/1.03 tff(2250,plain,
% 0.87/1.03 (~c0_1(a1338)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2207, 2217])).
% 0.87/1.04 tff(2251,plain,
% 0.87/1.04 (c0_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[99, 2248])).
% 0.87/1.04 tff(2252,plain,
% 0.87/1.04 (c3_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[107, 2248])).
% 0.87/1.04 tff(2253,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2055, 2252, 2251, 2037, 2250, 2233, 2225, 2086, 2085, 2249, 2224, 2084, 2039, 2038, 22])).
% 0.87/1.04 tff(2254,plain,(hskp17 | c3_1(a1319) | (~c2_1(a1319)) | c0_1(a1319) | hskp27 | c1_1(a1339) | c2_1(a1339) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2255,plain,
% 0.87/1.04 (hskp1),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2254, 2195, 2075, 2074, 22, 385, 23, 2073])).
% 0.87/1.04 tff(2256,plain,
% 0.87/1.04 (~c2_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[895, 2255])).
% 0.87/1.04 tff(2257,plain,
% 0.87/1.04 (c3_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[352, 2255])).
% 0.87/1.04 tff(2258,plain,
% 0.87/1.04 (~c1_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[344, 2255])).
% 0.87/1.04 tff(2259,plain,
% 0.87/1.04 (~hskp3),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1808, 2258, 2179, 416, 2181, 2180, 22, 2257, 2256])).
% 0.87/1.04 tff(2260,plain,
% 0.87/1.04 (hskp21),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1561, 2259, 918])).
% 0.87/1.04 tff(2261,plain,
% 0.87/1.04 (~c2_1(a1352)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1567, 2260])).
% 0.87/1.04 tff(2262,plain,
% 0.87/1.04 (~c0_1(a1352)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1573, 2260])).
% 0.87/1.04 tff(2263,plain,
% 0.87/1.04 (c3_1(a1352)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1583, 2260])).
% 0.87/1.04 tff(2264,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2265,plain,
% 0.87/1.04 (((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352))) <=> (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2266,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2265])).
% 0.87/1.04 tff(2267,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2266, 2264])).
% 0.87/1.04 tff(2268,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1338) | (~c1_1(a1338)) | (~c3_1(a1338)) | c0_1(a1352) | c2_1(a1352) | (~c3_1(a1352)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2269,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1339) | c0_1(a1352) | c2_1(a1352) | (~c0_1(a1339)) | (~ndr1_0) | (~c3_1(a1339)) | c0_1(a1338) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1352))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 0.87/1.04 tff(2270,plain,
% 0.87/1.04 (~c3_1(a1339)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2269, 384, 2086, 2085, 2263, 385, 2262, 2261, 2064, 35, 2208])).
% 0.87/1.04 tff(2271,plain,
% 0.87/1.04 (hskp11),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2246, 384, 385, 2199, 23, 2198, 57, 2270, 2206])).
% 0.87/1.04 tff(2272,plain,
% 0.87/1.04 (~c1_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[91, 2271])).
% 0.87/1.04 tff(2273,plain,
% 0.87/1.04 (c3_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[107, 2271])).
% 0.87/1.04 tff(2274,plain,
% 0.87/1.04 (c0_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[99, 2271])).
% 0.87/1.04 tff(2275,plain,
% 0.87/1.04 (c3_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1104, 2215])).
% 0.87/1.04 tff(2276,plain,
% 0.87/1.04 (~c1_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1134, 2215])).
% 0.87/1.04 tff(2277,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2055, 2276, 2275, 2073, 2208, 2274, 2273, 2086, 2085, 2272, 2216, 2084, 2075, 2074, 22])).
% 0.87/1.04 tff(2278,plain,(hskp27 | c1_1(a1339) | c2_1(a1339) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2279,plain,
% 0.87/1.04 (hskp27),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2278, 918, 23, 385])).
% 0.87/1.04 tff(2280,plain,
% 0.87/1.04 (c2_1(a1307)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[424, 2279])).
% 0.87/1.04 tff(2281,plain,
% 0.87/1.04 (c1_1(a1307)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[432, 2279])).
% 0.87/1.04 tff(2282,plain,
% 0.87/1.04 (c0_1(a1307)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[440, 2279])).
% 0.87/1.04 tff(2283,plain,
% 0.87/1.04 (hskp17),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1882, 384, 2086, 2084, 2085, 2282, 2281, 2280, 992])).
% 0.87/1.04 tff(2284,plain,
% 0.87/1.04 (~c0_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[783, 2283])).
% 0.87/1.04 tff(2285,plain,
% 0.87/1.04 (c3_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[792, 2283])).
% 0.87/1.04 tff(2286,plain,
% 0.87/1.04 (c2_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[800, 2283])).
% 0.87/1.04 tff(2287,plain,
% 0.87/1.04 (~c0_1(a1338)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1902, 384, 2086, 2085, 2286, 2285, 2075, 2284, 2074, 2073, 10])).
% 0.87/1.04 tff(2288,plain,
% 0.87/1.04 (~c3_1(a1307)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1909, 384, 2282, 2281, 2286, 2285, 2075, 2284, 2074, 2073, 10])).
% 0.87/1.04 tff(2289,plain,
% 0.87/1.04 (hskp30 | c3_1(a1307)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1916, 416, 384, 2282, 2280, 1744])).
% 0.87/1.04 tff(2290,plain,
% 0.87/1.04 (hskp30),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2289, 2288])).
% 0.87/1.04 tff(2291,plain,
% 0.87/1.04 (c3_1(a1372)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1758, 2290])).
% 0.87/1.04 tff(2292,plain,
% 0.87/1.04 (c1_1(a1372)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1766, 2290])).
% 0.87/1.04 tff(2293,plain,
% 0.87/1.04 (c0_1(a1372)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1774, 2290])).
% 0.87/1.04 tff(2294,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1927, 384, 2293, 2292, 2291, 2084, 2085, 2075, 2074, 2073, 10, 2287])).
% 0.87/1.04 tff(2295,plain,(hskp7 | c2_1(a1339) | c1_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2296,plain,
% 0.87/1.04 (hskp7),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2295, 385, 23])).
% 0.87/1.04 tff(2297,plain,
% 0.87/1.04 (~c3_1(a1316)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[281, 2296])).
% 0.87/1.04 tff(2298,plain,
% 0.87/1.04 (~c0_1(a1316)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1302, 2296])).
% 0.87/1.04 tff(2299,plain,
% 0.87/1.04 (~c2_1(a1316)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[275, 2296])).
% 0.87/1.04 tff(2300,plain,
% 0.87/1.04 (~hskp27),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1929, 2299, 2085, 416, 2086, 2084, 2298, 2297])).
% 0.87/1.04 tff(2301,plain,
% 0.87/1.04 (~c1_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1134, 1959])).
% 0.87/1.04 tff(2302,plain,
% 0.87/1.04 (hskp1 | c2_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2231, 384, 22, 1960, 2301, 1940])).
% 0.87/1.04 tff(2303,plain,
% 0.87/1.04 (hskp1),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2302, 1969])).
% 0.87/1.04 tff(2304,plain,
% 0.87/1.04 (~c2_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[895, 2303])).
% 0.87/1.04 tff(2305,plain,
% 0.87/1.04 (hskp14),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[461, 22, 706])).
% 0.87/1.04 tff(2306,plain,
% 0.87/1.04 (c0_1(a1330)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[220, 2305])).
% 0.87/1.04 tff(2307,plain,
% 0.87/1.04 (~c2_1(a1330)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[199, 2305])).
% 0.87/1.04 tff(2308,plain,
% 0.87/1.04 (hskp3),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2019, 933, 283, 284, 1304, 2307, 2306])).
% 0.87/1.04 tff(2309,plain,
% 0.87/1.04 (~c1_1(a1330)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[205, 2305])).
% 0.87/1.04 tff(2310,plain,
% 0.87/1.04 (c3_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[352, 2303])).
% 0.87/1.04 tff(2311,plain,
% 0.87/1.04 (~c1_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[344, 2303])).
% 0.87/1.04 tff(2312,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1808, 2311, 2310, 2307, 706, 2306, 2309, 22, 2308, 2304])).
% 0.87/1.04 tff(2313,plain,(hskp8 | hskp18 | hskp27 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2314,plain,
% 0.87/1.04 (hskp8),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2313, 416, 2300, 2298, 2299, 2297])).
% 0.87/1.04 tff(2315,plain,
% 0.87/1.04 (~c0_1(a1319)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1024, 2314])).
% 0.87/1.04 tff(2316,plain,
% 0.87/1.04 (c2_1(a1319)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1112, 2314])).
% 0.87/1.04 tff(2317,plain,
% 0.87/1.04 (hskp6),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1958, 384, 770, 762, 626, 2298, 2299, 2297, 1049])).
% 0.87/1.04 tff(2318,plain,
% 0.87/1.04 (~c0_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1062, 2317])).
% 0.87/1.04 tff(2319,plain,
% 0.87/1.04 (~c3_1(a1319)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1018, 2314])).
% 0.87/1.04 tff(2320,plain,
% 0.87/1.04 (~c0_1(a1333)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2205, 384, 2300, 2221, 2220, 2219, 533])).
% 0.87/1.04 tff(2321,plain,
% 0.87/1.04 (hskp1),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2254, 2217, 2316, 2315, 2300, 385, 23, 2319])).
% 0.87/1.04 tff(2322,plain,
% 0.87/1.04 (~c2_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[895, 2321])).
% 0.87/1.04 tff(2323,plain,
% 0.87/1.04 (c3_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[352, 2321])).
% 0.87/1.04 tff(2324,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2325,plain,
% 0.87/1.04 (((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333))) <=> (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2326,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2325])).
% 0.87/1.04 tff(2327,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2326, 2324])).
% 0.87/1.04 tff(2328,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1333) | c3_1(a1333) | (~c1_1(a1333)) | c2_1(a1308) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | c2_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2329,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1333) | c3_1(a1333) | c2_1(a1308) | (~ndr1_0) | c0_1(a1308) | (~c3_1(a1308)) | c0_1(a1333) | (~c1_1(a1333))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 0.87/1.04 tff(2330,plain,
% 0.87/1.04 (c0_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2329, 384, 2221, 2323, 2220, 2219, 2322, 302, 2320])).
% 0.87/1.04 tff(2331,plain,
% 0.87/1.04 (~c1_1(a1308)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[344, 2321])).
% 0.87/1.04 tff(2332,plain,
% 0.87/1.04 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(2333,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[2332])).
% 0.87/1.04 tff(2334,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2335,plain,
% 0.87/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(2336,plain,
% 0.87/1.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[2335])).
% 0.87/1.04 tff(2337,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.87/1.04 tff(2338,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 0.87/1.04 tff(2339,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2338, 2334])).
% 0.87/1.04 tff(2340,plain,(
% 0.87/1.04 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(skolemize,[status(sab)],[2339])).
% 0.87/1.04 tff(2341,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2340, 2333])).
% 0.87/1.04 tff(2342,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2343,plain,
% 0.87/1.04 ((hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333))) <=> (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2344,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2343])).
% 0.87/1.04 tff(2345,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2344, 2342])).
% 0.87/1.04 tff(2346,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c3_1(a1338)) | c2_1(a1333) | c0_1(a1333) | (~c1_1(a1333)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2347,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1333) | (~ndr1_0) | c0_1(a1333) | (~c3_1(a1338)) | (~c1_1(a1338)) | (~c2_1(a1338)) | (~c1_1(a1333))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 0.87/1.04 tff(2348,plain,
% 0.87/1.04 (hskp12),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2347, 384, 2086, 2084, 2085, 2221, 2220, 2341, 2320])).
% 0.87/1.04 tff(2349,plain,
% 0.87/1.04 (~c0_1(a1325)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1208, 2348])).
% 0.87/1.04 tff(2350,plain,
% 0.87/1.04 (c3_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1104, 2317])).
% 0.87/1.04 tff(2351,plain,
% 0.87/1.04 (c3_1(a1325)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1216, 2348])).
% 0.87/1.04 tff(2352,plain,
% 0.87/1.04 (c1_1(a1325)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1224, 2348])).
% 0.87/1.04 tff(2353,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2354,plain,
% 0.87/1.04 (((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2355,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2354])).
% 0.87/1.04 tff(2356,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2355, 2353])).
% 0.87/1.04 tff(2357,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2358,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c0_1(a1315) | c1_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | c2_1(a1315) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 0.87/1.04 tff(2359,plain,
% 0.87/1.04 (c2_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2358, 384, 2352, 2351, 2350, 2323, 2349, 2318, 2331, 35, 2330])).
% 0.87/1.04 tff(2360,plain,
% 0.87/1.04 (~c1_1(a1315)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1134, 2317])).
% 0.87/1.04 tff(2361,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2362,plain,
% 0.87/1.04 ((hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315))) <=> (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2363,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2362])).
% 0.87/1.04 tff(2364,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2363, 2361])).
% 0.87/1.04 tff(2365,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1308) | (~c0_1(a1308)) | (~c3_1(a1308)) | c1_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2366,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1315) | c2_1(a1308) | (~ndr1_0) | (~c3_1(a1308)) | (~c0_1(a1308)) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 0.87/1.04 tff(2367,plain,
% 0.87/1.04 ((~c0_1(a1308)) | (~c2_1(a1315))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2366, 384, 2300, 2350, 2323, 2360, 2322, 1710])).
% 0.87/1.04 tff(2368,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2367, 2359, 2330])).
% 0.87/1.04 tff(2369,plain,(hskp17 | c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2370,plain,
% 0.87/1.04 (hskp17),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2369, 385, 23])).
% 0.87/1.04 tff(2371,plain,
% 0.87/1.04 (~c0_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[783, 2370])).
% 0.87/1.04 tff(2372,plain,
% 0.87/1.04 (c3_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[792, 2370])).
% 0.87/1.04 tff(2373,plain,
% 0.87/1.04 (c2_1(a1334)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[800, 2370])).
% 0.87/1.04 tff(2374,plain,
% 0.87/1.04 (~c0_1(a1338)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1902, 384, 2086, 2085, 2373, 2372, 2316, 2371, 2315, 2319, 10])).
% 0.87/1.04 tff(2375,plain,
% 0.87/1.04 (hskp4),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2093, 384, 2086, 2085, 2316, 2315, 2319, 928, 2374])).
% 0.87/1.04 tff(2376,plain,
% 0.87/1.04 (~c3_1(a1312)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1078, 2375])).
% 0.87/1.04 tff(2377,plain,
% 0.87/1.04 (~c1_1(a1312)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[686, 2375])).
% 0.87/1.04 tff(2378,plain,
% 0.87/1.04 (c0_1(a1312)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[694, 2375])).
% 0.87/1.04 tff(2379,plain,
% 0.87/1.04 (hskp15),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2110, 384, 385, 2378, 2064, 23, 2377, 2376, 1601])).
% 0.87/1.04 tff(2380,plain,
% 0.87/1.04 (c1_1(a1331)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1178, 2379])).
% 0.87/1.04 tff(2381,plain,
% 0.87/1.04 (~c3_1(a1331)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1161, 2379])).
% 0.87/1.04 tff(2382,plain,
% 0.87/1.04 (~c2_1(a1312)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2102, 384, 2373, 2372, 2316, 2378, 2371, 2315, 2319, 2377, 395])).
% 0.87/1.04 tff(2383,plain,
% 0.87/1.04 (~c0_1(a1331)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2119, 384, 2300, 2380, 2378, 2381, 2376, 533, 2382])).
% 0.87/1.04 tff(2384,plain,
% 0.87/1.04 (~hskp22),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2135, 2383, 2382, 2377, 2376, 2381, 2380])).
% 0.87/1.04 tff(2385,plain,
% 0.87/1.04 (hskp11),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2137, 2384])).
% 0.87/1.04 tff(2386,plain,
% 0.87/1.04 (~c1_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[91, 2385])).
% 0.87/1.04 tff(2387,plain,
% 0.87/1.04 (c0_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[99, 2385])).
% 0.87/1.04 tff(2388,plain,
% 0.87/1.04 (c3_1(a1324)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[107, 2385])).
% 0.87/1.04 tff(2389,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2055, 2388, 2387, 2350, 2360, 2319, 2374, 2086, 2085, 2386, 2318, 2084, 2316, 2315, 2300])).
% 0.87/1.04 tff(2390,plain,(c1_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2391,plain,
% 0.87/1.04 (c1_1(a1339)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2390, 23])).
% 0.87/1.04 tff(2392,plain,
% 0.87/1.04 (~hskp13),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[174, 46, 384, 2391, 24, 23])).
% 0.87/1.04 tff(2393,plain,
% 0.87/1.04 (~hskp28),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[268, 2392, 2391, 24, 23, 25, 384])).
% 0.87/1.04 tff(2394,plain,
% 0.87/1.04 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(2395,plain,
% 0.87/1.04 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[2394])).
% 0.87/1.04 tff(2396,plain,
% 0.87/1.04 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2397,plain,
% 0.87/1.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(2398,plain,
% 0.87/1.04 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[2397])).
% 0.87/1.04 tff(2399,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.87/1.04 tff(2400,plain,
% 0.87/1.04 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2399, 2398])).
% 0.87/1.04 tff(2401,plain,
% 0.87/1.04 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2400, 2396])).
% 0.87/1.04 tff(2402,plain,(
% 0.87/1.04 ![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(skolemize,[status(sab)],[2401])).
% 0.87/1.04 tff(2403,plain,
% 0.87/1.04 (![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2402, 2395])).
% 0.87/1.04 tff(2404,plain,
% 0.87/1.04 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2405,plain,
% 0.87/1.04 ((hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348))) <=> (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2406,plain,
% 0.87/1.04 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348)))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2405])).
% 0.87/1.04 tff(2407,plain,
% 0.87/1.04 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2406, 2404])).
% 0.87/1.04 tff(2408,plain,
% 0.87/1.04 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2409,plain,
% 0.87/1.04 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1348) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 0.87/1.04 tff(2410,plain,
% 0.87/1.04 (hskp28 | c3_1(a1348)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2409, 384, 770, 626, 2403])).
% 0.87/1.04 tff(2411,plain,
% 0.87/1.04 (c3_1(a1348)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2410, 2393])).
% 0.87/1.04 tff(2412,plain,
% 0.87/1.04 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2413,plain,
% 0.87/1.04 ((hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2414,plain,
% 0.87/1.04 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2413])).
% 0.87/1.04 tff(2415,plain,
% 0.87/1.04 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2414, 2412])).
% 0.87/1.04 tff(2416,plain,
% 0.87/1.04 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1348)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2417,plain,
% 0.87/1.04 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c3_1(a1348)) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 0.87/1.04 tff(2418,plain,
% 0.87/1.04 (hskp22 | hskp11 | (~c3_1(a1348))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2417, 384, 770, 762, 415])).
% 0.87/1.05 tff(2419,plain,
% 0.87/1.05 (hskp22),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2418, 2411, 46])).
% 0.87/1.05 tff(2420,plain,
% 0.87/1.05 (c1_1(a1356)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[510, 2419])).
% 0.87/1.05 tff(2421,plain,
% 0.87/1.05 (c0_1(a1356)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[518, 2419])).
% 0.87/1.05 tff(2422,plain,
% 0.87/1.05 (~c2_1(a1356)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[522, 384, 2392, 2421, 2420, 45])).
% 0.87/1.05 tff(2423,plain,
% 0.87/1.05 (~c3_1(a1356)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[538, 2419])).
% 0.87/1.05 tff(2424,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2425,plain,
% 0.87/1.05 (((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2426,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356)))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2425])).
% 0.87/1.05 tff(2427,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2426, 2424])).
% 0.87/1.05 tff(2428,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1356) | c3_1(a1356) | (~c1_1(a1356)) | c2_1(a1339) | c0_1(a1339) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2429,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a1356) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c1_1(a1356)) | c2_1(a1356)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 0.87/1.05 tff(2430,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2429, 384, 2420, 2391, 2423, 24, 23, 302, 25, 2422])).
% 0.87/1.05 tff(2431,plain,(hskp11 | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2432,plain,
% 0.87/1.05 (hskp11),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2431, 25, 23, 24])).
% 0.87/1.05 tff(2433,plain,
% 0.87/1.05 (~c1_1(a1324)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[91, 2432])).
% 0.87/1.05 tff(2434,plain,
% 0.87/1.05 (c3_1(a1324)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[107, 2432])).
% 0.87/1.05 tff(2435,plain,
% 0.87/1.05 (c0_1(a1324)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[99, 2432])).
% 0.87/1.05 tff(2436,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[121, 384, 2391, 2435, 2434, 24, 23, 2433, 35, 25])).
% 0.87/1.05 tff(2437,plain,((~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2438,plain,
% 0.87/1.05 (~c3_1(a1339)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2437, 24, 23])).
% 0.87/1.05 tff(2439,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2440,plain,
% 0.87/1.05 ((hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339))) <=> (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2441,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2440])).
% 0.87/1.05 tff(2442,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2441, 2439])).
% 0.87/1.05 tff(2443,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1339) | c3_1(a1339) | (~c1_1(a1339)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2444,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 0.87/1.05 tff(2445,plain,
% 0.87/1.05 (hskp9 | c3_1(a1339)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2444, 384, 2391, 24, 23, 1384])).
% 0.87/1.05 tff(2446,plain,
% 0.87/1.05 (hskp9),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2445, 2438])).
% 0.87/1.05 tff(2447,plain,
% 0.87/1.05 (c2_1(a1320)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1410, 2446])).
% 0.87/1.05 tff(2448,plain,
% 0.87/1.05 (~c0_1(a1320)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1402, 2446])).
% 0.87/1.05 tff(2449,plain,
% 0.87/1.05 (~c1_1(a1320)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1396, 2446])).
% 0.87/1.05 tff(2450,assumption,(~c3_1(a1320)), introduced(assumption)).
% 0.87/1.05 tff(2451,assumption,(~c1_1(a1320)), introduced(assumption)).
% 0.87/1.05 tff(2452,assumption,(~c0_1(a1320)), introduced(assumption)).
% 0.87/1.05 tff(2453,assumption,(c2_1(a1320)), introduced(assumption)).
% 0.87/1.05 tff(2454,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2455,plain,
% 0.87/1.05 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320)) <=> (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2456,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320)))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2455])).
% 0.87/1.05 tff(2457,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2456, 2454])).
% 0.87/1.05 tff(2458,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1320) | c1_1(a1320) | c0_1(a1320))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2459,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | c3_1(a1320)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 0.87/1.05 tff(2460,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2459, 384, 2453, 2452, 2451, 1285, 2450])).
% 0.87/1.05 tff(2461,plain,(c3_1(a1320) | (~c2_1(a1320)) | c0_1(a1320) | c1_1(a1320)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2462,plain,
% 0.87/1.05 (c3_1(a1320)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2461, 2449, 2448, 2447])).
% 0.87/1.05 tff(2463,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2464,plain,
% 0.87/1.05 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339)) <=> (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2465,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2464])).
% 0.87/1.05 tff(2466,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2465, 2463])).
% 0.87/1.05 tff(2467,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1339) | c0_1(a1339) | c3_1(a1339))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2468,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1339) | c2_1(a1339) | c0_1(a1320) | (~ndr1_0) | c3_1(a1339) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 0.87/1.05 tff(2469,plain,
% 0.87/1.05 (hskp8),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2468, 384, 2447, 24, 23, 2448, 973, 2438, 2462])).
% 0.87/1.05 tff(2470,plain,
% 0.87/1.05 (~c3_1(a1319)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1018, 2469])).
% 0.87/1.05 tff(2471,plain,
% 0.87/1.05 (~c0_1(a1319)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1024, 2469])).
% 0.87/1.05 tff(2472,plain,
% 0.87/1.05 (c2_1(a1319)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1112, 2469])).
% 0.87/1.05 tff(2473,plain,
% 0.87/1.05 (hskp14 | hskp13 | c3_1(a1339) | (~c1_1(a1339))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[192, 384, 23, 186])).
% 0.87/1.05 tff(2474,plain,
% 0.87/1.05 (c3_1(a1339)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2473, 637, 2391, 248])).
% 0.87/1.05 tff(2475,plain,
% 0.87/1.05 (~hskp28),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[268, 2474, 2391, 24, 23, 248, 384])).
% 0.87/1.05 tff(2476,plain,
% 0.87/1.05 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2477,plain,
% 0.87/1.05 ((hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319))) <=> (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2478,plain,
% 0.87/1.05 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2477])).
% 0.87/1.05 tff(2479,plain,
% 0.87/1.05 (((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2478, 2476])).
% 0.87/1.05 tff(2480,plain,
% 0.87/1.05 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c0_1(a1319) | c3_1(a1319) | (~c1_1(a1319)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2481,plain,
% 0.87/1.05 ((~![U: $i] : (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1319))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 0.87/1.05 tff(2482,plain,
% 0.87/1.05 (hskp28 | c0_1(a1319) | (~c1_1(a1319))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2481, 384, 2037, 2403])).
% 0.87/1.05 tff(2483,plain,
% 0.87/1.05 (~c1_1(a1319)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2482, 2475, 2038])).
% 0.87/1.05 tff(2484,assumption,(~hskp28), introduced(assumption)).
% 0.87/1.05 tff(2485,plain,
% 0.87/1.05 (hskp1),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[338, 2484, 918])).
% 0.87/1.05 tff(2486,plain,
% 0.87/1.05 (~c2_1(a1308)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[895, 2485])).
% 0.87/1.05 tff(2487,plain,
% 0.87/1.05 (~c1_1(a1308)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[344, 2485])).
% 0.87/1.05 tff(2488,plain,
% 0.87/1.05 ((hskp28 | hskp25 | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2489,plain,
% 0.87/1.05 (((hskp28 | hskp25) | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2490,plain,
% 0.87/1.05 ((hskp28 | hskp25) <=> (hskp28 | hskp25)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2491,plain,
% 0.87/1.05 (((hskp28 | hskp25) | hskp14) <=> ((hskp28 | hskp25) | hskp14)),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2490])).
% 0.87/1.05 tff(2492,plain,
% 0.87/1.05 (((hskp28 | hskp25) | hskp14) <=> (hskp28 | hskp25 | hskp14)),
% 0.87/1.05 inference(transitivity,[status(thm)],[2491, 2489])).
% 0.87/1.05 tff(2493,axiom,((hskp28 | hskp25) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.87/1.05 tff(2494,plain,
% 0.87/1.05 (hskp28 | hskp25 | hskp14),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 0.87/1.05 tff(2495,plain,
% 0.87/1.05 (hskp28 | hskp25 | hskp14),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2494, 2488])).
% 0.87/1.05 tff(2496,plain,
% 0.87/1.05 (hskp28 | hskp25 | hskp14),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2495, 2488])).
% 0.87/1.05 tff(2497,plain,
% 0.87/1.05 (hskp28 | hskp25 | hskp14),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2496, 2488])).
% 0.87/1.05 tff(2498,plain,
% 0.87/1.05 (hskp28 | hskp25 | hskp14),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2497, 2488])).
% 0.87/1.05 tff(2499,plain,
% 0.87/1.05 (hskp25),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2498, 2484, 637])).
% 0.87/1.05 tff(2500,plain,
% 0.87/1.05 (((~hskp25) | (~c3_1(a1394))) <=> ((~hskp25) | (~c3_1(a1394)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2501,plain,
% 0.87/1.05 (((~c3_1(a1394)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1394)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2502,axiom,((~c3_1(a1394)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.87/1.05 tff(2503,plain,
% 0.87/1.05 ((~hskp25) | (~c3_1(a1394))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 0.87/1.05 tff(2504,plain,
% 0.87/1.05 ((~hskp25) | (~c3_1(a1394))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2503, 2500])).
% 0.87/1.05 tff(2505,plain,
% 0.87/1.05 (~c3_1(a1394)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2504, 2499])).
% 0.87/1.05 tff(2506,plain,
% 0.87/1.05 (((~hskp25) | c2_1(a1394)) <=> ((~hskp25) | c2_1(a1394))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2507,axiom,((~hskp25) | c2_1(a1394)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.87/1.05 tff(2508,plain,
% 0.87/1.05 ((~hskp25) | c2_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 0.87/1.05 tff(2509,plain,
% 0.87/1.05 ((~hskp25) | c2_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2508, 2506])).
% 0.87/1.05 tff(2510,plain,
% 0.87/1.05 ((~hskp25) | c2_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2509, 2506])).
% 0.87/1.05 tff(2511,plain,
% 0.87/1.05 ((~hskp25) | c2_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2510, 2506])).
% 0.87/1.05 tff(2512,plain,
% 0.87/1.05 ((~hskp25) | c2_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2511, 2506])).
% 0.87/1.05 tff(2513,plain,
% 0.87/1.05 (c2_1(a1394)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2512, 2499])).
% 0.87/1.05 tff(2514,plain,
% 0.87/1.05 (((~hskp25) | c0_1(a1394)) <=> ((~hskp25) | c0_1(a1394))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2515,axiom,((~hskp25) | c0_1(a1394)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.87/1.05 tff(2516,plain,
% 0.87/1.05 ((~hskp25) | c0_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 0.87/1.05 tff(2517,plain,
% 0.87/1.05 ((~hskp25) | c0_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2516, 2514])).
% 0.87/1.05 tff(2518,plain,
% 0.87/1.05 ((~hskp25) | c0_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2517, 2514])).
% 0.87/1.05 tff(2519,plain,
% 0.87/1.05 ((~hskp25) | c0_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2518, 2514])).
% 0.87/1.05 tff(2520,plain,
% 0.87/1.05 ((~hskp25) | c0_1(a1394)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2519, 2514])).
% 0.87/1.05 tff(2521,plain,
% 0.87/1.05 (c0_1(a1394)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2520, 2499])).
% 0.87/1.05 tff(2522,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2523,plain,
% 0.87/1.05 ((hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308))) <=> (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2524,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2523])).
% 0.87/1.05 tff(2525,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2524, 2522])).
% 0.87/1.05 tff(2526,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1394) | (~c2_1(a1394)) | (~c0_1(a1394)) | c2_1(a1308) | c1_1(a1308) | (~c0_1(a1308)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2527,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a1394) | c1_1(a1308) | c2_1(a1308) | (~ndr1_0) | (~c0_1(a1308)) | (~c0_1(a1394)) | (~c2_1(a1394))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 0.87/1.05 tff(2528,plain,
% 0.87/1.05 (~c0_1(a1308)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2527, 166, 637, 2521, 2513, 2505, 2487, 2486, 828])).
% 0.87/1.05 tff(2529,plain,
% 0.87/1.05 (c3_1(a1308)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[352, 2485])).
% 0.87/1.05 tff(2530,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[376, 166, 918, 165, 2529, 23, 2487, 370, 25, 2528])).
% 0.87/1.05 tff(2531,plain,(hskp28 | (~ndr1_0) | hskp7 | (~c1_1(a1339)) | c2_1(a1339) | (~c3_1(a1339)) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2532,plain,
% 0.87/1.05 (hskp7),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2531, 2475, 2391, 637, 23, 2474, 384])).
% 0.87/1.05 tff(2533,plain,
% 0.87/1.05 (~c3_1(a1316)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[281, 2532])).
% 0.87/1.05 tff(2534,plain,
% 0.87/1.05 (~c0_1(a1316)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1302, 2532])).
% 0.87/1.05 tff(2535,assumption,(~c2_1(a1319)), introduced(assumption)).
% 0.87/1.05 tff(2536,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2537,plain,
% 0.87/1.05 ((hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2538,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2537])).
% 0.87/1.05 tff(2539,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2538, 2536])).
% 0.87/1.05 tff(2540,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2541,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 0.87/1.05 tff(2542,plain,
% 0.87/1.05 (hskp6),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2541, 384, 770, 762, 2535, 626, 2038, 2037, 1049])).
% 0.87/1.05 tff(2543,plain,
% 0.87/1.05 (~c0_1(a1315)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1062, 2542])).
% 0.87/1.05 tff(2544,plain,
% 0.87/1.05 (c3_1(a1315)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1104, 2542])).
% 0.87/1.05 tff(2545,plain,
% 0.87/1.05 (~hskp8),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1112, 2535])).
% 0.87/1.05 tff(2546,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2547,plain,
% 0.87/1.05 ((hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2548,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2547])).
% 0.87/1.05 tff(2549,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2548, 2546])).
% 0.87/1.05 tff(2550,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1315) | (~c2_1(a1315)) | (~c3_1(a1315)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2551,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | (~c2_1(a1315))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 0.87/1.05 tff(2552,plain,
% 0.87/1.05 (~c2_1(a1315)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2551, 384, 2545, 2535, 2544, 2038, 2037, 2543, 973])).
% 0.87/1.05 tff(2553,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2554,plain,
% 0.87/1.06 ((hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2555,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2554])).
% 0.87/1.06 tff(2556,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2555, 2553])).
% 0.87/1.06 tff(2557,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1348) | (~c2_1(a1348)) | (~c3_1(a1348)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2558,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2557, 2556])).
% 0.87/1.06 tff(2559,plain,
% 0.87/1.06 (~c3_1(a1348)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2558, 384, 2545, 762, 2535, 626, 2038, 2037, 973])).
% 0.87/1.06 tff(2560,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2561,plain,
% 0.87/1.06 ((hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339))) <=> (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2562,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348)))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2561])).
% 0.87/1.06 tff(2563,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2562, 2560])).
% 0.87/1.06 tff(2564,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c2_1(a1339) | c0_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2565,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1348) | c0_1(a1339) | c2_1(a1339) | (~ndr1_0) | (~c1_1(a1339)) | (~c1_1(a1348)) | c3_1(a1348)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 0.87/1.06 tff(2566,plain,
% 0.87/1.06 (hskp9 | c0_1(a1339) | (~c1_1(a1339)) | c3_1(a1348)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2565, 384, 770, 626, 23, 1384])).
% 0.87/1.06 tff(2567,plain,
% 0.87/1.06 (hskp9),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2566, 2559, 2391, 24])).
% 0.87/1.06 tff(2568,plain,
% 0.87/1.06 (~c0_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1402, 2567])).
% 0.87/1.06 tff(2569,plain,
% 0.87/1.06 (c2_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1410, 2567])).
% 0.87/1.06 tff(2570,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2571,plain,
% 0.87/1.06 ((hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2572,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2571])).
% 0.87/1.06 tff(2573,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2572, 2570])).
% 0.87/1.06 tff(2574,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1320) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2575,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a1319) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 0.87/1.06 tff(2576,plain,
% 0.87/1.06 (~c3_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2575, 384, 2545, 2569, 2535, 2568, 2038, 2037, 973])).
% 0.87/1.06 tff(2577,plain,
% 0.87/1.06 (~c1_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1396, 2567])).
% 0.87/1.06 tff(2578,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2579,plain,
% 0.87/1.06 (((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319)) <=> (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2580,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320)))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2579])).
% 0.87/1.06 tff(2581,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2580, 2578])).
% 0.87/1.06 tff(2582,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1320) | c3_1(a1320) | (~c2_1(a1320)) | c1_1(a1320) | c0_1(a1320) | (~c2_1(a1320)) | c3_1(a1319) | c1_1(a1319) | c0_1(a1319))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2583,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1320) | c1_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c1_1(a1319) | (~c2_1(a1320)) | c3_1(a1320)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 0.87/1.06 tff(2584,plain,
% 0.87/1.06 (c1_1(a1319)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2583, 384, 2569, 2568, 2577, 2038, 2037, 1285, 2576])).
% 0.87/1.06 tff(2585,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2586,plain,
% 0.87/1.06 (((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339))) <=> (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2587,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2586])).
% 0.87/1.06 tff(2588,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2587, 2585])).
% 0.87/1.06 tff(2589,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1319) | c3_1(a1319) | (~c1_1(a1319)) | c2_1(a1315) | c0_1(a1315) | (~c3_1(a1315)) | c0_1(a1339) | c2_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2590,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1315)) | c2_1(a1315) | (~c1_1(a1319))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 0.87/1.06 tff(2591,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2590, 384, 2391, 2535, 2544, 24, 23, 2037, 2543, 302, 2584, 2552])).
% 0.87/1.06 tff(2592,plain,(c2_1(a1319) | c0_1(a1339) | c2_1(a1339) | c3_1(a1319) | c0_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2593,plain,
% 0.87/1.06 (c2_1(a1319)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2592, 2038, 23, 2037, 24])).
% 0.87/1.06 tff(2594,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2595,plain,
% 0.87/1.06 (((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316)) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2596,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2595])).
% 0.87/1.06 tff(2597,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2596, 2594])).
% 0.87/1.06 tff(2598,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1319) | c3_1(a1319) | (~c2_1(a1319)) | c1_1(a1319) | c0_1(a1319) | (~c2_1(a1319)) | c3_1(a1316) | c1_1(a1316) | c0_1(a1316))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2599,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | c1_1(a1316) | c1_1(a1319) | (~c2_1(a1319))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 0.87/1.06 tff(2600,plain,
% 0.87/1.06 (c1_1(a1316)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2599, 384, 2593, 2038, 2037, 2534, 2533, 1285, 2483])).
% 0.87/1.06 tff(2601,plain,
% 0.87/1.06 (~c2_1(a1316)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[275, 2532])).
% 0.87/1.06 tff(2602,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[316, 384, 637, 248, 2601, 2533, 186, 2600])).
% 0.87/1.06 tff(2603,plain,(hskp14 | hskp13 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339) | c0_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2604,plain,
% 0.87/1.06 (hskp14),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2603, 2392, 2038, 2037, 23, 24])).
% 0.87/1.06 tff(2605,plain,
% 0.87/1.06 (~c2_1(a1330)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[199, 2604])).
% 0.87/1.06 tff(2606,plain,
% 0.87/1.06 (~c1_1(a1330)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[205, 2604])).
% 0.87/1.06 tff(2607,plain,
% 0.87/1.06 (c3_1(a1330)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[212, 384, 46, 2391, 24, 23, 2606, 2605, 57])).
% 0.87/1.06 tff(2608,plain,
% 0.87/1.06 (c0_1(a1330)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[220, 2604])).
% 0.87/1.06 tff(2609,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2610,plain,
% 0.87/1.06 (((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339))) <=> (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2611,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2610])).
% 0.87/1.06 tff(2612,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2611, 2609])).
% 0.87/1.06 tff(2613,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c0_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c0_1(a1339) | c2_1(a1339) | (~c3_1(a1339)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2614,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1339) | c2_1(a1339) | c1_1(a1330) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1330)) | (~c0_1(a1330))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 0.87/1.06 tff(2615,plain,
% 0.87/1.06 ((~c3_1(a1339)) | (~c3_1(a1330))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2614, 384, 2391, 2608, 24, 23, 2606, 35])).
% 0.87/1.06 tff(2616,plain,
% 0.87/1.06 (~c3_1(a1339)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2615, 2607])).
% 0.87/1.06 tff(2617,plain,
% 0.87/1.06 (hskp9),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2445, 2616])).
% 0.87/1.06 tff(2618,plain,
% 0.87/1.06 (c2_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1410, 2617])).
% 0.87/1.06 tff(2619,plain,
% 0.87/1.06 (~c0_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1402, 2617])).
% 0.87/1.06 tff(2620,plain,
% 0.87/1.06 (~c1_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1396, 2617])).
% 0.87/1.06 tff(2621,plain,
% 0.87/1.06 (c3_1(a1320)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2461, 2620, 2619, 2618])).
% 0.87/1.06 tff(2622,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2623,plain,
% 0.87/1.06 ((hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320))) <=> (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2624,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2623])).
% 0.87/1.06 tff(2625,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2624, 2622])).
% 0.87/1.06 tff(2626,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1330) | (~c0_1(a1330)) | (~c3_1(a1330)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2627,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c2_1(a1330) | c1_1(a1320) | (~ndr1_0) | (~c3_1(a1330)) | (~c0_1(a1330)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 0.87/1.06 tff(2628,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2627, 384, 22, 2608, 2618, 2605, 2620, 1710, 2607, 2621])).
% 0.87/1.06 tff(2629,plain,(hskp11 | hskp27 | c0_1(a1339) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2630,plain,
% 0.87/1.06 (hskp11),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2629, 2038, 24, 23, 22, 2037])).
% 0.87/1.06 tff(2631,plain,
% 0.87/1.06 (~c1_1(a1324)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[91, 2630])).
% 0.87/1.06 tff(2632,plain,
% 0.87/1.06 (c3_1(a1324)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[107, 2630])).
% 0.87/1.07 tff(2633,plain,
% 0.87/1.07 (c0_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[99, 2630])).
% 0.87/1.07 tff(2634,plain,
% 0.87/1.07 (~c3_1(a1339)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[121, 384, 2391, 2633, 2632, 24, 23, 2631, 35])).
% 0.87/1.07 tff(2635,plain,
% 0.87/1.07 (hskp9),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2445, 2634])).
% 0.87/1.07 tff(2636,plain,
% 0.87/1.07 (~c0_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1402, 2635])).
% 0.87/1.07 tff(2637,plain,
% 0.87/1.07 (c2_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1410, 2635])).
% 0.87/1.07 tff(2638,plain,
% 0.87/1.07 (~c1_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1396, 2635])).
% 0.87/1.07 tff(2639,plain,
% 0.87/1.07 (c3_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2461, 2453, 2452, 2451])).
% 0.87/1.07 tff(2640,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2641,plain,
% 0.87/1.07 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2642,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2641])).
% 0.87/1.07 tff(2643,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2642, 2640])).
% 0.87/1.07 tff(2644,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2645,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1324) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 0.87/1.07 tff(2646,plain,
% 0.87/1.07 (~c2_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2645, 384, 100, 2453, 2039, 92, 2452, 2038, 2037, 395, 2639])).
% 0.87/1.07 tff(2647,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2648,plain,
% 0.87/1.07 ((hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320))) <=> (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2649,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2648])).
% 0.87/1.07 tff(2650,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2649, 2647])).
% 0.87/1.07 tff(2651,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c1_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2652,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a1320) | (~ndr1_0) | (~c2_1(a1320)) | (~c3_1(a1320)) | c2_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 0.87/1.07 tff(2653,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2652, 384, 22, 100, 108, 2453, 2451, 1710, 2639, 2646])).
% 0.87/1.07 tff(2654,plain,((~hskp11) | hskp27 | (~c2_1(a1320)) | c1_1(a1320) | (~c2_1(a1319)) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2655,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2654, 2638, 2637, 22, 2630, 2593, 2636, 2038, 2037])).
% 0.87/1.07 tff(2656,plain,(c0_1(a1319) | hskp27 | c3_1(a1319) | c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2657,plain,
% 0.87/1.07 (hskp27),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2656, 2470, 2471, 24, 23])).
% 0.87/1.07 tff(2658,plain,
% 0.87/1.07 (c1_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[432, 2657])).
% 0.87/1.07 tff(2659,plain,
% 0.87/1.07 (c0_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[440, 2657])).
% 0.87/1.07 tff(2660,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2661,plain,
% 0.87/1.07 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2662,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2661])).
% 0.87/1.07 tff(2663,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2662, 2660])).
% 0.87/1.07 tff(2664,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1320) | (~c3_1(a1320)) | (~c2_1(a1320)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2665,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1320) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)) | (~c2_1(a1320)) | (~c3_1(a1320))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 0.87/1.07 tff(2666,plain,
% 0.87/1.07 (~c3_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2665, 384, 2659, 2658, 2447, 2472, 2448, 2471, 2470, 10, 2462])).
% 0.87/1.07 tff(2667,plain,
% 0.87/1.07 (hskp13),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[449, 2657])).
% 0.87/1.07 tff(2668,plain,
% 0.87/1.07 (hskp11),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[174, 2667, 384, 2391, 24, 23])).
% 0.87/1.07 tff(2669,plain,
% 0.87/1.07 (~c1_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[91, 2668])).
% 0.87/1.07 tff(2670,plain,
% 0.87/1.07 (c0_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[99, 2668])).
% 0.87/1.07 tff(2671,plain,
% 0.87/1.07 (~c2_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2645, 384, 2670, 2447, 2472, 2669, 2448, 2471, 2470, 395, 2462])).
% 0.87/1.07 tff(2672,plain,
% 0.87/1.07 (c3_1(a1324)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[107, 2668])).
% 0.87/1.07 tff(2673,plain,
% 0.87/1.07 (c2_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[424, 2657])).
% 0.87/1.07 tff(2674,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2675,plain,
% 0.87/1.07 (((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2676,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2675])).
% 0.87/1.07 tff(2677,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2676, 2674])).
% 0.87/1.07 tff(2678,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2679,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1324) | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307) | c2_1(a1324) | (~c3_1(a1324))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2678, 2677])).
% 0.87/1.07 tff(2680,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2679, 384, 2659, 2658, 2673, 2672, 2669, 636, 2671, 2666])).
% 0.87/1.07 tff(2681,plain,(c0_1(a1339) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2682,plain,
% 0.87/1.07 (c0_1(a1339)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2681, 23])).
% 0.87/1.07 tff(2683,plain,
% 0.87/1.07 (~hskp18),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[76, 2682])).
% 0.87/1.07 tff(2684,plain,
% 0.87/1.07 (hskp7),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1257, 384, 933, 2306, 2309, 2307, 917])).
% 0.87/1.07 tff(2685,plain,
% 0.87/1.07 (~c3_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[281, 2684])).
% 0.87/1.07 tff(2686,plain,
% 0.87/1.07 (~c0_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1302, 2684])).
% 0.87/1.07 tff(2687,plain,
% 0.87/1.07 (~c2_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[275, 2684])).
% 0.87/1.07 tff(2688,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2313, 2687, 2686, 706, 933, 22, 2685])).
% 0.87/1.07 tff(2689,plain,(hskp27 | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2690,plain,
% 0.87/1.07 (hskp27),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2689, 933, 706])).
% 0.87/1.07 tff(2691,plain,
% 0.87/1.07 (hskp13),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[449, 2690])).
% 0.87/1.07 tff(2692,plain,
% 0.87/1.07 (~c3_1(a1326)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[151, 2691])).
% 0.87/1.07 tff(2693,plain,
% 0.87/1.07 (~c2_1(a1326)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[157, 2691])).
% 0.87/1.07 tff(2694,assumption,(c3_1(a1307)), introduced(assumption)).
% 0.87/1.07 tff(2695,plain,
% 0.87/1.07 (c2_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[424, 2690])).
% 0.87/1.07 tff(2696,plain,
% 0.87/1.07 (c1_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[432, 2690])).
% 0.87/1.07 tff(2697,plain,
% 0.87/1.07 (c0_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[440, 2690])).
% 0.87/1.07 tff(2698,plain,
% 0.87/1.07 (hskp17 | (~c3_1(a1307))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[999, 384, 2697, 2696, 2695, 992])).
% 0.87/1.07 tff(2699,plain,
% 0.87/1.07 (hskp17),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2698, 2694])).
% 0.87/1.07 tff(2700,plain,
% 0.87/1.07 (~c0_1(a1334)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[783, 2699])).
% 0.87/1.07 tff(2701,plain,
% 0.87/1.07 (c3_1(a1334)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[792, 2699])).
% 0.87/1.07 tff(2702,plain,
% 0.87/1.07 (c2_1(a1334)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[800, 2699])).
% 0.87/1.07 tff(2703,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2704,plain,
% 0.87/1.07 ((hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326)) <=> (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2705,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326)))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2704])).
% 0.87/1.07 tff(2706,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2705, 2703])).
% 0.87/1.07 tff(2707,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a1334) | (~c2_1(a1334)) | (~c3_1(a1334)) | c2_1(a1326) | c0_1(a1326) | c3_1(a1326))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2708,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a1334) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | c0_1(a1326)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 0.87/1.07 tff(2709,plain,
% 0.87/1.07 (c0_1(a1326)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2708, 384, 933, 2702, 2701, 2700, 2693, 2692, 973])).
% 0.87/1.07 tff(2710,plain,
% 0.87/1.07 (~c1_1(a1326)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[163, 2691])).
% 0.87/1.07 tff(2711,plain,
% 0.87/1.07 (hskp7 | (~c0_1(a1326))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[961, 384, 933, 2710, 2693, 917])).
% 0.87/1.07 tff(2712,plain,
% 0.87/1.07 (hskp7),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2711, 2709])).
% 0.87/1.07 tff(2713,plain,
% 0.87/1.07 (~c3_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[281, 2712])).
% 0.87/1.07 tff(2714,plain,
% 0.87/1.07 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(2715,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[2714])).
% 0.87/1.07 tff(2716,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2717,plain,
% 0.87/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp29) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(2718,plain,
% 0.87/1.07 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[2717])).
% 0.87/1.07 tff(2719,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 0.87/1.07 tff(2720,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 0.87/1.07 tff(2721,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2720, 2716])).
% 0.87/1.07 tff(2722,plain,(
% 0.87/1.07 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(skolemize,[status(sab)],[2721])).
% 0.87/1.07 tff(2723,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2722, 2715])).
% 0.87/1.07 tff(2724,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2725,plain,
% 0.87/1.07 ((hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307))) <=> (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2726,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2725])).
% 0.87/1.07 tff(2727,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2726, 2724])).
% 0.87/1.07 tff(2728,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c0_1(a1307)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2729,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2728, 2727])).
% 0.87/1.07 tff(2730,plain,
% 0.87/1.07 (hskp29 | (~c3_1(a1307))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2729, 384, 2697, 2696, 2695, 2723])).
% 0.87/1.07 tff(2731,plain,
% 0.87/1.07 (hskp29),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2730, 2694])).
% 0.87/1.07 tff(2732,plain,
% 0.87/1.07 (c1_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[495, 2731])).
% 0.87/1.07 tff(2733,plain,
% 0.87/1.07 (c2_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[487, 2731])).
% 0.87/1.07 tff(2734,plain,
% 0.87/1.07 (c3_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[479, 2731])).
% 0.87/1.07 tff(2735,plain,
% 0.87/1.07 (~c0_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1302, 2712])).
% 0.87/1.07 tff(2736,plain,
% 0.87/1.07 (~c2_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[275, 2712])).
% 0.87/1.07 tff(2737,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1929, 2736, 2735, 2690, 706, 2734, 2733, 2732, 2713])).
% 0.87/1.07 tff(2738,plain,((~c3_1(a1307)) | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2739,plain,
% 0.87/1.07 (~c3_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2738, 933, 706])).
% 0.87/1.07 tff(2740,plain,
% 0.87/1.07 (hskp14 | c3_1(a1307)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[951, 384, 933, 2697, 2696, 943])).
% 0.87/1.07 tff(2741,plain,
% 0.87/1.07 (hskp14),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2740, 2739])).
% 0.87/1.07 tff(2742,plain,
% 0.87/1.07 (~c2_1(a1330)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[199, 2741])).
% 0.87/1.07 tff(2743,plain,
% 0.87/1.07 (~c1_1(a1330)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[205, 2741])).
% 0.87/1.07 tff(2744,plain,
% 0.87/1.07 (c0_1(a1330)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[220, 2741])).
% 0.87/1.07 tff(2745,plain,
% 0.87/1.07 (hskp7),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1257, 384, 933, 2744, 2743, 2742, 917])).
% 0.87/1.07 tff(2746,plain,
% 0.87/1.07 (~c3_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[281, 2745])).
% 0.87/1.07 tff(2747,plain,
% 0.87/1.07 (hskp29),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[471, 706, 384, 2744, 2743, 2742, 21])).
% 0.87/1.07 tff(2748,plain,
% 0.87/1.07 (c1_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[495, 2747])).
% 0.87/1.07 tff(2749,plain,
% 0.87/1.07 (c2_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[487, 2747])).
% 0.87/1.07 tff(2750,plain,
% 0.87/1.07 (c3_1(a1338)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[479, 2747])).
% 0.87/1.07 tff(2751,plain,
% 0.87/1.07 (~c0_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1302, 2745])).
% 0.87/1.07 tff(2752,plain,
% 0.87/1.07 (~c2_1(a1316)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[275, 2745])).
% 0.87/1.07 tff(2753,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1929, 2752, 2751, 2690, 706, 2750, 2749, 2748, 2746])).
% 0.87/1.07 tff(2754,plain,(hskp8 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2755,plain,
% 0.87/1.07 (hskp8),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2754, 2683])).
% 0.87/1.07 tff(2756,plain,
% 0.87/1.07 (~c0_1(a1319)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1024, 2755])).
% 0.87/1.07 tff(2757,plain,
% 0.87/1.07 (~c3_1(a1319)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1018, 2755])).
% 0.87/1.07 tff(2758,assumption,(hskp9), introduced(assumption)).
% 0.87/1.07 tff(2759,plain,
% 0.87/1.07 (c2_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1410, 2758])).
% 0.87/1.07 tff(2760,plain,
% 0.87/1.07 (~c0_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1402, 2758])).
% 0.87/1.07 tff(2761,plain,
% 0.87/1.07 (~c1_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1396, 2758])).
% 0.87/1.07 tff(2762,plain,
% 0.87/1.07 (c3_1(a1320)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2461, 2761, 2760, 2759])).
% 0.87/1.07 tff(2763,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2575, 384, 2545, 2759, 2535, 2760, 2038, 2037, 973, 2762])).
% 0.87/1.07 tff(2764,plain,((~hskp9) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2765,plain,
% 0.87/1.07 (~hskp9),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2764, 2535, 2038, 2037])).
% 0.87/1.07 tff(2766,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2767,plain,
% 0.87/1.07 ((hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319)) <=> (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2768,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339)))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2767])).
% 0.87/1.07 tff(2769,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2768, 2766])).
% 0.87/1.07 tff(2770,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)) | c2_1(a1319) | c0_1(a1319) | c3_1(a1319))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2771,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp9 | c2_1(a1319) | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | c3_1(a1339)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 0.87/1.08 tff(2772,plain,
% 0.87/1.08 (hskp9 | c3_1(a1339)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2771, 384, 2535, 2682, 23, 2038, 2037, 1993])).
% 0.87/1.08 tff(2773,plain,
% 0.87/1.08 (c3_1(a1339)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2772, 2765])).
% 0.87/1.08 tff(2774,plain,
% 0.87/1.08 (~c1_1(a1315)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1134, 2542])).
% 0.87/1.08 tff(2775,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2776,plain,
% 0.87/1.08 ((hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315))) <=> (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2777,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2776])).
% 0.87/1.08 tff(2778,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2777, 2775])).
% 0.87/1.08 tff(2779,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1339) | (~c1_1(a1339)) | (~c3_1(a1339)) | c1_1(a1315) | c0_1(a1315) | (~c3_1(a1315)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2780,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a1339) | c0_1(a1315) | c1_1(a1315) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1339)) | (~c3_1(a1315))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 0.87/1.08 tff(2781,plain,
% 0.87/1.08 (hskp7 | (~c3_1(a1339))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2780, 384, 2391, 2544, 23, 2543, 2774, 370])).
% 0.87/1.08 tff(2782,plain,
% 0.87/1.08 (hskp7),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2781, 2773])).
% 0.87/1.08 tff(2783,plain,
% 0.87/1.08 (~c3_1(a1316)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[281, 2782])).
% 0.87/1.08 tff(2784,plain,
% 0.87/1.08 (~c0_1(a1316)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1302, 2782])).
% 0.87/1.08 tff(2785,plain,
% 0.87/1.08 (~c2_1(a1316)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[275, 2782])).
% 0.87/1.08 tff(2786,plain,
% 0.87/1.08 (hskp27),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2313, 2785, 2683, 2545, 2784, 2783])).
% 0.87/1.08 tff(2787,plain,
% 0.87/1.08 (c0_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[440, 2786])).
% 0.87/1.08 tff(2788,plain,
% 0.87/1.08 (c1_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[432, 2786])).
% 0.87/1.08 tff(2789,plain,
% 0.87/1.08 (c2_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[424, 2786])).
% 0.87/1.08 tff(2790,plain,
% 0.87/1.08 (hskp14),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1314, 2789, 2545, 2784, 2788, 2787, 2785, 2783])).
% 0.87/1.08 tff(2791,plain,
% 0.87/1.08 (~c2_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[199, 2790])).
% 0.87/1.08 tff(2792,plain,
% 0.87/1.08 (~c1_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[205, 2790])).
% 0.87/1.08 tff(2793,plain,
% 0.87/1.08 (c0_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[220, 2790])).
% 0.87/1.08 tff(2794,plain,
% 0.87/1.08 (hskp29),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[471, 2683, 384, 2793, 2792, 2791, 21])).
% 0.87/1.08 tff(2795,plain,
% 0.87/1.08 (c2_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[487, 2794])).
% 0.87/1.08 tff(2796,plain,
% 0.87/1.08 (c1_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[495, 2794])).
% 0.87/1.08 tff(2797,plain,
% 0.87/1.08 (c3_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[479, 2794])).
% 0.87/1.08 tff(2798,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1929, 2797, 2796, 2785, 2683, 2786, 2795, 2784, 2783])).
% 0.87/1.08 tff(2799,plain,(c2_1(a1319) | c2_1(a1339) | c0_1(a1319) | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2800,plain,
% 0.87/1.08 (c2_1(a1319)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2799, 2037, 2038, 23])).
% 0.87/1.08 tff(2801,plain,
% 0.87/1.08 (hskp14),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[461, 706, 22])).
% 0.87/1.08 tff(2802,plain,
% 0.87/1.08 (~c2_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[199, 2801])).
% 0.87/1.08 tff(2803,plain,
% 0.87/1.08 (~c1_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[205, 2801])).
% 0.87/1.08 tff(2804,plain,
% 0.87/1.08 (c0_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[220, 2801])).
% 0.87/1.08 tff(2805,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[471, 706, 384, 11, 2804, 2803, 2802, 21])).
% 0.87/1.08 tff(2806,plain,(hskp18 | hskp29 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2807,plain,
% 0.87/1.08 (hskp29),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2806, 22, 2683])).
% 0.87/1.08 tff(2808,plain,
% 0.87/1.08 (c3_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[479, 2807])).
% 0.87/1.08 tff(2809,plain,
% 0.87/1.08 (c2_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[487, 2807])).
% 0.87/1.08 tff(2810,plain,
% 0.87/1.08 (c1_1(a1338)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[495, 2807])).
% 0.87/1.08 tff(2811,plain,
% 0.87/1.08 (hskp22),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[502, 384, 46, 2810, 2809, 2808, 415])).
% 0.87/1.08 tff(2812,plain,
% 0.87/1.08 (~c3_1(a1356)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[538, 2811])).
% 0.87/1.08 tff(2813,plain,
% 0.87/1.08 (c1_1(a1356)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[510, 2811])).
% 0.87/1.08 tff(2814,plain,
% 0.87/1.08 (c0_1(a1356)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[518, 2811])).
% 0.87/1.08 tff(2815,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2816,plain,
% 0.87/1.08 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339))) <=> (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2817,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2816])).
% 0.87/1.08 tff(2818,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2817, 2815])).
% 0.87/1.08 tff(2819,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2820,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 0.87/1.08 tff(2821,plain,
% 0.87/1.08 (c3_1(a1339)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2820, 384, 22, 2814, 2813, 2812, 2682, 23, 533])).
% 0.87/1.08 tff(2822,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2823,plain,
% 0.87/1.08 (((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2824,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2823])).
% 0.87/1.08 tff(2825,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2824, 2822])).
% 0.87/1.08 tff(2826,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1339)) | (~c0_1(a1339)) | (~c3_1(a1339)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2827,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | (~c0_1(a1339)) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c1_1(a1339)) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 0.87/1.08 tff(2828,plain,
% 0.87/1.08 ((~c3_1(a1348)) | (~c3_1(a1339)) | (~c2_1(a1319))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2827, 384, 762, 2391, 626, 2682, 2038, 2037, 10])).
% 0.87/1.08 tff(2829,plain,
% 0.87/1.08 (~c3_1(a1348)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2828, 2821, 2800])).
% 0.87/1.08 tff(2830,plain,
% 0.87/1.08 (hskp14),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[461, 22, 2683])).
% 0.87/1.08 tff(2831,plain,
% 0.87/1.08 (~c2_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[199, 2830])).
% 0.87/1.08 tff(2832,plain,
% 0.87/1.08 (c0_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[220, 2830])).
% 0.87/1.08 tff(2833,plain,
% 0.87/1.08 (c3_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[545, 384, 22, 2814, 2813, 2832, 2812, 2831, 533])).
% 0.87/1.08 tff(2834,plain,
% 0.87/1.08 (~c1_1(a1330)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[205, 2830])).
% 0.87/1.08 tff(2835,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2836,plain,
% 0.87/1.08 (((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2837,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2836])).
% 0.87/1.08 tff(2838,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2837, 2835])).
% 0.87/1.08 tff(2839,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1348) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2840,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c1_1(a1348)) | (~c2_1(a1348)) | c3_1(a1348) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c0_1(a1356))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 0.87/1.08 tff(2841,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2840, 384, 2814, 2813, 770, 762, 2812, 2834, 2831, 636, 2833, 2829])).
% 0.87/1.08 tff(2842,plain,(hskp27 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2843,plain,
% 0.87/1.08 (hskp27),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2842, 46, 2037, 23, 2038])).
% 0.87/1.08 tff(2844,plain,
% 0.87/1.08 (c2_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[424, 2843])).
% 0.87/1.08 tff(2845,plain,
% 0.87/1.08 (c0_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[440, 2843])).
% 0.87/1.08 tff(2846,assumption,(~c3_1(a1307)), introduced(assumption)).
% 0.87/1.08 tff(2847,plain,
% 0.87/1.08 (hskp30 | c3_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1916, 706, 384, 945, 993, 1744])).
% 0.87/1.08 tff(2848,plain,
% 0.87/1.08 (hskp30),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2847, 2846])).
% 0.87/1.08 tff(2849,plain,
% 0.87/1.08 (c3_1(a1372)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1758, 2848])).
% 0.87/1.08 tff(2850,plain,
% 0.87/1.08 (c1_1(a1372)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1766, 2848])).
% 0.87/1.08 tff(2851,plain,
% 0.87/1.08 (c0_1(a1372)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1774, 2848])).
% 0.87/1.08 tff(2852,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2853,plain,
% 0.87/1.08 ((hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2854,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2853])).
% 0.87/1.08 tff(2855,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2854, 2852])).
% 0.87/1.08 tff(2856,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c3_1(a1307) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2857,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | c3_1(a1307) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 0.87/1.08 tff(2858,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2857, 384, 46, 2851, 2850, 2849, 945, 993, 1073, 2846])).
% 0.87/1.08 tff(2859,plain,(c3_1(a1307) | hskp11 | (~c0_1(a1307)) | (~c2_1(a1307)) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2860,plain,
% 0.87/1.08 (c3_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2859, 46, 2845, 2844, 2683])).
% 0.87/1.08 tff(2861,plain,
% 0.87/1.08 (c1_1(a1307)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[432, 2843])).
% 0.87/1.08 tff(2862,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2863,plain,
% 0.87/1.08 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2864,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2863])).
% 0.87/1.08 tff(2865,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2864, 2862])).
% 0.87/1.08 tff(2866,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2867,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c2_1(a1319))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 0.87/1.08 tff(2868,plain,
% 0.87/1.08 ((~c3_1(a1348)) | (~c3_1(a1307))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2867, 384, 2845, 2861, 762, 2800, 626, 2038, 2037, 10])).
% 0.87/1.08 tff(2869,plain,
% 0.87/1.08 (~c3_1(a1348)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2868, 2860])).
% 0.87/1.08 tff(2870,plain,
% 0.87/1.08 (hskp17 | (~c3_1(a1307))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[999, 384, 2845, 2861, 2844, 992])).
% 0.87/1.08 tff(2871,plain,
% 0.87/1.08 (hskp17),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2870, 2860])).
% 0.87/1.08 tff(2872,plain,
% 0.87/1.08 (~c0_1(a1334)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[783, 2871])).
% 0.87/1.08 tff(2873,plain,
% 0.87/1.08 (c3_1(a1334)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[792, 2871])).
% 0.87/1.08 tff(2874,plain,
% 0.87/1.08 (c2_1(a1334)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[800, 2871])).
% 0.87/1.08 tff(2875,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1010, 384, 2845, 2861, 762, 2874, 2873, 626, 2872, 10, 2869, 2860])).
% 0.87/1.08 tff(2876,plain,(hskp11 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2877,plain,
% 0.87/1.08 (hskp11),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2876, 2037, 2038, 23])).
% 0.87/1.08 tff(2878,plain,
% 0.87/1.08 (~c1_1(a1324)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[91, 2877])).
% 0.87/1.08 tff(2879,plain,
% 0.87/1.08 (c0_1(a1324)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[99, 2877])).
% 0.87/1.08 tff(2880,plain,
% 0.87/1.08 (c3_1(a1324)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[107, 2877])).
% 0.87/1.08 tff(2881,assumption,(~hskp9), introduced(assumption)).
% 0.87/1.08 tff(2882,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2883,plain,
% 0.87/1.08 ((hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2884,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2883])).
% 0.87/1.08 tff(2885,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2884, 2882])).
% 0.87/1.08 tff(2886,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339)) | (~c0_1(a1339)) | c2_1(a1339) | c3_1(a1339) | (~c0_1(a1339)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2887,plain,
% 0.87/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | (~ndr1_0) | c3_1(a1339) | (~c1_1(a1339))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 0.87/1.08 tff(2888,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2887, 384, 22, 2391, 2682, 23, 533, 176])).
% 0.87/1.08 tff(2889,plain,(c3_1(a1339) | hskp27 | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2890,plain,
% 0.87/1.08 (c3_1(a1339)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2889, 22, 23])).
% 0.87/1.08 tff(2891,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2892,plain,
% 0.87/1.08 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2893,plain,
% 0.87/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2892])).
% 0.87/1.09 tff(2894,plain,
% 0.87/1.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2893, 2891])).
% 0.87/1.09 tff(2895,plain,
% 0.87/1.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1311) | (~c3_1(a1311)) | (~c2_1(a1311)))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2896,plain,
% 0.87/1.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1311) | (~ndr1_0) | (~c3_1(a1339)) | (~c3_1(a1311)) | (~c2_1(a1311))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 0.87/1.09 tff(2897,plain,
% 0.87/1.09 (~c3_1(a1311)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2896, 384, 22, 1692, 2682, 23, 1690, 1710, 2890])).
% 0.87/1.09 tff(2898,plain,
% 0.87/1.09 (hskp30 | c3_1(a1311)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1750, 2683, 384, 1693, 1692, 1744])).
% 0.87/1.09 tff(2899,plain,
% 0.87/1.09 (hskp30),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2898, 2897])).
% 0.87/1.09 tff(2900,plain,
% 0.87/1.09 (c0_1(a1372)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1774, 2899])).
% 0.87/1.09 tff(2901,plain,
% 0.87/1.09 (hskp15),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1723, 384, 2832, 1693, 2834, 2831, 1690, 1601, 2897])).
% 0.87/1.09 tff(2902,plain,
% 0.87/1.09 (~c3_1(a1331)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1161, 2901])).
% 0.87/1.09 tff(2903,plain,
% 0.87/1.09 (c1_1(a1372)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1766, 2899])).
% 0.87/1.09 tff(2904,plain,
% 0.87/1.09 (c3_1(a1372)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1758, 2899])).
% 0.87/1.09 tff(2905,plain,
% 0.87/1.09 (c2_1(a1331)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1170, 2901])).
% 0.87/1.09 tff(2906,plain,
% 0.87/1.09 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.87/1.09 inference(bind,[status(th)],[])).
% 0.87/1.09 tff(2907,plain,
% 0.87/1.09 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(quant_intro,[status(thm)],[2906])).
% 0.87/1.09 tff(2908,plain,
% 0.87/1.09 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2909,plain,
% 0.87/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> ((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.87/1.09 inference(bind,[status(th)],[])).
% 0.87/1.09 tff(2910,plain,
% 0.87/1.09 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(quant_intro,[status(thm)],[2909])).
% 0.87/1.09 tff(2911,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.87/1.09 tff(2912,plain,
% 0.87/1.09 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 0.87/1.09 tff(2913,plain,
% 0.87/1.09 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2912, 2908])).
% 0.87/1.09 tff(2914,plain,(
% 0.87/1.09 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(skolemize,[status(sab)],[2913])).
% 0.87/1.09 tff(2915,plain,
% 0.87/1.09 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2914, 2907])).
% 0.87/1.09 tff(2916,plain,
% 0.87/1.09 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2917,plain,
% 0.87/1.09 ((hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311))) <=> (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2918,plain,
% 0.87/1.09 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2917])).
% 0.87/1.09 tff(2919,plain,
% 0.87/1.09 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311)))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2918, 2916])).
% 0.87/1.09 tff(2920,plain,
% 0.87/1.09 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c3_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2921,plain,
% 0.87/1.09 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp9 | hskp6 | (~ndr1_0) | (~c0_1(a1311)) | c3_1(a1311) | (~c2_1(a1311))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 0.87/1.09 tff(2922,plain,
% 0.87/1.09 (hskp6 | c3_1(a1311)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2921, 384, 2881, 1693, 1692, 2915])).
% 0.87/1.09 tff(2923,plain,
% 0.87/1.09 (hskp6),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2922, 2897])).
% 0.87/1.09 tff(2924,plain,
% 0.87/1.09 (~c0_1(a1315)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1062, 2923])).
% 0.87/1.09 tff(2925,plain,
% 0.87/1.09 (c3_1(a1315)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1104, 2923])).
% 0.87/1.09 tff(2926,plain,
% 0.87/1.09 (~c1_1(a1315)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1134, 2923])).
% 0.87/1.09 tff(2927,plain,
% 0.87/1.09 (c0_1(a1338)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2055, 2926, 2037, 2879, 2880, 2810, 2925, 2808, 2878, 2924, 2809, 2800, 2038, 22])).
% 0.87/1.09 tff(2928,plain,
% 0.87/1.09 (hskp17 | (~c0_1(a1338))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1655, 384, 2810, 2809, 2808, 992])).
% 0.87/1.09 tff(2929,plain,
% 0.87/1.09 (hskp17),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2928, 2927])).
% 0.87/1.09 tff(2930,plain,
% 0.87/1.09 (c0_1(a1331)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1793, 2929, 2905, 2904, 2903, 2902, 2900])).
% 0.87/1.09 tff(2931,plain,
% 0.87/1.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2932,plain,
% 0.87/1.09 ((hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324))) <=> (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2933,plain,
% 0.87/1.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2932])).
% 0.87/1.09 tff(2934,plain,
% 0.87/1.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324)))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2933, 2931])).
% 0.87/1.09 tff(2935,plain,
% 0.87/1.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1324) | (~c3_1(a1324)) | (~c2_1(a1324)))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2936,plain,
% 0.87/1.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | (~c0_1(a1339)) | c2_1(a1339) | c1_1(a1324) | (~ndr1_0) | (~c3_1(a1339)) | (~c2_1(a1324)) | (~c3_1(a1324))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 0.87/1.09 tff(2937,plain,
% 0.87/1.09 (hskp27 | (~c3_1(a1339)) | (~c2_1(a1324))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2936, 384, 2880, 2682, 23, 2878, 1710])).
% 0.87/1.09 tff(2938,plain,
% 0.87/1.09 (~c2_1(a1324)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2937, 2890, 22])).
% 0.87/1.09 tff(2939,plain,
% 0.87/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2940,plain,
% 0.87/1.09 (((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324))) <=> (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2941,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[2940])).
% 0.93/1.09 tff(2942,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[2941, 2939])).
% 0.93/1.09 tff(2943,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1330) | c3_1(a1330) | (~c0_1(a1330)) | c1_1(a1311) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1324) | c2_1(a1324) | (~c3_1(a1324)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(2944,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1330) | c1_1(a1324) | c1_1(a1311) | (~ndr1_0) | c3_1(a1330) | (~c0_1(a1330)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c2_1(a1324) | (~c3_1(a1324))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 0.93/1.09 tff(2945,plain,
% 0.93/1.09 (c3_1(a1330)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2944, 384, 2832, 2880, 1693, 1692, 2831, 2878, 1690, 556, 2938])).
% 0.93/1.09 tff(2946,plain,
% 0.93/1.09 (c1_1(a1331)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1178, 2901])).
% 0.93/1.09 tff(2947,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1733, 384, 2946, 2905, 2902, 2834, 2831, 636, 2945, 2930])).
% 0.93/1.09 tff(2948,plain,((~hskp3) | c3_1(a1319) | c0_1(a1319) | hskp27 | hskp9 | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(2949,plain,
% 0.93/1.09 (~hskp3),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2948, 2881, 2038, 22, 2037, 23])).
% 0.93/1.09 tff(2950,plain,
% 0.93/1.09 (hskp7),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1668, 2949, 2880, 2809, 2879, 2808, 2878, 2832, 2834, 2831, 2810])).
% 0.93/1.09 tff(2951,plain,
% 0.93/1.09 (~c3_1(a1316)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[281, 2950])).
% 0.93/1.09 tff(2952,plain,
% 0.93/1.09 (~c2_1(a1316)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[275, 2950])).
% 0.93/1.09 tff(2953,plain,
% 0.93/1.09 (~c0_1(a1316)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1302, 2950])).
% 0.93/1.09 tff(2954,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2955,plain,
% 0.93/1.09 ((hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316))) <=> (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2956,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[2955])).
% 0.93/1.09 tff(2957,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[2956, 2954])).
% 0.93/1.09 tff(2958,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1316) | c3_1(a1316) | (~c1_1(a1316)) | c2_1(a1316) | c0_1(a1316) | (~c1_1(a1316)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(2959,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1316) | c2_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c1_1(a1316))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[2958, 2957])).
% 0.93/1.09 tff(2960,plain,
% 0.93/1.09 (~c1_1(a1316)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2959, 384, 2881, 2953, 2952, 2951, 1384])).
% 0.93/1.09 tff(2961,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2962,plain,
% 0.93/1.09 ((hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316)) <=> (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2963,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316)))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[2962])).
% 0.93/1.09 tff(2964,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316))),
% 0.93/1.09 inference(transitivity,[status(thm)],[2963, 2961])).
% 0.93/1.09 tff(2965,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a1339) | (~c0_1(a1339)) | (~c3_1(a1339)) | c1_1(a1316) | c0_1(a1316) | c3_1(a1316))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(2966,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | (~c0_1(a1339)) | c2_1(a1339) | c0_1(a1316) | c3_1(a1316) | (~ndr1_0) | (~c3_1(a1339)) | c1_1(a1316)),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[2965, 2964])).
% 0.93/1.09 tff(2967,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2966, 384, 2949, 2682, 23, 2953, 2951, 578, 2890, 2960])).
% 0.93/1.09 tff(2968,plain,(hskp9 | c2_1(a1339) | c0_1(a1319) | hskp27 | c3_1(a1319)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(2969,plain,
% 0.93/1.09 (hskp9),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2968, 22, 2038, 23, 2037])).
% 0.93/1.09 tff(2970,plain,
% 0.93/1.09 (~c0_1(a1320)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1402, 2969])).
% 0.93/1.09 tff(2971,plain,
% 0.93/1.09 (c2_1(a1320)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1410, 2969])).
% 0.93/1.09 tff(2972,plain,
% 0.93/1.09 (~c1_1(a1320)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1396, 2969])).
% 0.93/1.09 tff(2973,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2654, 2972, 2971, 2877, 22, 2800, 2038, 2970, 2037])).
% 0.93/1.09 tff(2974,plain,(hskp27 | c0_1(a1319) | c3_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(2975,plain,
% 0.93/1.09 (hskp27),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2974, 2037, 2038, 23])).
% 0.93/1.09 tff(2976,plain,
% 0.93/1.09 (c2_1(a1307)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[424, 2975])).
% 0.93/1.09 tff(2977,plain,
% 0.93/1.09 (c1_1(a1307)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[432, 2975])).
% 0.93/1.09 tff(2978,plain,
% 0.93/1.09 (c0_1(a1307)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[440, 2975])).
% 0.93/1.09 tff(2979,assumption,(c3_1(a1348)), introduced(assumption)).
% 0.93/1.09 tff(2980,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2981,plain,
% 0.93/1.09 (((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(2982,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[2981])).
% 0.93/1.09 tff(2983,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[2982, 2980])).
% 0.93/1.09 tff(2984,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c2_1(a1324)) | (~c0_1(a1324)) | c0_1(a1348) | (~c3_1(a1348)) | (~c2_1(a1348)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(2985,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c1_1(a1324) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c3_1(a1348)) | (~c2_1(a1348)) | (~c2_1(a1319)) | (~c2_1(a1324)) | (~c0_1(a1324))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 0.93/1.09 tff(2986,plain,
% 0.93/1.09 ((~c3_1(a1348)) | (~c2_1(a1324))),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2985, 384, 762, 1576, 2039, 626, 109, 2038, 2037, 395])).
% 0.93/1.09 tff(2987,plain,
% 0.93/1.09 (~c2_1(a1324)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2986, 2979])).
% 0.93/1.09 tff(2988,plain,
% 0.93/1.09 ((~c3_1(a1348)) | (~c3_1(a1307))),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2867, 384, 945, 944, 762, 2039, 626, 2038, 2037, 10])).
% 0.93/1.09 tff(2989,plain,
% 0.93/1.09 (~c3_1(a1307)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2988, 2979])).
% 0.93/1.09 tff(2990,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2679, 384, 945, 944, 993, 1575, 109, 636, 2989, 2987])).
% 0.93/1.09 tff(2991,plain,((~c3_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1324)) | c1_1(a1324) | (~c2_1(a1319)) | c0_1(a1319) | c3_1(a1319) | (~c0_1(a1324))), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(2992,plain,
% 0.93/1.09 (~c3_1(a1348)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2991, 2978, 2977, 2976, 2880, 2878, 2800, 2038, 2037, 2879])).
% 0.93/1.09 tff(2993,plain,
% 0.93/1.09 (hskp12 | c3_1(a1348)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1859, 384, 2978, 2977, 2976, 770, 626, 1196])).
% 0.93/1.09 tff(2994,plain,
% 0.93/1.09 (hskp12),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[2993, 2992])).
% 0.93/1.09 tff(2995,plain,
% 0.93/1.09 (~c0_1(a1325)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1208, 2994])).
% 0.93/1.09 tff(2996,plain,
% 0.93/1.09 (c3_1(a1325)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1216, 2994])).
% 0.93/1.09 tff(2997,plain,
% 0.93/1.09 (c1_1(a1325)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1224, 2994])).
% 0.93/1.09 tff(2998,plain,
% 0.93/1.09 (c2_1(a1325)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1472, 384, 2997, 2996, 2879, 2880, 2995, 2878, 35])).
% 0.93/1.09 tff(2999,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(3000,plain,
% 0.93/1.09 ((hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(3001,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[3000])).
% 0.93/1.09 tff(3002,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[3001, 2999])).
% 0.93/1.09 tff(3003,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c1_1(a1325)) | (~c2_1(a1325)) | (~c3_1(a1325)) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c2_1(a1307)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3004,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a1307)) | (~c2_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)) | (~c1_1(a1325))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3003, 3002])).
% 0.93/1.10 tff(3005,plain,
% 0.93/1.10 (hskp17),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3004, 384, 2978, 2977, 2976, 2997, 2996, 992, 2998])).
% 0.93/1.10 tff(3006,plain,
% 0.93/1.10 (~c0_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[783, 3005])).
% 0.93/1.10 tff(3007,plain,
% 0.93/1.10 (c3_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[792, 3005])).
% 0.93/1.10 tff(3008,plain,
% 0.93/1.10 (c2_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[800, 3005])).
% 0.93/1.10 tff(3009,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3010,plain,
% 0.93/1.10 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348))) <=> (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3011,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3010])).
% 0.93/1.10 tff(3012,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3011, 3009])).
% 0.93/1.10 tff(3013,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1325) | (~c3_1(a1325)) | (~c2_1(a1325)) | c3_1(a1348) | c0_1(a1348) | (~c2_1(a1348)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3014,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1348) | c0_1(a1325) | (~ndr1_0) | (~c2_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | (~c3_1(a1325)) | (~c2_1(a1325))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3013, 3012])).
% 0.93/1.10 tff(3015,plain,
% 0.93/1.10 ((~c3_1(a1307)) | (~c2_1(a1325))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3014, 384, 2978, 2977, 762, 2996, 626, 2995, 10, 2992])).
% 0.93/1.10 tff(3016,plain,
% 0.93/1.10 (~c3_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3015, 2998])).
% 0.93/1.10 tff(3017,plain,
% 0.93/1.10 (hskp30 | c3_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1916, 2683, 384, 2978, 2976, 1744])).
% 0.93/1.10 tff(3018,plain,
% 0.93/1.10 (hskp30),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3017, 3016])).
% 0.93/1.10 tff(3019,plain,
% 0.93/1.10 (c3_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1758, 3018])).
% 0.93/1.10 tff(3020,plain,
% 0.93/1.10 (c1_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1766, 3018])).
% 0.93/1.10 tff(3021,plain,
% 0.93/1.10 (c0_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1774, 3018])).
% 0.93/1.10 tff(3022,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3023,plain,
% 0.93/1.10 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3024,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3023])).
% 0.93/1.10 tff(3025,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3024, 3022])).
% 0.93/1.10 tff(3026,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1334) | (~c3_1(a1334)) | (~c2_1(a1334)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3027,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1334) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c2_1(a1334)) | (~c3_1(a1334)) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c2_1(a1319))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3026, 3025])).
% 0.93/1.10 tff(3028,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3027, 384, 3021, 3020, 3019, 3008, 3007, 2800, 3006, 2038, 2037, 10])).
% 0.93/1.10 tff(3029,plain,(c3_1(a1319) | c0_1(a1319) | c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3030,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3029, 2757, 2756, 23])).
% 0.93/1.10 tff(3031,plain,(c2_1(a1339)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3032,plain,
% 0.93/1.10 (~hskp18),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[70, 3031])).
% 0.93/1.10 tff(3033,plain,
% 0.93/1.10 (hskp29 | hskp27),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2806, 3032])).
% 0.93/1.10 tff(3034,plain,
% 0.93/1.10 (hskp29),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3033, 22])).
% 0.93/1.10 tff(3035,plain,
% 0.93/1.10 (c2_1(a1338)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[487, 3034])).
% 0.93/1.10 tff(3036,plain,
% 0.93/1.10 (c1_1(a1338)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[495, 3034])).
% 0.93/1.10 tff(3037,plain,
% 0.93/1.10 (hskp27 | hskp14),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[461, 3032])).
% 0.93/1.10 tff(3038,plain,
% 0.93/1.10 (hskp14),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3037, 22])).
% 0.93/1.10 tff(3039,plain,
% 0.93/1.10 (~c2_1(a1330)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[199, 3038])).
% 0.93/1.10 tff(3040,plain,
% 0.93/1.10 (~c1_1(a1330)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[205, 3038])).
% 0.93/1.10 tff(3041,plain,
% 0.93/1.10 (c0_1(a1330)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[220, 3038])).
% 0.93/1.10 tff(3042,plain,
% 0.93/1.10 (c3_1(a1330)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[545, 384, 22, 2127, 2126, 3041, 2124, 3039, 533])).
% 0.93/1.10 tff(3043,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3044,plain,
% 0.93/1.10 (((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330))) <=> (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3045,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3044])).
% 0.93/1.10 tff(3046,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3045, 3043])).
% 0.93/1.10 tff(3047,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c2_1(a1356)) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c1_1(a1330) | c2_1(a1330) | (~c3_1(a1330)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3048,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1356) | c1_1(a1330) | c2_1(a1330) | (~ndr1_0) | (~c3_1(a1330)) | (~c1_1(a1356)) | (~c2_1(a1356)) | (~c0_1(a1356))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3047, 3046])).
% 0.93/1.10 tff(3049,plain,
% 0.93/1.10 ((~c3_1(a1330)) | (~c2_1(a1356))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3048, 384, 2127, 2126, 2124, 3040, 3039, 636])).
% 0.93/1.10 tff(3050,plain,
% 0.93/1.10 (~c2_1(a1356)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3049, 3042])).
% 0.93/1.10 tff(3051,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3052,plain,
% 0.93/1.10 ((hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356))) <=> (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3053,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3052])).
% 0.93/1.10 tff(3054,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3053, 3051])).
% 0.93/1.10 tff(3055,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1356) | (~c1_1(a1356)) | (~c0_1(a1356)) | c2_1(a1356) | c3_1(a1356) | (~c0_1(a1356)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3056,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp27 | c3_1(a1356) | (~ndr1_0) | (~c1_1(a1356)) | c2_1(a1356) | (~c0_1(a1356))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 0.93/1.10 tff(3057,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3056, 384, 22, 2127, 2126, 2124, 533, 3050])).
% 0.93/1.10 tff(3058,plain,((~hskp22) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3059,plain,
% 0.93/1.10 (~hskp22),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3058, 22])).
% 0.93/1.10 tff(3060,plain,
% 0.93/1.10 (c3_1(a1338)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[479, 3034])).
% 0.93/1.10 tff(3061,plain,
% 0.93/1.10 (hskp22 | hskp11),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[502, 384, 3036, 3035, 3060, 415])).
% 0.93/1.10 tff(3062,plain,
% 0.93/1.10 (hskp11),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3061, 3059])).
% 0.93/1.10 tff(3063,plain,
% 0.93/1.10 (~c1_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[91, 3062])).
% 0.93/1.10 tff(3064,plain,
% 0.93/1.10 (c0_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[99, 3062])).
% 0.93/1.10 tff(3065,plain,
% 0.93/1.10 (c3_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[107, 3062])).
% 0.93/1.10 tff(3066,assumption,(c0_1(a1338)), introduced(assumption)).
% 0.93/1.10 tff(3067,plain,
% 0.93/1.10 (hskp8),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2754, 3032])).
% 0.93/1.10 tff(3068,plain,
% 0.93/1.10 (~c3_1(a1319)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1018, 3067])).
% 0.93/1.10 tff(3069,plain,
% 0.93/1.10 (~c0_1(a1319)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1024, 3067])).
% 0.93/1.10 tff(3070,plain,
% 0.93/1.10 (hskp17),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1656, 3066])).
% 0.93/1.10 tff(3071,plain,
% 0.93/1.10 (~c0_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[783, 3070])).
% 0.93/1.10 tff(3072,plain,
% 0.93/1.10 (c2_1(a1319)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1112, 3067])).
% 0.93/1.10 tff(3073,plain,
% 0.93/1.10 (c3_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[792, 3070])).
% 0.93/1.10 tff(3074,plain,
% 0.93/1.10 (c2_1(a1334)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[800, 3070])).
% 0.93/1.10 tff(3075,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1902, 384, 1634, 1635, 3074, 3073, 3072, 3071, 3069, 3068, 10, 3066])).
% 0.93/1.10 tff(3076,plain,((~c0_1(a1338)) | (~c1_1(a1338)) | (~c3_1(a1338)) | (~c2_1(a1338))), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3077,plain,
% 0.93/1.10 (~c0_1(a1338)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3076, 3036, 3060, 3035])).
% 0.93/1.10 tff(3078,assumption,(~c1_1(a1311)), introduced(assumption)).
% 0.93/1.10 tff(3079,assumption,(c2_1(a1311)), introduced(assumption)).
% 0.93/1.10 tff(3080,assumption,(c0_1(a1311)), introduced(assumption)).
% 0.93/1.10 tff(3081,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3082,plain,
% 0.93/1.10 (((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3083,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3082])).
% 0.93/1.10 tff(3084,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3083, 3081])).
% 0.93/1.10 tff(3085,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1311) | (~c2_1(a1311)) | (~c0_1(a1311)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3086,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c1_1(a1311) | (~ndr1_0) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | (~c2_1(a1319))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 0.93/1.10 tff(3087,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3086, 384, 1649, 1635, 3072, 3080, 3079, 3069, 3068, 3078, 395, 1636])).
% 0.93/1.10 tff(3088,plain,(c0_1(a1338) | (~c2_1(a1338)) | (~c3_1(a1338)) | (~c0_1(a1311)) | (~c2_1(a1311)) | c1_1(a1311)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3089,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3088, 1692, 1693, 1635, 1649, 1636, 1690])).
% 0.93/1.10 tff(3090,plain,((~hskp3) | (~c3_1(a1338)) | (~c2_1(a1338)) | c0_1(a1338)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3091,plain,
% 0.93/1.10 (~hskp3),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3090, 3060, 3035, 3077])).
% 0.93/1.10 tff(3092,plain,
% 0.93/1.10 (hskp7),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1668, 3091, 3065, 3035, 3064, 3060, 3063, 3041, 3040, 3039, 3036])).
% 0.93/1.10 tff(3093,plain,
% 0.93/1.10 (~c3_1(a1316)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[281, 3092])).
% 0.93/1.10 tff(3094,plain,
% 0.93/1.10 (~c2_1(a1316)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[275, 3092])).
% 0.93/1.10 tff(3095,plain,
% 0.93/1.10 (~c0_1(a1316)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1302, 3092])).
% 0.93/1.10 tff(3096,plain,
% 0.93/1.10 (hskp6),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1958, 384, 770, 762, 626, 3095, 3094, 3093, 1049])).
% 0.93/1.10 tff(3097,plain,
% 0.93/1.10 (~c0_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1062, 3096])).
% 0.93/1.10 tff(3098,plain,
% 0.93/1.10 (c3_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1104, 3096])).
% 0.93/1.10 tff(3099,plain,
% 0.93/1.10 (~c1_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1134, 3096])).
% 0.93/1.10 tff(3100,plain,
% 0.93/1.10 (c0_1(a1338) | hskp27 | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1315)) | c1_1(a1315) | (~c1_1(a1338)) | (~c3_1(a1338)) | c1_1(a1324) | c0_1(a1315) | (~c2_1(a1338))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2055, 3068, 3072, 3069])).
% 0.93/1.10 tff(3101,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3100, 3099, 3098, 3065, 3064, 3077, 3036, 3060, 3063, 3097, 3035, 22])).
% 0.93/1.10 tff(3102,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(3103,plain,
% 0.93/1.10 (hskp13),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[449, 3102])).
% 0.93/1.10 tff(3104,plain,
% 0.93/1.10 (~c2_1(a1326)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[157, 3103])).
% 0.93/1.10 tff(3105,plain,
% 0.93/1.10 (~c1_1(a1326)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[163, 3103])).
% 0.93/1.10 tff(3106,plain,
% 0.93/1.10 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3107,plain,
% 0.93/1.10 ((hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326))) <=> (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3108,plain,
% 0.93/1.10 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3107])).
% 0.93/1.10 tff(3109,plain,
% 0.93/1.10 (((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))) <=> ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3108, 3106])).
% 0.93/1.10 tff(3110,plain,
% 0.93/1.10 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp18 | hskp29 | (~ndr1_0) | c2_1(a1326) | c1_1(a1326) | (~c0_1(a1326)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3111,plain,
% 0.93/1.10 ((~![U: $i] : (hskp18 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp18 | hskp29 | c1_1(a1326) | c2_1(a1326) | (~ndr1_0) | (~c0_1(a1326))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 0.93/1.10 tff(3112,plain,
% 0.93/1.10 (hskp29 | (~c0_1(a1326))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3111, 3032, 384, 3105, 3104, 21])).
% 0.93/1.10 tff(3113,plain,
% 0.93/1.10 (~c0_1(a1326)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3112, 11])).
% 0.93/1.10 tff(3114,plain,
% 0.93/1.10 (~c3_1(a1326)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[151, 3103])).
% 0.93/1.10 tff(3115,plain,
% 0.93/1.10 (hskp6 | c0_1(a1326)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1827, 384, 770, 762, 626, 3104, 3114, 1049])).
% 0.93/1.10 tff(3116,plain,
% 0.93/1.10 (hskp6),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3115, 3113])).
% 0.93/1.10 tff(3117,plain,
% 0.93/1.10 (~c0_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1062, 3116])).
% 0.93/1.10 tff(3118,plain,
% 0.93/1.10 (c3_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1104, 3116])).
% 0.93/1.10 tff(3119,plain,
% 0.93/1.10 (c2_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[424, 3102])).
% 0.93/1.10 tff(3120,plain,
% 0.93/1.10 (c1_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[432, 3102])).
% 0.93/1.10 tff(3121,plain,
% 0.93/1.10 (c0_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[440, 3102])).
% 0.93/1.10 tff(3122,plain,
% 0.93/1.10 (hskp29 | (~c3_1(a1307))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2729, 384, 3121, 3120, 3119, 2723])).
% 0.93/1.10 tff(3123,plain,
% 0.93/1.10 (~c3_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3122, 11])).
% 0.93/1.10 tff(3124,plain,
% 0.93/1.10 (hskp30 | c3_1(a1307)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1916, 3032, 384, 3121, 3119, 1744])).
% 0.93/1.10 tff(3125,plain,
% 0.93/1.10 (hskp30),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3124, 3123])).
% 0.93/1.10 tff(3126,plain,
% 0.93/1.10 (c3_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1758, 3125])).
% 0.93/1.10 tff(3127,plain,
% 0.93/1.10 (c1_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1766, 3125])).
% 0.93/1.10 tff(3128,plain,
% 0.93/1.10 (c0_1(a1372)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1774, 3125])).
% 0.93/1.10 tff(3129,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3130,plain,
% 0.93/1.10 (((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3131,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3130])).
% 0.93/1.10 tff(3132,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[3131, 3129])).
% 0.93/1.10 tff(3133,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1372)) | c0_1(a1315) | (~c3_1(a1315)) | (~c2_1(a1315)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(3134,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1372)) | (~c1_1(a1372)) | (~c0_1(a1372)) | (~c3_1(a1315)) | (~c2_1(a1315)) | (~c2_1(a1319))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[3133, 3132])).
% 0.93/1.10 tff(3135,plain,
% 0.93/1.10 (~c2_1(a1315)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3134, 384, 3128, 3127, 3126, 3072, 3118, 3069, 3068, 3117, 10])).
% 0.93/1.10 tff(3136,plain,
% 0.93/1.10 (c3_1(a1307) | hskp11 | (~c0_1(a1307)) | (~c2_1(a1307))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2859, 3032])).
% 0.93/1.10 tff(3137,plain,
% 0.93/1.10 (hskp11),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3136, 3123, 3119, 3121])).
% 0.93/1.10 tff(3138,plain,
% 0.93/1.10 (~c1_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[91, 3137])).
% 0.93/1.10 tff(3139,plain,
% 0.93/1.10 (c0_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[99, 3137])).
% 0.93/1.10 tff(3140,plain,
% 0.93/1.10 (c3_1(a1324)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[107, 3137])).
% 0.93/1.10 tff(3141,plain,
% 0.93/1.10 ((~c3_1(a1348)) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c2_1(a1307)) | (~c3_1(a1324)) | c1_1(a1324) | (~c0_1(a1324))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[2991, 3072, 3068, 3069])).
% 0.93/1.10 tff(3142,plain,
% 0.93/1.10 (~c3_1(a1348)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3141, 3138, 3121, 3120, 3119, 3140, 3139])).
% 0.93/1.10 tff(3143,plain,
% 0.93/1.10 (hskp12 | c3_1(a1348)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1859, 384, 3121, 3120, 3119, 770, 626, 1196])).
% 0.93/1.10 tff(3144,plain,
% 0.93/1.10 (hskp12),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[3143, 3142])).
% 0.93/1.10 tff(3145,plain,
% 0.93/1.10 (~c0_1(a1325)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1208, 3144])).
% 0.93/1.10 tff(3146,plain,
% 0.93/1.10 (c3_1(a1325)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1216, 3144])).
% 0.93/1.10 tff(3147,plain,
% 0.93/1.10 (c1_1(a1325)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1224, 3144])).
% 0.93/1.10 tff(3148,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3149,plain,
% 0.93/1.10 (((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315))) <=> (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(3150,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[3149])).
% 0.93/1.10 tff(3151,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[3150, 3148])).
% 0.93/1.11 tff(3152,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1324) | (~c0_1(a1324)) | (~c3_1(a1324)) | c0_1(a1325) | (~c1_1(a1325)) | (~c3_1(a1325)) | c0_1(a1315) | c2_1(a1315) | (~c3_1(a1315)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(3153,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1325) | c1_1(a1324) | c0_1(a1315) | (~ndr1_0) | (~c3_1(a1315)) | c2_1(a1315) | (~c0_1(a1324)) | (~c3_1(a1324)) | (~c3_1(a1325)) | (~c1_1(a1325))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[3152, 3151])).
% 0.93/1.11 tff(3154,plain,
% 0.93/1.11 ($false),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3153, 384, 3147, 3146, 3139, 3140, 3118, 3145, 3138, 3117, 35, 3135])).
% 0.93/1.11 tff(3155,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 0.93/1.11 tff(3156,plain,
% 0.93/1.11 (c2_1(a1338)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[487, 3155])).
% 0.93/1.11 tff(3157,plain,
% 0.93/1.11 (c3_1(a1338)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[479, 3155])).
% 0.93/1.11 tff(3158,plain,
% 0.93/1.11 (c1_1(a1338)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[495, 3155])).
% 0.93/1.11 tff(3159,plain,
% 0.93/1.11 (~c0_1(a1338)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3076, 3158, 3157, 3156])).
% 0.93/1.11 tff(3160,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(3161,plain,
% 0.93/1.11 (((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319))) <=> (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(3162,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[3161])).
% 0.93/1.11 tff(3163,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[3162, 3160])).
% 0.93/1.11 tff(3164,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1307)) | (~c0_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | c3_1(a1319) | c0_1(a1319) | (~c2_1(a1319)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(3165,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1319) | c3_1(a1319) | (~ndr1_0) | (~c0_1(a1307)) | (~c1_1(a1307)) | (~c3_1(a1307)) | c0_1(a1338) | (~c3_1(a1338)) | (~c2_1(a1338)) | (~c2_1(a1319))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 0.93/1.11 tff(3166,plain,
% 0.93/1.11 (~c3_1(a1307)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3165, 384, 3156, 3157, 3121, 3120, 3072, 3069, 3068, 10, 3159])).
% 0.93/1.11 tff(3167,plain,
% 0.93/1.11 (hskp11),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3136, 3166, 3119, 3121])).
% 0.93/1.11 tff(3168,plain,
% 0.93/1.11 (c0_1(a1324)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[99, 3167])).
% 0.93/1.11 tff(3169,plain,
% 0.93/1.11 (c3_1(a1324)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[107, 3167])).
% 0.93/1.11 tff(3170,plain,
% 0.93/1.11 (~c1_1(a1324)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[91, 3167])).
% 0.93/1.11 tff(3171,plain,
% 0.93/1.11 (~c3_1(a1348)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3141, 3170, 3121, 3120, 3119, 3169, 3168])).
% 0.93/1.11 tff(3172,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(3173,plain,
% 0.93/1.11 (((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326)) <=> (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(3174,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[3173])).
% 0.93/1.11 tff(3175,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307))),
% 0.93/1.11 inference(transitivity,[status(thm)],[3174, 3172])).
% 0.93/1.11 tff(3176,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1307) | (~c1_1(a1307)) | (~c0_1(a1307)) | c0_1(a1348) | c3_1(a1348) | (~c1_1(a1348)) | c3_1(a1326) | c1_1(a1326) | c2_1(a1326))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(3177,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1348) | c1_1(a1326) | c2_1(a1326) | c3_1(a1326) | (~ndr1_0) | (~c1_1(a1348)) | c3_1(a1348) | (~c0_1(a1307)) | (~c1_1(a1307)) | c3_1(a1307)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 0.93/1.11 tff(3178,plain,
% 0.93/1.11 ($false),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[3177, 384, 3121, 3120, 770, 626, 3105, 3104, 3114, 405, 3171, 3166])).
% 0.93/1.11 % SZS output end Proof
% 0.93/1.11 % E exiting
%------------------------------------------------------------------------------