%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN479-1 : 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 1.48s 1.67s
% Output : Proof 1.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN479-1 : TPTP v9.0.0. Released v2.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:35:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.48/1.67 % SZS status Unsatisfiable
% 1.48/1.67 % SZS output start Proof
% 1.48/1.67 tff(hskp0_type, type, (
% 1.48/1.67 hskp0: $o)).
% 1.48/1.67 tff(c3_1_type, type, (
% 1.48/1.67 c3_1: $i > $o)).
% 1.48/1.67 tff(a1435_type, type, (
% 1.48/1.67 a1435: $i)).
% 1.48/1.67 tff(hskp5_type, type, (
% 1.48/1.67 hskp5: $o)).
% 1.48/1.67 tff(a1457_type, type, (
% 1.48/1.67 a1457: $i)).
% 1.48/1.67 tff(c1_1_type, type, (
% 1.48/1.67 c1_1: $i > $o)).
% 1.48/1.67 tff(c0_1_type, type, (
% 1.48/1.67 c0_1: $i > $o)).
% 1.48/1.67 tff(c2_1_type, type, (
% 1.48/1.67 c2_1: $i > $o)).
% 1.48/1.67 tff(ndr1_0_type, type, (
% 1.48/1.67 ndr1_0: $o)).
% 1.48/1.67 tff(a1448_type, type, (
% 1.48/1.67 a1448: $i)).
% 1.48/1.67 tff(hskp12_type, type, (
% 1.48/1.67 hskp12: $o)).
% 1.48/1.67 tff(hskp11_type, type, (
% 1.48/1.67 hskp11: $o)).
% 1.48/1.67 tff(hskp2_type, type, (
% 1.48/1.67 hskp2: $o)).
% 1.48/1.67 tff(a1430_type, type, (
% 1.48/1.67 a1430: $i)).
% 1.48/1.67 tff(a1438_type, type, (
% 1.48/1.67 a1438: $i)).
% 1.48/1.67 tff(hskp7_type, type, (
% 1.48/1.67 hskp7: $o)).
% 1.48/1.67 tff(a1466_type, type, (
% 1.48/1.67 a1466: $i)).
% 1.48/1.67 tff(a1458_type, type, (
% 1.48/1.67 a1458: $i)).
% 1.48/1.67 tff(a1447_type, type, (
% 1.48/1.67 a1447: $i)).
% 1.48/1.67 tff(a1445_type, type, (
% 1.48/1.67 a1445: $i)).
% 1.48/1.67 tff(hskp10_type, type, (
% 1.48/1.67 hskp10: $o)).
% 1.48/1.67 tff(a1431_type, type, (
% 1.48/1.67 a1431: $i)).
% 1.48/1.67 tff(hskp3_type, type, (
% 1.48/1.67 hskp3: $o)).
% 1.48/1.67 tff(hskp17_type, type, (
% 1.48/1.67 hskp17: $o)).
% 1.48/1.67 tff(a1465_type, type, (
% 1.48/1.67 a1465: $i)).
% 1.48/1.67 tff(a1441_type, type, (
% 1.48/1.67 a1441: $i)).
% 1.48/1.67 tff(a1477_type, type, (
% 1.48/1.67 a1477: $i)).
% 1.48/1.67 tff(hskp23_type, type, (
% 1.48/1.67 hskp23: $o)).
% 1.48/1.67 tff(a1507_type, type, (
% 1.48/1.67 a1507: $i)).
% 1.48/1.67 tff(hskp30_type, type, (
% 1.48/1.67 hskp30: $o)).
% 1.48/1.67 tff(hskp24_type, type, (
% 1.48/1.67 hskp24: $o)).
% 1.48/1.67 tff(a1429_type, type, (
% 1.48/1.67 a1429: $i)).
% 1.48/1.67 tff(hskp4_type, type, (
% 1.48/1.67 hskp4: $o)).
% 1.48/1.67 tff(a1434_type, type, (
% 1.48/1.67 a1434: $i)).
% 1.48/1.67 tff(a1451_type, type, (
% 1.48/1.67 a1451: $i)).
% 1.48/1.67 tff(hskp14_type, type, (
% 1.48/1.67 hskp14: $o)).
% 1.48/1.67 tff(a1504_type, type, (
% 1.48/1.67 a1504: $i)).
% 1.48/1.67 tff(hskp25_type, type, (
% 1.48/1.67 hskp25: $o)).
% 1.48/1.67 tff(hskp18_type, type, (
% 1.48/1.67 hskp18: $o)).
% 1.48/1.67 tff(hskp1_type, type, (
% 1.48/1.67 hskp1: $o)).
% 1.48/1.67 tff(a1468_type, type, (
% 1.48/1.67 a1468: $i)).
% 1.48/1.67 tff(hskp22_type, type, (
% 1.48/1.67 hskp22: $o)).
% 1.48/1.67 tff(a1487_type, type, (
% 1.48/1.67 a1487: $i)).
% 1.48/1.67 tff(a1444_type, type, (
% 1.48/1.67 a1444: $i)).
% 1.48/1.67 tff(hskp9_type, type, (
% 1.48/1.67 hskp9: $o)).
% 1.48/1.67 tff(a1483_type, type, (
% 1.48/1.67 a1483: $i)).
% 1.48/1.67 tff(hskp29_type, type, (
% 1.48/1.67 hskp29: $o)).
% 1.48/1.67 tff(a1460_type, type, (
% 1.48/1.67 a1460: $i)).
% 1.48/1.67 tff(hskp19_type, type, (
% 1.48/1.67 hskp19: $o)).
% 1.48/1.67 tff(a1427_type, type, (
% 1.48/1.67 a1427: $i)).
% 1.48/1.67 tff(hskp20_type, type, (
% 1.48/1.67 hskp20: $o)).
% 1.48/1.67 tff(hskp8_type, type, (
% 1.48/1.67 hskp8: $o)).
% 1.48/1.67 tff(a1454_type, type, (
% 1.48/1.67 a1454: $i)).
% 1.48/1.67 tff(hskp16_type, type, (
% 1.48/1.67 hskp16: $o)).
% 1.48/1.67 tff(a1437_type, type, (
% 1.48/1.67 a1437: $i)).
% 1.48/1.67 tff(hskp6_type, type, (
% 1.48/1.67 hskp6: $o)).
% 1.48/1.67 tff(hskp21_type, type, (
% 1.48/1.67 hskp21: $o)).
% 1.48/1.67 tff(a1452_type, type, (
% 1.48/1.67 a1452: $i)).
% 1.48/1.67 tff(hskp15_type, type, (
% 1.48/1.67 hskp15: $o)).
% 1.48/1.67 tff(a1517_type, type, (
% 1.48/1.67 a1517: $i)).
% 1.48/1.67 tff(hskp26_type, type, (
% 1.48/1.67 hskp26: $o)).
% 1.48/1.67 tff(a1456_type, type, (
% 1.48/1.67 a1456: $i)).
% 1.48/1.67 tff(hskp28_type, type, (
% 1.48/1.67 hskp28: $o)).
% 1.48/1.67 tff(a1449_type, type, (
% 1.48/1.67 a1449: $i)).
% 1.48/1.67 tff(hskp13_type, type, (
% 1.48/1.67 hskp13: $o)).
% 1.48/1.67 tff(1,plain,
% 1.48/1.67 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(2,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[1])).
% 1.48/1.67 tff(3,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(4,plain,
% 1.48/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(5,plain,
% 1.48/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[4])).
% 1.48/1.67 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.48/1.67 tff(7,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.48/1.67 tff(8,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.48/1.67 tff(9,plain,(
% 1.48/1.67 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(skolemize,[status(sab)],[8])).
% 1.48/1.67 tff(10,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.48/1.67 tff(11,assumption,(~hskp5), introduced(assumption)).
% 1.48/1.67 tff(12,assumption,(~c0_1(a1430)), introduced(assumption)).
% 1.48/1.67 tff(13,assumption,(~hskp7), introduced(assumption)).
% 1.48/1.67 tff(14,plain,
% 1.48/1.67 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(15,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[14])).
% 1.48/1.67 tff(16,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(17,plain,
% 1.48/1.67 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(18,plain,
% 1.48/1.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[17])).
% 1.48/1.68 tff(19,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.48/1.68 tff(20,plain,
% 1.48/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.48/1.68 tff(21,plain,
% 1.48/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.48/1.68 tff(22,plain,(
% 1.48/1.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.68 inference(skolemize,[status(sab)],[21])).
% 1.48/1.68 tff(23,plain,
% 1.48/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.48/1.68 tff(24,assumption,(~c1_1(a1438)), introduced(assumption)).
% 1.48/1.68 tff(25,plain,
% 1.48/1.68 (^[U: $i] : refl((hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(26,plain,
% 1.48/1.68 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[25])).
% 1.48/1.68 tff(27,plain,
% 1.48/1.68 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(28,plain,
% 1.48/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp11) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp11) <=> (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(29,plain,
% 1.48/1.68 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp11) <=> ![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[28])).
% 1.48/1.68 tff(30,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.48/1.68 tff(31,plain,
% 1.48/1.68 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.48/1.68 tff(32,plain,
% 1.48/1.68 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.48/1.68 tff(33,plain,(
% 1.48/1.68 ![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[32])).
% 1.48/1.68 tff(34,plain,
% 1.48/1.68 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.48/1.68 tff(35,assumption,(~c3_1(a1430)), introduced(assumption)).
% 1.48/1.68 tff(36,assumption,(~hskp17), introduced(assumption)).
% 1.48/1.68 tff(37,assumption,(~c0_1(a1438)), introduced(assumption)).
% 1.48/1.68 tff(38,plain,
% 1.48/1.68 (((~hskp2) | c3_1(a1430)) <=> ((~hskp2) | c3_1(a1430))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(39,axiom,((~hskp2) | c3_1(a1430)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.48/1.68 tff(40,plain,
% 1.48/1.68 ((~hskp2) | c3_1(a1430)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.48/1.68 tff(41,plain,
% 1.48/1.68 ((~hskp2) | c3_1(a1430)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[40, 38])).
% 1.48/1.68 tff(42,plain,
% 1.48/1.68 ((~hskp2) | c3_1(a1430)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[41, 38])).
% 1.48/1.68 tff(43,plain,
% 1.48/1.68 ((~hskp2) | c3_1(a1430)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.48/1.68 tff(44,plain,
% 1.48/1.68 ((~hskp2) | c3_1(a1430)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[43, 38])).
% 1.48/1.68 tff(45,plain,
% 1.48/1.68 (~hskp2),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[44, 35])).
% 1.48/1.68 tff(46,assumption,(~c3_1(a1438)), introduced(assumption)).
% 1.48/1.68 tff(47,assumption,(~c2_1(a1438)), introduced(assumption)).
% 1.48/1.68 tff(48,plain,
% 1.48/1.68 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(49,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[48])).
% 1.48/1.68 tff(50,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(51,plain,
% 1.48/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | 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))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | 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) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(52,plain,
% 1.48/1.68 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[51])).
% 1.48/1.68 tff(53,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.48/1.68 tff(54,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.48/1.68 tff(55,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.48/1.68 tff(56,plain,(
% 1.48/1.68 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(skolemize,[status(sab)],[55])).
% 1.48/1.68 tff(57,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.48/1.68 tff(58,assumption,(~hskp2), introduced(assumption)).
% 1.48/1.68 tff(59,assumption,(~ndr1_0), introduced(assumption)).
% 1.48/1.68 tff(60,plain,
% 1.48/1.68 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(61,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.48/1.68 tff(62,plain,
% 1.48/1.68 ((~hskp30) | ndr1_0),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.48/1.68 tff(63,plain,
% 1.48/1.68 ((~hskp30) | ndr1_0),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[62, 60])).
% 1.48/1.68 tff(64,plain,
% 1.48/1.68 ((~hskp30) | ndr1_0),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.48/1.68 tff(65,plain,
% 1.48/1.68 ((~hskp30) | ndr1_0),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.48/1.68 tff(66,plain,
% 1.48/1.68 ((~hskp30) | ndr1_0),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[65, 60])).
% 1.48/1.68 tff(67,plain,
% 1.48/1.68 (~hskp30),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[66, 59])).
% 1.48/1.68 tff(68,plain,
% 1.48/1.68 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(69,plain,
% 1.48/1.68 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(70,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 1.48/1.68 tff(71,plain,
% 1.48/1.68 (ndr1_0 | (~hskp24)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.48/1.68 tff(72,plain,
% 1.48/1.68 (ndr1_0 | (~hskp24)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[71, 68])).
% 1.48/1.68 tff(73,plain,
% 1.48/1.68 (~hskp24),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[72, 59])).
% 1.48/1.68 tff(74,plain,
% 1.48/1.68 ((hskp30 | hskp24) <=> (hskp30 | hskp24)),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(75,axiom,(hskp30 | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.48/1.68 tff(76,plain,
% 1.48/1.68 (hskp30 | hskp24),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.48/1.68 tff(77,plain,
% 1.48/1.68 (hskp30 | hskp24),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[76, 74])).
% 1.48/1.68 tff(78,plain,
% 1.48/1.68 (hskp30 | hskp24),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[77, 74])).
% 1.48/1.68 tff(79,plain,
% 1.48/1.68 (hskp30 | hskp24),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[78, 74])).
% 1.48/1.68 tff(80,plain,
% 1.48/1.68 (hskp30 | hskp24),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[79, 74])).
% 1.48/1.68 tff(81,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[80, 73, 67])).
% 1.48/1.68 tff(82,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(83,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(84,plain,
% 1.48/1.68 ((hskp2 | (~ndr1_0) | c2_1(a1438) | c1_1(a1438) | c3_1(a1438) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438)) <=> (hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(85,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1438) | c1_1(a1438) | c3_1(a1438) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438)))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[84])).
% 1.48/1.68 tff(86,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1438) | c1_1(a1438) | c3_1(a1438) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438))),
% 1.48/1.68 inference(transitivity,[status(thm)],[85, 83])).
% 1.48/1.68 tff(87,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1438) | c1_1(a1438) | c3_1(a1438) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(88,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.48/1.68 tff(89,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[88, 82, 58, 46, 37, 24, 57, 47])).
% 1.48/1.68 tff(90,plain,(c2_1(a1438) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(91,plain,
% 1.48/1.68 (c2_1(a1438)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[90, 46, 37, 45, 24])).
% 1.48/1.68 tff(92,plain,
% 1.48/1.68 (((~hskp7) | c3_1(a1438)) <=> ((~hskp7) | c3_1(a1438))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(93,axiom,((~hskp7) | c3_1(a1438)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.48/1.68 tff(94,plain,
% 1.48/1.68 ((~hskp7) | c3_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.48/1.68 tff(95,plain,
% 1.48/1.68 ((~hskp7) | c3_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[94, 92])).
% 1.48/1.68 tff(96,plain,
% 1.48/1.68 ((~hskp7) | c3_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[95, 92])).
% 1.48/1.68 tff(97,plain,
% 1.48/1.68 ((~hskp7) | c3_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[96, 92])).
% 1.48/1.68 tff(98,plain,
% 1.48/1.68 ((~hskp7) | c3_1(a1438)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[97, 92])).
% 1.48/1.68 tff(99,plain,
% 1.48/1.68 (~hskp7),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[98, 46])).
% 1.48/1.68 tff(100,assumption,(~c2_1(a1435)), introduced(assumption)).
% 1.48/1.68 tff(101,assumption,(~c3_1(a1435)), introduced(assumption)).
% 1.48/1.68 tff(102,assumption,(c0_1(a1435)), introduced(assumption)).
% 1.48/1.68 tff(103,plain,
% 1.48/1.68 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(104,plain,
% 1.48/1.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[103])).
% 1.48/1.68 tff(105,plain,
% 1.48/1.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(106,plain,
% 1.48/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | 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)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(107,plain,
% 1.48/1.68 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[106])).
% 1.48/1.68 tff(108,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.48/1.68 tff(109,plain,
% 1.48/1.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.48/1.68 tff(110,plain,
% 1.48/1.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.48/1.68 tff(111,plain,(
% 1.48/1.68 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[110])).
% 1.48/1.68 tff(112,plain,
% 1.48/1.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[111, 104])).
% 1.48/1.68 tff(113,plain,
% 1.48/1.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(114,plain,
% 1.48/1.68 ((hskp7 | hskp4 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435))) <=> (hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(115,plain,
% 1.48/1.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[114])).
% 1.48/1.68 tff(116,plain,
% 1.48/1.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[115, 113])).
% 1.48/1.68 tff(117,plain,
% 1.48/1.68 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(118,plain,
% 1.48/1.68 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.48/1.68 tff(119,plain,
% 1.48/1.68 (hskp7 | hskp4 | c2_1(a1435) | (~c0_1(a1435))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[118, 82, 101, 112])).
% 1.48/1.68 tff(120,plain,
% 1.48/1.68 (hskp4),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[119, 13, 102, 100])).
% 1.48/1.68 tff(121,plain,
% 1.48/1.68 (((~hskp4) | (~c2_1(a1434))) <=> ((~hskp4) | (~c2_1(a1434)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(122,plain,
% 1.48/1.68 (((~c2_1(a1434)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1434)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(123,axiom,((~c2_1(a1434)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.48/1.68 tff(124,plain,
% 1.48/1.68 ((~hskp4) | (~c2_1(a1434))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.48/1.68 tff(125,plain,
% 1.48/1.68 ((~hskp4) | (~c2_1(a1434))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[124, 121])).
% 1.48/1.68 tff(126,plain,
% 1.48/1.68 (~c2_1(a1434)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[125, 120])).
% 1.48/1.68 tff(127,assumption,(c1_1(a1435)), introduced(assumption)).
% 1.48/1.68 tff(128,assumption,(hskp4), introduced(assumption)).
% 1.48/1.68 tff(129,plain,
% 1.48/1.68 (((~hskp4) | c1_1(a1434)) <=> ((~hskp4) | c1_1(a1434))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(130,axiom,((~hskp4) | c1_1(a1434)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.48/1.68 tff(131,plain,
% 1.48/1.68 ((~hskp4) | c1_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.48/1.68 tff(132,plain,
% 1.48/1.68 ((~hskp4) | c1_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[131, 129])).
% 1.48/1.68 tff(133,plain,
% 1.48/1.68 ((~hskp4) | c1_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[132, 129])).
% 1.48/1.68 tff(134,plain,
% 1.48/1.68 ((~hskp4) | c1_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.48/1.68 tff(135,plain,
% 1.48/1.68 ((~hskp4) | c1_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[134, 129])).
% 1.48/1.68 tff(136,plain,
% 1.48/1.68 (c1_1(a1434)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[135, 128])).
% 1.48/1.68 tff(137,plain,
% 1.48/1.68 (((~hskp4) | c3_1(a1434)) <=> ((~hskp4) | c3_1(a1434))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(138,axiom,((~hskp4) | c3_1(a1434)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.48/1.68 tff(139,plain,
% 1.48/1.68 ((~hskp4) | c3_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.48/1.68 tff(140,plain,
% 1.48/1.68 ((~hskp4) | c3_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[139, 137])).
% 1.48/1.68 tff(141,plain,
% 1.48/1.68 ((~hskp4) | c3_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[140, 137])).
% 1.48/1.68 tff(142,plain,
% 1.48/1.68 ((~hskp4) | c3_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.48/1.68 tff(143,plain,
% 1.48/1.68 ((~hskp4) | c3_1(a1434)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[142, 137])).
% 1.48/1.68 tff(144,plain,
% 1.48/1.68 (c3_1(a1434)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[143, 128])).
% 1.48/1.68 tff(145,plain,
% 1.48/1.68 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(146,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[145])).
% 1.48/1.68 tff(147,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(148,plain,
% 1.48/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(149,plain,
% 1.48/1.68 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[148])).
% 1.48/1.68 tff(150,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.48/1.68 tff(151,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.48/1.68 tff(152,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.48/1.68 tff(153,plain,(
% 1.48/1.68 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[152])).
% 1.48/1.68 tff(154,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[153, 146])).
% 1.48/1.68 tff(155,assumption,(~c2_1(a1434)), introduced(assumption)).
% 1.48/1.68 tff(156,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(157,plain,
% 1.48/1.68 ((hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435))) <=> (hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(158,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[157])).
% 1.48/1.68 tff(159,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[158, 156])).
% 1.48/1.68 tff(160,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(161,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.48/1.68 tff(162,plain,
% 1.48/1.68 (hskp7 | c2_1(a1435) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[161, 82, 101, 155, 154])).
% 1.48/1.68 tff(163,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[162, 144, 136, 13, 100, 127])).
% 1.48/1.68 tff(164,plain,((~hskp4) | hskp7 | c2_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1434)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(165,plain,
% 1.48/1.68 (~c1_1(a1435)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[164, 126, 100, 120, 101, 13])).
% 1.48/1.68 tff(166,plain,
% 1.48/1.68 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(167,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[166])).
% 1.48/1.68 tff(168,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(169,plain,
% 1.48/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(170,plain,
% 1.48/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[169])).
% 1.48/1.68 tff(171,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.48/1.68 tff(172,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.48/1.68 tff(173,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[172, 168])).
% 1.48/1.68 tff(174,plain,(
% 1.48/1.68 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[173])).
% 1.48/1.68 tff(175,plain,
% 1.48/1.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[174, 167])).
% 1.48/1.68 tff(176,plain,
% 1.48/1.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(177,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_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) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[176])).
% 1.48/1.69 tff(178,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_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) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(179,plain,
% 1.48/1.69 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_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) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(180,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[179])).
% 1.48/1.69 tff(181,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.48/1.69 tff(182,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.48/1.69 tff(183,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[182, 178])).
% 1.48/1.69 tff(184,plain,(
% 1.48/1.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(skolemize,[status(sab)],[183])).
% 1.48/1.69 tff(185,plain,
% 1.48/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[184, 177])).
% 1.48/1.69 tff(186,assumption,(~c2_1(a1430)), introduced(assumption)).
% 1.48/1.69 tff(187,plain,
% 1.48/1.69 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(188,plain,
% 1.48/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[187])).
% 1.48/1.69 tff(189,plain,
% 1.48/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(190,plain,
% 1.48/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(191,plain,
% 1.48/1.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[190])).
% 1.48/1.69 tff(192,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.48/1.69 tff(193,plain,
% 1.48/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.48/1.69 tff(194,plain,
% 1.48/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[193, 189])).
% 1.48/1.69 tff(195,plain,(
% 1.48/1.69 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(skolemize,[status(sab)],[194])).
% 1.48/1.69 tff(196,plain,
% 1.48/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[195, 188])).
% 1.48/1.69 tff(197,assumption,(hskp12), introduced(assumption)).
% 1.48/1.69 tff(198,plain,
% 1.48/1.69 (((~hskp12) | (~c2_1(a1448))) <=> ((~hskp12) | (~c2_1(a1448)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(199,plain,
% 1.48/1.69 (((~c2_1(a1448)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a1448)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(200,axiom,((~c2_1(a1448)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.48/1.69 tff(201,plain,
% 1.48/1.69 ((~hskp12) | (~c2_1(a1448))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.48/1.69 tff(202,plain,
% 1.48/1.69 ((~hskp12) | (~c2_1(a1448))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[201, 198])).
% 1.48/1.69 tff(203,plain,
% 1.48/1.69 (~c2_1(a1448)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[202, 197])).
% 1.48/1.69 tff(204,plain,
% 1.48/1.69 (((~hskp12) | c0_1(a1448)) <=> ((~hskp12) | c0_1(a1448))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(205,axiom,((~hskp12) | c0_1(a1448)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.48/1.69 tff(206,plain,
% 1.48/1.69 ((~hskp12) | c0_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.48/1.69 tff(207,plain,
% 1.48/1.69 ((~hskp12) | c0_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[206, 204])).
% 1.48/1.69 tff(208,plain,
% 1.48/1.69 ((~hskp12) | c0_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[207, 204])).
% 1.48/1.69 tff(209,plain,
% 1.48/1.69 ((~hskp12) | c0_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.48/1.69 tff(210,plain,
% 1.48/1.69 ((~hskp12) | c0_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[209, 204])).
% 1.48/1.69 tff(211,plain,
% 1.48/1.69 (c0_1(a1448)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[210, 197])).
% 1.48/1.69 tff(212,plain,
% 1.48/1.69 (((~hskp12) | c3_1(a1448)) <=> ((~hskp12) | c3_1(a1448))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(213,axiom,((~hskp12) | c3_1(a1448)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.48/1.69 tff(214,plain,
% 1.48/1.69 ((~hskp12) | c3_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.48/1.69 tff(215,plain,
% 1.48/1.69 ((~hskp12) | c3_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[214, 212])).
% 1.48/1.69 tff(216,plain,
% 1.48/1.69 ((~hskp12) | c3_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.48/1.69 tff(217,plain,
% 1.48/1.69 ((~hskp12) | c3_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.48/1.69 tff(218,plain,
% 1.48/1.69 ((~hskp12) | c3_1(a1448)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.48/1.69 tff(219,plain,
% 1.48/1.69 (c3_1(a1448)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[218, 197])).
% 1.48/1.69 tff(220,plain,
% 1.48/1.69 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(221,plain,
% 1.48/1.69 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[220])).
% 1.48/1.69 tff(222,plain,
% 1.48/1.69 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(223,plain,
% 1.48/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(224,plain,
% 1.48/1.69 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[223])).
% 1.48/1.69 tff(225,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.48/1.69 tff(226,plain,
% 1.48/1.69 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.48/1.69 tff(227,plain,
% 1.48/1.69 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.48/1.69 tff(228,plain,(
% 1.48/1.69 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(skolemize,[status(sab)],[227])).
% 1.48/1.69 tff(229,plain,
% 1.48/1.69 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[228, 221])).
% 1.48/1.69 tff(230,assumption,(~c2_1(a1448)), introduced(assumption)).
% 1.48/1.69 tff(231,plain,
% 1.48/1.69 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(232,plain,
% 1.48/1.69 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448))) <=> (hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(233,plain,
% 1.48/1.69 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[232])).
% 1.48/1.69 tff(234,plain,
% 1.48/1.69 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.48/1.69 inference(transitivity,[status(thm)],[233, 231])).
% 1.48/1.69 tff(235,plain,
% 1.48/1.69 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(236,plain,
% 1.48/1.69 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.48/1.69 tff(237,plain,
% 1.48/1.69 (hskp17 | hskp5 | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[236, 82, 230, 229])).
% 1.48/1.69 tff(238,plain,
% 1.48/1.69 ($false),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[237, 219, 211, 36, 11])).
% 1.48/1.69 tff(239,plain,((~hskp12) | hskp17 | hskp5 | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.69 tff(240,plain,
% 1.48/1.69 (hskp17),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[239, 11, 197, 203])).
% 1.48/1.69 tff(241,plain,
% 1.48/1.69 (((~hskp17) | (~c1_1(a1457))) <=> ((~hskp17) | (~c1_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(242,plain,
% 1.48/1.69 (((~c1_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(243,axiom,((~c1_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.48/1.69 tff(244,plain,
% 1.48/1.69 ((~hskp17) | (~c1_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.48/1.69 tff(245,plain,
% 1.48/1.69 ((~hskp17) | (~c1_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[244, 241])).
% 1.48/1.69 tff(246,plain,
% 1.48/1.69 (~c1_1(a1457)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[245, 240])).
% 1.48/1.69 tff(247,plain,
% 1.48/1.69 (((~hskp17) | (~c0_1(a1457))) <=> ((~hskp17) | (~c0_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(248,plain,
% 1.48/1.69 (((~c0_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(249,axiom,((~c0_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.48/1.69 tff(250,plain,
% 1.48/1.69 ((~hskp17) | (~c0_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.48/1.69 tff(251,plain,
% 1.48/1.69 ((~hskp17) | (~c0_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[250, 247])).
% 1.48/1.69 tff(252,plain,
% 1.48/1.69 (~c0_1(a1457)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[251, 240])).
% 1.48/1.69 tff(253,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(254,plain,
% 1.48/1.69 ((hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(255,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[254])).
% 1.48/1.69 tff(256,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457)))),
% 1.48/1.69 inference(transitivity,[status(thm)],[255, 253])).
% 1.48/1.69 tff(257,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(258,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[257, 256])).
% 1.48/1.69 tff(259,plain,
% 1.48/1.69 (~c3_1(a1457)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[258, 82, 11, 211, 219, 252, 246, 203, 10])).
% 1.48/1.69 tff(260,plain,
% 1.48/1.69 (((~hskp17) | (~c2_1(a1457))) <=> ((~hskp17) | (~c2_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(261,plain,
% 1.48/1.69 (((~c2_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1457)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(262,axiom,((~c2_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.48/1.69 tff(263,plain,
% 1.48/1.69 ((~hskp17) | (~c2_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.48/1.69 tff(264,plain,
% 1.48/1.69 ((~hskp17) | (~c2_1(a1457))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[263, 260])).
% 1.48/1.69 tff(265,plain,
% 1.48/1.69 (~c2_1(a1457)),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[264, 240])).
% 1.48/1.69 tff(266,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(267,plain,
% 1.48/1.69 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430)) <=> (hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(268,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457)))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[267])).
% 1.48/1.69 tff(269,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457))),
% 1.48/1.69 inference(transitivity,[status(thm)],[268, 266])).
% 1.48/1.69 tff(270,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(271,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457)),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[270, 269])).
% 1.48/1.69 tff(272,plain,
% 1.48/1.69 ($false),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[271, 82, 45, 35, 246, 265, 12, 186, 57, 259])).
% 1.48/1.69 tff(273,plain,(hskp5 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~hskp12)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.69 tff(274,plain,
% 1.48/1.69 (~hskp12),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[273, 35, 12, 186, 11])).
% 1.48/1.69 tff(275,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(276,plain,
% 1.48/1.69 ((hskp12 | (~ndr1_0) | c2_1(a1430) | c3_1(a1430) | (~c1_1(a1430)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430))) <=> (hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(277,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1430) | c3_1(a1430) | (~c1_1(a1430)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[276])).
% 1.48/1.69 tff(278,plain,
% 1.48/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1430) | c3_1(a1430) | (~c1_1(a1430)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.48/1.69 inference(transitivity,[status(thm)],[277, 275])).
% 1.48/1.69 tff(279,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1430) | c3_1(a1430) | (~c1_1(a1430)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(280,plain,
% 1.48/1.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.54/1.69 tff(281,plain,
% 1.54/1.69 (~c1_1(a1430)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[280, 82, 274, 35, 12, 186, 196])).
% 1.54/1.69 tff(282,plain,
% 1.54/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(283,plain,
% 1.54/1.69 ((hskp2 | (~ndr1_0) | c2_1(a1430) | c1_1(a1430) | c3_1(a1430) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430)) <=> (hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(284,plain,
% 1.54/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1430) | c1_1(a1430) | c3_1(a1430) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430)))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[283])).
% 1.54/1.69 tff(285,plain,
% 1.54/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1430) | c1_1(a1430) | c3_1(a1430) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430))),
% 1.54/1.69 inference(transitivity,[status(thm)],[284, 282])).
% 1.54/1.69 tff(286,plain,
% 1.54/1.69 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1430) | c1_1(a1430) | c3_1(a1430) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(287,plain,
% 1.54/1.69 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430)),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.54/1.69 tff(288,plain,
% 1.54/1.69 ($false),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[287, 82, 45, 35, 12, 186, 57, 281])).
% 1.54/1.69 tff(289,plain,(c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.69 tff(290,plain,
% 1.54/1.69 (hskp5),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[289, 186, 35, 12])).
% 1.54/1.69 tff(291,plain,
% 1.54/1.69 (((~hskp5) | (~c3_1(a1435))) <=> ((~hskp5) | (~c3_1(a1435)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(292,plain,
% 1.54/1.69 (((~c3_1(a1435)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1435)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(293,axiom,((~c3_1(a1435)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.54/1.69 tff(294,plain,
% 1.54/1.69 ((~hskp5) | (~c3_1(a1435))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.54/1.69 tff(295,plain,
% 1.54/1.69 ((~hskp5) | (~c3_1(a1435))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[294, 291])).
% 1.54/1.69 tff(296,plain,
% 1.54/1.69 (~c3_1(a1435)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[295, 290])).
% 1.54/1.69 tff(297,plain,
% 1.54/1.69 (((~hskp5) | (~c2_1(a1435))) <=> ((~hskp5) | (~c2_1(a1435)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(298,plain,
% 1.54/1.69 (((~c2_1(a1435)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1435)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(299,axiom,((~c2_1(a1435)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.54/1.69 tff(300,plain,
% 1.54/1.69 ((~hskp5) | (~c2_1(a1435))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.54/1.69 tff(301,plain,
% 1.54/1.69 ((~hskp5) | (~c2_1(a1435))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[300, 297])).
% 1.54/1.69 tff(302,plain,
% 1.54/1.69 (~c2_1(a1435)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[301, 290])).
% 1.54/1.69 tff(303,plain,
% 1.54/1.69 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(304,plain,
% 1.54/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[303])).
% 1.54/1.69 tff(305,plain,
% 1.54/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(306,plain,
% 1.54/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(307,plain,
% 1.54/1.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[306])).
% 1.54/1.69 tff(308,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.54/1.70 tff(309,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.54/1.70 tff(310,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[309, 305])).
% 1.54/1.70 tff(311,plain,(
% 1.54/1.70 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.70 inference(skolemize,[status(sab)],[310])).
% 1.54/1.70 tff(312,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[311, 304])).
% 1.54/1.70 tff(313,assumption,(~c1_1(a1435)), introduced(assumption)).
% 1.54/1.70 tff(314,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(315,plain,
% 1.54/1.70 ((hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430)) <=> (hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(316,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[315])).
% 1.54/1.70 tff(317,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.70 inference(transitivity,[status(thm)],[316, 314])).
% 1.54/1.70 tff(318,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(319,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.54/1.70 tff(320,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[319, 82, 45, 35, 100, 101, 12, 186, 57, 313])).
% 1.54/1.70 tff(321,plain,(c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(322,plain,
% 1.54/1.70 (c1_1(a1435)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[321, 296, 35, 12, 186, 302])).
% 1.54/1.70 tff(323,plain,
% 1.54/1.70 (c1_1(a1430)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[287, 82, 45, 35, 12, 186, 57])).
% 1.54/1.70 tff(324,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(325,plain,
% 1.54/1.70 ((hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430))) <=> (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(326,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[325])).
% 1.54/1.70 tff(327,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[326, 324])).
% 1.54/1.70 tff(328,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1430) | c0_1(a1430) | (~c1_1(a1430)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(329,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.54/1.70 tff(330,plain,
% 1.54/1.70 (hskp12),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[329, 82, 35, 302, 296, 12, 196, 323, 322])).
% 1.54/1.70 tff(331,plain,
% 1.54/1.70 (~c2_1(a1448)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[202, 330])).
% 1.54/1.70 tff(332,assumption,(hskp17), introduced(assumption)).
% 1.54/1.70 tff(333,plain,
% 1.54/1.70 (~c2_1(a1457)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[264, 332])).
% 1.54/1.70 tff(334,plain,
% 1.54/1.70 (~c1_1(a1457)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[245, 332])).
% 1.54/1.70 tff(335,plain,
% 1.54/1.70 (c3_1(a1457)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[271, 82, 45, 35, 334, 333, 12, 186, 57])).
% 1.54/1.70 tff(336,plain,
% 1.54/1.70 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(337,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[336])).
% 1.54/1.70 tff(338,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(339,plain,
% 1.54/1.70 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(340,plain,
% 1.54/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[339])).
% 1.54/1.70 tff(341,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.54/1.70 tff(342,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.54/1.70 tff(343,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[342, 338])).
% 1.54/1.70 tff(344,plain,(
% 1.54/1.70 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(skolemize,[status(sab)],[343])).
% 1.54/1.70 tff(345,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[344, 337])).
% 1.54/1.70 tff(346,plain,
% 1.54/1.70 (~c0_1(a1457)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[251, 332])).
% 1.54/1.70 tff(347,plain,
% 1.54/1.70 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(348,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[347])).
% 1.54/1.70 tff(349,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(350,plain,
% 1.54/1.70 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_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)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(351,plain,
% 1.54/1.70 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[350])).
% 1.54/1.70 tff(352,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.54/1.70 tff(353,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.54/1.70 tff(354,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.54/1.70 tff(355,plain,(
% 1.54/1.70 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(skolemize,[status(sab)],[354])).
% 1.54/1.70 tff(356,plain,
% 1.54/1.70 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[355, 348])).
% 1.54/1.70 tff(357,plain,
% 1.54/1.70 (((~hskp5) | c0_1(a1435)) <=> ((~hskp5) | c0_1(a1435))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(358,axiom,((~hskp5) | c0_1(a1435)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.54/1.70 tff(359,plain,
% 1.54/1.70 ((~hskp5) | c0_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[358, 357])).
% 1.54/1.70 tff(360,plain,
% 1.54/1.70 ((~hskp5) | c0_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[359, 357])).
% 1.54/1.70 tff(361,plain,
% 1.54/1.70 ((~hskp5) | c0_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[360, 357])).
% 1.54/1.70 tff(362,plain,
% 1.54/1.70 ((~hskp5) | c0_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[361, 357])).
% 1.54/1.70 tff(363,plain,
% 1.54/1.70 ((~hskp5) | c0_1(a1435)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[362, 357])).
% 1.54/1.70 tff(364,plain,
% 1.54/1.70 (c0_1(a1435)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[363, 290])).
% 1.54/1.70 tff(365,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(366,plain,
% 1.54/1.70 ((hskp18 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435))) <=> (hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(367,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[366])).
% 1.54/1.70 tff(368,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[367, 365])).
% 1.54/1.70 tff(369,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(370,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.54/1.70 tff(371,plain,
% 1.54/1.70 (hskp18),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[370, 82, 364, 302, 296, 356, 322])).
% 1.54/1.70 tff(372,plain,
% 1.54/1.70 (((~hskp18) | (~c2_1(a1458))) <=> ((~hskp18) | (~c2_1(a1458)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(373,plain,
% 1.54/1.70 (((~c2_1(a1458)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1458)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(374,axiom,((~c2_1(a1458)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.54/1.70 tff(375,plain,
% 1.54/1.70 ((~hskp18) | (~c2_1(a1458))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.54/1.70 tff(376,plain,
% 1.54/1.70 ((~hskp18) | (~c2_1(a1458))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[375, 372])).
% 1.54/1.70 tff(377,plain,
% 1.54/1.70 (~c2_1(a1458)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[376, 371])).
% 1.54/1.70 tff(378,plain,
% 1.54/1.70 (((~hskp18) | c1_1(a1458)) <=> ((~hskp18) | c1_1(a1458))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(379,axiom,((~hskp18) | c1_1(a1458)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.54/1.70 tff(380,plain,
% 1.54/1.70 ((~hskp18) | c1_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[379, 378])).
% 1.54/1.70 tff(381,plain,
% 1.54/1.70 ((~hskp18) | c1_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[380, 378])).
% 1.54/1.70 tff(382,plain,
% 1.54/1.70 ((~hskp18) | c1_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[381, 378])).
% 1.54/1.70 tff(383,plain,
% 1.54/1.70 ((~hskp18) | c1_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[382, 378])).
% 1.54/1.70 tff(384,plain,
% 1.54/1.70 ((~hskp18) | c1_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[383, 378])).
% 1.54/1.70 tff(385,plain,
% 1.54/1.70 (c1_1(a1458)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[384, 371])).
% 1.54/1.70 tff(386,plain,
% 1.54/1.70 (((~hskp18) | c0_1(a1458)) <=> ((~hskp18) | c0_1(a1458))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(387,axiom,((~hskp18) | c0_1(a1458)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.54/1.70 tff(388,plain,
% 1.54/1.70 ((~hskp18) | c0_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.54/1.70 tff(389,plain,
% 1.54/1.70 ((~hskp18) | c0_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[388, 386])).
% 1.54/1.70 tff(390,plain,
% 1.54/1.70 ((~hskp18) | c0_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[389, 386])).
% 1.54/1.70 tff(391,plain,
% 1.54/1.70 ((~hskp18) | c0_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[390, 386])).
% 1.54/1.70 tff(392,plain,
% 1.54/1.70 ((~hskp18) | c0_1(a1458)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[391, 386])).
% 1.54/1.70 tff(393,plain,
% 1.54/1.70 (c0_1(a1458)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[392, 371])).
% 1.54/1.70 tff(394,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(395,plain,
% 1.54/1.70 ((hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457))) <=> (hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(396,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[395])).
% 1.54/1.70 tff(397,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[396, 394])).
% 1.54/1.70 tff(398,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(399,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c0_1(a1458)) | (~c1_1(a1458))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.54/1.70 tff(400,plain,
% 1.54/1.70 (hskp10 | (~c3_1(a1457))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[399, 82, 393, 385, 377, 346, 333, 345])).
% 1.54/1.70 tff(401,plain,
% 1.54/1.70 (hskp10),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[400, 335])).
% 1.54/1.70 tff(402,plain,
% 1.54/1.70 (((~hskp10) | (~c3_1(a1445))) <=> ((~hskp10) | (~c3_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(403,plain,
% 1.54/1.70 (((~c3_1(a1445)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(404,axiom,((~c3_1(a1445)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.54/1.70 tff(405,plain,
% 1.54/1.70 ((~hskp10) | (~c3_1(a1445))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[404, 403])).
% 1.54/1.70 tff(406,plain,
% 1.54/1.70 ((~hskp10) | (~c3_1(a1445))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[405, 402])).
% 1.54/1.70 tff(407,plain,
% 1.54/1.70 (~c3_1(a1445)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[406, 401])).
% 1.54/1.70 tff(408,plain,
% 1.54/1.70 (((~hskp10) | (~c1_1(a1445))) <=> ((~hskp10) | (~c1_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(409,plain,
% 1.54/1.70 (((~c1_1(a1445)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(410,axiom,((~c1_1(a1445)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.54/1.70 tff(411,plain,
% 1.54/1.70 ((~hskp10) | (~c1_1(a1445))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.54/1.70 tff(412,plain,
% 1.54/1.70 ((~hskp10) | (~c1_1(a1445))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[411, 408])).
% 1.54/1.70 tff(413,plain,
% 1.54/1.70 (~c1_1(a1445)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[412, 401])).
% 1.54/1.70 tff(414,plain,
% 1.54/1.70 (((~hskp10) | c0_1(a1445)) <=> ((~hskp10) | c0_1(a1445))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(415,axiom,((~hskp10) | c0_1(a1445)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.54/1.70 tff(416,plain,
% 1.54/1.70 ((~hskp10) | c0_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.54/1.70 tff(417,plain,
% 1.54/1.70 ((~hskp10) | c0_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[416, 414])).
% 1.54/1.70 tff(418,plain,
% 1.54/1.70 ((~hskp10) | c0_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[417, 414])).
% 1.54/1.70 tff(419,plain,
% 1.54/1.70 ((~hskp10) | c0_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[418, 414])).
% 1.54/1.70 tff(420,plain,
% 1.54/1.70 ((~hskp10) | c0_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[419, 414])).
% 1.54/1.70 tff(421,plain,
% 1.54/1.70 (c0_1(a1445)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[420, 401])).
% 1.54/1.70 tff(422,plain,
% 1.54/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(423,plain,
% 1.54/1.70 (((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(424,plain,
% 1.54/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[423])).
% 1.54/1.70 tff(425,plain,
% 1.54/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[424, 422])).
% 1.54/1.70 tff(426,plain,
% 1.54/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(427,plain,
% 1.54/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.54/1.70 tff(428,plain,
% 1.54/1.70 (~c2_1(a1445)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[427, 82, 421, 346, 334, 333, 413, 407, 23])).
% 1.54/1.70 tff(429,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(430,plain,
% 1.54/1.70 ((hskp2 | (~ndr1_0) | c2_1(a1445) | c1_1(a1445) | c3_1(a1445) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430)) <=> (hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(431,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1445) | c1_1(a1445) | c3_1(a1445) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[430])).
% 1.54/1.70 tff(432,plain,
% 1.54/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1445) | c1_1(a1445) | c3_1(a1445) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445))),
% 1.54/1.70 inference(transitivity,[status(thm)],[431, 429])).
% 1.54/1.70 tff(433,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1445) | c1_1(a1445) | c3_1(a1445) | c3_1(a1430) | c2_1(a1430) | c0_1(a1430))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(434,plain,
% 1.54/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.54/1.70 tff(435,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[434, 82, 45, 35, 413, 407, 12, 186, 57, 428])).
% 1.54/1.70 tff(436,plain,((~hskp17) | c3_1(a1430) | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(437,plain,
% 1.54/1.70 (~hskp17),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[436, 186, 12, 35])).
% 1.54/1.70 tff(438,plain,
% 1.54/1.70 ((hskp25 | hskp17 | hskp2) <=> (hskp25 | hskp17 | hskp2)),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(439,plain,
% 1.54/1.70 (((hskp25 | hskp2) | hskp17) <=> (hskp25 | hskp17 | hskp2)),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(440,plain,
% 1.54/1.70 ((hskp25 | hskp2) <=> (hskp25 | hskp2)),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(441,plain,
% 1.54/1.70 (((hskp25 | hskp2) | hskp17) <=> ((hskp25 | hskp2) | hskp17)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[440])).
% 1.54/1.71 tff(442,plain,
% 1.54/1.71 (((hskp25 | hskp2) | hskp17) <=> (hskp25 | hskp17 | hskp2)),
% 1.54/1.71 inference(transitivity,[status(thm)],[441, 439])).
% 1.54/1.71 tff(443,axiom,((hskp25 | hskp2) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.54/1.71 tff(444,plain,
% 1.54/1.71 (hskp25 | hskp17 | hskp2),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.54/1.71 tff(445,plain,
% 1.54/1.71 (hskp25 | hskp17 | hskp2),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[444, 438])).
% 1.54/1.71 tff(446,plain,
% 1.54/1.71 (hskp25 | hskp17 | hskp2),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[445, 438])).
% 1.54/1.71 tff(447,plain,
% 1.54/1.71 (hskp25 | hskp17 | hskp2),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[446, 438])).
% 1.54/1.71 tff(448,plain,
% 1.54/1.71 (hskp25 | hskp17 | hskp2),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[447, 438])).
% 1.54/1.71 tff(449,plain,
% 1.54/1.71 (hskp25),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[448, 437, 45])).
% 1.54/1.71 tff(450,plain,
% 1.54/1.71 (((~hskp25) | (~c0_1(a1504))) <=> ((~hskp25) | (~c0_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(451,plain,
% 1.54/1.71 (((~c0_1(a1504)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(452,axiom,((~c0_1(a1504)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.54/1.71 tff(453,plain,
% 1.54/1.71 ((~hskp25) | (~c0_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.54/1.71 tff(454,plain,
% 1.54/1.71 ((~hskp25) | (~c0_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[453, 450])).
% 1.54/1.71 tff(455,plain,
% 1.54/1.71 (~c0_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[454, 449])).
% 1.54/1.71 tff(456,plain,
% 1.54/1.71 (c3_1(a1448)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[218, 330])).
% 1.54/1.71 tff(457,plain,
% 1.54/1.71 (c0_1(a1448)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[210, 330])).
% 1.54/1.71 tff(458,plain,
% 1.54/1.71 (((~hskp25) | c1_1(a1504)) <=> ((~hskp25) | c1_1(a1504))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(459,axiom,((~hskp25) | c1_1(a1504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.54/1.71 tff(460,plain,
% 1.54/1.71 ((~hskp25) | c1_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.54/1.71 tff(461,plain,
% 1.54/1.71 ((~hskp25) | c1_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[460, 458])).
% 1.54/1.71 tff(462,plain,
% 1.54/1.71 ((~hskp25) | c1_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[461, 458])).
% 1.54/1.71 tff(463,plain,
% 1.54/1.71 ((~hskp25) | c1_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[462, 458])).
% 1.54/1.71 tff(464,plain,
% 1.54/1.71 ((~hskp25) | c1_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[463, 458])).
% 1.54/1.71 tff(465,plain,
% 1.54/1.71 (c1_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[464, 449])).
% 1.54/1.71 tff(466,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(467,plain,
% 1.54/1.71 ((hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504))) <=> (hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(468,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[467])).
% 1.54/1.71 tff(469,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[468, 466])).
% 1.54/1.71 tff(470,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(471,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1504) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[470, 469])).
% 1.54/1.71 tff(472,plain,
% 1.54/1.71 (~c3_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[471, 82, 437, 465, 457, 456, 455, 331, 312])).
% 1.54/1.71 tff(473,plain,
% 1.54/1.71 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(474,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[473])).
% 1.54/1.71 tff(475,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(476,plain,
% 1.54/1.71 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(477,plain,
% 1.54/1.71 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[476])).
% 1.54/1.71 tff(478,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.54/1.71 tff(479,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.54/1.71 tff(480,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[479, 475])).
% 1.54/1.71 tff(481,plain,(
% 1.54/1.71 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(skolemize,[status(sab)],[480])).
% 1.54/1.71 tff(482,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[481, 474])).
% 1.54/1.71 tff(483,plain,
% 1.54/1.71 (((~hskp25) | c2_1(a1504)) <=> ((~hskp25) | c2_1(a1504))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(484,axiom,((~hskp25) | c2_1(a1504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.54/1.71 tff(485,plain,
% 1.54/1.71 ((~hskp25) | c2_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.54/1.71 tff(486,plain,
% 1.54/1.71 ((~hskp25) | c2_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[485, 483])).
% 1.54/1.71 tff(487,plain,
% 1.54/1.71 ((~hskp25) | c2_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.54/1.71 tff(488,plain,
% 1.54/1.71 ((~hskp25) | c2_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[487, 483])).
% 1.54/1.71 tff(489,plain,
% 1.54/1.71 ((~hskp25) | c2_1(a1504)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[488, 483])).
% 1.54/1.71 tff(490,plain,
% 1.54/1.71 (c2_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[489, 449])).
% 1.54/1.71 tff(491,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(492,plain,
% 1.54/1.71 ((hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1504) | c0_1(a1504) | (~c2_1(a1504))) <=> (hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(493,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1504) | c0_1(a1504) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[492])).
% 1.54/1.71 tff(494,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1504) | c0_1(a1504) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[493, 491])).
% 1.54/1.71 tff(495,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1504) | c0_1(a1504) | (~c2_1(a1504)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(496,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1504) | (~ndr1_0) | c3_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.54/1.71 tff(497,plain,
% 1.54/1.71 (hskp14),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[496, 82, 465, 490, 455, 482, 472])).
% 1.54/1.71 tff(498,plain,
% 1.54/1.71 (((~hskp14) | (~c3_1(a1451))) <=> ((~hskp14) | (~c3_1(a1451)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(499,plain,
% 1.54/1.71 (((~c3_1(a1451)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1451)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(500,axiom,((~c3_1(a1451)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.54/1.71 tff(501,plain,
% 1.54/1.71 ((~hskp14) | (~c3_1(a1451))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.54/1.71 tff(502,plain,
% 1.54/1.71 ((~hskp14) | (~c3_1(a1451))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[501, 498])).
% 1.54/1.71 tff(503,plain,
% 1.54/1.71 (~c3_1(a1451)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[502, 497])).
% 1.54/1.71 tff(504,plain,
% 1.54/1.71 (((~hskp14) | (~c1_1(a1451))) <=> ((~hskp14) | (~c1_1(a1451)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(505,plain,
% 1.54/1.71 (((~c1_1(a1451)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1451)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(506,axiom,((~c1_1(a1451)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.54/1.71 tff(507,plain,
% 1.54/1.71 ((~hskp14) | (~c1_1(a1451))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.54/1.71 tff(508,plain,
% 1.54/1.71 ((~hskp14) | (~c1_1(a1451))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[507, 504])).
% 1.54/1.71 tff(509,plain,
% 1.54/1.71 (~c1_1(a1451)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[508, 497])).
% 1.54/1.71 tff(510,plain,
% 1.54/1.71 (((~hskp14) | c2_1(a1451)) <=> ((~hskp14) | c2_1(a1451))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(511,axiom,((~hskp14) | c2_1(a1451)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.54/1.71 tff(512,plain,
% 1.54/1.71 ((~hskp14) | c2_1(a1451)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.54/1.71 tff(513,plain,
% 1.54/1.71 ((~hskp14) | c2_1(a1451)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[512, 510])).
% 1.54/1.71 tff(514,plain,
% 1.54/1.71 ((~hskp14) | c2_1(a1451)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[513, 510])).
% 1.54/1.71 tff(515,plain,
% 1.54/1.71 ((~hskp14) | c2_1(a1451)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[514, 510])).
% 1.54/1.71 tff(516,plain,
% 1.54/1.71 ((~hskp14) | c2_1(a1451)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[515, 510])).
% 1.54/1.71 tff(517,plain,
% 1.54/1.71 (c2_1(a1451)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[516, 497])).
% 1.54/1.71 tff(518,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(519,plain,
% 1.54/1.71 (((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504))) <=> (c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(520,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[519])).
% 1.54/1.71 tff(521,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[520, 518])).
% 1.54/1.71 tff(522,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(523,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.54/1.71 tff(524,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[523, 82, 465, 490, 517, 364, 455, 509, 503, 302, 296, 185])).
% 1.54/1.71 tff(525,plain,(c2_1(a1430) | c0_1(a1430) | c3_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(526,plain,
% 1.54/1.71 (c2_1(a1430)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[525, 35, 12])).
% 1.54/1.71 tff(527,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(528,plain,
% 1.54/1.71 ((hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430))) <=> (hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(529,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[528])).
% 1.54/1.71 tff(530,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[529, 527])).
% 1.54/1.71 tff(531,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(532,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1435) | (~c0_1(a1435))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.54/1.71 tff(533,plain,
% 1.54/1.71 (~c1_1(a1430)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[532, 82, 13, 102, 101, 12, 526, 175, 165])).
% 1.54/1.71 tff(534,plain,
% 1.54/1.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(535,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[534])).
% 1.54/1.71 tff(536,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(537,plain,
% 1.54/1.71 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(538,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[537])).
% 1.54/1.71 tff(539,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.54/1.71 tff(540,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.54/1.71 tff(541,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[540, 536])).
% 1.54/1.71 tff(542,plain,(
% 1.54/1.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(skolemize,[status(sab)],[541])).
% 1.54/1.71 tff(543,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[542, 535])).
% 1.54/1.71 tff(544,assumption,(~c1_1(a1430)), introduced(assumption)).
% 1.54/1.71 tff(545,assumption,(c2_1(a1430)), introduced(assumption)).
% 1.54/1.71 tff(546,assumption,(hskp25), introduced(assumption)).
% 1.54/1.71 tff(547,plain,
% 1.54/1.71 (~c0_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[454, 546])).
% 1.54/1.71 tff(548,plain,
% 1.54/1.71 (c2_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[489, 546])).
% 1.54/1.71 tff(549,plain,
% 1.54/1.71 (c1_1(a1504)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[464, 546])).
% 1.54/1.71 tff(550,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(551,plain,
% 1.54/1.71 (((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1430) | c1_1(a1430) | (~c2_1(a1430)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504))) <=> (c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(552,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1430) | c1_1(a1430) | (~c2_1(a1430)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[551])).
% 1.54/1.71 tff(553,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1430) | c1_1(a1430) | (~c2_1(a1430)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[552, 550])).
% 1.54/1.71 tff(554,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c3_1(a1430) | c1_1(a1430) | (~c2_1(a1430)) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(555,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.54/1.71 tff(556,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[555, 82, 549, 548, 102, 35, 547, 100, 101, 545, 185, 544])).
% 1.54/1.71 tff(557,plain,((~hskp25) | (~c0_1(a1435)) | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | c1_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(558,plain,
% 1.54/1.71 (~hskp25),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[557, 533, 35, 100, 101, 526, 102])).
% 1.54/1.71 tff(559,plain,
% 1.54/1.71 (hskp17),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[448, 558, 45])).
% 1.54/1.71 tff(560,plain,
% 1.54/1.71 (~c2_1(a1457)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[264, 559])).
% 1.54/1.71 tff(561,plain,
% 1.54/1.71 (~c0_1(a1457)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[251, 559])).
% 1.54/1.71 tff(562,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(563,plain,
% 1.54/1.71 (((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457))) <=> (c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(564,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[563])).
% 1.54/1.71 tff(565,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[564, 562])).
% 1.54/1.71 tff(566,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(567,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1430) | c0_1(a1457) | c2_1(a1457) | c2_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | c1_1(a1435) | (~c0_1(a1435)) | (~c3_1(a1457))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[566, 565])).
% 1.54/1.71 tff(568,plain,
% 1.54/1.71 (~c3_1(a1457)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[567, 82, 102, 35, 561, 560, 100, 526, 543, 533, 165])).
% 1.54/1.71 tff(569,plain,
% 1.54/1.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(570,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[569])).
% 1.54/1.71 tff(571,plain,
% 1.54/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(572,plain,
% 1.54/1.71 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(573,plain,
% 1.54/1.72 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[572])).
% 1.54/1.72 tff(574,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.54/1.72 tff(575,plain,
% 1.54/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.54/1.72 tff(576,plain,
% 1.54/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[575, 571])).
% 1.54/1.72 tff(577,plain,(
% 1.54/1.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.72 inference(skolemize,[status(sab)],[576])).
% 1.54/1.72 tff(578,plain,
% 1.54/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[577, 570])).
% 1.54/1.72 tff(579,plain,
% 1.54/1.72 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(580,plain,
% 1.54/1.72 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[579])).
% 1.54/1.72 tff(581,plain,
% 1.54/1.72 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(582,plain,
% 1.54/1.72 (^[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)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(583,plain,
% 1.54/1.72 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[582])).
% 1.54/1.72 tff(584,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.54/1.72 tff(585,plain,
% 1.54/1.72 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.54/1.72 tff(586,plain,
% 1.54/1.72 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[585, 581])).
% 1.54/1.72 tff(587,plain,(
% 1.54/1.72 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(skolemize,[status(sab)],[586])).
% 1.54/1.72 tff(588,plain,
% 1.54/1.72 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[587, 580])).
% 1.54/1.72 tff(589,plain,
% 1.54/1.72 (~c1_1(a1457)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[245, 559])).
% 1.54/1.72 tff(590,plain,
% 1.54/1.72 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(591,plain,
% 1.54/1.72 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c0_1(a1457)) <=> (hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(592,plain,
% 1.54/1.72 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c0_1(a1457))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[591])).
% 1.54/1.72 tff(593,plain,
% 1.54/1.72 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c0_1(a1457))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0))),
% 1.54/1.72 inference(transitivity,[status(thm)],[592, 590])).
% 1.54/1.72 tff(594,plain,
% 1.54/1.72 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c0_1(a1457))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(595,plain,
% 1.54/1.72 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[594, 593])).
% 1.54/1.72 tff(596,plain,
% 1.54/1.72 (hskp1),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[595, 82, 45, 561, 589, 560, 588])).
% 1.54/1.72 tff(597,plain,
% 1.54/1.72 (((~hskp1) | (~c0_1(a1429))) <=> ((~hskp1) | (~c0_1(a1429)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(598,plain,
% 1.54/1.72 (((~c0_1(a1429)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1429)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(599,axiom,((~c0_1(a1429)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.54/1.72 tff(600,plain,
% 1.54/1.72 ((~hskp1) | (~c0_1(a1429))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.54/1.72 tff(601,plain,
% 1.54/1.72 ((~hskp1) | (~c0_1(a1429))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[600, 597])).
% 1.54/1.72 tff(602,plain,
% 1.54/1.72 (~c0_1(a1429)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[601, 596])).
% 1.54/1.72 tff(603,plain,
% 1.54/1.72 (((~hskp1) | c3_1(a1429)) <=> ((~hskp1) | c3_1(a1429))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(604,axiom,((~hskp1) | c3_1(a1429)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.54/1.72 tff(605,plain,
% 1.54/1.72 ((~hskp1) | c3_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.54/1.72 tff(606,plain,
% 1.54/1.72 ((~hskp1) | c3_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[605, 603])).
% 1.54/1.72 tff(607,plain,
% 1.54/1.72 ((~hskp1) | c3_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[606, 603])).
% 1.54/1.72 tff(608,plain,
% 1.54/1.72 ((~hskp1) | c3_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[607, 603])).
% 1.54/1.72 tff(609,plain,
% 1.54/1.72 ((~hskp1) | c3_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[608, 603])).
% 1.54/1.72 tff(610,plain,
% 1.54/1.72 (c3_1(a1429)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[609, 596])).
% 1.54/1.72 tff(611,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(612,plain,
% 1.54/1.72 (((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457)) <=> (c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(613,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[612])).
% 1.54/1.72 tff(614,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457))),
% 1.54/1.72 inference(transitivity,[status(thm)],[613, 611])).
% 1.54/1.72 tff(615,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(616,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | (~c2_1(a1430)) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c1_1(a1430) | c3_1(a1457)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[615, 614])).
% 1.54/1.72 tff(617,plain,
% 1.54/1.72 (c1_1(a1429)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[616, 82, 35, 610, 589, 560, 526, 602, 578, 533, 568])).
% 1.54/1.72 tff(618,plain,
% 1.54/1.72 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(619,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[618])).
% 1.54/1.72 tff(620,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(621,plain,
% 1.54/1.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(622,plain,
% 1.54/1.72 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[621])).
% 1.54/1.72 tff(623,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.54/1.72 tff(624,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[623, 622])).
% 1.54/1.72 tff(625,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[624, 620])).
% 1.54/1.72 tff(626,plain,(
% 1.54/1.72 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(skolemize,[status(sab)],[625])).
% 1.54/1.72 tff(627,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[626, 619])).
% 1.54/1.72 tff(628,plain,
% 1.54/1.72 (((~hskp1) | c2_1(a1429)) <=> ((~hskp1) | c2_1(a1429))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(629,axiom,((~hskp1) | c2_1(a1429)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.54/1.72 tff(630,plain,
% 1.54/1.72 ((~hskp1) | c2_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.54/1.72 tff(631,plain,
% 1.54/1.72 ((~hskp1) | c2_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[630, 628])).
% 1.54/1.72 tff(632,plain,
% 1.54/1.72 ((~hskp1) | c2_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[631, 628])).
% 1.54/1.72 tff(633,plain,
% 1.54/1.72 ((~hskp1) | c2_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[632, 628])).
% 1.54/1.72 tff(634,plain,
% 1.54/1.72 ((~hskp1) | c2_1(a1429)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[633, 628])).
% 1.54/1.72 tff(635,plain,
% 1.54/1.72 (c2_1(a1429)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[634, 596])).
% 1.54/1.72 tff(636,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(637,plain,
% 1.54/1.72 ((hskp7 | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457)) <=> (hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(638,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[637])).
% 1.54/1.72 tff(639,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457))),
% 1.54/1.72 inference(transitivity,[status(thm)],[638, 636])).
% 1.54/1.72 tff(640,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(641,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.54/1.72 tff(642,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[641, 82, 13, 635, 610, 589, 560, 627, 568, 617])).
% 1.54/1.72 tff(643,plain,(hskp7 | c3_1(a1430) | (~c0_1(a1435)) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(644,plain,
% 1.54/1.72 (~c0_1(a1435)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[643, 101, 35, 13, 100, 12])).
% 1.54/1.72 tff(645,plain,
% 1.54/1.72 (~hskp5),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[363, 644])).
% 1.54/1.72 tff(646,assumption,(~c0_1(a1435)), introduced(assumption)).
% 1.54/1.72 tff(647,assumption,(~hskp12), introduced(assumption)).
% 1.54/1.72 tff(648,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(649,plain,
% 1.54/1.72 ((hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c1_1(a1435))) <=> (hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(650,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[649])).
% 1.54/1.72 tff(651,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[650, 648])).
% 1.54/1.72 tff(652,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c1_1(a1435)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(653,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.54/1.72 tff(654,plain,
% 1.54/1.72 (hskp12 | c0_1(a1435) | (~c1_1(a1435))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[653, 82, 100, 101, 196])).
% 1.54/1.72 tff(655,plain,
% 1.54/1.72 (~c1_1(a1435)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[654, 646, 647])).
% 1.54/1.72 tff(656,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(657,plain,
% 1.54/1.72 ((hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435)) <=> (hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(658,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[657])).
% 1.54/1.72 tff(659,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.54/1.72 inference(transitivity,[status(thm)],[658, 656])).
% 1.54/1.72 tff(660,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(661,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.54/1.72 tff(662,plain,
% 1.54/1.72 (c0_1(a1435) | c1_1(a1435)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[661, 82, 58, 100, 101, 57])).
% 1.54/1.72 tff(663,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[662, 655, 646])).
% 1.54/1.72 tff(664,plain,(c0_1(a1435) | hskp2 | c2_1(a1435) | c3_1(a1435) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(665,plain,
% 1.54/1.72 (hskp12),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[664, 646, 100, 101, 58])).
% 1.54/1.72 tff(666,plain,
% 1.54/1.72 (~c2_1(a1448)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[202, 665])).
% 1.54/1.72 tff(667,plain,
% 1.54/1.72 (hskp17),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[239, 666, 11, 665])).
% 1.54/1.72 tff(668,plain,
% 1.54/1.72 (~c1_1(a1457)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[245, 667])).
% 1.54/1.72 tff(669,plain,
% 1.54/1.72 (~c0_1(a1457)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[251, 667])).
% 1.54/1.72 tff(670,plain,
% 1.54/1.72 (c3_1(a1448)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[218, 665])).
% 1.54/1.72 tff(671,plain,
% 1.54/1.72 (c0_1(a1448)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[210, 665])).
% 1.54/1.72 tff(672,plain,
% 1.54/1.72 (~c3_1(a1457)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[258, 82, 11, 671, 670, 669, 668, 666, 10])).
% 1.54/1.72 tff(673,plain,
% 1.54/1.72 (~c2_1(a1457)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[264, 667])).
% 1.54/1.72 tff(674,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(675,plain,
% 1.54/1.72 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435)) <=> (hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(676,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[675])).
% 1.54/1.72 tff(677,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.72 inference(transitivity,[status(thm)],[676, 674])).
% 1.54/1.72 tff(678,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1435) | c2_1(a1435) | c0_1(a1435))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(679,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.54/1.72 tff(680,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[679, 82, 58, 646, 668, 673, 100, 101, 57, 672])).
% 1.54/1.72 tff(681,plain,(c0_1(a1435) | hskp2 | c2_1(a1435) | c3_1(a1435) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(682,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[681, 645, 644, 100, 101, 45])).
% 1.54/1.72 tff(683,plain,(c3_1(a1435) | c2_1(a1435) | c3_1(a1430) | hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(684,plain,
% 1.54/1.72 (c3_1(a1435)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[683, 100, 35, 99, 12])).
% 1.54/1.72 tff(685,plain,
% 1.54/1.72 (~hskp5),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[295, 684])).
% 1.54/1.72 tff(686,assumption,(hskp11), introduced(assumption)).
% 1.54/1.72 tff(687,plain,
% 1.54/1.72 (((~hskp11) | (~c2_1(a1447))) <=> ((~hskp11) | (~c2_1(a1447)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(688,plain,
% 1.54/1.72 (((~c2_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1447)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(689,axiom,((~c2_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.54/1.72 tff(690,plain,
% 1.54/1.72 ((~hskp11) | (~c2_1(a1447))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[689, 688])).
% 1.54/1.73 tff(691,plain,
% 1.54/1.73 ((~hskp11) | (~c2_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[690, 687])).
% 1.54/1.73 tff(692,plain,
% 1.54/1.73 (~c2_1(a1447)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[691, 686])).
% 1.54/1.73 tff(693,plain,
% 1.54/1.73 (((~hskp11) | (~c0_1(a1447))) <=> ((~hskp11) | (~c0_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(694,plain,
% 1.54/1.73 (((~c0_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(695,axiom,((~c0_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.54/1.73 tff(696,plain,
% 1.54/1.73 ((~hskp11) | (~c0_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.54/1.73 tff(697,plain,
% 1.54/1.73 ((~hskp11) | (~c0_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[696, 693])).
% 1.54/1.73 tff(698,plain,
% 1.54/1.73 (~c0_1(a1447)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[697, 686])).
% 1.54/1.73 tff(699,plain,
% 1.54/1.73 (((~hskp11) | (~c3_1(a1447))) <=> ((~hskp11) | (~c3_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(700,plain,
% 1.54/1.73 (((~c3_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(701,axiom,((~c3_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.54/1.73 tff(702,plain,
% 1.54/1.73 ((~hskp11) | (~c3_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.54/1.73 tff(703,plain,
% 1.54/1.73 ((~hskp11) | (~c3_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[702, 699])).
% 1.54/1.73 tff(704,plain,
% 1.54/1.73 (~c3_1(a1447)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[703, 686])).
% 1.54/1.73 tff(705,assumption,(~c0_1(a1447)), introduced(assumption)).
% 1.54/1.73 tff(706,assumption,(~c3_1(a1447)), introduced(assumption)).
% 1.54/1.73 tff(707,assumption,(~c2_1(a1447)), introduced(assumption)).
% 1.54/1.73 tff(708,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(709,plain,
% 1.54/1.73 ((hskp2 | (~ndr1_0) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(710,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[709])).
% 1.54/1.73 tff(711,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447))),
% 1.54/1.73 inference(transitivity,[status(thm)],[710, 708])).
% 1.54/1.73 tff(712,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(713,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.54/1.73 tff(714,plain,
% 1.54/1.73 (c0_1(a1447) | c1_1(a1447)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[713, 82, 58, 707, 706, 57])).
% 1.54/1.73 tff(715,plain,
% 1.54/1.73 (c1_1(a1447)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[714, 705])).
% 1.54/1.73 tff(716,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(717,plain,
% 1.54/1.73 ((hskp12 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447))) <=> (hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(718,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[717])).
% 1.54/1.73 tff(719,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[718, 716])).
% 1.54/1.73 tff(720,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(721,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.54/1.73 tff(722,plain,
% 1.54/1.73 (hskp12 | c0_1(a1447) | (~c1_1(a1447))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[721, 82, 707, 706, 196])).
% 1.54/1.73 tff(723,plain,
% 1.54/1.73 (hskp12),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[722, 715, 705])).
% 1.54/1.73 tff(724,plain,
% 1.54/1.73 (~c2_1(a1448)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[202, 723])).
% 1.54/1.73 tff(725,plain,
% 1.54/1.73 (hskp17),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[239, 724, 11, 723])).
% 1.54/1.73 tff(726,plain,
% 1.54/1.73 (~c1_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[245, 725])).
% 1.54/1.73 tff(727,plain,
% 1.54/1.73 (~c0_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[251, 725])).
% 1.54/1.73 tff(728,plain,
% 1.54/1.73 (c3_1(a1448)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[218, 723])).
% 1.54/1.73 tff(729,plain,
% 1.54/1.73 (c0_1(a1448)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[210, 723])).
% 1.54/1.73 tff(730,plain,
% 1.54/1.73 (~c3_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[258, 82, 11, 729, 728, 727, 726, 724, 10])).
% 1.54/1.73 tff(731,plain,
% 1.54/1.73 (~c2_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[264, 725])).
% 1.54/1.73 tff(732,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(733,plain,
% 1.54/1.73 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(734,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[733])).
% 1.54/1.73 tff(735,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.73 inference(transitivity,[status(thm)],[734, 732])).
% 1.54/1.73 tff(736,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(737,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.54/1.73 tff(738,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[737, 82, 58, 726, 731, 705, 707, 706, 57, 730])).
% 1.54/1.73 tff(739,plain,(c0_1(a1447) | hskp2 | c2_1(a1447) | c3_1(a1447) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(740,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[739, 704, 698, 692, 58, 11])).
% 1.54/1.73 tff(741,plain,((~hskp11) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(742,plain,
% 1.54/1.73 (~hskp11),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[741, 685, 45])).
% 1.54/1.73 tff(743,plain,
% 1.54/1.73 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(744,plain,
% 1.54/1.73 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1435) | c0_1(a1435) | (~c3_1(a1435))) <=> (hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(745,plain,
% 1.54/1.73 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1435) | c0_1(a1435) | (~c3_1(a1435)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[744])).
% 1.54/1.73 tff(746,plain,
% 1.54/1.73 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1435) | c0_1(a1435) | (~c3_1(a1435)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0))),
% 1.54/1.73 inference(transitivity,[status(thm)],[745, 743])).
% 1.54/1.73 tff(747,plain,
% 1.54/1.73 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1435) | c0_1(a1435) | (~c3_1(a1435)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(748,plain,
% 1.54/1.73 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1435) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[747, 746])).
% 1.54/1.73 tff(749,plain,
% 1.54/1.73 (hskp11 | hskp5 | c0_1(a1435) | (~c3_1(a1435))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[748, 82, 100, 34])).
% 1.54/1.73 tff(750,plain,
% 1.54/1.73 (c0_1(a1435)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[749, 742, 685, 684])).
% 1.54/1.73 tff(751,plain,
% 1.54/1.73 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(752,plain,
% 1.54/1.73 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435))) <=> (hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(753,plain,
% 1.54/1.73 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[752])).
% 1.54/1.73 tff(754,plain,
% 1.54/1.73 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[753, 751])).
% 1.54/1.73 tff(755,plain,
% 1.54/1.73 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(756,plain,
% 1.54/1.73 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.54/1.73 tff(757,plain,
% 1.54/1.73 (hskp17 | hskp5 | (~c3_1(a1435)) | (~c0_1(a1435))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[756, 82, 100, 229])).
% 1.54/1.73 tff(758,plain,
% 1.54/1.73 (hskp17),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[757, 750, 685, 684])).
% 1.54/1.73 tff(759,plain,
% 1.54/1.73 (~c1_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[245, 758])).
% 1.54/1.73 tff(760,plain,
% 1.54/1.73 (~c0_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[251, 758])).
% 1.54/1.73 tff(761,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(762,plain,
% 1.54/1.73 ((hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(763,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[762])).
% 1.54/1.73 tff(764,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[763, 761])).
% 1.54/1.73 tff(765,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1435) | (~c3_1(a1435)) | (~c0_1(a1435)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(766,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1435) | (~c3_1(a1435)) | (~ndr1_0) | (~c0_1(a1435)) | (~c3_1(a1457))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.54/1.73 tff(767,plain,
% 1.54/1.73 (~c3_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[766, 82, 685, 750, 760, 759, 100, 684, 10])).
% 1.54/1.73 tff(768,assumption,(c2_1(a1438)), introduced(assumption)).
% 1.54/1.73 tff(769,plain,
% 1.54/1.73 (~c2_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[264, 758])).
% 1.54/1.73 tff(770,plain,
% 1.54/1.73 (hskp1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[595, 82, 45, 760, 759, 769, 588])).
% 1.54/1.73 tff(771,plain,
% 1.54/1.73 (~c0_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[601, 770])).
% 1.54/1.73 tff(772,plain,
% 1.54/1.73 (c3_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[609, 770])).
% 1.54/1.73 tff(773,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(774,plain,
% 1.54/1.73 (((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457)) <=> (c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(775,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[774])).
% 1.54/1.73 tff(776,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457))),
% 1.54/1.73 inference(transitivity,[status(thm)],[775, 773])).
% 1.54/1.73 tff(777,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(778,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.54/1.73 tff(779,plain,
% 1.54/1.73 (c1_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[778, 82, 46, 772, 759, 769, 24, 771, 578, 768, 767])).
% 1.54/1.73 tff(780,plain,
% 1.54/1.73 (c2_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[634, 770])).
% 1.54/1.73 tff(781,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[641, 82, 99, 780, 772, 759, 769, 627, 767, 779])).
% 1.54/1.73 tff(782,plain,(c2_1(a1435) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(783,plain,
% 1.54/1.73 (c2_1(a1435)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[782, 46, 24, 91, 35, 12])).
% 1.54/1.73 tff(784,plain,
% 1.54/1.73 (~hskp5),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[301, 783])).
% 1.54/1.73 tff(785,plain,
% 1.54/1.73 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(786,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[785])).
% 1.54/1.73 tff(787,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(788,plain,
% 1.54/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_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) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_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) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_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) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(789,plain,
% 1.54/1.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[788])).
% 1.54/1.73 tff(790,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.54/1.73 tff(791,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.54/1.73 tff(792,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[791, 787])).
% 1.54/1.73 tff(793,plain,(
% 1.54/1.73 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(skolemize,[status(sab)],[792])).
% 1.54/1.73 tff(794,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[793, 786])).
% 1.54/1.73 tff(795,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(796,plain,
% 1.54/1.73 ((hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(797,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[796])).
% 1.54/1.73 tff(798,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[797, 795])).
% 1.54/1.73 tff(799,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(800,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.54/1.73 tff(801,plain,
% 1.54/1.73 (~c3_1(a1457)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[800, 82, 11, 46, 346, 334, 24, 794, 768])).
% 1.54/1.73 tff(802,plain,
% 1.54/1.73 (hskp1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[595, 82, 58, 346, 334, 333, 588])).
% 1.54/1.73 tff(803,plain,
% 1.54/1.73 (~c0_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[601, 802])).
% 1.54/1.73 tff(804,plain,
% 1.54/1.73 (c3_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[609, 802])).
% 1.54/1.73 tff(805,plain,
% 1.54/1.73 (c1_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[778, 82, 46, 804, 334, 333, 24, 803, 578, 768, 801])).
% 1.54/1.73 tff(806,plain,
% 1.54/1.73 (c2_1(a1429)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[634, 802])).
% 1.54/1.73 tff(807,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[641, 82, 99, 806, 804, 334, 333, 627, 801, 805])).
% 1.54/1.73 tff(808,plain,((~hskp17) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(809,plain,
% 1.54/1.73 (~hskp17),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[808, 46, 24, 91, 45, 784])).
% 1.54/1.73 tff(810,plain,
% 1.54/1.73 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(811,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[810])).
% 1.54/1.73 tff(812,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(813,plain,
% 1.54/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(814,plain,
% 1.54/1.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[813])).
% 1.54/1.73 tff(815,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.54/1.73 tff(816,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.54/1.73 tff(817,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[816, 812])).
% 1.54/1.73 tff(818,plain,(
% 1.54/1.73 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(skolemize,[status(sab)],[817])).
% 1.54/1.73 tff(819,plain,
% 1.54/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[818, 811])).
% 1.54/1.73 tff(820,assumption,(~hskp3), introduced(assumption)).
% 1.54/1.73 tff(821,plain,
% 1.54/1.73 ((hskp22 | hskp17 | hskp3) <=> (hskp22 | hskp17 | hskp3)),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(822,plain,
% 1.54/1.73 (((hskp22 | hskp3) | hskp17) <=> (hskp22 | hskp17 | hskp3)),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(823,axiom,((hskp22 | hskp3) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.54/1.73 tff(824,plain,
% 1.54/1.73 (hskp22 | hskp17 | hskp3),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[823, 822])).
% 1.54/1.73 tff(825,plain,
% 1.54/1.73 (hskp22 | hskp17 | hskp3),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[824, 821])).
% 1.54/1.73 tff(826,plain,
% 1.54/1.73 (hskp22 | hskp17 | hskp3),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[825, 821])).
% 1.54/1.73 tff(827,plain,
% 1.54/1.73 (hskp22 | hskp17 | hskp3),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[826, 821])).
% 1.54/1.73 tff(828,plain,
% 1.54/1.73 (hskp22 | hskp17 | hskp3),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[827, 821])).
% 1.54/1.73 tff(829,plain,
% 1.54/1.73 (hskp22),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[828, 820, 36])).
% 1.54/1.73 tff(830,plain,
% 1.54/1.73 (((~hskp22) | (~c0_1(a1468))) <=> ((~hskp22) | (~c0_1(a1468)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(831,plain,
% 1.54/1.73 (((~c0_1(a1468)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1468)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(832,axiom,((~c0_1(a1468)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.54/1.73 tff(833,plain,
% 1.54/1.73 ((~hskp22) | (~c0_1(a1468))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.54/1.73 tff(834,plain,
% 1.54/1.73 ((~hskp22) | (~c0_1(a1468))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[833, 830])).
% 1.54/1.73 tff(835,plain,
% 1.54/1.73 (~c0_1(a1468)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[834, 829])).
% 1.54/1.73 tff(836,plain,
% 1.54/1.73 (((~hskp22) | c3_1(a1468)) <=> ((~hskp22) | c3_1(a1468))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(837,axiom,((~hskp22) | c3_1(a1468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.54/1.73 tff(838,plain,
% 1.54/1.73 ((~hskp22) | c3_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.54/1.73 tff(839,plain,
% 1.54/1.73 ((~hskp22) | c3_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[838, 836])).
% 1.54/1.73 tff(840,plain,
% 1.54/1.73 ((~hskp22) | c3_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[839, 836])).
% 1.54/1.73 tff(841,plain,
% 1.54/1.73 ((~hskp22) | c3_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[840, 836])).
% 1.54/1.73 tff(842,plain,
% 1.54/1.73 ((~hskp22) | c3_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[841, 836])).
% 1.54/1.73 tff(843,plain,
% 1.54/1.73 (c3_1(a1468)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[842, 829])).
% 1.54/1.73 tff(844,plain,
% 1.54/1.73 (((~hskp22) | c1_1(a1468)) <=> ((~hskp22) | c1_1(a1468))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(845,axiom,((~hskp22) | c1_1(a1468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.54/1.73 tff(846,plain,
% 1.54/1.73 ((~hskp22) | c1_1(a1468)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.54/1.74 tff(847,plain,
% 1.54/1.74 ((~hskp22) | c1_1(a1468)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[846, 844])).
% 1.54/1.74 tff(848,plain,
% 1.54/1.74 ((~hskp22) | c1_1(a1468)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[847, 844])).
% 1.54/1.74 tff(849,plain,
% 1.54/1.74 ((~hskp22) | c1_1(a1468)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[848, 844])).
% 1.54/1.74 tff(850,plain,
% 1.54/1.74 ((~hskp22) | c1_1(a1468)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[849, 844])).
% 1.54/1.74 tff(851,plain,
% 1.54/1.74 (c1_1(a1468)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[850, 829])).
% 1.54/1.74 tff(852,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(853,plain,
% 1.54/1.74 ((hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)) <=> (hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(854,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[853])).
% 1.54/1.74 tff(855,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[854, 852])).
% 1.54/1.74 tff(856,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(857,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.54/1.74 tff(858,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[857, 82, 820, 851, 843, 46, 835, 37, 24, 819])).
% 1.54/1.74 tff(859,plain,(hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(860,plain,
% 1.54/1.74 (hskp3),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[859, 809, 37, 24, 46])).
% 1.54/1.74 tff(861,plain,
% 1.54/1.74 (((~hskp3) | (~c2_1(a1431))) <=> ((~hskp3) | (~c2_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(862,plain,
% 1.54/1.74 (((~c2_1(a1431)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(863,axiom,((~c2_1(a1431)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.54/1.74 tff(864,plain,
% 1.54/1.74 ((~hskp3) | (~c2_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.54/1.74 tff(865,plain,
% 1.54/1.74 ((~hskp3) | (~c2_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[864, 861])).
% 1.54/1.74 tff(866,plain,
% 1.54/1.74 (~c2_1(a1431)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[865, 860])).
% 1.54/1.74 tff(867,plain,
% 1.54/1.74 (((~hskp3) | (~c0_1(a1431))) <=> ((~hskp3) | (~c0_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(868,plain,
% 1.54/1.74 (((~c0_1(a1431)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(869,axiom,((~c0_1(a1431)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.54/1.74 tff(870,plain,
% 1.54/1.74 ((~hskp3) | (~c0_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.54/1.74 tff(871,plain,
% 1.54/1.74 ((~hskp3) | (~c0_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[870, 867])).
% 1.54/1.74 tff(872,plain,
% 1.54/1.74 (~c0_1(a1431)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[871, 860])).
% 1.54/1.74 tff(873,plain,
% 1.54/1.74 (~hskp11),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[741, 784, 45])).
% 1.54/1.74 tff(874,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(875,plain,
% 1.54/1.74 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431))) <=> (hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(876,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[875])).
% 1.54/1.74 tff(877,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[876, 874])).
% 1.54/1.74 tff(878,plain,
% 1.54/1.74 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(879,plain,
% 1.54/1.74 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.54/1.74 tff(880,plain,
% 1.54/1.74 (~c3_1(a1431)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[879, 82, 873, 784, 872, 866, 34])).
% 1.54/1.74 tff(881,plain,
% 1.54/1.74 (((~hskp3) | c1_1(a1431)) <=> ((~hskp3) | c1_1(a1431))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(882,axiom,((~hskp3) | c1_1(a1431)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.54/1.74 tff(883,plain,
% 1.54/1.74 ((~hskp3) | c1_1(a1431)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.54/1.74 tff(884,plain,
% 1.54/1.74 ((~hskp3) | c1_1(a1431)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[883, 881])).
% 1.54/1.74 tff(885,plain,
% 1.54/1.74 ((~hskp3) | c1_1(a1431)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[884, 881])).
% 1.54/1.74 tff(886,plain,
% 1.54/1.74 ((~hskp3) | c1_1(a1431)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[885, 881])).
% 1.54/1.74 tff(887,plain,
% 1.54/1.74 ((~hskp3) | c1_1(a1431)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[886, 881])).
% 1.54/1.74 tff(888,plain,
% 1.54/1.74 (c1_1(a1431)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[887, 860])).
% 1.54/1.74 tff(889,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(890,plain,
% 1.54/1.74 ((hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1431) | c0_1(a1431) | (~c1_1(a1431))) <=> (hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(891,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1431) | c0_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[890])).
% 1.54/1.74 tff(892,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1431) | c0_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[891, 889])).
% 1.54/1.74 tff(893,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1431) | c0_1(a1431) | (~c1_1(a1431)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(894,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.54/1.74 tff(895,plain,
% 1.54/1.74 (hskp12),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[894, 82, 888, 872, 866, 196, 880])).
% 1.54/1.74 tff(896,plain,
% 1.54/1.74 (~c2_1(a1448)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[202, 895])).
% 1.54/1.74 tff(897,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[239, 896, 895, 784, 809])).
% 1.54/1.74 tff(898,plain,(c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(899,plain,
% 1.54/1.74 (c3_1(a1438)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[898, 37, 24, 35, 12])).
% 1.54/1.74 tff(900,assumption,(hskp24), introduced(assumption)).
% 1.54/1.74 tff(901,plain,
% 1.54/1.74 (((~hskp24) | (~c2_1(a1487))) <=> ((~hskp24) | (~c2_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(902,plain,
% 1.54/1.74 (((~c2_1(a1487)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(903,axiom,((~c2_1(a1487)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.54/1.74 tff(904,plain,
% 1.54/1.74 ((~hskp24) | (~c2_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.54/1.74 tff(905,plain,
% 1.54/1.74 ((~hskp24) | (~c2_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[904, 901])).
% 1.54/1.74 tff(906,plain,
% 1.54/1.74 (~c2_1(a1487)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[905, 900])).
% 1.54/1.74 tff(907,plain,
% 1.54/1.74 (((~hskp24) | c3_1(a1487)) <=> ((~hskp24) | c3_1(a1487))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(908,axiom,((~hskp24) | c3_1(a1487)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.54/1.74 tff(909,plain,
% 1.54/1.74 ((~hskp24) | c3_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[908, 907])).
% 1.54/1.74 tff(910,plain,
% 1.54/1.74 ((~hskp24) | c3_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[909, 907])).
% 1.54/1.74 tff(911,plain,
% 1.54/1.74 ((~hskp24) | c3_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[910, 907])).
% 1.54/1.74 tff(912,plain,
% 1.54/1.74 ((~hskp24) | c3_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[911, 907])).
% 1.54/1.74 tff(913,plain,
% 1.54/1.74 ((~hskp24) | c3_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[912, 907])).
% 1.54/1.74 tff(914,plain,
% 1.54/1.74 (c3_1(a1487)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[913, 900])).
% 1.54/1.74 tff(915,plain,
% 1.54/1.74 (~hskp11),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[741, 11, 58])).
% 1.54/1.74 tff(916,assumption,(~c2_1(a1487)), introduced(assumption)).
% 1.54/1.74 tff(917,assumption,(c3_1(a1487)), introduced(assumption)).
% 1.54/1.74 tff(918,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(919,plain,
% 1.54/1.74 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487))) <=> (hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(920,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[919])).
% 1.54/1.74 tff(921,plain,
% 1.54/1.74 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.74 inference(transitivity,[status(thm)],[920, 918])).
% 1.54/1.74 tff(922,plain,
% 1.54/1.74 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(923,plain,
% 1.54/1.74 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[922, 921])).
% 1.54/1.74 tff(924,plain,
% 1.54/1.74 (hskp11 | hskp5 | c0_1(a1487)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[923, 82, 917, 916, 34])).
% 1.54/1.74 tff(925,plain,
% 1.54/1.74 (c0_1(a1487)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[924, 915, 11])).
% 1.54/1.74 tff(926,plain,
% 1.54/1.74 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(927,plain,
% 1.54/1.74 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487))) <=> (hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(928,plain,
% 1.54/1.74 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[927])).
% 1.54/1.74 tff(929,plain,
% 1.54/1.74 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[928, 926])).
% 1.54/1.74 tff(930,plain,
% 1.54/1.74 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(931,plain,
% 1.54/1.74 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1487) | (~ndr1_0) | (~c3_1(a1487)) | (~c0_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.54/1.74 tff(932,plain,
% 1.54/1.74 (hskp17 | hskp5 | (~c0_1(a1487))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[931, 82, 917, 916, 229])).
% 1.54/1.74 tff(933,plain,
% 1.54/1.74 (hskp17),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[932, 925, 11])).
% 1.54/1.74 tff(934,plain,
% 1.54/1.74 (~c1_1(a1457)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[245, 933])).
% 1.54/1.74 tff(935,plain,
% 1.54/1.74 (~c0_1(a1457)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[251, 933])).
% 1.54/1.74 tff(936,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(937,plain,
% 1.54/1.74 ((hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(938,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[937])).
% 1.54/1.74 tff(939,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[938, 936])).
% 1.54/1.74 tff(940,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(941,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c3_1(a1487)) | (~c0_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.54/1.74 tff(942,plain,
% 1.54/1.74 (~c3_1(a1457)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[941, 82, 11, 917, 916, 935, 934, 10, 925])).
% 1.54/1.74 tff(943,plain,
% 1.54/1.74 (~c2_1(a1457)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[264, 933])).
% 1.54/1.74 tff(944,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(945,plain,
% 1.54/1.74 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1457) | c2_1(a1457) | c0_1(a1457)) <=> (hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(946,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1457) | c2_1(a1457) | c0_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[945])).
% 1.54/1.74 tff(947,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1457) | c2_1(a1457) | c0_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.54/1.74 inference(transitivity,[status(thm)],[946, 944])).
% 1.54/1.74 tff(948,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1457) | c2_1(a1457) | c0_1(a1457))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(949,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.54/1.74 tff(950,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[949, 82, 58, 935, 934, 943, 57, 942])).
% 1.54/1.74 tff(951,plain,(hskp5 | hskp2 | (~c3_1(a1487)) | c2_1(a1487)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(952,plain,
% 1.54/1.74 (hskp5),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[951, 914, 45, 906])).
% 1.54/1.74 tff(953,plain,
% 1.54/1.74 (~c3_1(a1435)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[295, 952])).
% 1.54/1.74 tff(954,plain,
% 1.54/1.74 (((~hskp24) | (~c1_1(a1487))) <=> ((~hskp24) | (~c1_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(955,plain,
% 1.54/1.74 (((~c1_1(a1487)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1487)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(956,axiom,((~c1_1(a1487)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.54/1.74 tff(957,plain,
% 1.54/1.74 ((~hskp24) | (~c1_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.54/1.74 tff(958,plain,
% 1.54/1.74 ((~hskp24) | (~c1_1(a1487))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[957, 954])).
% 1.54/1.74 tff(959,plain,
% 1.54/1.74 (~c1_1(a1487)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[958, 900])).
% 1.54/1.74 tff(960,plain,
% 1.54/1.74 (~c2_1(a1435)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[301, 952])).
% 1.54/1.74 tff(961,assumption,(~c1_1(a1487)), introduced(assumption)).
% 1.54/1.74 tff(962,plain,
% 1.54/1.74 (c0_1(a1435)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[681, 11, 100, 101, 45])).
% 1.54/1.74 tff(963,plain,
% 1.54/1.74 (hskp4),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[119, 102, 13, 100])).
% 1.54/1.74 tff(964,plain,
% 1.54/1.74 (~c2_1(a1434)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[125, 963])).
% 1.54/1.74 tff(965,plain,
% 1.54/1.74 (~c1_1(a1435)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[164, 964, 100, 963, 101, 13])).
% 1.54/1.74 tff(966,plain,
% 1.54/1.74 (^[U: $i] : refl((hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(967,plain,
% 1.54/1.74 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[966])).
% 1.54/1.74 tff(968,plain,
% 1.54/1.74 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(969,plain,
% 1.54/1.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | 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)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp29) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp29))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp29) <=> (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp29) <=> (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(970,plain,
% 1.54/1.74 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp29) <=> ![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[969])).
% 1.54/1.74 tff(971,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.54/1.74 tff(972,plain,
% 1.54/1.74 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.54/1.74 tff(973,plain,
% 1.54/1.74 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[972, 968])).
% 1.54/1.74 tff(974,plain,(
% 1.54/1.74 ![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(skolemize,[status(sab)],[973])).
% 1.54/1.74 tff(975,plain,
% 1.54/1.74 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[974, 967])).
% 1.54/1.74 tff(976,plain,
% 1.54/1.74 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(977,plain,
% 1.54/1.74 ((hskp29 | hskp5 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435))) <=> (hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(978,plain,
% 1.54/1.74 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[977])).
% 1.54/1.74 tff(979,plain,
% 1.54/1.74 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[978, 976])).
% 1.54/1.74 tff(980,plain,
% 1.54/1.74 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(981,plain,
% 1.54/1.74 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.54/1.74 tff(982,plain,
% 1.54/1.74 (hskp29 | hskp5 | c2_1(a1435) | (~c0_1(a1435))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[981, 82, 101, 975])).
% 1.54/1.74 tff(983,plain,
% 1.54/1.74 (hskp29),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[982, 102, 11, 100])).
% 1.54/1.74 tff(984,plain,
% 1.54/1.74 (((~hskp29) | c3_1(a1483)) <=> ((~hskp29) | c3_1(a1483))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(985,axiom,((~hskp29) | c3_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.54/1.74 tff(986,plain,
% 1.54/1.74 ((~hskp29) | c3_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[985, 984])).
% 1.54/1.74 tff(987,plain,
% 1.54/1.74 ((~hskp29) | c3_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[986, 984])).
% 1.54/1.74 tff(988,plain,
% 1.54/1.74 ((~hskp29) | c3_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[987, 984])).
% 1.54/1.74 tff(989,plain,
% 1.54/1.74 ((~hskp29) | c3_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[988, 984])).
% 1.54/1.74 tff(990,plain,
% 1.54/1.74 ((~hskp29) | c3_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[989, 984])).
% 1.54/1.74 tff(991,plain,
% 1.54/1.74 (c3_1(a1483)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[990, 983])).
% 1.54/1.74 tff(992,plain,
% 1.54/1.74 (((~hskp29) | c2_1(a1483)) <=> ((~hskp29) | c2_1(a1483))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(993,axiom,((~hskp29) | c2_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.54/1.74 tff(994,plain,
% 1.54/1.74 ((~hskp29) | c2_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.54/1.74 tff(995,plain,
% 1.54/1.74 ((~hskp29) | c2_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[994, 992])).
% 1.54/1.74 tff(996,plain,
% 1.54/1.74 ((~hskp29) | c2_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[995, 992])).
% 1.54/1.74 tff(997,plain,
% 1.54/1.74 ((~hskp29) | c2_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[996, 992])).
% 1.54/1.74 tff(998,plain,
% 1.54/1.74 ((~hskp29) | c2_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[997, 992])).
% 1.54/1.74 tff(999,plain,
% 1.54/1.74 (c2_1(a1483)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[998, 983])).
% 1.54/1.74 tff(1000,plain,
% 1.54/1.74 (((~hskp29) | c1_1(a1483)) <=> ((~hskp29) | c1_1(a1483))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1001,axiom,((~hskp29) | c1_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.54/1.74 tff(1002,plain,
% 1.54/1.74 ((~hskp29) | c1_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.54/1.74 tff(1003,plain,
% 1.54/1.74 ((~hskp29) | c1_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1002, 1000])).
% 1.54/1.74 tff(1004,plain,
% 1.54/1.74 ((~hskp29) | c1_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1003, 1000])).
% 1.54/1.74 tff(1005,plain,
% 1.54/1.74 ((~hskp29) | c1_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1004, 1000])).
% 1.54/1.74 tff(1006,plain,
% 1.54/1.74 ((~hskp29) | c1_1(a1483)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1005, 1000])).
% 1.54/1.74 tff(1007,plain,
% 1.54/1.74 (c1_1(a1483)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1006, 983])).
% 1.54/1.74 tff(1008,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1009,plain,
% 1.54/1.75 ((hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1435) | c2_1(a1435) | c1_1(a1435)) <=> (hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1010,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1435) | c2_1(a1435) | c1_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1009])).
% 1.54/1.75 tff(1011,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1435) | c2_1(a1435) | c1_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1010, 1008])).
% 1.54/1.75 tff(1012,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1435) | c2_1(a1435) | c1_1(a1435))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1013,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.54/1.75 tff(1014,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1013, 82, 13, 1007, 999, 991, 100, 101, 627, 965])).
% 1.54/1.75 tff(1015,plain,((~c0_1(a1435)) | hskp7 | c2_1(a1435) | c3_1(a1435) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(1016,plain,
% 1.54/1.75 (hskp7),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1015, 962, 100, 101, 11])).
% 1.54/1.75 tff(1017,plain,
% 1.54/1.75 (((~hskp7) | (~c0_1(a1438))) <=> ((~hskp7) | (~c0_1(a1438)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1018,plain,
% 1.54/1.75 (((~c0_1(a1438)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a1438)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1019,axiom,((~c0_1(a1438)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.54/1.75 tff(1020,plain,
% 1.54/1.75 ((~hskp7) | (~c0_1(a1438))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.54/1.75 tff(1021,plain,
% 1.54/1.75 ((~hskp7) | (~c0_1(a1438))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1020, 1017])).
% 1.54/1.75 tff(1022,plain,
% 1.54/1.75 (~c0_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1021, 1016])).
% 1.54/1.75 tff(1023,plain,
% 1.54/1.75 (c3_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[98, 1016])).
% 1.54/1.75 tff(1024,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1025,plain,
% 1.54/1.75 ((hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1026,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1025])).
% 1.54/1.75 tff(1027,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1026, 1024])).
% 1.54/1.75 tff(1028,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1029,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.54/1.75 tff(1030,plain,
% 1.54/1.75 (~c0_1(a1487)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1029, 82, 11, 917, 1023, 916, 1022, 24, 10])).
% 1.54/1.75 tff(1031,plain,
% 1.54/1.75 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1032,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1031])).
% 1.54/1.75 tff(1033,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1034,plain,
% 1.54/1.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1035,plain,
% 1.54/1.75 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_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) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1034])).
% 1.54/1.75 tff(1036,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.54/1.75 tff(1037,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.54/1.75 tff(1038,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 1.54/1.75 tff(1039,plain,(
% 1.54/1.75 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(skolemize,[status(sab)],[1038])).
% 1.54/1.75 tff(1040,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 1.54/1.75 tff(1041,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1042,plain,
% 1.54/1.75 ((hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487))) <=> (hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1043,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1042])).
% 1.54/1.75 tff(1044,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1043, 1041])).
% 1.54/1.75 tff(1045,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1487) | c0_1(a1487) | (~c3_1(a1487)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1046,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c2_1(a1487) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1487)) | c0_1(a1487)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.54/1.75 tff(1047,plain,
% 1.54/1.75 (hskp9 | c0_1(a1487)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1046, 82, 917, 35, 916, 12, 526, 1040])).
% 1.54/1.75 tff(1048,plain,
% 1.54/1.75 (hskp9),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1047, 1030])).
% 1.54/1.75 tff(1049,plain,
% 1.54/1.75 (((~hskp9) | (~c3_1(a1444))) <=> ((~hskp9) | (~c3_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1050,plain,
% 1.54/1.75 (((~c3_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1051,axiom,((~c3_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.54/1.75 tff(1052,plain,
% 1.54/1.75 ((~hskp9) | (~c3_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.54/1.75 tff(1053,plain,
% 1.54/1.75 ((~hskp9) | (~c3_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1052, 1049])).
% 1.54/1.75 tff(1054,plain,
% 1.54/1.75 (~c3_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1053, 1048])).
% 1.54/1.75 tff(1055,plain,
% 1.54/1.75 (((~hskp9) | (~c2_1(a1444))) <=> ((~hskp9) | (~c2_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1056,plain,
% 1.54/1.75 (((~c2_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1057,axiom,((~c2_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.54/1.75 tff(1058,plain,
% 1.54/1.75 ((~hskp9) | (~c2_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.54/1.75 tff(1059,plain,
% 1.54/1.75 ((~hskp9) | (~c2_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1058, 1055])).
% 1.54/1.75 tff(1060,plain,
% 1.54/1.75 (~c2_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1059, 1048])).
% 1.54/1.75 tff(1061,plain,
% 1.54/1.75 (((~hskp9) | (~c1_1(a1444))) <=> ((~hskp9) | (~c1_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1062,plain,
% 1.54/1.75 (((~c1_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1444)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1063,axiom,((~c1_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.54/1.75 tff(1064,plain,
% 1.54/1.75 ((~hskp9) | (~c1_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.54/1.75 tff(1065,plain,
% 1.54/1.75 ((~hskp9) | (~c1_1(a1444))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1064, 1061])).
% 1.54/1.75 tff(1066,plain,
% 1.54/1.75 (~c1_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1065, 1048])).
% 1.54/1.75 tff(1067,plain,
% 1.54/1.75 (hskp11),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[924, 1030, 11])).
% 1.54/1.75 tff(1068,plain,
% 1.54/1.75 (~c3_1(a1447)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[703, 1067])).
% 1.54/1.75 tff(1069,plain,
% 1.54/1.75 (~c2_1(a1447)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[691, 1067])).
% 1.54/1.75 tff(1070,plain,
% 1.54/1.75 (~c0_1(a1447)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[697, 1067])).
% 1.54/1.75 tff(1071,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1072,plain,
% 1.54/1.75 ((hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1073,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1072])).
% 1.54/1.75 tff(1074,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1073, 1071])).
% 1.54/1.75 tff(1075,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1076,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.54/1.75 tff(1077,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1076, 82, 45, 1070, 1069, 1068, 1066, 1060, 1054, 57])).
% 1.54/1.75 tff(1078,plain,(hskp5 | (~c3_1(a1487)) | c2_1(a1487) | c3_1(a1430) | c0_1(a1430) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(1079,plain,
% 1.54/1.75 (hskp5),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1078, 100, 916, 35, 12, 24, 917, 101])).
% 1.54/1.75 tff(1080,plain,
% 1.54/1.75 (c0_1(a1435)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[363, 1079])).
% 1.54/1.75 tff(1081,plain,
% 1.54/1.75 (hskp7),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[643, 1080, 35, 100, 101, 12])).
% 1.54/1.75 tff(1082,plain,
% 1.54/1.75 (~c0_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1021, 1081])).
% 1.54/1.75 tff(1083,plain,
% 1.54/1.75 (c3_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[98, 1081])).
% 1.54/1.75 tff(1084,plain,
% 1.54/1.75 (hskp7),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[643, 102, 35, 100, 101, 12])).
% 1.54/1.75 tff(1085,plain,
% 1.54/1.75 (~c0_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1021, 1084])).
% 1.54/1.75 tff(1086,plain,
% 1.54/1.75 (c3_1(a1438)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[98, 1084])).
% 1.54/1.75 tff(1087,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1088,plain,
% 1.54/1.75 ((hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438))) <=> (hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1089,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1088])).
% 1.54/1.75 tff(1090,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1089, 1087])).
% 1.54/1.75 tff(1091,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1430) | c3_1(a1430) | (~c2_1(a1430)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1092,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.54/1.75 tff(1093,plain,
% 1.54/1.75 (hskp9),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1092, 82, 1086, 35, 1085, 12, 526, 1040, 47])).
% 1.54/1.75 tff(1094,plain,
% 1.54/1.75 (~c3_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1053, 1093])).
% 1.54/1.75 tff(1095,plain,
% 1.54/1.75 (~c2_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1059, 1093])).
% 1.54/1.75 tff(1096,plain,
% 1.54/1.75 (~c1_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1065, 1093])).
% 1.54/1.75 tff(1097,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1098,plain,
% 1.54/1.75 ((hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444)) <=> (hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1099,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1098])).
% 1.54/1.75 tff(1100,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1099, 1097])).
% 1.54/1.75 tff(1101,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1102,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.54/1.75 tff(1103,plain,
% 1.54/1.75 (c0_1(a1444)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1102, 82, 45, 1096, 1095, 1094, 57])).
% 1.54/1.75 tff(1104,plain,
% 1.54/1.75 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1105,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1104])).
% 1.54/1.75 tff(1106,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1107,plain,
% 1.54/1.75 (^[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)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~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)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1108,plain,
% 1.54/1.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1107])).
% 1.54/1.75 tff(1109,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)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.54/1.75 tff(1110,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 1.54/1.75 tff(1111,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 1.54/1.75 tff(1112,plain,(
% 1.54/1.75 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(skolemize,[status(sab)],[1111])).
% 1.54/1.75 tff(1113,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1112, 1105])).
% 1.54/1.75 tff(1114,plain,
% 1.54/1.75 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1115,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1114])).
% 1.54/1.75 tff(1116,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1117,plain,
% 1.54/1.75 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(1118,plain,
% 1.54/1.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[1117])).
% 1.54/1.75 tff(1119,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.54/1.75 tff(1120,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 1.54/1.75 tff(1121,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1120, 1116])).
% 1.54/1.75 tff(1122,plain,(
% 1.54/1.75 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(skolemize,[status(sab)],[1121])).
% 1.54/1.75 tff(1123,plain,
% 1.54/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1122, 1115])).
% 1.54/1.75 tff(1124,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1125,plain,
% 1.54/1.75 ((hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | c1_1(a1438)) <=> (hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1126,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1125])).
% 1.54/1.76 tff(1127,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1126, 1124])).
% 1.54/1.76 tff(1128,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | c1_1(a1438))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1129,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c2_1(a1438)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.54/1.76 tff(1130,plain,
% 1.54/1.76 (hskp0),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1129, 82, 102, 1085, 24, 100, 101, 1123, 47])).
% 1.54/1.76 tff(1131,plain,
% 1.54/1.76 (((~hskp0) | (~c3_1(a1427))) <=> ((~hskp0) | (~c3_1(a1427)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1132,plain,
% 1.54/1.76 (((~c3_1(a1427)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1427)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1133,axiom,((~c3_1(a1427)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.54/1.76 tff(1134,plain,
% 1.54/1.76 ((~hskp0) | (~c3_1(a1427))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.54/1.76 tff(1135,plain,
% 1.54/1.76 ((~hskp0) | (~c3_1(a1427))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1134, 1131])).
% 1.54/1.76 tff(1136,plain,
% 1.54/1.76 (~c3_1(a1427)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1135, 1130])).
% 1.54/1.76 tff(1137,plain,
% 1.54/1.76 (((~hskp0) | c2_1(a1427)) <=> ((~hskp0) | c2_1(a1427))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1138,axiom,((~hskp0) | c2_1(a1427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.54/1.76 tff(1139,plain,
% 1.54/1.76 ((~hskp0) | c2_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.54/1.76 tff(1140,plain,
% 1.54/1.76 ((~hskp0) | c2_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1139, 1137])).
% 1.54/1.76 tff(1141,plain,
% 1.54/1.76 ((~hskp0) | c2_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1140, 1137])).
% 1.54/1.76 tff(1142,plain,
% 1.54/1.76 ((~hskp0) | c2_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1141, 1137])).
% 1.54/1.76 tff(1143,plain,
% 1.54/1.76 ((~hskp0) | c2_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1142, 1137])).
% 1.54/1.76 tff(1144,plain,
% 1.54/1.76 (c2_1(a1427)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1143, 1130])).
% 1.54/1.76 tff(1145,plain,
% 1.54/1.76 (((~hskp0) | c0_1(a1427)) <=> ((~hskp0) | c0_1(a1427))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1146,axiom,((~hskp0) | c0_1(a1427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.54/1.76 tff(1147,plain,
% 1.54/1.76 ((~hskp0) | c0_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.54/1.76 tff(1148,plain,
% 1.54/1.76 ((~hskp0) | c0_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1147, 1145])).
% 1.54/1.76 tff(1149,plain,
% 1.54/1.76 ((~hskp0) | c0_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1148, 1145])).
% 1.54/1.76 tff(1150,plain,
% 1.54/1.76 ((~hskp0) | c0_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 1.54/1.76 tff(1151,plain,
% 1.54/1.76 ((~hskp0) | c0_1(a1427)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1150, 1145])).
% 1.54/1.76 tff(1152,plain,
% 1.54/1.76 (c0_1(a1427)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1151, 1130])).
% 1.54/1.76 tff(1153,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1154,plain,
% 1.54/1.76 ((hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444))) <=> (hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1155,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1154])).
% 1.54/1.76 tff(1156,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1155, 1153])).
% 1.54/1.76 tff(1157,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1158,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1444) | c2_1(a1444) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1444))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.54/1.76 tff(1159,plain,
% 1.54/1.76 (hskp19 | (~c0_1(a1444))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1158, 82, 1152, 1144, 1096, 1095, 1136, 1113])).
% 1.54/1.76 tff(1160,plain,
% 1.54/1.76 (hskp19),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1159, 1103])).
% 1.54/1.76 tff(1161,plain,
% 1.54/1.76 (((~hskp19) | (~c3_1(a1460))) <=> ((~hskp19) | (~c3_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1162,plain,
% 1.54/1.76 (((~c3_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1163,axiom,((~c3_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.54/1.76 tff(1164,plain,
% 1.54/1.76 ((~hskp19) | (~c3_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.54/1.76 tff(1165,plain,
% 1.54/1.76 ((~hskp19) | (~c3_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1164, 1161])).
% 1.54/1.76 tff(1166,plain,
% 1.54/1.76 (~c3_1(a1460)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1165, 1160])).
% 1.54/1.76 tff(1167,plain,
% 1.54/1.76 (((~hskp19) | (~c0_1(a1460))) <=> ((~hskp19) | (~c0_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1168,plain,
% 1.54/1.76 (((~c0_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1169,axiom,((~c0_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.54/1.76 tff(1170,plain,
% 1.54/1.76 ((~hskp19) | (~c0_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 1.54/1.76 tff(1171,plain,
% 1.54/1.76 ((~hskp19) | (~c0_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1170, 1167])).
% 1.54/1.76 tff(1172,plain,
% 1.54/1.76 (~c0_1(a1460)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1171, 1160])).
% 1.54/1.76 tff(1173,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1174,plain,
% 1.54/1.76 ((hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460)) <=> (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1175,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1174])).
% 1.54/1.76 tff(1176,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1175, 1173])).
% 1.54/1.76 tff(1177,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1178,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c2_1(a1460)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.54/1.76 tff(1179,plain,
% 1.54/1.76 (c2_1(a1460)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1178, 82, 45, 1172, 1166, 1096, 1095, 1094, 57])).
% 1.54/1.76 tff(1180,plain,
% 1.54/1.76 (((~hskp19) | (~c1_1(a1460))) <=> ((~hskp19) | (~c1_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1181,plain,
% 1.54/1.76 (((~c1_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1182,axiom,((~c1_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.54/1.76 tff(1183,plain,
% 1.54/1.76 ((~hskp19) | (~c1_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.54/1.76 tff(1184,plain,
% 1.54/1.76 ((~hskp19) | (~c1_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1183, 1180])).
% 1.54/1.76 tff(1185,plain,
% 1.54/1.76 (~c1_1(a1460)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1184, 1160])).
% 1.54/1.76 tff(1186,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1187,plain,
% 1.54/1.76 (((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1188,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1187])).
% 1.54/1.76 tff(1189,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1188, 1186])).
% 1.54/1.76 tff(1190,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1191,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.54/1.76 tff(1192,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1191, 82, 1086, 1185, 1166, 1096, 1095, 1085, 543, 47, 1103, 1179])).
% 1.54/1.76 tff(1193,plain,(c2_1(a1438) | (~c0_1(a1435)) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1194,plain,
% 1.54/1.76 (c2_1(a1438)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1193, 1080, 24, 100, 101, 35, 12])).
% 1.54/1.76 tff(1195,plain,
% 1.54/1.76 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1196,plain,
% 1.54/1.76 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1195])).
% 1.54/1.76 tff(1197,plain,
% 1.54/1.76 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1198,plain,
% 1.54/1.76 (^[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)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp11) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1199,plain,
% 1.54/1.76 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp11) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1198])).
% 1.54/1.76 tff(1200,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.54/1.76 tff(1201,plain,
% 1.54/1.76 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.54/1.76 tff(1202,plain,
% 1.54/1.76 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1201, 1197])).
% 1.54/1.76 tff(1203,plain,(
% 1.54/1.76 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[1202])).
% 1.54/1.76 tff(1204,plain,
% 1.54/1.76 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1203, 1196])).
% 1.54/1.76 tff(1205,plain,
% 1.54/1.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1206,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_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) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1205])).
% 1.54/1.76 tff(1207,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_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) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1208,plain,
% 1.54/1.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1209,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1208])).
% 1.54/1.76 tff(1210,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.54/1.76 tff(1211,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 1.54/1.76 tff(1212,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1211, 1207])).
% 1.54/1.76 tff(1213,plain,(
% 1.54/1.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[1212])).
% 1.54/1.76 tff(1214,plain,
% 1.54/1.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1213, 1206])).
% 1.54/1.76 tff(1215,assumption,(c3_1(a1438)), introduced(assumption)).
% 1.54/1.76 tff(1216,assumption,(~hskp11), introduced(assumption)).
% 1.54/1.76 tff(1217,plain,
% 1.54/1.76 (^[U: $i] : refl((hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1218,plain,
% 1.54/1.76 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1217])).
% 1.54/1.76 tff(1219,plain,
% 1.54/1.76 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1220,plain,
% 1.54/1.76 (^[U: $i] : 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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp11) <=> ((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite(((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp11) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(1221,plain,
% 1.54/1.76 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp11) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[1220])).
% 1.54/1.76 tff(1222,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.54/1.76 tff(1223,plain,
% 1.54/1.76 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.54/1.76 tff(1224,plain,
% 1.54/1.76 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1223, 1219])).
% 1.54/1.76 tff(1225,plain,(
% 1.54/1.76 ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[1224])).
% 1.54/1.76 tff(1226,plain,
% 1.54/1.76 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1225, 1218])).
% 1.54/1.76 tff(1227,plain,
% 1.54/1.76 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1228,plain,
% 1.54/1.76 ((hskp20 | hskp11 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c3_1(a1438))) <=> (hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1229,plain,
% 1.54/1.76 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1228])).
% 1.54/1.76 tff(1230,plain,
% 1.54/1.76 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1229, 1227])).
% 1.54/1.76 tff(1231,plain,
% 1.54/1.76 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1232,plain,
% 1.54/1.76 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp11 | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.54/1.76 tff(1233,plain,
% 1.54/1.76 (hskp20 | hskp11 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1232, 82, 24, 1226])).
% 1.54/1.76 tff(1234,plain,
% 1.54/1.76 (hskp20),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1233, 1216, 1215, 768])).
% 1.54/1.76 tff(1235,plain,
% 1.54/1.76 (((~hskp20) | (~c1_1(a1465))) <=> ((~hskp20) | (~c1_1(a1465)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1236,plain,
% 1.54/1.76 (((~c1_1(a1465)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1465)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1237,axiom,((~c1_1(a1465)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.54/1.76 tff(1238,plain,
% 1.54/1.76 ((~hskp20) | (~c1_1(a1465))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.54/1.76 tff(1239,plain,
% 1.54/1.76 ((~hskp20) | (~c1_1(a1465))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 1.54/1.76 tff(1240,plain,
% 1.54/1.76 (~c1_1(a1465)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1239, 1234])).
% 1.54/1.76 tff(1241,plain,
% 1.54/1.76 (((~hskp20) | c3_1(a1465)) <=> ((~hskp20) | c3_1(a1465))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1242,axiom,((~hskp20) | c3_1(a1465)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.54/1.76 tff(1243,plain,
% 1.54/1.76 ((~hskp20) | c3_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 1.54/1.76 tff(1244,plain,
% 1.54/1.76 ((~hskp20) | c3_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1243, 1241])).
% 1.54/1.76 tff(1245,plain,
% 1.54/1.76 ((~hskp20) | c3_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1244, 1241])).
% 1.54/1.76 tff(1246,plain,
% 1.54/1.76 ((~hskp20) | c3_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1245, 1241])).
% 1.54/1.76 tff(1247,plain,
% 1.54/1.76 ((~hskp20) | c3_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1246, 1241])).
% 1.54/1.76 tff(1248,plain,
% 1.54/1.76 (c3_1(a1465)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1247, 1234])).
% 1.54/1.76 tff(1249,plain,
% 1.54/1.76 (((~hskp20) | c2_1(a1465)) <=> ((~hskp20) | c2_1(a1465))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1250,axiom,((~hskp20) | c2_1(a1465)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.54/1.76 tff(1251,plain,
% 1.54/1.76 ((~hskp20) | c2_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.54/1.76 tff(1252,plain,
% 1.54/1.76 ((~hskp20) | c2_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1251, 1249])).
% 1.54/1.76 tff(1253,plain,
% 1.54/1.76 ((~hskp20) | c2_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1252, 1249])).
% 1.54/1.76 tff(1254,plain,
% 1.54/1.76 ((~hskp20) | c2_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 1.54/1.76 tff(1255,plain,
% 1.54/1.76 ((~hskp20) | c2_1(a1465)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1254, 1249])).
% 1.54/1.76 tff(1256,plain,
% 1.54/1.76 (c2_1(a1465)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1255, 1234])).
% 1.54/1.76 tff(1257,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1258,plain,
% 1.54/1.77 (((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1259,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1258])).
% 1.54/1.77 tff(1260,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1259, 1257])).
% 1.54/1.77 tff(1261,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1262,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 1.54/1.77 tff(1263,plain,
% 1.54/1.77 (~c0_1(a1465)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1262, 82, 1256, 1248, 1240, 37, 24, 1214, 768])).
% 1.54/1.77 tff(1264,plain,
% 1.54/1.77 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1265,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1264])).
% 1.54/1.77 tff(1266,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1267,plain,
% 1.54/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1268,plain,
% 1.54/1.77 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1267])).
% 1.54/1.77 tff(1269,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.54/1.77 tff(1270,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.54/1.77 tff(1271,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1270, 1266])).
% 1.54/1.77 tff(1272,plain,(
% 1.54/1.77 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(skolemize,[status(sab)],[1271])).
% 1.54/1.77 tff(1273,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1272, 1265])).
% 1.54/1.77 tff(1274,assumption,(~c0_1(a1465)), introduced(assumption)).
% 1.54/1.77 tff(1275,plain,
% 1.54/1.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1276,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1275])).
% 1.54/1.77 tff(1277,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1278,plain,
% 1.54/1.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1279,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1278])).
% 1.54/1.77 tff(1280,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.54/1.77 tff(1281,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.54/1.77 tff(1282,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 1.54/1.77 tff(1283,plain,(
% 1.54/1.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(skolemize,[status(sab)],[1282])).
% 1.54/1.77 tff(1284,plain,
% 1.54/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 1.54/1.77 tff(1285,assumption,(~c1_1(a1465)), introduced(assumption)).
% 1.54/1.77 tff(1286,plain,
% 1.54/1.77 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1287,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1286])).
% 1.54/1.77 tff(1288,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1289,plain,
% 1.54/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1290,plain,
% 1.54/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1289])).
% 1.54/1.77 tff(1291,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.54/1.77 tff(1292,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.54/1.77 tff(1293,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1292, 1288])).
% 1.54/1.77 tff(1294,plain,(
% 1.54/1.77 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(skolemize,[status(sab)],[1293])).
% 1.54/1.77 tff(1295,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1294, 1287])).
% 1.54/1.77 tff(1296,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1297,plain,
% 1.54/1.77 ((hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1487) | c1_1(a1487) | (~c3_1(a1487))) <=> (hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1298,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1487) | c1_1(a1487) | (~c3_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1297])).
% 1.54/1.77 tff(1299,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1487) | c1_1(a1487) | (~c3_1(a1487)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1298, 1296])).
% 1.54/1.77 tff(1300,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1487) | c1_1(a1487) | (~c3_1(a1487)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1301,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a1487) | c2_1(a1487) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1487))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.54/1.77 tff(1302,plain,
% 1.54/1.77 (hskp22),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1301, 82, 917, 211, 219, 961, 916, 203, 1295])).
% 1.54/1.77 tff(1303,plain,
% 1.54/1.77 (~c0_1(a1468)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[834, 1302])).
% 1.54/1.77 tff(1304,assumption,(c2_1(a1465)), introduced(assumption)).
% 1.54/1.77 tff(1305,plain,
% 1.54/1.77 (c3_1(a1468)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[842, 1302])).
% 1.54/1.77 tff(1306,plain,
% 1.54/1.77 (c1_1(a1468)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[850, 1302])).
% 1.54/1.77 tff(1307,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1308,plain,
% 1.54/1.77 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465))) <=> (c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1309,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1308])).
% 1.54/1.77 tff(1310,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.54/1.77 tff(1311,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1312,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.54/1.77 tff(1313,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1312, 82, 1306, 1305, 1304, 211, 219, 1303, 1285, 203, 1284, 1274])).
% 1.54/1.77 tff(1314,plain,((~hskp12) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1315,plain,
% 1.54/1.77 (~hskp12),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1314, 1263, 1240, 1256, 917, 961, 916])).
% 1.54/1.77 tff(1316,plain,
% 1.54/1.77 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1317,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1316])).
% 1.54/1.77 tff(1318,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1319,plain,
% 1.54/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(1320,plain,
% 1.54/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[1319])).
% 1.54/1.77 tff(1321,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.54/1.77 tff(1322,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 1.54/1.77 tff(1323,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 1.54/1.77 tff(1324,plain,(
% 1.54/1.77 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(skolemize,[status(sab)],[1323])).
% 1.54/1.77 tff(1325,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1324, 1317])).
% 1.54/1.77 tff(1326,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1327,plain,
% 1.54/1.77 ((hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438))) <=> (hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1328,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1327])).
% 1.54/1.77 tff(1329,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1328, 1326])).
% 1.54/1.77 tff(1330,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1331,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 1.54/1.77 tff(1332,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1331, 82, 647, 1215, 102, 37, 101, 1325, 313, 768])).
% 1.54/1.77 tff(1333,plain,(c1_1(a1435) | hskp12 | (~c3_1(a1438)) | (~c0_1(a1435)) | c0_1(a1438) | c3_1(a1435) | (~c2_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1334,plain,
% 1.54/1.77 (c1_1(a1435)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1333, 1315, 1215, 102, 37, 101, 768])).
% 1.54/1.77 tff(1335,plain,
% 1.54/1.77 (hskp18 | (~c1_1(a1435)) | (~c0_1(a1435))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[370, 82, 100, 101, 356])).
% 1.54/1.77 tff(1336,plain,
% 1.54/1.77 (hskp18),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1335, 1334, 102])).
% 1.54/1.77 tff(1337,plain,
% 1.54/1.77 (~c2_1(a1458)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[376, 1336])).
% 1.54/1.77 tff(1338,plain,
% 1.54/1.77 (c1_1(a1458)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[384, 1336])).
% 1.54/1.77 tff(1339,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1340,plain,
% 1.54/1.77 ((hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465))) <=> (hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1341,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1340])).
% 1.54/1.77 tff(1342,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1341, 1339])).
% 1.54/1.77 tff(1343,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1344,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.54/1.77 tff(1345,plain,
% 1.54/1.77 (~c3_1(a1458)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1344, 82, 1315, 1256, 1248, 1338, 1337, 1273, 1263])).
% 1.54/1.77 tff(1346,plain,
% 1.54/1.77 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.62/1.78 inference(bind,[status(th)],[])).
% 1.62/1.78 tff(1347,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(quant_intro,[status(thm)],[1346])).
% 1.62/1.78 tff(1348,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1349,plain,
% 1.62/1.78 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.62/1.78 inference(bind,[status(th)],[])).
% 1.62/1.78 tff(1350,plain,
% 1.62/1.78 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(quant_intro,[status(thm)],[1349])).
% 1.62/1.78 tff(1351,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.62/1.78 tff(1352,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.62/1.78 tff(1353,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1352, 1348])).
% 1.62/1.78 tff(1354,plain,(
% 1.62/1.78 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(skolemize,[status(sab)],[1353])).
% 1.62/1.78 tff(1355,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1354, 1347])).
% 1.62/1.78 tff(1356,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1357,plain,
% 1.62/1.78 ((hskp12 | (~ndr1_0) | c3_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435))) <=> (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1358,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435))))),
% 1.62/1.78 inference(monotonicity,[status(thm)],[1357])).
% 1.62/1.78 tff(1359,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435)))),
% 1.62/1.78 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.62/1.78 tff(1360,plain,
% 1.62/1.78 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1435) | c2_1(a1435) | (~c1_1(a1435)))),
% 1.62/1.78 inference(quant_inst,[status(thm)],[])).
% 1.62/1.78 tff(1361,plain,
% 1.62/1.78 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c1_1(a1435))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.62/1.78 tff(1362,plain,
% 1.62/1.78 (hskp12 | c2_1(a1435) | (~c1_1(a1430)) | (~c1_1(a1435))),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1361, 82, 35, 101, 545, 1355])).
% 1.62/1.78 tff(1363,plain,
% 1.62/1.78 (~c1_1(a1430)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1362, 1334, 100, 1315])).
% 1.62/1.78 tff(1364,plain,
% 1.62/1.78 (~hskp25),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[557, 1363, 35, 100, 101, 545, 102])).
% 1.62/1.78 tff(1365,plain,
% 1.62/1.78 (hskp17),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[448, 1364, 45])).
% 1.62/1.78 tff(1366,plain,
% 1.62/1.78 (~c2_1(a1457)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[264, 1365])).
% 1.62/1.78 tff(1367,plain,
% 1.62/1.78 (~c1_1(a1457)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[245, 1365])).
% 1.62/1.78 tff(1368,plain,
% 1.62/1.78 (~c0_1(a1457)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[251, 1365])).
% 1.62/1.78 tff(1369,plain,
% 1.62/1.78 (c0_1(a1458)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[392, 1336])).
% 1.62/1.78 tff(1370,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1371,plain,
% 1.63/1.78 ((hskp0 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457)) <=> (hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1372,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1371])).
% 1.63/1.78 tff(1373,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.63/1.78 tff(1374,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(1375,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1458) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1458) | (~c0_1(a1458))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.63/1.78 tff(1376,plain,
% 1.63/1.78 (hskp0),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1375, 82, 1369, 1337, 1368, 1367, 1366, 1123, 1345])).
% 1.63/1.78 tff(1377,plain,
% 1.63/1.78 (~c3_1(a1427)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1135, 1376])).
% 1.63/1.78 tff(1378,plain,
% 1.63/1.78 (c2_1(a1427)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1143, 1376])).
% 1.63/1.78 tff(1379,plain,
% 1.63/1.78 (c0_1(a1427)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1151, 1376])).
% 1.63/1.78 tff(1380,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1381,plain,
% 1.63/1.78 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427))) <=> (hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1382,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1381])).
% 1.63/1.78 tff(1383,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[1382, 1380])).
% 1.63/1.78 tff(1384,plain,
% 1.63/1.78 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(1385,plain,
% 1.63/1.78 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.63/1.78 tff(1386,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1385, 82, 1315, 1216, 1379, 1378, 1377, 1204])).
% 1.63/1.78 tff(1387,plain,(hskp11 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~c0_1(a1435)) | (~c3_1(a1438)) | c0_1(a1438) | (~c2_1(a1438)) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(1388,plain,
% 1.63/1.78 (hskp11),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1387, 100, 35, 101, 526, 1080, 1083, 1082, 1194, 917, 961, 916, 24])).
% 1.63/1.78 tff(1389,plain,
% 1.63/1.78 (~c2_1(a1447)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[691, 1388])).
% 1.63/1.78 tff(1390,plain,
% 1.63/1.78 (~c0_1(a1447)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[697, 1388])).
% 1.63/1.78 tff(1391,plain,
% 1.63/1.78 (~c3_1(a1447)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[703, 1388])).
% 1.63/1.78 tff(1392,plain,
% 1.63/1.78 (c0_1(a1447) | c1_1(a1447)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[713, 82, 45, 707, 706, 57])).
% 1.63/1.78 tff(1393,plain,
% 1.63/1.78 (c1_1(a1447)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1392, 705])).
% 1.63/1.78 tff(1394,plain,
% 1.63/1.78 (hskp12),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[722, 1393, 705])).
% 1.63/1.78 tff(1395,plain,
% 1.63/1.78 (~c2_1(a1448)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[202, 1394])).
% 1.63/1.78 tff(1396,plain,
% 1.63/1.78 (c3_1(a1448)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[218, 1394])).
% 1.63/1.78 tff(1397,plain,
% 1.63/1.78 (c0_1(a1448)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[210, 1394])).
% 1.63/1.78 tff(1398,plain,
% 1.63/1.78 (hskp22),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1301, 82, 917, 1397, 1396, 961, 916, 1395, 1295])).
% 1.63/1.78 tff(1399,plain,
% 1.63/1.78 (~c0_1(a1468)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[834, 1398])).
% 1.63/1.78 tff(1400,plain,
% 1.63/1.78 (c3_1(a1468)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[842, 1398])).
% 1.63/1.78 tff(1401,plain,
% 1.63/1.78 (c1_1(a1468)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[850, 1398])).
% 1.63/1.78 tff(1402,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1403,plain,
% 1.63/1.78 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1404,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1403])).
% 1.63/1.78 tff(1405,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[1404, 1402])).
% 1.63/1.78 tff(1406,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(1407,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 1.63/1.78 tff(1408,plain,
% 1.63/1.78 (~c2_1(a1438)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1407, 82, 1401, 1400, 1397, 1396, 1399, 1395, 37, 24, 1284])).
% 1.63/1.78 tff(1409,plain,
% 1.63/1.78 (hskp9),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1092, 82, 1215, 35, 37, 12, 526, 1040, 1408])).
% 1.63/1.78 tff(1410,plain,
% 1.63/1.78 (~c3_1(a1444)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1053, 1409])).
% 1.63/1.78 tff(1411,plain,
% 1.63/1.78 (~c2_1(a1444)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1059, 1409])).
% 1.63/1.78 tff(1412,plain,
% 1.63/1.78 (~c1_1(a1444)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1065, 1409])).
% 1.63/1.78 tff(1413,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1076, 82, 45, 705, 707, 706, 1412, 1411, 1410, 57])).
% 1.63/1.78 tff(1414,plain,(c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~c3_1(a1438)) | c3_1(a1430) | c0_1(a1438) | c0_1(a1430) | c1_1(a1438) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(1415,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1414, 1391, 1390, 1389, 1083, 35, 1082, 12, 24, 917, 961, 916])).
% 1.63/1.78 tff(1416,plain,(c2_1(a1435) | c3_1(a1430) | c0_1(a1430) | c1_1(a1438) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(1417,plain,
% 1.63/1.78 (c1_1(a1438)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1416, 960, 12, 35, 914, 959, 906, 953])).
% 1.63/1.78 tff(1418,plain,
% 1.63/1.78 (c0_1(a1435)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[363, 952])).
% 1.63/1.78 tff(1419,plain,
% 1.63/1.78 (hskp7),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[643, 960, 35, 1418, 953, 12])).
% 1.63/1.78 tff(1420,plain,
% 1.63/1.78 (((~hskp7) | (~c1_1(a1438))) <=> ((~hskp7) | (~c1_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1421,plain,
% 1.63/1.78 (((~c1_1(a1438)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1422,axiom,((~c1_1(a1438)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.63/1.78 tff(1423,plain,
% 1.63/1.78 ((~hskp7) | (~c1_1(a1438))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.63/1.78 tff(1424,plain,
% 1.63/1.78 ((~hskp7) | (~c1_1(a1438))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1423, 1420])).
% 1.63/1.78 tff(1425,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1424, 1419, 1417])).
% 1.63/1.78 tff(1426,plain,((~hskp24) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(1427,plain,
% 1.63/1.78 (~hskp24),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1426, 35, 12])).
% 1.63/1.78 tff(1428,plain,
% 1.63/1.78 (hskp30),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[80, 1427])).
% 1.63/1.78 tff(1429,plain,
% 1.63/1.78 (((~hskp30) | c2_1(a1507)) <=> ((~hskp30) | c2_1(a1507))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1430,axiom,((~hskp30) | c2_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.63/1.78 tff(1431,plain,
% 1.63/1.78 ((~hskp30) | c2_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.63/1.78 tff(1432,plain,
% 1.63/1.78 ((~hskp30) | c2_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1431, 1429])).
% 1.63/1.78 tff(1433,plain,
% 1.63/1.78 ((~hskp30) | c2_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1432, 1429])).
% 1.63/1.78 tff(1434,plain,
% 1.63/1.78 ((~hskp30) | c2_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1433, 1429])).
% 1.63/1.78 tff(1435,plain,
% 1.63/1.78 ((~hskp30) | c2_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1434, 1429])).
% 1.63/1.78 tff(1436,plain,
% 1.63/1.78 (c2_1(a1507)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1435, 1428])).
% 1.63/1.78 tff(1437,plain,
% 1.63/1.78 (((~hskp30) | c0_1(a1507)) <=> ((~hskp30) | c0_1(a1507))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1438,axiom,((~hskp30) | c0_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.63/1.78 tff(1439,plain,
% 1.63/1.78 ((~hskp30) | c0_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 1.63/1.78 tff(1440,plain,
% 1.63/1.78 ((~hskp30) | c0_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1439, 1437])).
% 1.63/1.78 tff(1441,plain,
% 1.63/1.78 ((~hskp30) | c0_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1440, 1437])).
% 1.63/1.78 tff(1442,plain,
% 1.63/1.78 ((~hskp30) | c0_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1441, 1437])).
% 1.63/1.78 tff(1443,plain,
% 1.63/1.78 ((~hskp30) | c0_1(a1507)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1442, 1437])).
% 1.63/1.78 tff(1444,plain,
% 1.63/1.78 (c0_1(a1507)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1443, 1428])).
% 1.63/1.78 tff(1445,plain,
% 1.63/1.78 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1446,plain,
% 1.63/1.78 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438))) <=> (hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1447,plain,
% 1.63/1.78 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1446])).
% 1.63/1.78 tff(1448,plain,
% 1.63/1.78 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[1447, 1445])).
% 1.63/1.78 tff(1449,plain,
% 1.63/1.78 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(1450,plain,
% 1.63/1.78 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 1.63/1.78 tff(1451,plain,
% 1.63/1.78 (hskp11 | hskp5 | c2_1(a1438) | (~c3_1(a1438))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1450, 82, 37, 34])).
% 1.63/1.78 tff(1452,plain,
% 1.63/1.78 (c2_1(a1438)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1451, 915, 1215, 11])).
% 1.63/1.78 tff(1453,assumption,(c2_1(a1507)), introduced(assumption)).
% 1.63/1.78 tff(1454,assumption,(c0_1(a1507)), introduced(assumption)).
% 1.63/1.78 tff(1455,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1456,plain,
% 1.63/1.78 (((~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1457,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1456])).
% 1.63/1.78 tff(1458,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.63/1.78 tff(1459,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(1460,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.63/1.78 tff(1461,plain,
% 1.63/1.78 (c0_1(a1438) | (~c3_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1460, 82, 1454, 1453, 24, 1214])).
% 1.63/1.78 tff(1462,plain,
% 1.63/1.78 (~c3_1(a1507)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1461, 1452, 37, 1215])).
% 1.63/1.78 tff(1463,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1464,plain,
% 1.63/1.78 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(1465,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[1464])).
% 1.63/1.78 tff(1466,plain,
% 1.63/1.78 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.63/1.79 tff(1467,plain,
% 1.63/1.79 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(1468,plain,
% 1.63/1.79 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.63/1.79 tff(1469,plain,
% 1.63/1.79 (hskp12 | hskp11 | c3_1(a1507)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1468, 82, 1454, 1453, 1204])).
% 1.63/1.79 tff(1470,plain,
% 1.63/1.79 (hskp12),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1469, 1462, 915])).
% 1.63/1.79 tff(1471,plain,
% 1.63/1.79 (~c2_1(a1448)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[202, 1470])).
% 1.63/1.79 tff(1472,plain,
% 1.63/1.79 (c3_1(a1448)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[218, 1470])).
% 1.63/1.79 tff(1473,plain,
% 1.63/1.79 (c0_1(a1448)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[210, 1470])).
% 1.63/1.79 tff(1474,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1475,plain,
% 1.63/1.79 ((hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1476,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[1475])).
% 1.63/1.79 tff(1477,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[1476, 1474])).
% 1.63/1.79 tff(1478,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(1479,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.63/1.79 tff(1480,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1479, 82, 11, 1473, 1472, 1215, 1471, 37, 24, 10])).
% 1.63/1.79 tff(1481,plain,(hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1507)) | (~c2_1(a1507)) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(1482,plain,
% 1.63/1.79 (hskp5),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1481, 899, 37, 24, 1444, 1436, 45])).
% 1.63/1.79 tff(1483,plain,
% 1.63/1.79 (~c3_1(a1435)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[295, 1482])).
% 1.63/1.79 tff(1484,plain,
% 1.63/1.79 (~c2_1(a1435)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[301, 1482])).
% 1.63/1.79 tff(1485,plain,
% 1.63/1.79 (c0_1(a1435)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[363, 1482])).
% 1.63/1.79 tff(1486,plain,
% 1.63/1.79 (c2_1(a1438)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1193, 1485, 24, 1484, 1483, 35, 12])).
% 1.63/1.79 tff(1487,plain,
% 1.63/1.79 (c0_1(a1438) | (~c3_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1460, 82, 1444, 1436, 24, 1214])).
% 1.63/1.79 tff(1488,plain,
% 1.63/1.79 (~c3_1(a1507)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1487, 1486, 37, 899])).
% 1.63/1.79 tff(1489,plain,
% 1.63/1.79 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1490,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1489])).
% 1.63/1.79 tff(1491,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1492,plain,
% 1.63/1.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1493,plain,
% 1.63/1.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1492])).
% 1.63/1.79 tff(1494,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.63/1.79 tff(1495,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.63/1.79 tff(1496,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1495, 1491])).
% 1.63/1.79 tff(1497,plain,(
% 1.63/1.79 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(skolemize,[status(sab)],[1496])).
% 1.63/1.79 tff(1498,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1497, 1490])).
% 1.63/1.79 tff(1499,plain,
% 1.63/1.79 (((~hskp30) | c1_1(a1507)) <=> ((~hskp30) | c1_1(a1507))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1500,axiom,((~hskp30) | c1_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.63/1.79 tff(1501,plain,
% 1.63/1.79 ((~hskp30) | c1_1(a1507)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.63/1.79 tff(1502,plain,
% 1.63/1.79 ((~hskp30) | c1_1(a1507)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1501, 1499])).
% 1.63/1.79 tff(1503,plain,
% 1.63/1.79 ((~hskp30) | c1_1(a1507)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1502, 1499])).
% 1.63/1.79 tff(1504,plain,
% 1.63/1.79 ((~hskp30) | c1_1(a1507)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1503, 1499])).
% 1.63/1.79 tff(1505,plain,
% 1.63/1.79 ((~hskp30) | c1_1(a1507)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1504, 1499])).
% 1.63/1.79 tff(1506,plain,
% 1.63/1.79 (c1_1(a1507)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1505, 1428])).
% 1.63/1.79 tff(1507,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1508,plain,
% 1.63/1.79 ((hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507))) <=> (hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1509,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[1508])).
% 1.63/1.79 tff(1510,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[1509, 1507])).
% 1.63/1.79 tff(1511,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(1512,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1507))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 1.63/1.79 tff(1513,plain,
% 1.63/1.79 (hskp23),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1512, 82, 1444, 1506, 1436, 1498, 1488])).
% 1.63/1.79 tff(1514,plain,
% 1.63/1.79 (((~hskp23) | c2_1(a1477)) <=> ((~hskp23) | c2_1(a1477))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1515,axiom,((~hskp23) | c2_1(a1477)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.63/1.79 tff(1516,plain,
% 1.63/1.79 ((~hskp23) | c2_1(a1477)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.63/1.79 tff(1517,plain,
% 1.63/1.79 ((~hskp23) | c2_1(a1477)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1516, 1514])).
% 1.63/1.79 tff(1518,plain,
% 1.63/1.79 ((~hskp23) | c2_1(a1477)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1517, 1514])).
% 1.63/1.79 tff(1519,plain,
% 1.63/1.79 ((~hskp23) | c2_1(a1477)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1518, 1514])).
% 1.63/1.79 tff(1520,plain,
% 1.63/1.79 ((~hskp23) | c2_1(a1477)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1519, 1514])).
% 1.63/1.79 tff(1521,plain,
% 1.63/1.79 (c2_1(a1477)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1520, 1513])).
% 1.63/1.79 tff(1522,plain,
% 1.63/1.79 (((~hskp23) | (~c1_1(a1477))) <=> ((~hskp23) | (~c1_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1523,plain,
% 1.63/1.79 (((~c1_1(a1477)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1524,axiom,((~c1_1(a1477)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.63/1.79 tff(1525,plain,
% 1.63/1.79 ((~hskp23) | (~c1_1(a1477))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 1.63/1.79 tff(1526,plain,
% 1.63/1.79 ((~hskp23) | (~c1_1(a1477))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1525, 1522])).
% 1.63/1.79 tff(1527,plain,
% 1.63/1.79 (~c1_1(a1477)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1526, 1513])).
% 1.63/1.79 tff(1528,plain,
% 1.63/1.79 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1529,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1528])).
% 1.63/1.79 tff(1530,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1531,plain,
% 1.63/1.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1532,plain,
% 1.63/1.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1531])).
% 1.63/1.79 tff(1533,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.63/1.79 tff(1534,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.63/1.79 tff(1535,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1534, 1530])).
% 1.63/1.79 tff(1536,plain,(
% 1.63/1.79 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(skolemize,[status(sab)],[1535])).
% 1.63/1.79 tff(1537,plain,
% 1.63/1.79 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1536, 1529])).
% 1.63/1.79 tff(1538,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1539,plain,
% 1.63/1.79 ((hskp8 | (~ndr1_0) | c3_1(a1507) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438))) <=> (hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1540,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1507) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[1539])).
% 1.63/1.79 tff(1541,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1507) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.63/1.79 tff(1542,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1507) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(1543,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c1_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.63/1.79 tff(1544,plain,
% 1.63/1.79 (hskp8),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1543, 82, 1444, 1506, 899, 24, 1537, 1488, 1486])).
% 1.63/1.79 tff(1545,plain,
% 1.63/1.79 (((~hskp8) | (~c1_1(a1441))) <=> ((~hskp8) | (~c1_1(a1441)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1546,plain,
% 1.63/1.79 (((~c1_1(a1441)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1441)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1547,axiom,((~c1_1(a1441)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.63/1.79 tff(1548,plain,
% 1.63/1.79 ((~hskp8) | (~c1_1(a1441))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.63/1.79 tff(1549,plain,
% 1.63/1.79 ((~hskp8) | (~c1_1(a1441))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1548, 1545])).
% 1.63/1.79 tff(1550,plain,
% 1.63/1.79 (~c1_1(a1441)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1549, 1544])).
% 1.63/1.79 tff(1551,plain,
% 1.63/1.79 (((~hskp8) | c3_1(a1441)) <=> ((~hskp8) | c3_1(a1441))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1552,axiom,((~hskp8) | c3_1(a1441)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.63/1.79 tff(1553,plain,
% 1.63/1.79 ((~hskp8) | c3_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.63/1.79 tff(1554,plain,
% 1.63/1.79 ((~hskp8) | c3_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1553, 1551])).
% 1.63/1.79 tff(1555,plain,
% 1.63/1.79 ((~hskp8) | c3_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1554, 1551])).
% 1.63/1.79 tff(1556,plain,
% 1.63/1.79 ((~hskp8) | c3_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1555, 1551])).
% 1.63/1.79 tff(1557,plain,
% 1.63/1.79 ((~hskp8) | c3_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1556, 1551])).
% 1.63/1.79 tff(1558,plain,
% 1.63/1.79 (c3_1(a1441)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1557, 1544])).
% 1.63/1.79 tff(1559,plain,
% 1.63/1.79 (((~hskp8) | c0_1(a1441)) <=> ((~hskp8) | c0_1(a1441))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1560,axiom,((~hskp8) | c0_1(a1441)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.63/1.79 tff(1561,plain,
% 1.63/1.79 ((~hskp8) | c0_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 1.63/1.79 tff(1562,plain,
% 1.63/1.79 ((~hskp8) | c0_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1561, 1559])).
% 1.63/1.79 tff(1563,plain,
% 1.63/1.79 ((~hskp8) | c0_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1562, 1559])).
% 1.63/1.79 tff(1564,plain,
% 1.63/1.79 ((~hskp8) | c0_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1563, 1559])).
% 1.63/1.79 tff(1565,plain,
% 1.63/1.79 ((~hskp8) | c0_1(a1441)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1564, 1559])).
% 1.63/1.79 tff(1566,plain,
% 1.63/1.79 (c0_1(a1441)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1565, 1544])).
% 1.63/1.79 tff(1567,plain,
% 1.63/1.79 (((~hskp23) | (~c0_1(a1477))) <=> ((~hskp23) | (~c0_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1568,plain,
% 1.63/1.79 (((~c0_1(a1477)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1569,axiom,((~c0_1(a1477)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.63/1.79 tff(1570,plain,
% 1.63/1.79 ((~hskp23) | (~c0_1(a1477))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 1.63/1.79 tff(1571,plain,
% 1.63/1.79 ((~hskp23) | (~c0_1(a1477))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1570, 1567])).
% 1.63/1.79 tff(1572,plain,
% 1.63/1.79 (~c0_1(a1477)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1571, 1513])).
% 1.63/1.79 tff(1573,assumption,(c2_1(a1441)), introduced(assumption)).
% 1.63/1.79 tff(1574,assumption,(~c1_1(a1441)), introduced(assumption)).
% 1.63/1.79 tff(1575,assumption,(~c1_1(a1477)), introduced(assumption)).
% 1.63/1.79 tff(1576,assumption,(~c0_1(a1477)), introduced(assumption)).
% 1.63/1.79 tff(1577,assumption,(c3_1(a1441)), introduced(assumption)).
% 1.63/1.79 tff(1578,assumption,(c0_1(a1441)), introduced(assumption)).
% 1.63/1.79 tff(1579,assumption,(c2_1(a1477)), introduced(assumption)).
% 1.63/1.79 tff(1580,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1581,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477))) <=> (c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1582,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[1581])).
% 1.63/1.79 tff(1583,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[1582, 1580])).
% 1.63/1.79 tff(1584,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(1585,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 1.63/1.79 tff(1586,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1585, 82, 1579, 1578, 1577, 1576, 1575, 1574, 1214, 1573])).
% 1.63/1.79 tff(1587,plain,((~c2_1(a1441)) | (~c2_1(a1477)) | (~c0_1(a1441)) | (~c3_1(a1441)) | c0_1(a1477) | c1_1(a1477) | c1_1(a1441)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(1588,plain,
% 1.63/1.79 (~c2_1(a1441)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1587, 1572, 1566, 1558, 1550, 1527, 1521])).
% 1.63/1.79 tff(1589,plain,
% 1.63/1.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1590,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_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)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1589])).
% 1.63/1.79 tff(1591,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_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)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1592,plain,
% 1.63/1.79 (^[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))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(1593,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[1592])).
% 1.63/1.79 tff(1594,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.63/1.79 tff(1595,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.63/1.79 tff(1596,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1595, 1591])).
% 1.63/1.79 tff(1597,plain,(
% 1.63/1.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(skolemize,[status(sab)],[1596])).
% 1.63/1.79 tff(1598,plain,
% 1.63/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 1.63/1.79 tff(1599,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1600,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441))) <=> (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(1601,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[1600])).
% 1.63/1.79 tff(1602,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.63/1.80 tff(1603,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1604,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.63/1.80 tff(1605,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1604, 82, 1444, 1506, 1436, 1558, 899, 1550, 24, 1598, 1486, 1588])).
% 1.63/1.80 tff(1606,plain,(c0_1(a1438) | c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(1607,plain,
% 1.63/1.80 (c0_1(a1438)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1606, 24, 35, 12])).
% 1.63/1.80 tff(1608,plain,
% 1.63/1.80 (~hskp7),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1021, 1607])).
% 1.63/1.80 tff(1609,assumption,(hskp5), introduced(assumption)).
% 1.63/1.80 tff(1610,plain,
% 1.63/1.80 (~c3_1(a1435)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[295, 1609])).
% 1.63/1.80 tff(1611,plain,
% 1.63/1.80 (c0_1(a1435)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[363, 1609])).
% 1.63/1.80 tff(1612,plain,
% 1.63/1.80 (~c2_1(a1435)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[301, 1609])).
% 1.63/1.80 tff(1613,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[643, 1612, 1611, 35, 13, 1610, 12])).
% 1.63/1.80 tff(1614,plain,((~hskp5) | c3_1(a1430) | hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(1615,plain,
% 1.63/1.80 (~hskp5),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1614, 1608, 35, 12])).
% 1.63/1.80 tff(1616,assumption,(c0_1(a1438)), introduced(assumption)).
% 1.63/1.80 tff(1617,plain,
% 1.63/1.80 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1618,plain,
% 1.63/1.80 ((hskp29 | hskp5 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438))) <=> (hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1619,plain,
% 1.63/1.80 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1618])).
% 1.63/1.80 tff(1620,plain,
% 1.63/1.80 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1619, 1617])).
% 1.63/1.80 tff(1621,plain,
% 1.63/1.80 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1622,plain,
% 1.63/1.80 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 1.63/1.80 tff(1623,plain,
% 1.63/1.80 (hskp29 | hskp5 | c3_1(a1438) | c2_1(a1438)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1622, 82, 1616, 975])).
% 1.63/1.80 tff(1624,plain,
% 1.63/1.80 (hskp29),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1623, 47, 46, 11])).
% 1.63/1.80 tff(1625,plain,
% 1.63/1.80 (c3_1(a1483)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[990, 1624])).
% 1.63/1.80 tff(1626,plain,
% 1.63/1.80 (c2_1(a1483)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[998, 1624])).
% 1.63/1.80 tff(1627,plain,
% 1.63/1.80 (c1_1(a1483)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1006, 1624])).
% 1.63/1.80 tff(1628,plain,
% 1.63/1.80 (~hskp7),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1021, 1616])).
% 1.63/1.80 tff(1629,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1630,plain,
% 1.63/1.80 ((hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1438) | c2_1(a1438) | c1_1(a1438)) <=> (hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1631,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1438) | c2_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1630])).
% 1.63/1.80 tff(1632,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1438) | c2_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1631, 1629])).
% 1.63/1.80 tff(1633,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1438) | c2_1(a1438) | c1_1(a1438))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1634,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.63/1.80 tff(1635,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1634, 82, 1628, 1627, 1626, 1625, 46, 24, 627, 47])).
% 1.63/1.80 tff(1636,plain,(c2_1(a1438) | c3_1(a1438) | c1_1(a1438) | hskp5 | (~c0_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(1637,plain,
% 1.63/1.80 (c2_1(a1438)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1636, 11, 24, 46, 1616])).
% 1.63/1.80 tff(1638,plain,
% 1.63/1.80 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1639,plain,
% 1.63/1.80 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438))) <=> (hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1640,plain,
% 1.63/1.80 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1639])).
% 1.63/1.80 tff(1641,plain,
% 1.63/1.80 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.63/1.80 tff(1642,plain,
% 1.63/1.80 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1643,plain,
% 1.63/1.80 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.63/1.80 tff(1644,plain,
% 1.63/1.80 (hskp12 | hskp11 | c3_1(a1438) | (~c2_1(a1438))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1643, 82, 1616, 1204])).
% 1.63/1.80 tff(1645,plain,
% 1.63/1.80 (hskp12),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1644, 1637, 46, 915])).
% 1.63/1.80 tff(1646,plain,
% 1.63/1.80 (~hskp17),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[808, 1637, 24, 46, 58, 11])).
% 1.63/1.80 tff(1647,plain,
% 1.63/1.80 (c2_1(a1448)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[239, 1646, 11, 1645])).
% 1.63/1.80 tff(1648,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[202, 1647, 1645])).
% 1.63/1.80 tff(1649,plain,(hskp5 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(1650,plain,
% 1.63/1.80 (c3_1(a1438)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1649, 1615, 1607, 24, 45])).
% 1.63/1.80 tff(1651,plain,
% 1.63/1.80 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1652,plain,
% 1.63/1.80 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438))) <=> (hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1653,plain,
% 1.63/1.80 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1652])).
% 1.63/1.80 tff(1654,plain,
% 1.63/1.80 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1653, 1651])).
% 1.63/1.80 tff(1655,plain,
% 1.63/1.80 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1656,plain,
% 1.63/1.80 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.63/1.80 tff(1657,plain,
% 1.63/1.80 (hskp17 | hskp5 | c2_1(a1438) | (~c3_1(a1438))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1656, 82, 1616, 229])).
% 1.63/1.80 tff(1658,plain,
% 1.63/1.80 (hskp17),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1657, 47, 11, 1215])).
% 1.63/1.80 tff(1659,plain,
% 1.63/1.80 (~c1_1(a1457)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[245, 1658])).
% 1.63/1.80 tff(1660,plain,
% 1.63/1.80 (~c0_1(a1457)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[251, 1658])).
% 1.63/1.80 tff(1661,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1662,plain,
% 1.63/1.80 ((hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1663,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1662])).
% 1.63/1.80 tff(1664,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1663, 1661])).
% 1.63/1.80 tff(1665,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1666,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 1.63/1.80 tff(1667,plain,
% 1.63/1.80 (~c3_1(a1457)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1666, 82, 11, 1215, 1660, 1659, 1616, 10, 47])).
% 1.63/1.80 tff(1668,plain,
% 1.63/1.80 (~c2_1(a1457)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[264, 1658])).
% 1.63/1.80 tff(1669,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[949, 82, 58, 1660, 1659, 1668, 57, 1667])).
% 1.63/1.80 tff(1670,plain,(c2_1(a1438) | hskp2 | hskp5 | (~c3_1(a1438)) | (~c0_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(1671,plain,
% 1.63/1.80 (c2_1(a1438)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1670, 1615, 45, 1650, 1607])).
% 1.63/1.80 tff(1672,plain,
% 1.63/1.80 (~hskp11),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[741, 1615, 45])).
% 1.63/1.80 tff(1673,plain,
% 1.63/1.80 (hskp20),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1233, 1671, 1672, 1650])).
% 1.63/1.80 tff(1674,plain,
% 1.63/1.80 (~c1_1(a1465)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1239, 1673])).
% 1.63/1.80 tff(1675,plain,
% 1.63/1.80 (c3_1(a1465)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1247, 1673])).
% 1.63/1.80 tff(1676,plain,
% 1.63/1.80 (c2_1(a1465)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1255, 1673])).
% 1.63/1.80 tff(1677,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1678,plain,
% 1.63/1.80 (((~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465))) <=> (c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1679,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1678])).
% 1.63/1.80 tff(1680,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1679, 1677])).
% 1.63/1.80 tff(1681,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1682,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 1.63/1.80 tff(1683,plain,
% 1.63/1.80 (c0_1(a1465)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1682, 82, 1676, 1675, 1650, 1674, 1607, 1214, 1671])).
% 1.63/1.80 tff(1684,plain,
% 1.63/1.80 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(1685,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[1684])).
% 1.63/1.80 tff(1686,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1687,plain,
% 1.63/1.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(1688,plain,
% 1.63/1.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[1687])).
% 1.63/1.80 tff(1689,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.63/1.80 tff(1690,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.63/1.80 tff(1691,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1690, 1686])).
% 1.63/1.80 tff(1692,plain,(
% 1.63/1.80 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(skolemize,[status(sab)],[1691])).
% 1.63/1.80 tff(1693,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1692, 1685])).
% 1.63/1.80 tff(1694,plain,
% 1.63/1.80 (^[U: $i] : refl((hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(1695,plain,
% 1.63/1.80 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[1694])).
% 1.63/1.80 tff(1696,plain,
% 1.63/1.80 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1697,plain,
% 1.63/1.80 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp11) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(1698,plain,
% 1.63/1.80 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp11) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[1697])).
% 1.63/1.80 tff(1699,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.63/1.80 tff(1700,plain,
% 1.63/1.80 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.63/1.80 tff(1701,plain,
% 1.63/1.80 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1700, 1696])).
% 1.63/1.80 tff(1702,plain,(
% 1.63/1.80 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(skolemize,[status(sab)],[1701])).
% 1.63/1.80 tff(1703,plain,
% 1.63/1.80 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1702, 1695])).
% 1.63/1.80 tff(1704,plain,
% 1.63/1.80 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1705,plain,
% 1.63/1.80 ((hskp11 | hskp0 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438))) <=> (hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1706,plain,
% 1.63/1.80 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1705])).
% 1.63/1.80 tff(1707,plain,
% 1.63/1.80 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1706, 1704])).
% 1.63/1.80 tff(1708,plain,
% 1.63/1.80 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(1709,plain,
% 1.63/1.80 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 1.63/1.80 tff(1710,plain,
% 1.63/1.80 (hskp11 | hskp0 | (~c0_1(a1438)) | (~c2_1(a1438))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1709, 82, 24, 1703])).
% 1.63/1.80 tff(1711,plain,
% 1.63/1.80 (hskp0),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1710, 1671, 1607, 1672])).
% 1.63/1.80 tff(1712,plain,
% 1.63/1.80 (~c3_1(a1427)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1135, 1711])).
% 1.63/1.80 tff(1713,plain,
% 1.63/1.80 (c2_1(a1427)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1143, 1711])).
% 1.63/1.80 tff(1714,plain,
% 1.63/1.80 (c0_1(a1427)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1151, 1711])).
% 1.63/1.80 tff(1715,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1716,plain,
% 1.63/1.80 ((hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465))) <=> (hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(1717,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1716])).
% 1.63/1.80 tff(1718,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[1717, 1715])).
% 1.63/1.80 tff(1719,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1720,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1465) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1465)) | (~c3_1(a1465))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 1.63/1.81 tff(1721,plain,
% 1.63/1.81 (hskp23),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1720, 82, 1676, 1675, 1714, 1713, 1674, 1712, 1693])).
% 1.63/1.81 tff(1722,plain,
% 1.63/1.81 (~c1_1(a1477)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1526, 1721])).
% 1.63/1.81 tff(1723,plain,
% 1.63/1.81 (~c0_1(a1477)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1571, 1721])).
% 1.63/1.81 tff(1724,plain,
% 1.63/1.81 (c2_1(a1477)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1520, 1721])).
% 1.63/1.81 tff(1725,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1726,plain,
% 1.63/1.81 (((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477))) <=> (c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1727,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1726])).
% 1.63/1.81 tff(1728,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1727, 1725])).
% 1.63/1.81 tff(1729,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1465)) | (~c3_1(a1465)) | (~c0_1(a1465)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1477) | c0_1(a1477) | (~c2_1(a1477)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1730,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 1.63/1.81 tff(1731,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1730, 82, 1724, 1676, 1675, 1723, 1722, 1674, 1214, 1683])).
% 1.63/1.81 tff(1732,plain,(c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(1733,plain,
% 1.63/1.81 (c1_1(a1438)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1732, 35, 12])).
% 1.63/1.81 tff(1734,plain,
% 1.63/1.81 (~hskp7),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1424, 1733])).
% 1.63/1.81 tff(1735,plain,
% 1.63/1.81 (~hskp5),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1614, 1734, 35, 12])).
% 1.63/1.81 tff(1736,plain,
% 1.63/1.81 (hskp25),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[448, 36, 45])).
% 1.63/1.81 tff(1737,plain,
% 1.63/1.81 (~c0_1(a1504)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[454, 1736])).
% 1.63/1.81 tff(1738,plain,
% 1.63/1.81 (c2_1(a1504)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[489, 1736])).
% 1.63/1.81 tff(1739,plain,
% 1.63/1.81 (c1_1(a1504)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[464, 1736])).
% 1.63/1.81 tff(1740,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1741,plain,
% 1.63/1.81 ((hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430))) <=> (hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1742,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1741])).
% 1.63/1.81 tff(1743,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1742, 1740])).
% 1.63/1.81 tff(1744,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1745,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.63/1.81 tff(1746,plain,
% 1.63/1.81 (hskp14),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1745, 82, 1739, 1738, 35, 1737, 12, 526, 482])).
% 1.63/1.81 tff(1747,plain,
% 1.63/1.81 (~c1_1(a1451)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[508, 1746])).
% 1.63/1.81 tff(1748,plain,
% 1.63/1.81 (~c3_1(a1451)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[502, 1746])).
% 1.63/1.81 tff(1749,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1750,plain,
% 1.63/1.81 ((hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504))) <=> (hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1751,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1750])).
% 1.63/1.81 tff(1752,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.63/1.81 tff(1753,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1754,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c0_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.63/1.81 tff(1755,plain,
% 1.63/1.81 (~c0_1(a1451)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1754, 82, 1734, 1739, 1738, 1737, 1747, 1748, 175])).
% 1.63/1.81 tff(1756,assumption,(~c0_1(a1451)), introduced(assumption)).
% 1.63/1.81 tff(1757,assumption,(~c3_1(a1451)), introduced(assumption)).
% 1.63/1.81 tff(1758,assumption,(~c1_1(a1451)), introduced(assumption)).
% 1.63/1.81 tff(1759,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1760,plain,
% 1.63/1.81 ((hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451)) <=> (hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1761,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1760])).
% 1.63/1.81 tff(1762,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.63/1.81 tff(1763,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1764,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.63/1.81 tff(1765,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1764, 82, 820, 851, 843, 835, 1758, 1757, 819, 1756])).
% 1.63/1.81 tff(1766,plain,(hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1451) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(1767,plain,
% 1.63/1.81 (hskp3),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1766, 1755, 36, 1748, 1747])).
% 1.63/1.81 tff(1768,plain,
% 1.63/1.81 (~c2_1(a1431)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[865, 1767])).
% 1.63/1.81 tff(1769,plain,
% 1.63/1.81 (~c0_1(a1431)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[871, 1767])).
% 1.63/1.81 tff(1770,plain,
% 1.63/1.81 (~hskp11),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[741, 1735, 45])).
% 1.63/1.81 tff(1771,plain,
% 1.63/1.81 (~c3_1(a1431)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[879, 82, 1770, 1735, 1769, 1768, 34])).
% 1.63/1.81 tff(1772,plain,
% 1.63/1.81 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.63/1.81 inference(bind,[status(th)],[])).
% 1.63/1.81 tff(1773,plain,
% 1.63/1.81 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(quant_intro,[status(thm)],[1772])).
% 1.63/1.81 tff(1774,plain,
% 1.63/1.81 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1775,plain,
% 1.63/1.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp7) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp7) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.63/1.81 inference(bind,[status(th)],[])).
% 1.63/1.81 tff(1776,plain,
% 1.63/1.81 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp7) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(quant_intro,[status(thm)],[1775])).
% 1.63/1.81 tff(1777,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.63/1.81 tff(1778,plain,
% 1.63/1.81 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.63/1.81 tff(1779,plain,
% 1.63/1.81 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1778, 1774])).
% 1.63/1.81 tff(1780,plain,(
% 1.63/1.81 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(skolemize,[status(sab)],[1779])).
% 1.63/1.81 tff(1781,plain,
% 1.63/1.81 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1780, 1773])).
% 1.63/1.81 tff(1782,plain,
% 1.63/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1783,plain,
% 1.63/1.81 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504))) <=> (hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1784,plain,
% 1.63/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1783])).
% 1.63/1.81 tff(1785,plain,
% 1.63/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1784, 1782])).
% 1.63/1.81 tff(1786,plain,
% 1.63/1.81 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1787,plain,
% 1.63/1.81 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1504) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.63/1.81 tff(1788,plain,
% 1.63/1.81 (hskp16),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1787, 82, 1734, 1739, 1738, 1737, 1781])).
% 1.63/1.81 tff(1789,plain,
% 1.63/1.81 (((~hskp16) | (~c3_1(a1454))) <=> ((~hskp16) | (~c3_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1790,plain,
% 1.63/1.81 (((~c3_1(a1454)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1791,axiom,((~c3_1(a1454)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.63/1.81 tff(1792,plain,
% 1.63/1.81 ((~hskp16) | (~c3_1(a1454))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.63/1.81 tff(1793,plain,
% 1.63/1.81 ((~hskp16) | (~c3_1(a1454))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1792, 1789])).
% 1.63/1.81 tff(1794,plain,
% 1.63/1.81 (~c3_1(a1454)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1793, 1788])).
% 1.63/1.81 tff(1795,plain,
% 1.63/1.81 (((~hskp16) | (~c0_1(a1454))) <=> ((~hskp16) | (~c0_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1796,plain,
% 1.63/1.81 (((~c0_1(a1454)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1797,axiom,((~c0_1(a1454)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.63/1.81 tff(1798,plain,
% 1.63/1.81 ((~hskp16) | (~c0_1(a1454))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.63/1.81 tff(1799,plain,
% 1.63/1.81 ((~hskp16) | (~c0_1(a1454))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1798, 1795])).
% 1.63/1.81 tff(1800,plain,
% 1.63/1.81 (~c0_1(a1454)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1799, 1788])).
% 1.63/1.81 tff(1801,plain,
% 1.63/1.81 (c1_1(a1431)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[887, 1767])).
% 1.63/1.81 tff(1802,plain,
% 1.63/1.81 (((~hskp16) | c1_1(a1454)) <=> ((~hskp16) | c1_1(a1454))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1803,axiom,((~hskp16) | c1_1(a1454)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.63/1.81 tff(1804,plain,
% 1.63/1.81 ((~hskp16) | c1_1(a1454)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 1.63/1.81 tff(1805,plain,
% 1.63/1.81 ((~hskp16) | c1_1(a1454)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1804, 1802])).
% 1.63/1.81 tff(1806,plain,
% 1.63/1.81 ((~hskp16) | c1_1(a1454)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1805, 1802])).
% 1.63/1.81 tff(1807,plain,
% 1.63/1.81 ((~hskp16) | c1_1(a1454)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1806, 1802])).
% 1.63/1.81 tff(1808,plain,
% 1.63/1.81 ((~hskp16) | c1_1(a1454)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1807, 1802])).
% 1.63/1.81 tff(1809,plain,
% 1.63/1.81 (c1_1(a1454)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1808, 1788])).
% 1.63/1.81 tff(1810,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1811,plain,
% 1.63/1.81 ((hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454))) <=> (hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1812,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1811])).
% 1.63/1.81 tff(1813,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.63/1.81 tff(1814,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1815,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.63/1.81 tff(1816,plain,
% 1.63/1.81 (hskp12),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1815, 82, 1809, 1801, 1800, 1794, 1768, 196, 1771])).
% 1.63/1.81 tff(1817,plain,
% 1.63/1.81 (~c2_1(a1448)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[202, 1816])).
% 1.63/1.81 tff(1818,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[239, 1817, 1816, 1735, 36])).
% 1.63/1.81 tff(1819,plain,(hskp17 | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(1820,plain,
% 1.63/1.81 (hskp17),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1819, 35, 12])).
% 1.63/1.81 tff(1821,plain,
% 1.63/1.81 (~c2_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[264, 1820])).
% 1.63/1.81 tff(1822,plain,
% 1.63/1.81 (~c0_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[251, 1820])).
% 1.63/1.81 tff(1823,plain,
% 1.63/1.81 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1824,plain,
% 1.63/1.81 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457))) <=> (hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1825,plain,
% 1.63/1.81 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1824])).
% 1.63/1.81 tff(1826,plain,
% 1.63/1.81 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1825, 1823])).
% 1.63/1.81 tff(1827,plain,
% 1.63/1.81 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | (~c3_1(a1457)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1828,plain,
% 1.63/1.81 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c3_1(a1457))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 1.63/1.81 tff(1829,plain,
% 1.63/1.81 (~c3_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1828, 82, 1770, 1735, 1822, 1821, 34])).
% 1.63/1.81 tff(1830,assumption,(~hskp24), introduced(assumption)).
% 1.63/1.81 tff(1831,plain,
% 1.63/1.81 (hskp30),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[80, 1830])).
% 1.63/1.81 tff(1832,plain,
% 1.63/1.81 (c2_1(a1507)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1435, 1831])).
% 1.63/1.81 tff(1833,plain,
% 1.63/1.81 (c1_1(a1507)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1505, 1831])).
% 1.63/1.81 tff(1834,plain,
% 1.63/1.81 (c0_1(a1507)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1443, 1831])).
% 1.63/1.81 tff(1835,assumption,(c1_1(a1438)), introduced(assumption)).
% 1.63/1.81 tff(1836,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1837,plain,
% 1.63/1.81 ((hskp12 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438))) <=> (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1838,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1837])).
% 1.63/1.81 tff(1839,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.63/1.81 tff(1840,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1841,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.63/1.81 tff(1842,plain,
% 1.63/1.81 (hskp12),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1841, 82, 46, 37, 1835, 196, 47])).
% 1.63/1.81 tff(1843,plain,
% 1.63/1.81 (~c2_1(a1448)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[202, 1842])).
% 1.63/1.81 tff(1844,plain,
% 1.63/1.81 (hskp17),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[239, 1843, 11, 1842])).
% 1.63/1.81 tff(1845,plain,
% 1.63/1.81 (~c1_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[245, 1844])).
% 1.63/1.81 tff(1846,plain,
% 1.63/1.81 (~c0_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[251, 1844])).
% 1.63/1.81 tff(1847,plain,
% 1.63/1.81 (c3_1(a1448)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[218, 1842])).
% 1.63/1.81 tff(1848,plain,
% 1.63/1.81 (c0_1(a1448)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[210, 1842])).
% 1.63/1.81 tff(1849,plain,
% 1.63/1.81 (~c3_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[258, 82, 11, 1848, 1847, 1846, 1845, 1843, 10])).
% 1.63/1.81 tff(1850,plain,
% 1.63/1.81 (~c2_1(a1457)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[264, 1844])).
% 1.63/1.81 tff(1851,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1852,plain,
% 1.63/1.81 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438)) <=> (hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1853,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1852])).
% 1.63/1.81 tff(1854,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457))),
% 1.63/1.81 inference(transitivity,[status(thm)],[1853, 1851])).
% 1.63/1.81 tff(1855,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(1856,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.63/1.81 tff(1857,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1856, 82, 58, 46, 1845, 1850, 37, 57, 47, 1849])).
% 1.63/1.81 tff(1858,plain,(c2_1(a1438) | hskp2 | c3_1(a1438) | c0_1(a1438) | hskp5 | (~c1_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(1859,plain,
% 1.63/1.81 (c2_1(a1438)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1858, 37, 46, 58, 11, 1835])).
% 1.63/1.81 tff(1860,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(1861,plain,
% 1.63/1.81 ((hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(1862,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1861])).
% 1.63/1.82 tff(1863,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[1862, 1860])).
% 1.63/1.82 tff(1864,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(1865,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.63/1.82 tff(1866,plain,
% 1.63/1.82 (hskp14 | (~c2_1(a1438))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1865, 82, 46, 37, 1835, 482])).
% 1.63/1.82 tff(1867,plain,
% 1.63/1.82 (hskp14),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1866, 1859])).
% 1.63/1.82 tff(1868,plain,
% 1.63/1.82 (~c3_1(a1451)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[502, 1867])).
% 1.63/1.82 tff(1869,plain,
% 1.63/1.82 (~c1_1(a1451)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[508, 1867])).
% 1.63/1.82 tff(1870,assumption,(c1_1(a1507)), introduced(assumption)).
% 1.63/1.82 tff(1871,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(1872,plain,
% 1.63/1.82 ((hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438))) <=> (hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(1873,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1872])).
% 1.63/1.82 tff(1874,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1873, 1871])).
% 1.66/1.82 tff(1875,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1876,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.66/1.82 tff(1877,plain,
% 1.66/1.82 (hskp23 | (~c2_1(a1438))),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1876, 82, 1454, 1870, 1453, 46, 1835, 1498])).
% 1.66/1.82 tff(1878,plain,
% 1.66/1.82 (hskp23),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1877, 1859])).
% 1.66/1.82 tff(1879,plain,
% 1.66/1.82 (~c1_1(a1477)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1526, 1878])).
% 1.66/1.82 tff(1880,plain,
% 1.66/1.82 (~c0_1(a1477)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1571, 1878])).
% 1.66/1.82 tff(1881,plain,
% 1.66/1.82 (c2_1(a1451)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[516, 1867])).
% 1.66/1.82 tff(1882,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1883,plain,
% 1.66/1.82 ((hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477))) <=> (hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1884,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477))))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1883])).
% 1.66/1.82 tff(1885,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477)))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1884, 1882])).
% 1.66/1.82 tff(1886,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1887,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c3_1(a1477))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.66/1.82 tff(1888,plain,
% 1.66/1.82 (~c3_1(a1477)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1887, 82, 11, 1881, 1880, 1879, 1869, 1868, 794])).
% 1.66/1.82 tff(1889,plain,
% 1.66/1.82 (~hskp7),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1424, 1835])).
% 1.66/1.82 tff(1890,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1891,plain,
% 1.66/1.82 ((hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438))) <=> (hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1892,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451))))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1891])).
% 1.66/1.82 tff(1893,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451)))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1892, 1890])).
% 1.66/1.82 tff(1894,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1451)) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1438)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1895,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1451))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 1.66/1.82 tff(1896,plain,
% 1.66/1.82 (~c0_1(a1451)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1895, 82, 1889, 1869, 1868, 37, 1835, 175, 1859])).
% 1.66/1.82 tff(1897,plain,
% 1.66/1.82 (hskp3),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1766, 36, 1757, 1756, 1758])).
% 1.66/1.82 tff(1898,plain,
% 1.66/1.82 (~c2_1(a1431)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[865, 1897])).
% 1.66/1.82 tff(1899,plain,
% 1.66/1.82 (~c0_1(a1431)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[871, 1897])).
% 1.66/1.82 tff(1900,plain,
% 1.66/1.82 (~c3_1(a1431)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[879, 82, 1216, 11, 1899, 1898, 34])).
% 1.66/1.82 tff(1901,plain,
% 1.66/1.82 (c1_1(a1431)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[887, 1897])).
% 1.66/1.82 tff(1902,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1903,plain,
% 1.66/1.82 ((hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438))) <=> (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1904,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1903])).
% 1.66/1.82 tff(1905,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1904, 1902])).
% 1.66/1.82 tff(1906,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1907,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 1.66/1.82 tff(1908,plain,
% 1.66/1.82 (hskp12),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1907, 82, 46, 1901, 37, 1835, 1898, 196, 1900])).
% 1.66/1.82 tff(1909,plain,
% 1.66/1.82 (~c2_1(a1448)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[202, 1908])).
% 1.66/1.82 tff(1910,plain,
% 1.66/1.82 ($false),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[239, 1909, 1908, 11, 36])).
% 1.66/1.82 tff(1911,plain,(hskp17 | hskp5 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | hskp11 | c3_1(a1451) | c0_1(a1451) | c1_1(a1451)), inference(lemma,lemma(discharge,[]))).
% 1.66/1.82 tff(1912,plain,
% 1.66/1.82 (hskp17),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1911, 37, 46, 11, 1835, 915, 1868, 1896, 1869])).
% 1.66/1.82 tff(1913,plain,
% 1.66/1.82 (~c1_1(a1457)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[245, 1912])).
% 1.66/1.82 tff(1914,plain,
% 1.66/1.82 (~c0_1(a1457)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[251, 1912])).
% 1.66/1.82 tff(1915,plain,
% 1.66/1.82 (c2_1(a1477)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1520, 1878])).
% 1.66/1.82 tff(1916,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1917,plain,
% 1.66/1.82 ((hskp5 | (~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1918,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477)))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1917])).
% 1.66/1.82 tff(1919,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1918, 1916])).
% 1.66/1.82 tff(1920,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1921,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1477) | c0_1(a1457) | c1_1(a1457) | (~ndr1_0) | (~c3_1(a1457)) | (~c2_1(a1477)) | c3_1(a1477)),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 1.66/1.82 tff(1922,plain,
% 1.66/1.82 (~c3_1(a1457)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1921, 82, 11, 1915, 1879, 1914, 1913, 794, 1888])).
% 1.66/1.82 tff(1923,plain,
% 1.66/1.82 (~c2_1(a1457)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[264, 1912])).
% 1.66/1.82 tff(1924,plain,
% 1.66/1.82 (hskp1),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[595, 82, 58, 1914, 1913, 1923, 588])).
% 1.66/1.82 tff(1925,plain,
% 1.66/1.82 (~c0_1(a1429)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[601, 1924])).
% 1.66/1.82 tff(1926,plain,
% 1.66/1.82 (c3_1(a1429)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[609, 1924])).
% 1.66/1.82 tff(1927,plain,
% 1.66/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1928,plain,
% 1.66/1.82 (((~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457)) <=> (c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1929,plain,
% 1.66/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477)))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1928])).
% 1.66/1.82 tff(1930,plain,
% 1.66/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1929, 1927])).
% 1.66/1.82 tff(1931,plain,
% 1.66/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1477) | c3_1(a1477) | (~c2_1(a1477)) | c0_1(a1429) | c1_1(a1429) | (~c3_1(a1429)) | c3_1(a1457) | c1_1(a1457) | c2_1(a1457))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1932,plain,
% 1.66/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477)),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.66/1.82 tff(1933,plain,
% 1.66/1.82 (c1_1(a1429)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1932, 82, 1915, 1926, 1879, 1913, 1923, 1925, 578, 1888, 1922])).
% 1.66/1.82 tff(1934,plain,
% 1.66/1.82 (c2_1(a1429)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[634, 1924])).
% 1.66/1.82 tff(1935,plain,
% 1.66/1.82 ($false),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[641, 82, 1889, 1934, 1926, 1913, 1923, 627, 1922, 1933])).
% 1.66/1.82 tff(1936,plain,(c0_1(a1438) | hskp2 | hskp5 | c3_1(a1438) | (~c1_1(a1438)) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.82 tff(1937,plain,
% 1.66/1.82 (c0_1(a1438)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1936, 46, 11, 58, 1835, 1834, 1833, 1832])).
% 1.66/1.82 tff(1938,plain,
% 1.66/1.82 (^[U: $i] : refl((hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.66/1.82 inference(bind,[status(th)],[])).
% 1.66/1.82 tff(1939,plain,
% 1.66/1.82 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(quant_intro,[status(thm)],[1938])).
% 1.66/1.82 tff(1940,plain,
% 1.66/1.82 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1941,plain,
% 1.66/1.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | 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)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp24) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.66/1.82 inference(bind,[status(th)],[])).
% 1.66/1.82 tff(1942,plain,
% 1.66/1.82 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp24) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(quant_intro,[status(thm)],[1941])).
% 1.66/1.82 tff(1943,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.66/1.82 tff(1944,plain,
% 1.66/1.82 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 1.66/1.82 tff(1945,plain,
% 1.66/1.82 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1944, 1940])).
% 1.66/1.82 tff(1946,plain,(
% 1.66/1.82 ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(skolemize,[status(sab)],[1945])).
% 1.66/1.82 tff(1947,plain,
% 1.66/1.82 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1946, 1939])).
% 1.66/1.82 tff(1948,plain,
% 1.66/1.82 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1949,plain,
% 1.66/1.82 ((hskp24 | hskp4 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438))) <=> (hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1950,plain,
% 1.66/1.82 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438)))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1949])).
% 1.66/1.82 tff(1951,plain,
% 1.66/1.82 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.66/1.82 tff(1952,plain,
% 1.66/1.82 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a1438) | c3_1(a1438) | (~c0_1(a1438)))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(1953,plain,
% 1.66/1.82 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp4 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438)),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.66/1.82 tff(1954,plain,
% 1.66/1.82 (hskp4 | (~c0_1(a1438)) | c2_1(a1438)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1953, 1830, 82, 46, 1947])).
% 1.66/1.82 tff(1955,plain,
% 1.66/1.82 (hskp4),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1954, 47, 1616])).
% 1.66/1.82 tff(1956,plain,
% 1.66/1.82 (~c2_1(a1434)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[125, 1955])).
% 1.66/1.82 tff(1957,plain,
% 1.66/1.82 (c3_1(a1434)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[143, 1955])).
% 1.66/1.82 tff(1958,plain,
% 1.66/1.82 (c1_1(a1434)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[135, 1955])).
% 1.66/1.82 tff(1959,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1960,plain,
% 1.66/1.82 ((hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | (~c1_1(a1438))) <=> (hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(1961,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438)))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[1960])).
% 1.66/1.82 tff(1962,plain,
% 1.66/1.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | (~c1_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.66/1.82 inference(transitivity,[status(thm)],[1961, 1959])).
% 1.66/1.82 tff(1963,plain,
% 1.66/1.82 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | (~c1_1(a1438)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(1964,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.66/1.83 tff(1965,plain,
% 1.66/1.83 ($false),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1964, 82, 1889, 46, 1958, 1957, 1835, 1956, 154, 47])).
% 1.66/1.83 tff(1966,plain,(c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | (~c0_1(a1438)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.66/1.83 tff(1967,plain,
% 1.66/1.83 (c2_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1966, 46, 1835, 1937, 1830])).
% 1.66/1.83 tff(1968,plain,
% 1.66/1.83 (hskp12 | (~c0_1(a1438)) | (~c2_1(a1438))),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1643, 82, 915, 46, 1204])).
% 1.66/1.83 tff(1969,plain,
% 1.66/1.83 (hskp12),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1968, 1967, 1937])).
% 1.66/1.83 tff(1970,plain,
% 1.66/1.83 (~c2_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[202, 1969])).
% 1.66/1.83 tff(1971,plain,
% 1.66/1.83 (hskp23 | (~c2_1(a1438))),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1876, 82, 1834, 1833, 1832, 46, 1835, 1498])).
% 1.66/1.83 tff(1972,plain,
% 1.66/1.83 (hskp23),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1971, 1967])).
% 1.66/1.83 tff(1973,plain,
% 1.66/1.83 (~c1_1(a1477)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1526, 1972])).
% 1.66/1.83 tff(1974,plain,
% 1.66/1.83 (~c0_1(a1477)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1571, 1972])).
% 1.66/1.83 tff(1975,plain,
% 1.66/1.83 (c3_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[218, 1969])).
% 1.66/1.83 tff(1976,plain,
% 1.66/1.83 (c0_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[210, 1969])).
% 1.66/1.83 tff(1977,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(1978,plain,
% 1.66/1.83 ((hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477))) <=> (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(1979,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[1978])).
% 1.66/1.83 tff(1980,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[1979, 1977])).
% 1.66/1.83 tff(1981,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(1982,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 1.66/1.83 tff(1983,plain,
% 1.66/1.83 (~c3_1(a1477)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1982, 82, 11, 1976, 1975, 1974, 1973, 1970, 10])).
% 1.66/1.83 tff(1984,plain,
% 1.66/1.83 (hskp17),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[239, 1970, 11, 1969])).
% 1.66/1.83 tff(1985,plain,
% 1.66/1.83 (~c1_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[245, 1984])).
% 1.66/1.83 tff(1986,plain,
% 1.66/1.83 (~c0_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[251, 1984])).
% 1.66/1.83 tff(1987,plain,
% 1.66/1.83 (~c3_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[258, 82, 11, 1976, 1975, 1986, 1985, 1970, 10])).
% 1.66/1.83 tff(1988,plain,
% 1.66/1.83 (~c2_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[264, 1984])).
% 1.66/1.83 tff(1989,plain,
% 1.66/1.83 (hskp1),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[595, 82, 58, 1986, 1985, 1988, 588])).
% 1.66/1.83 tff(1990,plain,
% 1.66/1.83 (~c0_1(a1429)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[601, 1989])).
% 1.66/1.83 tff(1991,plain,
% 1.66/1.83 (c3_1(a1429)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[609, 1989])).
% 1.66/1.83 tff(1992,plain,
% 1.66/1.83 (c2_1(a1477)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1520, 1972])).
% 1.66/1.83 tff(1993,plain,
% 1.66/1.83 (c1_1(a1429)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1932, 82, 1992, 1991, 1973, 1985, 1988, 1990, 578, 1987, 1983])).
% 1.66/1.83 tff(1994,plain,
% 1.66/1.83 (c2_1(a1429)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[634, 1989])).
% 1.66/1.83 tff(1995,plain,
% 1.66/1.83 ($false),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[641, 82, 1889, 1994, 1991, 1985, 1988, 627, 1987, 1993])).
% 1.66/1.83 tff(1996,plain,(c3_1(a1438) | hskp2 | hskp5 | (~c1_1(a1438)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.66/1.83 tff(1997,plain,
% 1.66/1.83 (c3_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1996, 45, 1735, 1733, 1427])).
% 1.66/1.83 tff(1998,plain,
% 1.66/1.83 (c0_1(a1438) | c2_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1450, 82, 1770, 1735, 1997, 34])).
% 1.66/1.83 tff(1999,plain,
% 1.66/1.83 (c2_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1998, 37])).
% 1.66/1.83 tff(2000,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2001,plain,
% 1.66/1.83 ((hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430))) <=> (hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2002,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2001])).
% 1.66/1.83 tff(2003,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2002, 2000])).
% 1.66/1.83 tff(2004,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2005,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a1430) | c0_1(a1438) | (~c1_1(a1438)) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c2_1(a1438))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.66/1.83 tff(2006,plain,
% 1.66/1.83 (hskp14),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2005, 82, 35, 37, 1733, 12, 526, 482, 1999])).
% 1.66/1.83 tff(2007,plain,
% 1.66/1.83 (~c3_1(a1451)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[502, 2006])).
% 1.66/1.83 tff(2008,plain,
% 1.66/1.83 (~c1_1(a1451)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[508, 2006])).
% 1.66/1.83 tff(2009,plain,
% 1.66/1.83 (~c0_1(a1451)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1895, 82, 1734, 2008, 2007, 37, 1733, 175, 1999])).
% 1.66/1.83 tff(2010,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2011,plain,
% 1.66/1.83 ((hskp3 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451)) <=> (hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2012,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451)))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2011])).
% 1.66/1.83 tff(2013,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.66/1.83 tff(2014,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2015,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.66/1.83 tff(2016,plain,
% 1.66/1.83 (hskp3),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2015, 82, 1997, 2008, 2007, 37, 1733, 819, 2009])).
% 1.66/1.83 tff(2017,plain,
% 1.66/1.83 (~c2_1(a1431)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[865, 2016])).
% 1.66/1.83 tff(2018,plain,
% 1.66/1.83 (~c0_1(a1431)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[871, 2016])).
% 1.66/1.83 tff(2019,plain,
% 1.66/1.83 (~c3_1(a1431)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[879, 82, 1770, 1735, 2018, 2017, 34])).
% 1.66/1.83 tff(2020,plain,
% 1.66/1.83 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2021,plain,
% 1.66/1.83 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438))) <=> (hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2022,plain,
% 1.66/1.83 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2021])).
% 1.66/1.83 tff(2023,plain,
% 1.66/1.83 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2022, 2020])).
% 1.66/1.83 tff(2024,plain,
% 1.66/1.83 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1438) | (~c2_1(a1438)) | (~c1_1(a1438)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2025,plain,
% 1.66/1.83 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 1.66/1.83 tff(2026,plain,
% 1.66/1.83 (hskp16 | c0_1(a1438) | (~c2_1(a1438))),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2025, 82, 1734, 1733, 1781])).
% 1.66/1.83 tff(2027,plain,
% 1.66/1.83 (hskp16),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2026, 1999, 37])).
% 1.66/1.83 tff(2028,plain,
% 1.66/1.83 (~c3_1(a1454)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1793, 2027])).
% 1.66/1.83 tff(2029,plain,
% 1.66/1.83 (~c0_1(a1454)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1799, 2027])).
% 1.66/1.83 tff(2030,plain,
% 1.66/1.83 (c1_1(a1431)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[887, 2016])).
% 1.66/1.83 tff(2031,plain,
% 1.66/1.83 (c1_1(a1454)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1808, 2027])).
% 1.66/1.83 tff(2032,plain,
% 1.66/1.83 (hskp12),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1815, 82, 2031, 2030, 2029, 2028, 2017, 196, 2019])).
% 1.66/1.83 tff(2033,plain,
% 1.66/1.83 (~c2_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[202, 2032])).
% 1.66/1.83 tff(2034,plain,
% 1.66/1.83 (hskp17),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[239, 2033, 1735, 2032])).
% 1.66/1.83 tff(2035,plain,
% 1.66/1.83 (~c2_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[264, 2034])).
% 1.66/1.83 tff(2036,plain,
% 1.66/1.83 (~c1_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[245, 2034])).
% 1.66/1.83 tff(2037,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2038,plain,
% 1.66/1.83 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1431) | c2_1(a1431) | c0_1(a1431)) <=> (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2039,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1431) | c2_1(a1431) | c0_1(a1431))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457)))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2038])).
% 1.66/1.83 tff(2040,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1431) | c2_1(a1431) | c0_1(a1431))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2039, 2037])).
% 1.66/1.83 tff(2041,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1431) | c2_1(a1431) | c0_1(a1431))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2042,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | c3_1(a1457)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.66/1.83 tff(2043,plain,
% 1.66/1.83 (c3_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2042, 82, 45, 2036, 2035, 2018, 2017, 57, 2019])).
% 1.66/1.83 tff(2044,plain,
% 1.66/1.83 (c3_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[218, 2032])).
% 1.66/1.83 tff(2045,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2046,plain,
% 1.66/1.83 ((hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1431) | c2_1(a1431) | (~c1_1(a1431))) <=> (hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2047,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1431) | c2_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2046])).
% 1.66/1.83 tff(2048,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1431) | c2_1(a1431) | (~c1_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2047, 2045])).
% 1.66/1.83 tff(2049,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1431) | c2_1(a1431) | (~c1_1(a1431)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2050,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 1.66/1.83 tff(2051,plain,
% 1.66/1.83 (~c1_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2050, 82, 1734, 2044, 2030, 2033, 2017, 154, 2019])).
% 1.66/1.83 tff(2052,plain,
% 1.66/1.83 (~c0_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[251, 2034])).
% 1.66/1.83 tff(2053,plain,
% 1.66/1.83 (c0_1(a1448)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[210, 2032])).
% 1.66/1.83 tff(2054,plain,
% 1.66/1.83 (c2_1(a1451)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[516, 2006])).
% 1.66/1.83 tff(2055,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2056,plain,
% 1.66/1.83 (((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457))) <=> (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2057,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2056])).
% 1.66/1.83 tff(2058,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2057, 2055])).
% 1.66/1.83 tff(2059,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2060,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 1.66/1.83 tff(2061,plain,
% 1.66/1.83 ($false),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2060, 82, 2054, 2053, 2052, 2035, 2008, 2007, 2033, 543, 2051, 2043])).
% 1.66/1.83 tff(2062,plain,(c0_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.66/1.83 tff(2063,plain,
% 1.66/1.83 (c0_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2062, 35, 12])).
% 1.66/1.83 tff(2064,plain,
% 1.66/1.83 (c2_1(a1438)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1670, 2063, 45, 1735, 1997])).
% 1.66/1.83 tff(2065,plain,
% 1.66/1.83 (~c1_1(a1457)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[245, 1820])).
% 1.66/1.83 tff(2066,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2067,plain,
% 1.66/1.83 ((hskp7 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457)) <=> (hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2068,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457)))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[2067])).
% 1.68/1.83 tff(2069,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457))),
% 1.68/1.83 inference(transitivity,[status(thm)],[2068, 2066])).
% 1.68/1.83 tff(2070,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(2071,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 1.68/1.83 tff(2072,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2071, 82, 1734, 1997, 2065, 1821, 1733, 627, 2064, 1829])).
% 1.68/1.83 tff(2073,plain,(c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(2074,plain,
% 1.68/1.83 (c3_1(a1430)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2073, 12])).
% 1.68/1.83 tff(2075,plain,
% 1.68/1.83 (~c1_1(a1447)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[721, 82, 647, 705, 707, 706, 196])).
% 1.68/1.83 tff(2076,plain,
% 1.68/1.83 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.68/1.83 inference(bind,[status(th)],[])).
% 1.68/1.83 tff(2077,plain,
% 1.68/1.83 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(quant_intro,[status(thm)],[2076])).
% 1.68/1.83 tff(2078,plain,
% 1.68/1.83 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2079,plain,
% 1.68/1.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.68/1.83 inference(bind,[status(th)],[])).
% 1.68/1.83 tff(2080,plain,
% 1.68/1.83 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(quant_intro,[status(thm)],[2079])).
% 1.68/1.83 tff(2081,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.68/1.83 tff(2082,plain,
% 1.68/1.83 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 1.68/1.83 tff(2083,plain,
% 1.68/1.83 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2082, 2078])).
% 1.68/1.83 tff(2084,plain,(
% 1.68/1.83 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(skolemize,[status(sab)],[2083])).
% 1.68/1.83 tff(2085,plain,
% 1.68/1.83 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2084, 2077])).
% 1.68/1.83 tff(2086,plain,
% 1.68/1.83 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2087,plain,
% 1.68/1.83 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a1430) | c0_1(a1430) | (~c3_1(a1430))) <=> (hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2088,plain,
% 1.68/1.83 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[2087])).
% 1.68/1.83 tff(2089,plain,
% 1.68/1.83 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[2088, 2086])).
% 1.68/1.83 tff(2090,plain,
% 1.68/1.83 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(2091,plain,
% 1.68/1.83 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 1.68/1.83 tff(2092,plain,
% 1.68/1.83 (hskp7 | hskp6 | c1_1(a1430) | (~c3_1(a1430))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2091, 82, 12, 2085])).
% 1.68/1.83 tff(2093,plain,
% 1.68/1.83 (hskp6),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2092, 544, 2074, 13])).
% 1.68/1.83 tff(2094,plain,
% 1.68/1.83 (((~hskp6) | (~c2_1(a1437))) <=> ((~hskp6) | (~c2_1(a1437)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2095,plain,
% 1.68/1.83 (((~c2_1(a1437)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1437)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(2096,axiom,((~c2_1(a1437)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.68/1.83 tff(2097,plain,
% 1.68/1.83 ((~hskp6) | (~c2_1(a1437))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 1.68/1.83 tff(2098,plain,
% 1.68/1.83 ((~hskp6) | (~c2_1(a1437))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[2097, 2094])).
% 1.68/1.83 tff(2099,plain,
% 1.68/1.83 (~c2_1(a1437)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2098, 2093])).
% 1.68/1.83 tff(2100,plain,
% 1.68/1.83 (((~hskp6) | c0_1(a1437)) <=> ((~hskp6) | c0_1(a1437))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2101,axiom,((~hskp6) | c0_1(a1437)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.68/1.84 tff(2102,plain,
% 1.68/1.84 ((~hskp6) | c0_1(a1437)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 1.68/1.84 tff(2103,plain,
% 1.68/1.84 ((~hskp6) | c0_1(a1437)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2102, 2100])).
% 1.68/1.84 tff(2104,plain,
% 1.68/1.84 ((~hskp6) | c0_1(a1437)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2103, 2100])).
% 1.68/1.84 tff(2105,plain,
% 1.68/1.84 ((~hskp6) | c0_1(a1437)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2104, 2100])).
% 1.68/1.84 tff(2106,plain,
% 1.68/1.84 ((~hskp6) | c0_1(a1437)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2105, 2100])).
% 1.68/1.84 tff(2107,plain,
% 1.68/1.84 (c0_1(a1437)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2106, 2093])).
% 1.68/1.84 tff(2108,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2109,plain,
% 1.68/1.84 ((hskp5 | (~ndr1_0) | c2_1(a1437) | (~c3_1(a1437)) | (~c0_1(a1437)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430))) <=> (hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2110,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1437) | (~c3_1(a1437)) | (~c0_1(a1437)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2109])).
% 1.68/1.84 tff(2111,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1437) | (~c3_1(a1437)) | (~c0_1(a1437)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.68/1.84 tff(2112,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1437) | (~c3_1(a1437)) | (~c0_1(a1437)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2113,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1437) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c0_1(a1437)) | (~c3_1(a1437))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.68/1.84 tff(2114,plain,
% 1.68/1.84 (~c3_1(a1437)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2113, 82, 11, 2107, 2074, 2099, 12, 10, 544])).
% 1.68/1.84 tff(2115,plain,
% 1.68/1.84 (((~hskp6) | (~c1_1(a1437))) <=> ((~hskp6) | (~c1_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2116,plain,
% 1.68/1.84 (((~c1_1(a1437)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2117,axiom,((~c1_1(a1437)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.68/1.84 tff(2118,plain,
% 1.68/1.84 ((~hskp6) | (~c1_1(a1437))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 1.68/1.84 tff(2119,plain,
% 1.68/1.84 ((~hskp6) | (~c1_1(a1437))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2118, 2115])).
% 1.68/1.84 tff(2120,plain,
% 1.68/1.84 (~c1_1(a1437)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2119, 2093])).
% 1.68/1.84 tff(2121,plain,
% 1.68/1.84 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2122,plain,
% 1.68/1.84 ((hskp29 | hskp5 | (~ndr1_0) | c2_1(a1437) | c3_1(a1437) | (~c0_1(a1437))) <=> (hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2123,plain,
% 1.68/1.84 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1437) | c3_1(a1437) | (~c0_1(a1437)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2122])).
% 1.68/1.84 tff(2124,plain,
% 1.68/1.84 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1437) | c3_1(a1437) | (~c0_1(a1437)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2123, 2121])).
% 1.68/1.84 tff(2125,plain,
% 1.68/1.84 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1437) | c3_1(a1437) | (~c0_1(a1437)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2126,plain,
% 1.68/1.84 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c0_1(a1437))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 1.68/1.84 tff(2127,plain,
% 1.68/1.84 (hskp29 | c3_1(a1437)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2126, 82, 11, 2107, 2099, 975])).
% 1.68/1.84 tff(2128,plain,
% 1.68/1.84 (hskp29),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2127, 2114])).
% 1.68/1.84 tff(2129,plain,
% 1.68/1.84 (c3_1(a1483)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[990, 2128])).
% 1.68/1.84 tff(2130,plain,
% 1.68/1.84 (c2_1(a1483)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[998, 2128])).
% 1.68/1.84 tff(2131,plain,
% 1.68/1.84 (c1_1(a1483)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1006, 2128])).
% 1.68/1.84 tff(2132,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2133,plain,
% 1.68/1.84 ((hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1437) | c2_1(a1437) | c1_1(a1437)) <=> (hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2134,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1437) | c2_1(a1437) | c1_1(a1437))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2133])).
% 1.68/1.84 tff(2135,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1437) | c2_1(a1437) | c1_1(a1437))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2134, 2132])).
% 1.68/1.84 tff(2136,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1437) | c2_1(a1437) | c1_1(a1437))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2137,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 1.68/1.84 tff(2138,plain,
% 1.68/1.84 ($false),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2137, 82, 13, 2131, 2130, 2129, 2120, 2099, 627, 2114])).
% 1.68/1.84 tff(2139,plain,(c1_1(a1430) | hskp7 | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.84 tff(2140,plain,
% 1.68/1.84 (c1_1(a1430)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2139, 99, 11, 12])).
% 1.68/1.84 tff(2141,plain,
% 1.68/1.84 (c2_1(a1438)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[90, 58, 24, 46, 37])).
% 1.68/1.84 tff(2142,plain,
% 1.68/1.84 (~hskp17),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[808, 2141, 24, 46, 58, 11])).
% 1.68/1.84 tff(2143,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2144,plain,
% 1.68/1.84 ((hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430))) <=> (hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2145,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2144])).
% 1.68/1.84 tff(2146,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.68/1.84 tff(2147,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2148,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1438))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.68/1.84 tff(2149,plain,
% 1.68/1.84 (c3_1(a1438) | c1_1(a1430) | (~c2_1(a1438))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2148, 82, 11, 2074, 24, 12, 794])).
% 1.68/1.84 tff(2150,plain,
% 1.68/1.84 (c1_1(a1430)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2149, 2141, 46])).
% 1.68/1.84 tff(2151,plain,
% 1.68/1.84 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.68/1.84 inference(bind,[status(th)],[])).
% 1.68/1.84 tff(2152,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(quant_intro,[status(thm)],[2151])).
% 1.68/1.84 tff(2153,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2154,plain,
% 1.68/1.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.68/1.84 inference(bind,[status(th)],[])).
% 1.68/1.84 tff(2155,plain,
% 1.68/1.84 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(quant_intro,[status(thm)],[2154])).
% 1.68/1.84 tff(2156,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.68/1.84 tff(2157,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.68/1.84 tff(2158,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2157, 2153])).
% 1.68/1.84 tff(2159,plain,(
% 1.68/1.84 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(skolemize,[status(sab)],[2158])).
% 1.68/1.84 tff(2160,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2159, 2152])).
% 1.68/1.84 tff(2161,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2162,plain,
% 1.68/1.84 ((hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438))) <=> (hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2163,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2162])).
% 1.68/1.84 tff(2164,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2163, 2161])).
% 1.68/1.84 tff(2165,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2166,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 1.68/1.84 tff(2167,plain,
% 1.68/1.84 (hskp0 | (~c1_1(a1430)) | (~c2_1(a1438))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2166, 82, 2074, 37, 24, 12, 2160])).
% 1.68/1.84 tff(2168,plain,
% 1.68/1.84 (hskp0),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2167, 2150, 2141])).
% 1.68/1.84 tff(2169,plain,
% 1.68/1.84 (~c3_1(a1427)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1135, 2168])).
% 1.68/1.84 tff(2170,plain,
% 1.68/1.84 (c2_1(a1427)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1143, 2168])).
% 1.68/1.84 tff(2171,plain,
% 1.68/1.84 (c0_1(a1427)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1151, 2168])).
% 1.68/1.84 tff(2172,plain,
% 1.68/1.84 (~hskp11),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[741, 58, 11])).
% 1.68/1.84 tff(2173,plain,
% 1.68/1.84 (hskp12),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1385, 82, 2172, 2171, 2170, 2169, 1204])).
% 1.68/1.84 tff(2174,plain,
% 1.68/1.84 (~c2_1(a1448)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[202, 2173])).
% 1.68/1.84 tff(2175,plain,
% 1.68/1.84 ($false),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[239, 2174, 2173, 11, 2142])).
% 1.68/1.84 tff(2176,plain,(hskp2 | hskp5 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | c3_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.84 tff(2177,plain,
% 1.68/1.84 (hskp2),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2176, 37, 11, 24, 12, 46])).
% 1.68/1.84 tff(2178,plain,
% 1.68/1.84 (((~hskp2) | (~c2_1(a1430))) <=> ((~hskp2) | (~c2_1(a1430)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2179,plain,
% 1.68/1.84 (((~c2_1(a1430)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1430)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2180,axiom,((~c2_1(a1430)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.68/1.84 tff(2181,plain,
% 1.68/1.84 ((~hskp2) | (~c2_1(a1430))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.68/1.84 tff(2182,plain,
% 1.68/1.84 ((~hskp2) | (~c2_1(a1430))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2181, 2178])).
% 1.68/1.84 tff(2183,plain,
% 1.68/1.84 (~c2_1(a1430)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2182, 2177])).
% 1.68/1.84 tff(2184,plain,
% 1.68/1.84 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2185,plain,
% 1.68/1.84 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430))) <=> (hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2186,plain,
% 1.68/1.84 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2185])).
% 1.68/1.84 tff(2187,plain,
% 1.68/1.84 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.68/1.84 tff(2188,plain,
% 1.68/1.84 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2189,plain,
% 1.68/1.84 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.68/1.84 tff(2190,plain,
% 1.68/1.84 (hskp11 | hskp5 | c2_1(a1430) | (~c3_1(a1430))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2189, 82, 12, 34])).
% 1.68/1.84 tff(2191,plain,
% 1.68/1.84 (hskp11),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2190, 2183, 2074, 11])).
% 1.68/1.84 tff(2192,plain,
% 1.68/1.84 (~c3_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[703, 2191])).
% 1.68/1.84 tff(2193,plain,
% 1.68/1.84 (~c2_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[691, 2191])).
% 1.68/1.84 tff(2194,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2195,plain,
% 1.68/1.84 ((hskp7 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447))) <=> (hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2196,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2195])).
% 1.68/1.84 tff(2197,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.68/1.84 tff(2198,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2199,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1447))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.68/1.84 tff(2200,plain,
% 1.68/1.84 (~c1_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2199, 82, 99, 2074, 2193, 2192, 2183, 154, 2140])).
% 1.68/1.84 tff(2201,plain,
% 1.68/1.84 (c3_1(a1430)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[289, 11, 186, 12])).
% 1.68/1.84 tff(2202,assumption,(~hskp8), introduced(assumption)).
% 1.68/1.84 tff(2203,plain,
% 1.68/1.84 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.68/1.84 inference(bind,[status(th)],[])).
% 1.68/1.84 tff(2204,plain,
% 1.68/1.84 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(quant_intro,[status(thm)],[2203])).
% 1.68/1.84 tff(2205,plain,
% 1.68/1.84 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2206,plain,
% 1.68/1.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | 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) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.68/1.84 inference(bind,[status(th)],[])).
% 1.68/1.84 tff(2207,plain,
% 1.68/1.84 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(quant_intro,[status(thm)],[2206])).
% 1.68/1.84 tff(2208,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.68/1.84 tff(2209,plain,
% 1.68/1.84 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 1.68/1.84 tff(2210,plain,
% 1.68/1.84 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2209, 2205])).
% 1.68/1.84 tff(2211,plain,(
% 1.68/1.84 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(skolemize,[status(sab)],[2210])).
% 1.68/1.84 tff(2212,plain,
% 1.68/1.84 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2211, 2204])).
% 1.68/1.84 tff(2213,plain,
% 1.68/1.84 (hskp11 | hskp5 | c0_1(a1430) | (~c3_1(a1430))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2189, 82, 186, 34])).
% 1.68/1.84 tff(2214,plain,
% 1.68/1.84 (hskp11),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2213, 2201, 11, 12])).
% 1.68/1.84 tff(2215,plain,
% 1.68/1.84 (~c3_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[703, 2214])).
% 1.68/1.84 tff(2216,plain,
% 1.68/1.84 (~c2_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[691, 2214])).
% 1.68/1.84 tff(2217,plain,
% 1.68/1.84 (~c0_1(a1447)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[697, 2214])).
% 1.68/1.84 tff(2218,plain,
% 1.68/1.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2219,plain,
% 1.68/1.84 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1447) | c0_1(a1447) | c3_1(a1447)) <=> (hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2220,plain,
% 1.68/1.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1447) | c0_1(a1447) | c3_1(a1447))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0)))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2219])).
% 1.68/1.84 tff(2221,plain,
% 1.68/1.84 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1447) | c0_1(a1447) | c3_1(a1447))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2220, 2218])).
% 1.68/1.84 tff(2222,plain,
% 1.68/1.84 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1447) | c0_1(a1447) | c3_1(a1447))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2223,plain,
% 1.68/1.84 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 1.68/1.84 tff(2224,plain,
% 1.68/1.84 (hskp8 | hskp7),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2223, 82, 2217, 2216, 2215, 2212])).
% 1.68/1.84 tff(2225,plain,
% 1.68/1.84 (hskp7),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2224, 2202])).
% 1.68/1.84 tff(2226,plain,
% 1.68/1.84 (c3_1(a1438)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[98, 2225])).
% 1.68/1.85 tff(2227,plain,
% 1.68/1.85 (~c0_1(a1438)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1021, 2225])).
% 1.68/1.85 tff(2228,plain,
% 1.68/1.85 (~c1_1(a1438)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1424, 2225])).
% 1.68/1.85 tff(2229,assumption,(c3_1(a1430)), introduced(assumption)).
% 1.68/1.85 tff(2230,plain,
% 1.68/1.85 (hskp11),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2213, 11, 2229, 12])).
% 1.68/1.85 tff(2231,plain,
% 1.68/1.85 (~c0_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[697, 2230])).
% 1.68/1.85 tff(2232,plain,
% 1.68/1.85 (~c3_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[703, 2230])).
% 1.68/1.85 tff(2233,plain,
% 1.68/1.85 (~c2_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[691, 2230])).
% 1.68/1.85 tff(2234,plain,
% 1.68/1.85 (hskp12 | (~c1_1(a1447))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[721, 82, 705, 707, 706, 196])).
% 1.68/1.85 tff(2235,plain,
% 1.68/1.85 (~c1_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2234, 647])).
% 1.68/1.85 tff(2236,plain,
% 1.68/1.85 ((hskp14 | hskp12 | hskp8) <=> (hskp14 | hskp12 | hskp8)),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2237,plain,
% 1.68/1.85 (((hskp12 | hskp8) | hskp14) <=> (hskp14 | hskp12 | hskp8)),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2238,plain,
% 1.68/1.85 ((hskp8 | hskp12) <=> (hskp12 | hskp8)),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2239,plain,
% 1.68/1.85 (((hskp8 | hskp12) | hskp14) <=> ((hskp12 | hskp8) | hskp14)),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2238])).
% 1.68/1.85 tff(2240,plain,
% 1.68/1.85 (((hskp8 | hskp12) | hskp14) <=> (hskp14 | hskp12 | hskp8)),
% 1.68/1.85 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.68/1.85 tff(2241,axiom,((hskp8 | hskp12) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.68/1.85 tff(2242,plain,
% 1.68/1.85 (hskp14 | hskp12 | hskp8),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.68/1.85 tff(2243,plain,
% 1.68/1.85 (hskp14 | hskp12 | hskp8),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2242, 2236])).
% 1.68/1.85 tff(2244,plain,
% 1.68/1.85 (hskp14 | hskp12 | hskp8),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2243, 2236])).
% 1.68/1.85 tff(2245,plain,
% 1.68/1.85 (hskp14 | hskp12 | hskp8),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2244, 2236])).
% 1.68/1.85 tff(2246,plain,
% 1.68/1.85 (hskp14 | hskp12 | hskp8),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2245, 2236])).
% 1.68/1.85 tff(2247,plain,
% 1.68/1.85 (hskp14),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2246, 647, 2202])).
% 1.68/1.85 tff(2248,plain,
% 1.68/1.85 (~c3_1(a1451)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[502, 2247])).
% 1.68/1.85 tff(2249,plain,
% 1.68/1.85 (~c1_1(a1451)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[508, 2247])).
% 1.68/1.85 tff(2250,plain,
% 1.68/1.85 (hskp7),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2223, 82, 2202, 705, 707, 706, 2212])).
% 1.68/1.85 tff(2251,plain,
% 1.68/1.85 (c3_1(a1438)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[98, 2250])).
% 1.68/1.85 tff(2252,plain,
% 1.68/1.85 (c2_1(a1451)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[516, 2247])).
% 1.68/1.85 tff(2253,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2254,plain,
% 1.68/1.85 (((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1447) | c1_1(a1447) | c2_1(a1447)) <=> (c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2255,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1447) | c1_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2254])).
% 1.68/1.85 tff(2256,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1447) | c1_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2255, 2253])).
% 1.68/1.85 tff(2257,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1447) | c1_1(a1447) | c2_1(a1447))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2258,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 1.68/1.85 tff(2259,plain,
% 1.68/1.85 ($false),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2258, 82, 2252, 2251, 2249, 2248, 707, 706, 37, 24, 578, 2235])).
% 1.68/1.85 tff(2260,plain,(hskp12 | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | c0_1(a1447) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.68/1.85 tff(2261,plain,
% 1.68/1.85 (hskp12),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2260, 2233, 37, 2232, 24, 2231, 2202])).
% 1.68/1.85 tff(2262,plain,
% 1.68/1.85 (~c2_1(a1448)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[202, 2261])).
% 1.68/1.85 tff(2263,plain,
% 1.68/1.85 (c3_1(a1448)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[218, 2261])).
% 1.68/1.85 tff(2264,plain,
% 1.68/1.85 (c0_1(a1448)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[210, 2261])).
% 1.68/1.85 tff(2265,plain,
% 1.68/1.85 ($false),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1479, 82, 11, 2264, 2263, 1215, 2262, 37, 24, 10])).
% 1.68/1.85 tff(2266,plain,(hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | hskp8 | (~c3_1(a1430)) | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.85 tff(2267,plain,
% 1.68/1.85 ($false),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2266, 2228, 2227, 11, 2202, 2226, 2201, 12, 186])).
% 1.68/1.85 tff(2268,plain,(hskp8 | hskp5 | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.85 tff(2269,plain,
% 1.68/1.85 (hskp8),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2268, 2183, 12, 11])).
% 1.68/1.85 tff(2270,plain,
% 1.68/1.85 (c3_1(a1441)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1557, 2269])).
% 1.68/1.85 tff(2271,plain,
% 1.68/1.85 (~c1_1(a1441)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1549, 2269])).
% 1.68/1.85 tff(2272,plain,
% 1.68/1.85 (c0_1(a1441)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1565, 2269])).
% 1.68/1.85 tff(2273,assumption,(~c1_1(a1447)), introduced(assumption)).
% 1.68/1.85 tff(2274,plain,
% 1.68/1.85 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2275,plain,
% 1.68/1.85 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441))) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2276,plain,
% 1.68/1.85 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2275])).
% 1.68/1.85 tff(2277,plain,
% 1.68/1.85 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2276, 2274])).
% 1.68/1.85 tff(2278,plain,
% 1.68/1.85 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2279,plain,
% 1.68/1.85 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.68/1.85 tff(2280,plain,
% 1.68/1.85 (hskp17 | c2_1(a1441)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2279, 82, 11, 1578, 1577, 229])).
% 1.68/1.85 tff(2281,plain,
% 1.68/1.85 (c2_1(a1441)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2280, 36])).
% 1.68/1.85 tff(2282,plain,
% 1.68/1.85 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2283,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2282])).
% 1.68/1.85 tff(2284,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2285,plain,
% 1.68/1.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2286,plain,
% 1.68/1.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2285])).
% 1.68/1.85 tff(2287,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.68/1.85 tff(2288,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 1.68/1.85 tff(2289,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2288, 2284])).
% 1.68/1.85 tff(2290,plain,(
% 1.68/1.85 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(skolemize,[status(sab)],[2289])).
% 1.68/1.85 tff(2291,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2290, 2283])).
% 1.68/1.85 tff(2292,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2293,plain,
% 1.68/1.85 ((hskp17 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447)) <=> (hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2294,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447)))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2293])).
% 1.68/1.85 tff(2295,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2294, 2292])).
% 1.68/1.85 tff(2296,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2297,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 1.68/1.85 tff(2298,plain,
% 1.68/1.85 (hskp17 | (~c2_1(a1441)) | c1_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2297, 82, 1578, 707, 706, 1574, 2291])).
% 1.68/1.85 tff(2299,plain,
% 1.68/1.85 ($false),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2298, 2281, 36, 2273])).
% 1.68/1.85 tff(2300,plain,(hskp17 | c1_1(a1447) | (~c0_1(a1441)) | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | hskp5 | (~c3_1(a1441))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.85 tff(2301,plain,
% 1.68/1.85 (hskp17),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2300, 2200, 2272, 2193, 2192, 2271, 11, 2270])).
% 1.68/1.85 tff(2302,plain,
% 1.68/1.85 (~c0_1(a1457)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[251, 2301])).
% 1.68/1.85 tff(2303,plain,
% 1.68/1.85 (~c2_1(a1457)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[264, 2301])).
% 1.68/1.85 tff(2304,plain,
% 1.68/1.85 (~c1_1(a1457)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[245, 2301])).
% 1.68/1.85 tff(2305,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2306,plain,
% 1.68/1.85 ((hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)) <=> (hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2307,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2306])).
% 1.68/1.85 tff(2308,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2307, 2305])).
% 1.68/1.85 tff(2309,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2310,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 1.68/1.85 tff(2311,plain,
% 1.68/1.85 (hskp3 | c0_1(a1438) | (~c1_1(a1430))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2310, 82, 46, 2074, 24, 12, 819])).
% 1.68/1.85 tff(2312,plain,
% 1.68/1.85 (hskp3),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2311, 37, 2140])).
% 1.68/1.85 tff(2313,plain,
% 1.68/1.85 (c1_1(a1431)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[887, 2312])).
% 1.68/1.85 tff(2314,plain,
% 1.68/1.85 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2315,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2314])).
% 1.68/1.85 tff(2316,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2317,plain,
% 1.68/1.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_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))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_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)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2318,plain,
% 1.68/1.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2317])).
% 1.68/1.85 tff(2319,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.68/1.85 tff(2320,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.68/1.85 tff(2321,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2320, 2316])).
% 1.68/1.85 tff(2322,plain,(
% 1.68/1.85 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(skolemize,[status(sab)],[2321])).
% 1.68/1.85 tff(2323,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2322, 2315])).
% 1.68/1.85 tff(2324,plain,
% 1.68/1.85 (~c0_1(a1447)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[697, 2191])).
% 1.68/1.85 tff(2325,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2326,plain,
% 1.68/1.85 ((hskp0 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2327,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2326])).
% 1.68/1.85 tff(2328,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2327, 2325])).
% 1.68/1.85 tff(2329,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2330,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2329, 2328])).
% 1.68/1.85 tff(2331,plain,
% 1.68/1.85 (hskp0),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2330, 82, 2074, 2324, 2193, 2192, 2183, 2323, 2140])).
% 1.68/1.85 tff(2332,plain,
% 1.68/1.85 (c2_1(a1427)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1143, 2331])).
% 1.68/1.85 tff(2333,plain,
% 1.68/1.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2334,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2333])).
% 1.68/1.85 tff(2335,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2336,plain,
% 1.68/1.85 (^[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)) | 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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2337,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2336])).
% 1.68/1.85 tff(2338,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.68/1.85 tff(2339,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.68/1.85 tff(2340,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2339, 2335])).
% 1.68/1.85 tff(2341,plain,(
% 1.68/1.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.85 inference(skolemize,[status(sab)],[2340])).
% 1.68/1.85 tff(2342,plain,
% 1.68/1.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2341, 2334])).
% 1.68/1.86 tff(2343,plain,
% 1.68/1.86 (~c2_1(a1431)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[865, 2312])).
% 1.68/1.86 tff(2344,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2345,plain,
% 1.68/1.86 (((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447)) <=> (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2346,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447)))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2345])).
% 1.68/1.86 tff(2347,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.68/1.86 tff(2348,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2349,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c1_1(a1447)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.68/1.86 tff(2350,plain,
% 1.68/1.86 (c3_1(a1431) | c1_1(a1447)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2349, 82, 2313, 2324, 2193, 2192, 2343, 2342])).
% 1.68/1.86 tff(2351,plain,
% 1.68/1.86 (c3_1(a1431)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2350, 2200])).
% 1.68/1.86 tff(2352,plain,
% 1.68/1.86 (~c0_1(a1431)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[871, 2312])).
% 1.68/1.86 tff(2353,plain,
% 1.68/1.86 (~c3_1(a1427)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1135, 2331])).
% 1.68/1.86 tff(2354,plain,
% 1.68/1.86 (c0_1(a1427)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1151, 2331])).
% 1.68/1.86 tff(2355,assumption,(c3_1(a1431)), introduced(assumption)).
% 1.68/1.86 tff(2356,assumption,(~c2_1(a1431)), introduced(assumption)).
% 1.68/1.86 tff(2357,assumption,(c1_1(a1431)), introduced(assumption)).
% 1.68/1.86 tff(2358,assumption,(~hskp10), introduced(assumption)).
% 1.68/1.86 tff(2359,assumption,(hskp1), introduced(assumption)).
% 1.68/1.86 tff(2360,plain,
% 1.68/1.86 (~c0_1(a1429)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[601, 2359])).
% 1.68/1.86 tff(2361,plain,
% 1.68/1.86 (c3_1(a1429)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[609, 2359])).
% 1.68/1.86 tff(2362,plain,
% 1.68/1.86 (c2_1(a1429)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[634, 2359])).
% 1.68/1.86 tff(2363,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2364,plain,
% 1.68/1.86 ((hskp12 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429))) <=> (hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2365,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2364])).
% 1.68/1.86 tff(2366,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.68/1.86 tff(2367,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2368,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.68/1.86 tff(2369,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2368, 82, 647, 2357, 2362, 2361, 2356, 2360, 1273, 2355])).
% 1.68/1.86 tff(2370,plain,((~hskp1) | hskp12 | (~c1_1(a1431)) | c2_1(a1431) | (~c3_1(a1431))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2371,plain,
% 1.68/1.86 (~hskp1),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2370, 647, 2357, 2356, 2355])).
% 1.68/1.86 tff(2372,plain,
% 1.68/1.86 ((hskp12 | hskp10 | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2373,plain,
% 1.68/1.86 (((hskp12 | hskp10) | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2374,plain,
% 1.68/1.86 ((hskp12 | hskp10) <=> (hskp12 | hskp10)),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2375,plain,
% 1.68/1.86 (((hskp12 | hskp10) | hskp1) <=> ((hskp12 | hskp10) | hskp1)),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2374])).
% 1.68/1.86 tff(2376,plain,
% 1.68/1.86 (((hskp12 | hskp10) | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 1.68/1.86 inference(transitivity,[status(thm)],[2375, 2373])).
% 1.68/1.86 tff(2377,axiom,((hskp12 | hskp10) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.68/1.86 tff(2378,plain,
% 1.68/1.86 (hskp12 | hskp10 | hskp1),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 1.68/1.86 tff(2379,plain,
% 1.68/1.86 (hskp12 | hskp10 | hskp1),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2378, 2372])).
% 1.68/1.86 tff(2380,plain,
% 1.68/1.86 (hskp12 | hskp10 | hskp1),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2379, 2372])).
% 1.68/1.86 tff(2381,plain,
% 1.68/1.86 (hskp12 | hskp10 | hskp1),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2380, 2372])).
% 1.68/1.86 tff(2382,plain,
% 1.68/1.86 (hskp12 | hskp10 | hskp1),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2381, 2372])).
% 1.68/1.86 tff(2383,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2382, 2371, 647, 2358])).
% 1.68/1.86 tff(2384,plain,(hskp12 | hskp10 | (~c1_1(a1431)) | c2_1(a1431) | (~c3_1(a1431))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2385,plain,
% 1.68/1.86 (hskp12),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2384, 2358, 2357, 2356, 2355])).
% 1.68/1.86 tff(2386,plain,
% 1.68/1.86 (~c2_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[202, 2385])).
% 1.68/1.86 tff(2387,assumption,(~c0_1(a1431)), introduced(assumption)).
% 1.68/1.86 tff(2388,plain,
% 1.68/1.86 (c0_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[210, 2385])).
% 1.68/1.86 tff(2389,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2390,plain,
% 1.68/1.86 ((hskp10 | (~ndr1_0) | c2_1(a1448) | (~c1_1(a1448)) | (~c0_1(a1448)) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431))) <=> (hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2391,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1448) | (~c1_1(a1448)) | (~c0_1(a1448)) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2390])).
% 1.68/1.86 tff(2392,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1448) | (~c1_1(a1448)) | (~c0_1(a1448)) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2391, 2389])).
% 1.68/1.86 tff(2393,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1448) | (~c1_1(a1448)) | (~c0_1(a1448)) | c2_1(a1431) | c0_1(a1431) | (~c3_1(a1431)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2394,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | (~c1_1(a1448))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 1.68/1.86 tff(2395,plain,
% 1.68/1.86 (~c1_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2394, 82, 2358, 2388, 2386, 2387, 2356, 345, 2355])).
% 1.68/1.86 tff(2396,assumption,(~c3_1(a1427)), introduced(assumption)).
% 1.68/1.86 tff(2397,assumption,(c2_1(a1427)), introduced(assumption)).
% 1.68/1.86 tff(2398,assumption,(c0_1(a1427)), introduced(assumption)).
% 1.68/1.86 tff(2399,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2400,plain,
% 1.68/1.86 ((hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448))) <=> (hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2401,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448)))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2400])).
% 1.68/1.86 tff(2402,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.68/1.86 tff(2403,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2404,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.68/1.86 tff(2405,plain,
% 1.68/1.86 (hskp19 | c1_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2404, 82, 2388, 2398, 2397, 2386, 2396, 1113])).
% 1.68/1.86 tff(2406,plain,
% 1.68/1.86 (hskp19),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2405, 2395])).
% 1.68/1.86 tff(2407,plain,
% 1.68/1.86 (~c1_1(a1460)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1184, 2406])).
% 1.68/1.86 tff(2408,plain,
% 1.68/1.86 (~c0_1(a1460)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1171, 2406])).
% 1.68/1.86 tff(2409,plain,
% 1.68/1.86 (c3_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[218, 2385])).
% 1.68/1.86 tff(2410,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2411,plain,
% 1.68/1.86 ((hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1448) | c1_1(a1448) | (~c3_1(a1448))) <=> (hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2412,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1448) | c1_1(a1448) | (~c3_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448)))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2411])).
% 1.68/1.86 tff(2413,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1448) | c1_1(a1448) | (~c3_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.68/1.86 tff(2414,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1448) | c1_1(a1448) | (~c3_1(a1448)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2415,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c1_1(a1448)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.68/1.86 tff(2416,plain,
% 1.68/1.86 (hskp22 | c1_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2415, 82, 2388, 2409, 2386, 1295])).
% 1.68/1.86 tff(2417,plain,
% 1.68/1.86 (hskp22),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2416, 2395])).
% 1.68/1.86 tff(2418,plain,
% 1.68/1.86 (~c0_1(a1468)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[834, 2417])).
% 1.68/1.86 tff(2419,plain,
% 1.68/1.86 (c3_1(a1468)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[842, 2417])).
% 1.68/1.86 tff(2420,plain,
% 1.68/1.86 (c1_1(a1468)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[850, 2417])).
% 1.68/1.86 tff(2421,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2422,plain,
% 1.68/1.86 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460))) <=> (c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2423,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2422])).
% 1.68/1.86 tff(2424,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2423, 2421])).
% 1.68/1.86 tff(2425,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2426,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.68/1.86 tff(2427,plain,
% 1.68/1.86 (~c2_1(a1460)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2426, 82, 2420, 2419, 2388, 2409, 2418, 2408, 2407, 2386, 1284])).
% 1.68/1.86 tff(2428,plain,
% 1.68/1.86 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.68/1.86 inference(bind,[status(th)],[])).
% 1.68/1.86 tff(2429,plain,
% 1.68/1.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(quant_intro,[status(thm)],[2428])).
% 1.68/1.86 tff(2430,plain,
% 1.68/1.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2431,plain,
% 1.68/1.86 (^[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)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~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)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.68/1.86 inference(bind,[status(th)],[])).
% 1.68/1.86 tff(2432,plain,
% 1.68/1.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(quant_intro,[status(thm)],[2431])).
% 1.68/1.86 tff(2433,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)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.68/1.86 tff(2434,plain,
% 1.68/1.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.68/1.86 tff(2435,plain,
% 1.68/1.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2434, 2430])).
% 1.68/1.86 tff(2436,plain,(
% 1.68/1.86 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(skolemize,[status(sab)],[2435])).
% 1.68/1.86 tff(2437,plain,
% 1.68/1.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2436, 2429])).
% 1.68/1.86 tff(2438,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2439,plain,
% 1.68/1.86 ((hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448))) <=> (hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2440,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448)))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2439])).
% 1.68/1.86 tff(2441,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2440, 2438])).
% 1.68/1.86 tff(2442,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2443,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1448)) | c1_1(a1448)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 1.68/1.86 tff(2444,plain,
% 1.68/1.86 (hskp21 | c1_1(a1448)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2443, 82, 2388, 2398, 2397, 2386, 2396, 2437])).
% 1.68/1.86 tff(2445,plain,
% 1.68/1.86 (hskp21),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2444, 2395])).
% 1.68/1.86 tff(2446,plain,
% 1.68/1.86 (((~hskp21) | (~c1_1(a1466))) <=> ((~hskp21) | (~c1_1(a1466)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2447,plain,
% 1.68/1.86 (((~c1_1(a1466)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1466)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2448,axiom,((~c1_1(a1466)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.68/1.86 tff(2449,plain,
% 1.68/1.86 ((~hskp21) | (~c1_1(a1466))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.68/1.86 tff(2450,plain,
% 1.68/1.86 ((~hskp21) | (~c1_1(a1466))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2449, 2446])).
% 1.68/1.86 tff(2451,plain,
% 1.68/1.86 (~c1_1(a1466)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2450, 2445])).
% 1.68/1.86 tff(2452,plain,
% 1.68/1.86 (((~hskp21) | c2_1(a1466)) <=> ((~hskp21) | c2_1(a1466))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2453,axiom,((~hskp21) | c2_1(a1466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.68/1.86 tff(2454,plain,
% 1.68/1.86 ((~hskp21) | c2_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2453, 2452])).
% 1.68/1.86 tff(2455,plain,
% 1.68/1.86 ((~hskp21) | c2_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2454, 2452])).
% 1.68/1.86 tff(2456,plain,
% 1.68/1.86 ((~hskp21) | c2_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2455, 2452])).
% 1.68/1.86 tff(2457,plain,
% 1.68/1.86 ((~hskp21) | c2_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2456, 2452])).
% 1.68/1.86 tff(2458,plain,
% 1.68/1.86 ((~hskp21) | c2_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2457, 2452])).
% 1.68/1.86 tff(2459,plain,
% 1.68/1.86 (c2_1(a1466)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2458, 2445])).
% 1.68/1.86 tff(2460,plain,
% 1.68/1.86 (((~hskp21) | c0_1(a1466)) <=> ((~hskp21) | c0_1(a1466))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2461,axiom,((~hskp21) | c0_1(a1466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.68/1.86 tff(2462,plain,
% 1.68/1.86 ((~hskp21) | c0_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.68/1.86 tff(2463,plain,
% 1.68/1.86 ((~hskp21) | c0_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2462, 2460])).
% 1.68/1.86 tff(2464,plain,
% 1.68/1.86 ((~hskp21) | c0_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2463, 2460])).
% 1.68/1.86 tff(2465,plain,
% 1.68/1.86 ((~hskp21) | c0_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2464, 2460])).
% 1.68/1.86 tff(2466,plain,
% 1.68/1.86 ((~hskp21) | c0_1(a1466)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2465, 2460])).
% 1.68/1.86 tff(2467,plain,
% 1.68/1.86 (c0_1(a1466)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2466, 2445])).
% 1.68/1.86 tff(2468,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2469,plain,
% 1.68/1.86 (((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460)) <=> (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2470,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2469])).
% 1.68/1.86 tff(2471,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2470, 2468])).
% 1.68/1.87 tff(2472,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2473,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.68/1.87 tff(2474,plain,
% 1.68/1.87 (c1_1(a1427)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2473, 82, 2467, 2459, 2398, 2451, 2408, 2407, 2396, 23, 2427])).
% 1.68/1.87 tff(2475,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2476,plain,
% 1.68/1.87 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431))) <=> (c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2477,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2476])).
% 1.68/1.87 tff(2478,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2477, 2475])).
% 1.68/1.87 tff(2479,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2480,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 1.68/1.87 tff(2481,plain,
% 1.68/1.87 (c3_1(a1466)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2480, 82, 2459, 2388, 2451, 2386, 2387, 2356, 543, 2355, 2395])).
% 1.68/1.87 tff(2482,plain,
% 1.68/1.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.68/1.87 inference(bind,[status(th)],[])).
% 1.68/1.87 tff(2483,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(quant_intro,[status(thm)],[2482])).
% 1.68/1.87 tff(2484,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2485,plain,
% 1.68/1.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.68/1.87 inference(bind,[status(th)],[])).
% 1.68/1.87 tff(2486,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(quant_intro,[status(thm)],[2485])).
% 1.68/1.87 tff(2487,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.68/1.87 tff(2488,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.68/1.87 tff(2489,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2488, 2484])).
% 1.68/1.87 tff(2490,plain,(
% 1.68/1.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(skolemize,[status(sab)],[2489])).
% 1.68/1.87 tff(2491,plain,
% 1.68/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2490, 2483])).
% 1.68/1.87 tff(2492,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2493,plain,
% 1.68/1.87 (((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448))) <=> (c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2494,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2493])).
% 1.68/1.87 tff(2495,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2494, 2492])).
% 1.68/1.87 tff(2496,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2497,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 1.68/1.87 tff(2498,plain,
% 1.68/1.87 ((~c1_1(a1427)) | (~c3_1(a1466))),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2497, 82, 2467, 2459, 2409, 2398, 2386, 2396, 2491, 2395])).
% 1.68/1.87 tff(2499,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2498, 2481, 2474])).
% 1.68/1.87 tff(2500,plain,(hskp10 | (~c0_1(a1427)) | c3_1(a1427) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)) | (~c2_1(a1427)) | (~c1_1(a1431))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2501,plain,
% 1.68/1.87 (hskp10),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2500, 2354, 2353, 2352, 2343, 2351, 2332, 2313])).
% 1.68/1.87 tff(2502,assumption,(hskp10), introduced(assumption)).
% 1.68/1.87 tff(2503,plain,
% 1.68/1.87 (~c3_1(a1445)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[406, 2502])).
% 1.68/1.87 tff(2504,plain,
% 1.68/1.87 (c0_1(a1445)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[420, 2502])).
% 1.68/1.87 tff(2505,assumption,(~hskp29), introduced(assumption)).
% 1.68/1.87 tff(2506,plain,
% 1.68/1.87 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2507,plain,
% 1.68/1.87 ((hskp29 | hskp5 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445))) <=> (hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2508,plain,
% 1.68/1.87 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2507])).
% 1.68/1.87 tff(2509,plain,
% 1.68/1.87 (((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)))) <=> ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2508, 2506])).
% 1.68/1.87 tff(2510,plain,
% 1.68/1.87 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | hskp5 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2511,plain,
% 1.68/1.87 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.68/1.87 tff(2512,plain,
% 1.68/1.87 (c2_1(a1445)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2511, 82, 2505, 11, 2504, 2503, 975])).
% 1.68/1.87 tff(2513,plain,
% 1.68/1.87 (~c1_1(a1445)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[412, 2502])).
% 1.68/1.87 tff(2514,assumption,(~c2_1(a1457)), introduced(assumption)).
% 1.68/1.87 tff(2515,assumption,(~c1_1(a1457)), introduced(assumption)).
% 1.68/1.87 tff(2516,assumption,(~c0_1(a1457)), introduced(assumption)).
% 1.68/1.87 tff(2517,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[427, 82, 2504, 2516, 2515, 2514, 2513, 2503, 23, 2512])).
% 1.68/1.87 tff(2518,plain,((~hskp10) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | hskp29 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2519,plain,
% 1.68/1.87 (hskp29),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2518, 2501, 2304, 2303, 2302, 11])).
% 1.68/1.87 tff(2520,plain,
% 1.68/1.87 (c3_1(a1483)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[990, 2519])).
% 1.68/1.87 tff(2521,plain,
% 1.68/1.87 (c2_1(a1483)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[998, 2519])).
% 1.68/1.87 tff(2522,plain,
% 1.68/1.87 (c1_1(a1483)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1006, 2519])).
% 1.68/1.87 tff(2523,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2524,plain,
% 1.68/1.87 ((hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447)) <=> (hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2525,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2524])).
% 1.68/1.87 tff(2526,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2525, 2523])).
% 1.68/1.87 tff(2527,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2528,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 1.68/1.87 tff(2529,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2528, 82, 99, 2522, 2521, 2520, 2193, 2192, 627, 2200])).
% 1.68/1.87 tff(2530,plain,(c0_1(a1438) | hskp5 | c0_1(a1430) | c3_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2531,plain,
% 1.68/1.87 (c0_1(a1438)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2530, 46, 12, 11, 24])).
% 1.68/1.87 tff(2532,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2533,plain,
% 1.68/1.87 ((hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430))) <=> (hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2534,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2533])).
% 1.68/1.87 tff(2535,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2534, 2532])).
% 1.68/1.87 tff(2536,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2537,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 1.68/1.87 tff(2538,plain,
% 1.68/1.87 (hskp7 | c3_1(a1438) | (~c0_1(a1438)) | (~c2_1(a1430)) | (~c1_1(a1430))),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2537, 82, 24, 12, 175])).
% 1.68/1.87 tff(2539,plain,
% 1.68/1.87 (~c2_1(a1430)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2538, 2531, 46, 99, 2140])).
% 1.68/1.87 tff(2540,plain,
% 1.68/1.87 (hskp11),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2190, 2539, 2074, 11])).
% 1.68/1.87 tff(2541,plain,
% 1.68/1.87 (~c3_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[703, 2540])).
% 1.68/1.87 tff(2542,plain,
% 1.68/1.87 (~c2_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[691, 2540])).
% 1.68/1.87 tff(2543,plain,
% 1.68/1.87 (~c1_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2199, 82, 99, 2074, 2542, 2541, 2539, 154, 2140])).
% 1.68/1.87 tff(2544,plain,
% 1.68/1.87 (c2_1(a1438)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1636, 2531, 24, 11, 46])).
% 1.68/1.87 tff(2545,plain,
% 1.68/1.87 (~c0_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[697, 2540])).
% 1.68/1.87 tff(2546,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2547,plain,
% 1.68/1.87 (((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1438) | c1_1(a1438) | (~c0_1(a1438)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447)) <=> (c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2548,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1438) | c1_1(a1438) | (~c0_1(a1438)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447)))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2547])).
% 1.68/1.87 tff(2549,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1438) | c1_1(a1438) | (~c0_1(a1438)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.68/1.87 tff(2550,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1438) | c1_1(a1438) | (~c0_1(a1438)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2551,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447)),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.68/1.87 tff(2552,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2551, 82, 46, 2545, 2542, 2531, 24, 23, 2544, 2543])).
% 1.68/1.87 tff(2553,plain,(c3_1(a1438) | c1_1(a1438) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2554,plain,
% 1.68/1.87 (c3_1(a1438)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2553, 24, 11, 12])).
% 1.68/1.87 tff(2555,plain,
% 1.68/1.87 (hskp11 | c0_1(a1438) | c2_1(a1438)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1450, 82, 11, 2554, 34])).
% 1.68/1.87 tff(2556,plain,
% 1.68/1.87 (hskp11),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2555, 47, 37])).
% 1.68/1.87 tff(2557,plain,
% 1.68/1.87 (hskp2),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[741, 2556, 11])).
% 1.68/1.87 tff(2558,plain,
% 1.68/1.87 (~c2_1(a1430)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2182, 2557])).
% 1.68/1.87 tff(2559,plain,
% 1.68/1.87 (hskp8),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2268, 2558, 12, 11])).
% 1.68/1.87 tff(2560,plain,
% 1.68/1.87 (c3_1(a1441)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1557, 2559])).
% 1.68/1.87 tff(2561,plain,
% 1.68/1.87 (c0_1(a1441)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1565, 2559])).
% 1.68/1.87 tff(2562,assumption,(~c2_1(a1441)), introduced(assumption)).
% 1.68/1.87 tff(2563,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2564,plain,
% 1.68/1.87 ((hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2565,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2564])).
% 1.68/1.87 tff(2566,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.68/1.87 tff(2567,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2568,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.68/1.87 tff(2569,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2568, 82, 11, 1578, 1577, 1215, 37, 24, 10, 2562])).
% 1.68/1.87 tff(2570,plain,(c2_1(a1441) | hskp5 | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2571,plain,
% 1.68/1.87 (c2_1(a1441)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2570, 2561, 11, 2560, 2554, 37, 24])).
% 1.68/1.87 tff(2572,plain,
% 1.68/1.87 (~c1_1(a1441)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1549, 2559])).
% 1.68/1.87 tff(2573,plain,
% 1.68/1.87 (~c3_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[703, 2556])).
% 1.68/1.87 tff(2574,plain,
% 1.68/1.87 (~c2_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[691, 2556])).
% 1.68/1.87 tff(2575,plain,
% 1.68/1.87 (~c0_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[697, 2556])).
% 1.68/1.87 tff(2576,plain,
% 1.68/1.87 (c1_1(a1447)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2300, 36, 1578, 707, 706, 1574, 11, 1577])).
% 1.68/1.87 tff(2577,plain,
% 1.68/1.87 (hskp12),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2234, 2576])).
% 1.68/1.87 tff(2578,plain,
% 1.68/1.87 (~c2_1(a1448)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[202, 2577])).
% 1.68/1.87 tff(2579,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[239, 2578, 2577, 11, 36])).
% 1.68/1.87 tff(2580,plain,(hskp17 | hskp5 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2581,plain,
% 1.68/1.87 (hskp17),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2580, 2575, 11, 2574, 2573, 2561, 2572, 2560])).
% 1.68/1.87 tff(2582,plain,
% 1.68/1.87 (~c2_1(a1457)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[264, 2581])).
% 1.68/1.87 tff(2583,plain,
% 1.68/1.87 (~c1_1(a1457)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[245, 2581])).
% 1.68/1.87 tff(2584,plain,
% 1.68/1.87 (~c0_1(a1457)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[251, 2581])).
% 1.68/1.87 tff(2585,assumption,(hskp0), introduced(assumption)).
% 1.68/1.87 tff(2586,plain,
% 1.68/1.87 (~c3_1(a1427)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1135, 2585])).
% 1.68/1.87 tff(2587,plain,
% 1.68/1.87 (c0_1(a1427)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1151, 2585])).
% 1.68/1.88 tff(2588,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2589,plain,
% 1.68/1.88 (((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2590,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2589])).
% 1.68/1.88 tff(2591,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2590, 2588])).
% 1.68/1.88 tff(2592,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2593,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 1.68/1.88 tff(2594,plain,
% 1.68/1.88 (~c1_1(a1427)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2593, 82, 1578, 1577, 1215, 2587, 24, 2586, 2491, 47, 1573])).
% 1.68/1.88 tff(2595,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2596,plain,
% 1.68/1.88 (((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2597,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2596])).
% 1.68/1.88 tff(2598,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2597, 2595])).
% 1.68/1.88 tff(2599,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2600,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 1.68/1.88 tff(2601,plain,
% 1.68/1.88 ($false),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2600, 82, 1578, 2587, 2516, 2515, 2514, 1574, 2586, 23, 1573, 2594])).
% 1.68/1.88 tff(2602,plain,((~hskp0) | (~c0_1(a1441)) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c3_1(a1438)) | c1_1(a1438) | c2_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.88 tff(2603,plain,
% 1.68/1.88 (~hskp0),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2602, 2561, 2584, 2583, 2582, 2572, 2571, 2560, 2554, 24, 47])).
% 1.68/1.88 tff(2604,plain,
% 1.68/1.88 (hskp0 | (~c1_1(a1430))),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2330, 82, 2074, 2575, 2574, 2573, 2558, 2323])).
% 1.68/1.88 tff(2605,plain,
% 1.68/1.88 (~c1_1(a1430)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2604, 2603])).
% 1.68/1.88 tff(2606,plain,
% 1.68/1.88 (hskp11 | c0_1(a1438) | c2_1(a1438)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1450, 82, 11, 1215, 34])).
% 1.68/1.88 tff(2607,plain,
% 1.68/1.88 (hskp11),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2606, 47, 37])).
% 1.68/1.88 tff(2608,plain,
% 1.68/1.88 (~c3_1(a1447)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[703, 2607])).
% 1.68/1.88 tff(2609,plain,
% 1.68/1.88 (~c2_1(a1447)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[691, 2607])).
% 1.68/1.88 tff(2610,plain,
% 1.68/1.88 (~c0_1(a1447)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[697, 2607])).
% 1.68/1.88 tff(2611,plain,
% 1.68/1.88 (hskp12 | (~c1_1(a1447))),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[721, 82, 2610, 2609, 2608, 196])).
% 1.68/1.88 tff(2612,plain,
% 1.68/1.88 (~c1_1(a1447)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2611, 647])).
% 1.68/1.88 tff(2613,plain,
% 1.68/1.88 (c2_1(a1441)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2570, 1578, 11, 1577, 1215, 37, 24])).
% 1.68/1.88 tff(2614,plain,
% 1.68/1.88 (hskp17),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2580, 2610, 11, 2609, 2608, 1578, 1574, 1577])).
% 1.68/1.88 tff(2615,plain,
% 1.68/1.88 (~c2_1(a1457)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[264, 2614])).
% 1.68/1.88 tff(2616,plain,
% 1.68/1.88 (~c1_1(a1457)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[245, 2614])).
% 1.68/1.88 tff(2617,plain,
% 1.68/1.88 (~c0_1(a1457)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[251, 2614])).
% 1.68/1.88 tff(2618,plain,
% 1.68/1.88 (~hskp0),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2602, 1578, 2617, 2616, 2615, 1574, 2613, 1577, 1215, 24, 47])).
% 1.68/1.88 tff(2619,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2620,plain,
% 1.68/1.88 (((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2621,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2620])).
% 1.68/1.88 tff(2622,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2621, 2619])).
% 1.68/1.88 tff(2623,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2624,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 1.68/1.88 tff(2625,plain,
% 1.68/1.88 ($false),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2624, 82, 2504, 1578, 2516, 2515, 2514, 2513, 2503, 1574, 23, 1573])).
% 1.68/1.88 tff(2626,plain,((~hskp10) | (~c0_1(a1441)) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c2_1(a1441))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.88 tff(2627,plain,
% 1.68/1.88 (~hskp10),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2626, 1578, 2617, 2616, 2615, 1574, 2613])).
% 1.68/1.88 tff(2628,plain,
% 1.68/1.88 (hskp1),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2382, 647, 2627])).
% 1.68/1.88 tff(2629,assumption,(~c1_1(a1431)), introduced(assumption)).
% 1.68/1.88 tff(2630,plain,
% 1.68/1.88 (~hskp3),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[887, 2629])).
% 1.68/1.88 tff(2631,assumption,(~hskp0), introduced(assumption)).
% 1.68/1.88 tff(2632,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2633,plain,
% 1.68/1.88 ((hskp3 | (~ndr1_0) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447)) <=> (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2634,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447)))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2633])).
% 1.68/1.88 tff(2635,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2634, 2632])).
% 1.68/1.88 tff(2636,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2637,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1447)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 1.68/1.88 tff(2638,plain,
% 1.68/1.88 (~c1_1(a1429)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2637, 82, 820, 2361, 705, 706, 2360, 819, 2273])).
% 1.68/1.88 tff(2639,plain,
% 1.68/1.88 (^[U: $i] : refl((hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.68/1.88 inference(bind,[status(th)],[])).
% 1.68/1.88 tff(2640,plain,
% 1.68/1.88 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(quant_intro,[status(thm)],[2639])).
% 1.68/1.88 tff(2641,plain,
% 1.68/1.88 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2642,plain,
% 1.68/1.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.68/1.88 inference(bind,[status(th)],[])).
% 1.68/1.88 tff(2643,plain,
% 1.68/1.88 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(quant_intro,[status(thm)],[2642])).
% 1.68/1.88 tff(2644,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.68/1.88 tff(2645,plain,
% 1.68/1.88 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 1.68/1.88 tff(2646,plain,
% 1.68/1.88 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2645, 2641])).
% 1.68/1.88 tff(2647,plain,(
% 1.68/1.88 ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(skolemize,[status(sab)],[2646])).
% 1.68/1.88 tff(2648,plain,
% 1.68/1.88 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2647, 2640])).
% 1.68/1.88 tff(2649,plain,
% 1.68/1.88 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2650,plain,
% 1.68/1.88 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a1429) | c0_1(a1429) | (~c2_1(a1429))) <=> (hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2651,plain,
% 1.68/1.88 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1429) | c0_1(a1429) | (~c2_1(a1429)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429)))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2650])).
% 1.68/1.88 tff(2652,plain,
% 1.68/1.88 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1429) | c0_1(a1429) | (~c2_1(a1429)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2651, 2649])).
% 1.68/1.88 tff(2653,plain,
% 1.68/1.88 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1429) | c0_1(a1429) | (~c2_1(a1429)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2654,plain,
% 1.68/1.88 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | c1_1(a1429)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 1.68/1.88 tff(2655,plain,
% 1.68/1.88 (hskp4 | c1_1(a1429)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2654, 82, 2631, 2362, 2360, 2648])).
% 1.68/1.88 tff(2656,plain,
% 1.68/1.88 (hskp4),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2655, 2638])).
% 1.68/1.88 tff(2657,plain,
% 1.68/1.88 (~c2_1(a1434)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[125, 2656])).
% 1.68/1.88 tff(2658,plain,
% 1.68/1.88 (c3_1(a1434)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[143, 2656])).
% 1.68/1.88 tff(2659,plain,
% 1.68/1.88 (c1_1(a1434)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[135, 2656])).
% 1.68/1.88 tff(2660,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2661,plain,
% 1.68/1.88 ((hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429))) <=> (hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2662,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2661])).
% 1.68/1.88 tff(2663,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.68/1.88 tff(2664,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2665,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.68/1.88 tff(2666,plain,
% 1.68/1.88 ($false),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2665, 82, 647, 2659, 2658, 2362, 2361, 2657, 2360, 1273])).
% 1.68/1.88 tff(2667,plain,((~hskp1) | hskp12 | hskp0 | hskp3 | c0_1(a1447) | c3_1(a1447) | c1_1(a1447)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.88 tff(2668,plain,
% 1.68/1.88 (~hskp1),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2667, 2631, 647, 2630, 705, 706, 2273])).
% 1.68/1.88 tff(2669,plain,
% 1.68/1.88 (hskp10),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2382, 2668, 647])).
% 1.68/1.88 tff(2670,plain,
% 1.68/1.88 (~c3_1(a1445)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[406, 2669])).
% 1.68/1.88 tff(2671,plain,
% 1.68/1.88 (~c1_1(a1445)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[412, 2669])).
% 1.68/1.88 tff(2672,plain,
% 1.68/1.88 (c0_1(a1445)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[420, 2669])).
% 1.68/1.88 tff(2673,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2674,plain,
% 1.68/1.88 (((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431)) <=> (c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2675,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2674])).
% 1.68/1.88 tff(2676,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2675, 2673])).
% 1.68/1.88 tff(2677,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2678,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1445) | c3_1(a1445) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c2_1(a1445)) | (~c0_1(a1445))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.68/1.88 tff(2679,plain,
% 1.68/1.88 (~c2_1(a1445)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2678, 82, 2672, 2629, 2671, 2670, 2387, 2356, 23])).
% 1.68/1.88 tff(2680,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2681,plain,
% 1.68/1.88 ((hskp0 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457)) <=> (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2682,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2681])).
% 1.68/1.88 tff(2683,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.68/1.88 tff(2684,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1445) | c3_1(a1445) | (~c0_1(a1445)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2685,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.68/1.88 tff(2686,plain,
% 1.68/1.88 ($false),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2685, 82, 2631, 2672, 2516, 2515, 2514, 2670, 1123, 2679])).
% 1.68/1.88 tff(2687,plain,(hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431) | hskp12 | c0_1(a1447) | c3_1(a1447) | c1_1(a1447)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.88 tff(2688,plain,
% 1.68/1.88 (hskp0),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2687, 2387, 2515, 2514, 2629, 2516, 2356, 647, 705, 706, 2273])).
% 1.68/1.88 tff(2689,plain,
% 1.68/1.88 (c2_1(a1427)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1143, 2688])).
% 1.68/1.88 tff(2690,plain,
% 1.68/1.88 (c0_1(a1427)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1151, 2688])).
% 1.68/1.88 tff(2691,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2692,plain,
% 1.68/1.88 (((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2693,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2692])).
% 1.68/1.88 tff(2694,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2693, 2691])).
% 1.68/1.88 tff(2695,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2696,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c3_1(a1441))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.68/1.89 tff(2697,plain,
% 1.68/1.89 (~c1_1(a1427)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2696, 82, 1577, 1215, 2690, 2689, 1574, 24, 1598, 47, 1573])).
% 1.68/1.89 tff(2698,plain,
% 1.68/1.89 (~c3_1(a1427)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1135, 2688])).
% 1.68/1.89 tff(2699,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2700,plain,
% 1.68/1.89 (((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431)) <=> (c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2701,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2700])).
% 1.68/1.89 tff(2702,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2701, 2699])).
% 1.68/1.89 tff(2703,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1431) | c0_1(a1431) | c2_1(a1431))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2704,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 1.68/1.89 tff(2705,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2704, 82, 1578, 2629, 2690, 1574, 2387, 2356, 2698, 23, 1573, 2697])).
% 1.68/1.89 tff(2706,plain,(c0_1(a1431) | (~c0_1(a1441)) | c1_1(a1431) | c1_1(a1441) | c2_1(a1431) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c3_1(a1438)) | c1_1(a1438) | c2_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1457) | hskp12 | c0_1(a1447) | c3_1(a1447) | c1_1(a1447)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2707,plain,
% 1.68/1.89 (c0_1(a1431)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2706, 2629, 1578, 1574, 2356, 2613, 1577, 1215, 24, 47, 2616, 2615, 2617, 647, 2610, 2608, 2612])).
% 1.68/1.89 tff(2708,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2709,plain,
% 1.68/1.89 ((hskp5 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c0_1(a1431)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2710,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c0_1(a1431)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2709])).
% 1.68/1.89 tff(2711,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c0_1(a1431)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2710, 2708])).
% 1.68/1.89 tff(2712,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c0_1(a1431)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2713,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1431)) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | (~c3_1(a1438))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 1.68/1.89 tff(2714,plain,
% 1.68/1.89 ((~c0_1(a1431)) | (~c3_1(a1431))),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2713, 82, 11, 1215, 37, 24, 2356, 10])).
% 1.68/1.89 tff(2715,plain,
% 1.68/1.89 (~c3_1(a1431)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2714, 2707])).
% 1.68/1.89 tff(2716,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2717,plain,
% 1.68/1.89 (((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1431) | c1_1(a1431) | (~c0_1(a1431)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2718,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1431) | c1_1(a1431) | (~c0_1(a1431)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2717])).
% 1.68/1.89 tff(2719,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1431) | c1_1(a1431) | (~c0_1(a1431)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2718, 2716])).
% 1.68/1.89 tff(2720,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)) | c3_1(a1431) | c1_1(a1431) | (~c0_1(a1431)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2721,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.68/1.89 tff(2722,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2721, 82, 1578, 2629, 2617, 2616, 2615, 1574, 2707, 23, 2715, 2613])).
% 1.68/1.89 tff(2723,plain,(c1_1(a1431) | (~c0_1(a1441)) | c1_1(a1441) | hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | c2_1(a1431) | (~c3_1(a1441)) | c2_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2724,plain,
% 1.68/1.89 (c1_1(a1431)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2723, 2356, 1574, 11, 1215, 37, 24, 1578, 1577, 47, 647])).
% 1.68/1.89 tff(2725,plain,
% 1.68/1.89 (c3_1(a1431)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2349, 82, 2724, 2610, 2609, 2608, 2356, 2342, 2612])).
% 1.68/1.89 tff(2726,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2727,plain,
% 1.68/1.89 ((hskp0 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2728,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2727])).
% 1.68/1.89 tff(2729,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2728, 2726])).
% 1.68/1.89 tff(2730,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1431) | (~c3_1(a1431)) | (~c1_1(a1431)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2731,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.68/1.89 tff(2732,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2731, 82, 2618, 2724, 2610, 2609, 2608, 2356, 2323, 2725])).
% 1.68/1.89 tff(2733,plain,(c2_1(a1431) | c1_1(a1441) | hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1441)) | (~c3_1(a1441)) | c2_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2734,plain,
% 1.68/1.89 (c2_1(a1431)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2733, 647, 11, 1215, 37, 24, 1578, 1577, 47, 1574])).
% 1.68/1.89 tff(2735,plain,
% 1.68/1.89 (~hskp3),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[865, 2734])).
% 1.68/1.89 tff(2736,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2667, 2735, 2628, 2618, 647, 2610, 2608, 2612])).
% 1.68/1.89 tff(2737,plain,(hskp12 | hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1441)) | (~c3_1(a1441)) | c2_1(a1438) | c1_1(a1441)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2738,plain,
% 1.68/1.89 (hskp12),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2737, 2561, 2554, 37, 24, 11, 2560, 47, 2572])).
% 1.68/1.89 tff(2739,plain,
% 1.68/1.89 (~c2_1(a1448)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[202, 2738])).
% 1.68/1.89 tff(2740,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2741,plain,
% 1.68/1.89 ((hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430))) <=> (hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2742,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2741])).
% 1.68/1.89 tff(2743,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2742, 2740])).
% 1.68/1.89 tff(2744,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2745,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 1.68/1.89 tff(2746,plain,
% 1.68/1.89 (hskp5 | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2745, 82, 2229, 230, 12, 10])).
% 1.68/1.89 tff(2747,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2746, 219, 211, 11, 544])).
% 1.68/1.89 tff(2748,plain,((~hskp12) | hskp5 | c1_1(a1430) | (~c3_1(a1430)) | c2_1(a1448) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2749,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2748, 2739, 2738, 12, 2074, 2605, 11])).
% 1.68/1.89 tff(2750,plain,(c2_1(a1438) | c0_1(a1430) | hskp5 | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2751,plain,
% 1.68/1.89 (c2_1(a1438)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2750, 37, 11, 12, 24])).
% 1.68/1.89 tff(2752,assumption,(hskp8), introduced(assumption)).
% 1.68/1.89 tff(2753,plain,
% 1.68/1.89 (c3_1(a1441)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1557, 2752])).
% 1.68/1.89 tff(2754,plain,
% 1.68/1.89 (c0_1(a1441)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1565, 2752])).
% 1.68/1.89 tff(2755,plain,
% 1.68/1.89 (c2_1(a1441)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2570, 2754, 11, 2753, 1215, 37, 24])).
% 1.68/1.89 tff(2756,plain,
% 1.68/1.89 (~c1_1(a1441)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1549, 2752])).
% 1.68/1.89 tff(2757,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2758,plain,
% 1.68/1.89 (((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2759,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2758])).
% 1.68/1.89 tff(2760,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2759, 2757])).
% 1.68/1.89 tff(2761,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1441)) | (~c3_1(a1441)) | (~c0_1(a1441)) | c1_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2762,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 1.68/1.89 tff(2763,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2762, 82, 2754, 2753, 2756, 37, 24, 1214, 768, 2755])).
% 1.68/1.89 tff(2764,plain,((~hskp8) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp5 | (~c3_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2765,plain,
% 1.68/1.89 (~hskp8),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2764, 37, 24, 2751, 11, 2554])).
% 1.68/1.89 tff(2766,assumption,(hskp14), introduced(assumption)).
% 1.68/1.89 tff(2767,plain,
% 1.68/1.89 (~c3_1(a1451)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[502, 2766])).
% 1.68/1.89 tff(2768,plain,
% 1.68/1.89 (~c1_1(a1451)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[508, 2766])).
% 1.68/1.89 tff(2769,plain,
% 1.68/1.89 (c2_1(a1451)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[516, 2766])).
% 1.68/1.89 tff(2770,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2771,plain,
% 1.68/1.89 ((hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2772,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2771])).
% 1.68/1.89 tff(2773,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.68/1.89 tff(2774,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2775,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.68/1.89 tff(2776,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2775, 82, 11, 2769, 1215, 2768, 2767, 37, 24, 794])).
% 1.68/1.89 tff(2777,plain,((~hskp14) | hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(2778,plain,
% 1.68/1.89 (~hskp14),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2777, 37, 2554, 11, 24])).
% 1.68/1.89 tff(2779,plain,
% 1.68/1.89 (hskp12),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2246, 2778, 2765])).
% 1.68/1.89 tff(2780,plain,
% 1.68/1.89 (~c2_1(a1448)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[202, 2779])).
% 1.68/1.89 tff(2781,plain,
% 1.68/1.89 (c1_1(a1430)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2748, 2780, 12, 2074, 2779, 11])).
% 1.68/1.89 tff(2782,plain,
% 1.68/1.89 (c2_1(a1430)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2268, 2765, 12, 11])).
% 1.68/1.89 tff(2783,plain,
% 1.68/1.89 ((hskp19 | hskp14 | hskp8) <=> (hskp19 | hskp14 | hskp8)),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2784,plain,
% 1.68/1.89 (((hskp14 | hskp8) | hskp19) <=> (hskp19 | hskp14 | hskp8)),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2785,plain,
% 1.68/1.89 ((hskp8 | hskp14) <=> (hskp14 | hskp8)),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2786,plain,
% 1.68/1.89 (((hskp8 | hskp14) | hskp19) <=> ((hskp14 | hskp8) | hskp19)),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2785])).
% 1.68/1.89 tff(2787,plain,
% 1.68/1.89 (((hskp8 | hskp14) | hskp19) <=> (hskp19 | hskp14 | hskp8)),
% 1.68/1.89 inference(transitivity,[status(thm)],[2786, 2784])).
% 1.68/1.89 tff(2788,axiom,((hskp8 | hskp14) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.68/1.89 tff(2789,plain,
% 1.68/1.89 (hskp19 | hskp14 | hskp8),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 1.68/1.89 tff(2790,plain,
% 1.68/1.89 (hskp19 | hskp14 | hskp8),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2789, 2783])).
% 1.68/1.89 tff(2791,plain,
% 1.68/1.89 (hskp19 | hskp14 | hskp8),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2790, 2783])).
% 1.68/1.89 tff(2792,plain,
% 1.68/1.89 (hskp19 | hskp14 | hskp8),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2791, 2783])).
% 1.68/1.89 tff(2793,plain,
% 1.68/1.89 (hskp19 | hskp14 | hskp8),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2792, 2783])).
% 1.68/1.89 tff(2794,plain,
% 1.68/1.89 (hskp19),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2793, 2778, 2765])).
% 1.68/1.89 tff(2795,plain,
% 1.68/1.89 (~c3_1(a1460)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1165, 2794])).
% 1.68/1.89 tff(2796,plain,
% 1.68/1.89 (~c0_1(a1460)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1171, 2794])).
% 1.68/1.89 tff(2797,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2798,plain,
% 1.68/1.89 ((hskp14 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1460) | c0_1(a1460) | (~c2_1(a1460))) <=> (hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(2799,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[2798])).
% 1.68/1.89 tff(2800,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.68/1.89 tff(2801,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)) | c3_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(2802,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1460) | c3_1(a1460) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c2_1(a1460))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.68/1.89 tff(2803,plain,
% 1.68/1.89 (~c2_1(a1460)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2802, 82, 2778, 2796, 2795, 12, 2782, 482, 2781])).
% 1.68/1.90 tff(2804,plain,
% 1.68/1.90 (hskp17),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[239, 2780, 11, 2779])).
% 1.68/1.90 tff(2805,plain,
% 1.68/1.90 (~c1_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[245, 2804])).
% 1.68/1.90 tff(2806,plain,
% 1.68/1.90 (~c0_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[251, 2804])).
% 1.68/1.90 tff(2807,plain,
% 1.68/1.90 (c3_1(a1448)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[218, 2779])).
% 1.68/1.90 tff(2808,plain,
% 1.68/1.90 (c0_1(a1448)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[210, 2779])).
% 1.68/1.90 tff(2809,plain,
% 1.68/1.90 (~c3_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[258, 82, 11, 2808, 2807, 2806, 2805, 2780, 10])).
% 1.68/1.90 tff(2810,plain,
% 1.68/1.90 (~c2_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[264, 2804])).
% 1.68/1.90 tff(2811,plain,
% 1.68/1.90 (~hskp2),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2182, 2782])).
% 1.68/1.90 tff(2812,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2813,plain,
% 1.68/1.90 ((hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460)) <=> (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2814,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460)))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2813])).
% 1.68/1.90 tff(2815,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2814, 2812])).
% 1.68/1.90 tff(2816,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c3_1(a1460) | c2_1(a1460) | c0_1(a1460))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2817,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460)),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2816, 2815])).
% 1.68/1.90 tff(2818,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2817, 82, 2811, 2796, 2795, 2805, 2810, 57, 2809, 2803])).
% 1.68/1.90 tff(2819,plain,(c0_1(a1438) | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(2820,plain,
% 1.68/1.90 (c0_1(a1438)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2819, 24, 11, 12])).
% 1.68/1.90 tff(2821,plain,
% 1.68/1.90 (c1_1(a1430)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2139, 1628, 11, 12])).
% 1.68/1.90 tff(2822,plain,
% 1.68/1.90 (hskp2),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1670, 47, 1616, 11, 1215])).
% 1.68/1.90 tff(2823,plain,
% 1.68/1.90 (~c2_1(a1430)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2182, 2822])).
% 1.68/1.90 tff(2824,plain,
% 1.68/1.90 (hskp11),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2190, 2823, 2074, 11])).
% 1.68/1.90 tff(2825,plain,
% 1.68/1.90 (~c3_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[703, 2824])).
% 1.68/1.90 tff(2826,plain,
% 1.68/1.90 (~c2_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[691, 2824])).
% 1.68/1.90 tff(2827,plain,
% 1.68/1.90 (~c1_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2199, 82, 1628, 2074, 2826, 2825, 2823, 154, 2821])).
% 1.68/1.90 tff(2828,plain,
% 1.68/1.90 (hskp17 | (~c0_1(a1438)) | c2_1(a1438)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1656, 82, 11, 1215, 229])).
% 1.68/1.90 tff(2829,plain,
% 1.68/1.90 (hskp17),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2828, 47, 1616])).
% 1.68/1.90 tff(2830,plain,
% 1.68/1.90 (~c0_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[251, 2829])).
% 1.68/1.90 tff(2831,plain,
% 1.68/1.90 (~c2_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[264, 2829])).
% 1.68/1.90 tff(2832,plain,
% 1.68/1.90 (~c1_1(a1457)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[245, 2829])).
% 1.68/1.90 tff(2833,plain,
% 1.68/1.90 (~c0_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[697, 2824])).
% 1.68/1.90 tff(2834,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2835,plain,
% 1.68/1.90 ((hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447)) <=> (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2836,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447)))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2835])).
% 1.68/1.90 tff(2837,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.68/1.90 tff(2838,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1447) | c0_1(a1447) | c1_1(a1447))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2839,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447)),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.68/1.90 tff(2840,plain,
% 1.68/1.90 (hskp3),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2839, 82, 2074, 2833, 2825, 12, 819, 2821, 2827])).
% 1.68/1.90 tff(2841,plain,
% 1.68/1.90 (c1_1(a1431)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[887, 2840])).
% 1.68/1.90 tff(2842,plain,
% 1.68/1.90 (~c2_1(a1431)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[865, 2840])).
% 1.68/1.90 tff(2843,plain,
% 1.68/1.90 (c3_1(a1431)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2349, 82, 2841, 2833, 2826, 2825, 2842, 2342, 2827])).
% 1.68/1.90 tff(2844,plain,
% 1.68/1.90 (hskp10),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2384, 2843, 2842, 647, 2841])).
% 1.68/1.90 tff(2845,plain,
% 1.68/1.90 (hskp29),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2518, 2844, 2832, 2831, 2830, 11])).
% 1.68/1.90 tff(2846,plain,
% 1.68/1.90 (c3_1(a1483)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[990, 2845])).
% 1.68/1.90 tff(2847,plain,
% 1.68/1.90 (c2_1(a1483)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[998, 2845])).
% 1.68/1.90 tff(2848,plain,
% 1.68/1.90 (c1_1(a1483)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1006, 2845])).
% 1.68/1.90 tff(2849,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2528, 82, 1628, 2848, 2847, 2846, 2826, 2825, 627, 2827])).
% 1.68/1.90 tff(2850,plain,(c2_1(a1438) | hskp5 | hskp12 | c0_1(a1430) | (~c0_1(a1438)) | (~c3_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(2851,plain,
% 1.68/1.90 (c2_1(a1438)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2850, 647, 11, 12, 2820, 2554])).
% 1.68/1.90 tff(2852,plain,
% 1.68/1.90 (hskp2),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[739, 707, 706, 705, 11])).
% 1.68/1.90 tff(2853,plain,
% 1.68/1.90 (~c2_1(a1430)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2182, 2852])).
% 1.68/1.90 tff(2854,plain,
% 1.68/1.90 (~hskp7),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1021, 2820])).
% 1.68/1.90 tff(2855,plain,
% 1.68/1.90 (c1_1(a1430)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2139, 2854, 11, 12])).
% 1.68/1.90 tff(2856,plain,
% 1.68/1.90 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(2857,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[2856])).
% 1.68/1.90 tff(2858,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2859,plain,
% 1.68/1.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(2860,plain,
% 1.68/1.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[2859])).
% 1.68/1.90 tff(2861,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.68/1.90 tff(2862,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 1.68/1.90 tff(2863,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2862, 2858])).
% 1.68/1.90 tff(2864,plain,(
% 1.68/1.90 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(skolemize,[status(sab)],[2863])).
% 1.68/1.90 tff(2865,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2864, 2857])).
% 1.68/1.90 tff(2866,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2867,plain,
% 1.68/1.90 ((hskp18 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2868,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2867])).
% 1.68/1.90 tff(2869,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2868, 2866])).
% 1.68/1.90 tff(2870,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2871,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.68/1.90 tff(2872,plain,
% 1.68/1.90 (hskp18),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2871, 82, 2554, 2074, 2820, 12, 2865, 2855, 2851])).
% 1.68/1.90 tff(2873,plain,
% 1.68/1.90 (~c2_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[376, 2872])).
% 1.68/1.90 tff(2874,plain,
% 1.68/1.90 (c1_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[384, 2872])).
% 1.68/1.90 tff(2875,plain,
% 1.68/1.90 (c0_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[392, 2872])).
% 1.68/1.90 tff(2876,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2877,plain,
% 1.68/1.90 ((hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430))) <=> (hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2878,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2877])).
% 1.68/1.90 tff(2879,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2878, 2876])).
% 1.68/1.90 tff(2880,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1430) | c0_1(a1430) | (~c3_1(a1430)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2881,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.68/1.90 tff(2882,plain,
% 1.68/1.90 (hskp10),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2881, 82, 2875, 2874, 2074, 2873, 12, 2853, 345])).
% 1.68/1.90 tff(2883,plain,
% 1.68/1.90 (~c3_1(a1445)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[406, 2882])).
% 1.68/1.90 tff(2884,plain,
% 1.68/1.90 (~c1_1(a1445)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[412, 2882])).
% 1.68/1.90 tff(2885,plain,
% 1.68/1.90 (c0_1(a1445)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[420, 2882])).
% 1.68/1.90 tff(2886,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2887,plain,
% 1.68/1.90 (((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447)) <=> (c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2888,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447)))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2887])).
% 1.68/1.90 tff(2889,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2888, 2886])).
% 1.68/1.90 tff(2890,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | (~c2_1(a1438)) | (~c0_1(a1438)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2891,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447)),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.68/1.90 tff(2892,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2891, 82, 2885, 705, 707, 2884, 2883, 2820, 24, 23, 2851, 2075])).
% 1.68/1.90 tff(2893,plain,(c2_1(a1447) | c0_1(a1447) | c1_1(a1438) | c0_1(a1430) | hskp12 | c3_1(a1447) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(2894,plain,
% 1.68/1.90 (c2_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2893, 705, 24, 12, 647, 706, 11])).
% 1.68/1.90 tff(2895,plain,
% 1.68/1.90 (~hskp11),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[691, 2894])).
% 1.68/1.90 tff(2896,plain,
% 1.68/1.90 (c2_1(a1430)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2190, 2895, 2074, 11])).
% 1.68/1.90 tff(2897,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2898,plain,
% 1.68/1.90 ((hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430))) <=> (hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2899,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2898])).
% 1.68/1.90 tff(2900,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.68/1.90 tff(2901,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2902,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | (~c3_1(a1458)) | (~c1_1(a1458))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.68/1.90 tff(2903,plain,
% 1.68/1.90 ((~c2_1(a1430)) | (~c3_1(a1458))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2902, 82, 647, 2874, 2074, 2873, 12, 1273])).
% 1.68/1.90 tff(2904,plain,
% 1.68/1.90 (~c3_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2903, 2896])).
% 1.68/1.90 tff(2905,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2906,plain,
% 1.68/1.90 (((~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c3_1(a1447) | c1_1(a1447) | (~c2_1(a1447)) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430))) <=> (c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2907,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c3_1(a1447) | c1_1(a1447) | (~c2_1(a1447)) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2906])).
% 1.68/1.90 tff(2908,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c3_1(a1447) | c1_1(a1447) | (~c2_1(a1447)) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2907, 2905])).
% 1.68/1.90 tff(2909,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c0_1(a1458)) | c3_1(a1447) | c1_1(a1447) | (~c2_1(a1447)) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2910,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1458) | (~c2_1(a1447)) | c3_1(a1447) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c1_1(a1447) | c3_1(a1458) | (~c0_1(a1458))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.68/1.90 tff(2911,plain,
% 1.68/1.90 ((~c2_1(a1447)) | (~c2_1(a1430)) | c1_1(a1447) | c3_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2910, 82, 2875, 2873, 706, 12, 185, 2855])).
% 1.68/1.90 tff(2912,plain,
% 1.68/1.90 (c1_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2911, 2896, 2894, 2904])).
% 1.68/1.90 tff(2913,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2914,plain,
% 1.68/1.90 ((hskp12 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c1_1(a1458)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447))) <=> (hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2915,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c1_1(a1458)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[2914])).
% 1.68/1.90 tff(2916,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c1_1(a1458)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[2915, 2913])).
% 1.68/1.90 tff(2917,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1458) | c3_1(a1458) | (~c1_1(a1458)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(2918,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.68/1.90 tff(2919,plain,
% 1.68/1.90 (c0_1(a1447) | (~c1_1(a1447)) | c3_1(a1458)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2918, 82, 647, 2874, 2873, 706, 196])).
% 1.68/1.90 tff(2920,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2919, 2912, 2904, 705])).
% 1.68/1.90 tff(2921,plain,(c0_1(a1447) | hskp12 | c3_1(a1447) | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(2922,plain,
% 1.68/1.90 (c0_1(a1447)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2921, 706, 647, 12, 11, 24])).
% 1.68/1.90 tff(2923,plain,
% 1.68/1.90 (~hskp11),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[697, 2922])).
% 1.68/1.90 tff(2924,plain,
% 1.68/1.90 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.68/1.90 inference(bind,[status(th)],[])).
% 1.68/1.90 tff(2925,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.90 inference(quant_intro,[status(thm)],[2924])).
% 1.68/1.90 tff(2926,plain,
% 1.68/1.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(2927,plain,
% 1.68/1.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(2928,plain,
% 1.68/1.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[2927])).
% 1.68/1.91 tff(2929,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.68/1.91 tff(2930,plain,
% 1.68/1.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.68/1.91 tff(2931,plain,
% 1.68/1.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2930, 2926])).
% 1.68/1.91 tff(2932,plain,(
% 1.68/1.91 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.91 inference(skolemize,[status(sab)],[2931])).
% 1.68/1.91 tff(2933,plain,
% 1.68/1.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2932, 2925])).
% 1.68/1.91 tff(2934,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2935,plain,
% 1.68/1.91 ((hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1447) | c2_1(a1447) | (~c0_1(a1447))) <=> (hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2936,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1447) | c2_1(a1447) | (~c0_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[2935])).
% 1.68/1.91 tff(2937,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1447) | c2_1(a1447) | (~c0_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[2936, 2934])).
% 1.68/1.91 tff(2938,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1447) | c2_1(a1447) | (~c0_1(a1447)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(2939,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 1.68/1.91 tff(2940,plain,
% 1.68/1.91 (hskp11 | (~c0_1(a1447)) | c2_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2939, 82, 2554, 706, 2820, 2933, 2851])).
% 1.68/1.91 tff(2941,plain,
% 1.68/1.91 (c2_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2940, 2923, 2922])).
% 1.68/1.91 tff(2942,plain,
% 1.68/1.91 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2943,plain,
% 1.68/1.91 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1447) | (~c2_1(a1447)) | (~c0_1(a1447))) <=> (hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2944,plain,
% 1.68/1.91 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1447) | (~c2_1(a1447)) | (~c0_1(a1447)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0)))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[2943])).
% 1.68/1.91 tff(2945,plain,
% 1.68/1.91 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1447) | (~c2_1(a1447)) | (~c0_1(a1447)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0))),
% 1.68/1.91 inference(transitivity,[status(thm)],[2944, 2942])).
% 1.68/1.91 tff(2946,plain,
% 1.68/1.91 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1447) | (~c2_1(a1447)) | (~c0_1(a1447)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(2947,plain,
% 1.68/1.91 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0)),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.68/1.91 tff(2948,plain,
% 1.68/1.91 (hskp11 | (~c0_1(a1447)) | (~c2_1(a1447))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2947, 82, 647, 706, 1204])).
% 1.68/1.91 tff(2949,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2948, 2941, 2923, 2922])).
% 1.68/1.91 tff(2950,plain,(c3_1(a1447) | hskp12 | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(2951,plain,
% 1.68/1.91 (c3_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2950, 647, 12, 11, 24])).
% 1.68/1.91 tff(2952,plain,
% 1.68/1.91 (~hskp11),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[703, 2951])).
% 1.68/1.91 tff(2953,plain,
% 1.68/1.91 (c2_1(a1430)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2190, 2952, 2074, 11])).
% 1.68/1.91 tff(2954,plain,
% 1.68/1.91 (~c3_1(a1458)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2903, 2953])).
% 1.68/1.91 tff(2955,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2956,plain,
% 1.68/1.91 ((hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1458) | c2_1(a1458) | (~c0_1(a1458))) <=> (hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2957,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1458) | c2_1(a1458) | (~c0_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[2956])).
% 1.68/1.91 tff(2958,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1458) | c2_1(a1458) | (~c0_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[2957, 2955])).
% 1.68/1.91 tff(2959,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1458) | c2_1(a1458) | (~c0_1(a1458)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(2960,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.68/1.91 tff(2961,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2960, 82, 2952, 2875, 2554, 2873, 2820, 2933, 2851, 2954])).
% 1.68/1.91 tff(2962,plain,(hskp12 | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(2963,plain,
% 1.68/1.91 (hskp12),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2962, 24, 11, 12])).
% 1.68/1.91 tff(2964,plain,
% 1.68/1.91 (~c2_1(a1448)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[202, 2963])).
% 1.68/1.91 tff(2965,plain,
% 1.68/1.91 (hskp17),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[239, 2964, 11, 2963])).
% 1.68/1.91 tff(2966,plain,
% 1.68/1.91 (~c1_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[245, 2965])).
% 1.68/1.91 tff(2967,plain,
% 1.68/1.91 (~c0_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[251, 2965])).
% 1.68/1.91 tff(2968,plain,
% 1.68/1.91 (c3_1(a1448)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[218, 2963])).
% 1.68/1.91 tff(2969,plain,
% 1.68/1.91 (c0_1(a1448)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[210, 2963])).
% 1.68/1.91 tff(2970,plain,
% 1.68/1.91 (~c3_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[258, 82, 11, 2969, 2968, 2967, 2966, 2964, 10])).
% 1.68/1.91 tff(2971,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2972,plain,
% 1.68/1.91 ((hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1457) | c0_1(a1457) | c1_1(a1457)) <=> (hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2973,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457)))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[2972])).
% 1.68/1.91 tff(2974,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457))),
% 1.68/1.91 inference(transitivity,[status(thm)],[2973, 2971])).
% 1.68/1.91 tff(2975,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c3_1(a1457) | c0_1(a1457) | c1_1(a1457))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(2976,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1457) | c1_1(a1457) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c3_1(a1457)),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 1.68/1.91 tff(2977,plain,
% 1.68/1.91 (hskp3),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2976, 82, 2074, 2967, 2966, 12, 819, 2855, 2970])).
% 1.68/1.91 tff(2978,plain,
% 1.68/1.91 (c1_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[887, 2977])).
% 1.68/1.91 tff(2979,plain,
% 1.68/1.91 (~c2_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[865, 2977])).
% 1.68/1.91 tff(2980,plain,
% 1.68/1.91 (~c2_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[264, 2965])).
% 1.68/1.91 tff(2981,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2982,plain,
% 1.68/1.91 (((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c1_1(a1457) | c0_1(a1457)) <=> (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(2983,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c1_1(a1457) | c0_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457)))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[2982])).
% 1.68/1.91 tff(2984,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c1_1(a1457) | c0_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457))),
% 1.68/1.91 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.68/1.91 tff(2985,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457) | c3_1(a1457) | c1_1(a1457) | c0_1(a1457))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(2986,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1457)),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.68/1.91 tff(2987,plain,
% 1.68/1.91 (c3_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2986, 82, 2978, 2967, 2966, 2980, 2979, 2342, 2970])).
% 1.68/1.91 tff(2988,plain,
% 1.68/1.91 (hskp2),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[949, 82, 2967, 2966, 2980, 57, 2970])).
% 1.68/1.91 tff(2989,plain,
% 1.68/1.91 (~c2_1(a1430)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2182, 2988])).
% 1.68/1.91 tff(2990,plain,
% 1.68/1.91 (hskp11),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2190, 2989, 2074, 11])).
% 1.68/1.91 tff(2991,plain,
% 1.68/1.91 (~c3_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[703, 2990])).
% 1.68/1.91 tff(2992,plain,
% 1.68/1.91 (~c2_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[691, 2990])).
% 1.68/1.91 tff(2993,plain,
% 1.68/1.91 (~c0_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[697, 2990])).
% 1.68/1.91 tff(2994,plain,
% 1.68/1.91 (hskp0),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2731, 82, 2978, 2993, 2992, 2991, 2979, 2323, 2987])).
% 1.68/1.91 tff(2995,plain,
% 1.68/1.91 (c2_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1143, 2994])).
% 1.68/1.91 tff(2996,plain,
% 1.68/1.91 (c0_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1151, 2994])).
% 1.68/1.91 tff(2997,plain,
% 1.68/1.91 (~c0_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[871, 2977])).
% 1.68/1.91 tff(2998,plain,
% 1.68/1.91 (~c3_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1135, 2994])).
% 1.68/1.91 tff(2999,plain,
% 1.68/1.91 (hskp10),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2500, 2998, 2987, 2997, 2979, 2996, 2995, 2978])).
% 1.68/1.91 tff(3000,plain,
% 1.68/1.91 (~c3_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[406, 2999])).
% 1.68/1.91 tff(3001,plain,
% 1.68/1.91 (~c1_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[412, 2999])).
% 1.68/1.91 tff(3002,plain,
% 1.68/1.91 (c0_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[420, 2999])).
% 1.68/1.91 tff(3003,plain,
% 1.68/1.91 (~c2_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[427, 82, 3002, 2967, 2966, 2980, 3001, 3000, 23])).
% 1.68/1.91 tff(3004,plain,
% 1.68/1.91 (hskp29),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2518, 2999, 2966, 2980, 2967, 11])).
% 1.68/1.91 tff(3005,plain,
% 1.68/1.91 (c3_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[990, 3004])).
% 1.68/1.91 tff(3006,plain,
% 1.68/1.91 (c2_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[998, 3004])).
% 1.68/1.91 tff(3007,plain,
% 1.68/1.91 (c1_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1006, 3004])).
% 1.68/1.91 tff(3008,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3009,plain,
% 1.68/1.91 ((hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1445) | c2_1(a1445) | c1_1(a1445)) <=> (hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3010,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1445) | c2_1(a1445) | c1_1(a1445))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3009])).
% 1.68/1.91 tff(3011,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1445) | c2_1(a1445) | c1_1(a1445))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3010, 3008])).
% 1.68/1.91 tff(3012,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1445) | c2_1(a1445) | c1_1(a1445))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3013,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 1.68/1.91 tff(3014,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3013, 82, 2854, 3007, 3006, 3005, 3001, 3000, 627, 3003])).
% 1.68/1.91 tff(3015,plain,(c1_1(a1438) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3016,plain,
% 1.68/1.91 (c1_1(a1438)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3015, 11, 12])).
% 1.68/1.91 tff(3017,plain,
% 1.68/1.91 (~hskp7),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1424, 3016])).
% 1.68/1.91 tff(3018,plain,
% 1.68/1.91 (c1_1(a1430)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2139, 3017, 11, 12])).
% 1.68/1.91 tff(3019,plain,
% 1.68/1.91 (hskp17),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[239, 203, 11, 197])).
% 1.68/1.91 tff(3020,plain,
% 1.68/1.91 (~c1_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[245, 3019])).
% 1.68/1.91 tff(3021,plain,
% 1.68/1.91 (~c0_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[251, 3019])).
% 1.68/1.91 tff(3022,plain,
% 1.68/1.91 (~c3_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[258, 82, 11, 211, 219, 3021, 3020, 203, 10])).
% 1.68/1.91 tff(3023,plain,
% 1.68/1.91 (hskp3),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2976, 82, 2074, 3021, 3020, 12, 819, 3018, 3022])).
% 1.68/1.91 tff(3024,plain,
% 1.68/1.91 (c1_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[887, 3023])).
% 1.68/1.91 tff(3025,plain,
% 1.68/1.91 (~c2_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[865, 3023])).
% 1.68/1.91 tff(3026,plain,
% 1.68/1.91 (~c2_1(a1457)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[264, 3019])).
% 1.68/1.91 tff(3027,plain,
% 1.68/1.91 (c3_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2986, 82, 3024, 3021, 3020, 3026, 3025, 2342, 3022])).
% 1.68/1.91 tff(3028,plain,
% 1.68/1.91 (hskp2),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[949, 82, 3021, 3020, 3026, 57, 3022])).
% 1.68/1.91 tff(3029,plain,
% 1.68/1.91 (~c2_1(a1430)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2182, 3028])).
% 1.68/1.91 tff(3030,plain,
% 1.68/1.91 (hskp11),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2190, 3029, 2074, 11])).
% 1.68/1.91 tff(3031,plain,
% 1.68/1.91 (~c3_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[703, 3030])).
% 1.68/1.91 tff(3032,plain,
% 1.68/1.91 (~c2_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[691, 3030])).
% 1.68/1.91 tff(3033,plain,
% 1.68/1.91 (~c0_1(a1447)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[697, 3030])).
% 1.68/1.91 tff(3034,plain,
% 1.68/1.91 (hskp0),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2731, 82, 3024, 3033, 3032, 3031, 3025, 2323, 3027])).
% 1.68/1.91 tff(3035,plain,
% 1.68/1.91 (c2_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1143, 3034])).
% 1.68/1.91 tff(3036,plain,
% 1.68/1.91 (c0_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1151, 3034])).
% 1.68/1.91 tff(3037,plain,
% 1.68/1.91 (~c0_1(a1431)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[871, 3023])).
% 1.68/1.91 tff(3038,plain,
% 1.68/1.91 (~c3_1(a1427)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1135, 3034])).
% 1.68/1.91 tff(3039,plain,
% 1.68/1.91 (hskp10),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2500, 3038, 3027, 3037, 3025, 3036, 3035, 3024])).
% 1.68/1.91 tff(3040,plain,
% 1.68/1.91 (~c3_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[406, 3039])).
% 1.68/1.91 tff(3041,plain,
% 1.68/1.91 (~c1_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[412, 3039])).
% 1.68/1.91 tff(3042,plain,
% 1.68/1.91 (c0_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[420, 3039])).
% 1.68/1.91 tff(3043,plain,
% 1.68/1.91 (~c2_1(a1445)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[427, 82, 3042, 3021, 3020, 3026, 3041, 3040, 23])).
% 1.68/1.91 tff(3044,plain,
% 1.68/1.91 (hskp29),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2518, 3039, 3020, 3026, 3021, 11])).
% 1.68/1.91 tff(3045,plain,
% 1.68/1.91 (c3_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[990, 3044])).
% 1.68/1.91 tff(3046,plain,
% 1.68/1.91 (c2_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[998, 3044])).
% 1.68/1.91 tff(3047,plain,
% 1.68/1.91 (c1_1(a1483)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1006, 3044])).
% 1.68/1.91 tff(3048,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3013, 82, 3017, 3047, 3046, 3045, 3041, 3040, 627, 3043])).
% 1.68/1.91 tff(3049,plain,((~hskp12) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3050,plain,
% 1.68/1.91 (~hskp12),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3049, 11, 12])).
% 1.68/1.91 tff(3051,plain,
% 1.68/1.91 (c2_1(a1430)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2190, 1216, 2074, 11])).
% 1.68/1.91 tff(3052,plain,
% 1.68/1.91 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.68/1.91 inference(bind,[status(th)],[])).
% 1.68/1.91 tff(3053,plain,
% 1.68/1.91 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.68/1.91 inference(quant_intro,[status(thm)],[3052])).
% 1.76/1.91 tff(3054,plain,
% 1.76/1.91 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3055,plain,
% 1.76/1.91 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.76/1.91 inference(bind,[status(th)],[])).
% 1.76/1.91 tff(3056,plain,
% 1.76/1.91 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(quant_intro,[status(thm)],[3055])).
% 1.76/1.91 tff(3057,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.76/1.91 tff(3058,plain,
% 1.76/1.91 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 1.76/1.91 tff(3059,plain,
% 1.76/1.91 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3058, 3054])).
% 1.76/1.91 tff(3060,plain,(
% 1.76/1.91 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(skolemize,[status(sab)],[3059])).
% 1.76/1.91 tff(3061,plain,
% 1.76/1.91 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3060, 3053])).
% 1.76/1.91 tff(3062,plain,
% 1.76/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3063,plain,
% 1.76/1.91 ((hskp15 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c3_1(a1430)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430))) <=> (hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3064,plain,
% 1.76/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c3_1(a1430)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))))),
% 1.76/1.91 inference(monotonicity,[status(thm)],[3063])).
% 1.76/1.91 tff(3065,plain,
% 1.76/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c3_1(a1430)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.91 inference(transitivity,[status(thm)],[3064, 3062])).
% 1.76/1.91 tff(3066,plain,
% 1.76/1.91 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c3_1(a1430)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))),
% 1.76/1.91 inference(quant_inst,[status(thm)],[])).
% 1.76/1.91 tff(3067,plain,
% 1.76/1.91 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 1.76/1.91 tff(3068,plain,
% 1.76/1.91 (hskp15 | (~c2_1(a1430)) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.76/1.91 inference(unit_resolution,[status(thm)],[3067, 82, 12, 3061])).
% 1.76/1.91 tff(3069,plain,
% 1.76/1.91 (hskp15),
% 1.76/1.91 inference(unit_resolution,[status(thm)],[3068, 3051, 2074, 3018])).
% 1.76/1.91 tff(3070,plain,
% 1.76/1.91 (((~hskp15) | (~c3_1(a1452))) <=> ((~hskp15) | (~c3_1(a1452)))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3071,plain,
% 1.76/1.91 (((~c3_1(a1452)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1452)))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3072,axiom,((~c3_1(a1452)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.76/1.91 tff(3073,plain,
% 1.76/1.91 ((~hskp15) | (~c3_1(a1452))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3072, 3071])).
% 1.76/1.91 tff(3074,plain,
% 1.76/1.91 ((~hskp15) | (~c3_1(a1452))),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3073, 3070])).
% 1.76/1.91 tff(3075,plain,
% 1.76/1.91 (~c3_1(a1452)),
% 1.76/1.91 inference(unit_resolution,[status(thm)],[3074, 3069])).
% 1.76/1.91 tff(3076,plain,
% 1.76/1.91 (((~hskp15) | c0_1(a1452)) <=> ((~hskp15) | c0_1(a1452))),
% 1.76/1.91 inference(rewrite,[status(thm)],[])).
% 1.76/1.91 tff(3077,axiom,((~hskp15) | c0_1(a1452)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.76/1.91 tff(3078,plain,
% 1.76/1.91 ((~hskp15) | c0_1(a1452)),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3077, 3076])).
% 1.76/1.91 tff(3079,plain,
% 1.76/1.91 ((~hskp15) | c0_1(a1452)),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3078, 3076])).
% 1.76/1.91 tff(3080,plain,
% 1.76/1.91 ((~hskp15) | c0_1(a1452)),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3079, 3076])).
% 1.76/1.91 tff(3081,plain,
% 1.76/1.91 ((~hskp15) | c0_1(a1452)),
% 1.76/1.91 inference(modus_ponens,[status(thm)],[3080, 3076])).
% 1.76/1.92 tff(3082,plain,
% 1.76/1.92 ((~hskp15) | c0_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3081, 3076])).
% 1.76/1.92 tff(3083,plain,
% 1.76/1.92 (c0_1(a1452)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3082, 3069])).
% 1.76/1.92 tff(3084,plain,
% 1.76/1.92 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3085,plain,
% 1.76/1.92 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1452) | (~c2_1(a1452)) | (~c0_1(a1452))) <=> (hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3086,plain,
% 1.76/1.92 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1452) | (~c2_1(a1452)) | (~c0_1(a1452)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3085])).
% 1.76/1.92 tff(3087,plain,
% 1.76/1.92 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1452) | (~c2_1(a1452)) | (~c0_1(a1452)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3086, 3084])).
% 1.76/1.92 tff(3088,plain,
% 1.76/1.92 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1452) | (~c2_1(a1452)) | (~c0_1(a1452)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3089,plain,
% 1.76/1.92 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1452) | (~ndr1_0) | (~c2_1(a1452)) | (~c0_1(a1452))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 1.76/1.92 tff(3090,plain,
% 1.76/1.92 (~c2_1(a1452)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3089, 82, 647, 1216, 3083, 3075, 1204])).
% 1.76/1.92 tff(3091,plain,
% 1.76/1.92 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3092,plain,
% 1.76/1.92 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430))) <=> (hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3093,plain,
% 1.76/1.92 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3092])).
% 1.76/1.92 tff(3094,plain,
% 1.76/1.92 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3093, 3091])).
% 1.76/1.92 tff(3095,plain,
% 1.76/1.92 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a1430) | (~c2_1(a1430)) | (~c1_1(a1430)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3096,plain,
% 1.76/1.92 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp7 | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3095, 3094])).
% 1.76/1.92 tff(3097,plain,
% 1.76/1.92 (hskp16 | hskp7 | (~c2_1(a1430)) | (~c1_1(a1430))),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3096, 82, 12, 1781])).
% 1.76/1.92 tff(3098,plain,
% 1.76/1.92 (hskp16),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3097, 3051, 3017, 3018])).
% 1.76/1.92 tff(3099,plain,
% 1.76/1.92 (~c3_1(a1454)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1793, 3098])).
% 1.76/1.92 tff(3100,plain,
% 1.76/1.92 (~c0_1(a1454)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1799, 3098])).
% 1.76/1.92 tff(3101,plain,
% 1.76/1.92 (((~hskp15) | c1_1(a1452)) <=> ((~hskp15) | c1_1(a1452))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3102,axiom,((~hskp15) | c1_1(a1452)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.76/1.92 tff(3103,plain,
% 1.76/1.92 ((~hskp15) | c1_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3102, 3101])).
% 1.76/1.92 tff(3104,plain,
% 1.76/1.92 ((~hskp15) | c1_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3103, 3101])).
% 1.76/1.92 tff(3105,plain,
% 1.76/1.92 ((~hskp15) | c1_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3104, 3101])).
% 1.76/1.92 tff(3106,plain,
% 1.76/1.92 ((~hskp15) | c1_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3105, 3101])).
% 1.76/1.92 tff(3107,plain,
% 1.76/1.92 ((~hskp15) | c1_1(a1452)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3106, 3101])).
% 1.76/1.92 tff(3108,plain,
% 1.76/1.92 (c1_1(a1452)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3107, 3069])).
% 1.76/1.92 tff(3109,plain,
% 1.76/1.92 (c1_1(a1454)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1808, 3098])).
% 1.76/1.92 tff(3110,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3111,plain,
% 1.76/1.92 ((hskp12 | (~ndr1_0) | c2_1(a1452) | c3_1(a1452) | (~c1_1(a1452)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454))) <=> (hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3112,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1452) | c3_1(a1452) | (~c1_1(a1452)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3111])).
% 1.76/1.92 tff(3113,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1452) | c3_1(a1452) | (~c1_1(a1452)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3112, 3110])).
% 1.76/1.92 tff(3114,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1452) | c3_1(a1452) | (~c1_1(a1452)) | c3_1(a1454) | c0_1(a1454) | (~c1_1(a1454)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3115,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 1.76/1.92 tff(3116,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3115, 82, 647, 3109, 3108, 3100, 3099, 3075, 196, 3090])).
% 1.76/1.92 tff(3117,plain,(hskp11 | hskp12 | c0_1(a1430) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3118,plain,
% 1.76/1.92 (hskp11),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3117, 3050, 12, 11])).
% 1.76/1.92 tff(3119,plain,
% 1.76/1.92 (hskp2),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[741, 3118, 11])).
% 1.76/1.92 tff(3120,plain,
% 1.76/1.92 (~c2_1(a1430)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2182, 3119])).
% 1.76/1.92 tff(3121,plain,
% 1.76/1.92 (~c3_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[703, 3118])).
% 1.76/1.92 tff(3122,plain,
% 1.76/1.92 (~c2_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[691, 3118])).
% 1.76/1.92 tff(3123,plain,
% 1.76/1.92 (~c1_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2199, 82, 3017, 2074, 3122, 3121, 3120, 154, 3018])).
% 1.76/1.92 tff(3124,plain,
% 1.76/1.92 (~c0_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[697, 3118])).
% 1.76/1.92 tff(3125,plain,
% 1.76/1.92 (hskp3),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2839, 82, 2074, 3124, 3121, 12, 819, 3018, 3123])).
% 1.76/1.92 tff(3126,plain,
% 1.76/1.92 (c1_1(a1431)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[887, 3125])).
% 1.76/1.92 tff(3127,plain,
% 1.76/1.92 (~c2_1(a1431)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[865, 3125])).
% 1.76/1.92 tff(3128,plain,
% 1.76/1.92 (c3_1(a1431)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2349, 82, 3126, 3124, 3122, 3121, 3127, 2342, 3123])).
% 1.76/1.92 tff(3129,plain,
% 1.76/1.92 (hskp10),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2384, 3128, 3050, 3127, 3126])).
% 1.76/1.92 tff(3130,plain,
% 1.76/1.92 (~c3_1(a1445)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[406, 3129])).
% 1.76/1.92 tff(3131,plain,
% 1.76/1.92 (~c1_1(a1445)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[412, 3129])).
% 1.76/1.92 tff(3132,plain,
% 1.76/1.92 (hskp8),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2268, 3120, 12, 11])).
% 1.76/1.92 tff(3133,plain,
% 1.76/1.92 (c3_1(a1441)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1557, 3132])).
% 1.76/1.92 tff(3134,plain,
% 1.76/1.92 (~c1_1(a1441)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1549, 3132])).
% 1.76/1.92 tff(3135,plain,
% 1.76/1.92 (c0_1(a1441)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1565, 3132])).
% 1.76/1.92 tff(3136,plain,
% 1.76/1.92 (hskp17),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2580, 3135, 11, 3124, 3121, 3122, 3134, 3133])).
% 1.76/1.92 tff(3137,plain,
% 1.76/1.92 (~c2_1(a1457)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[264, 3136])).
% 1.76/1.92 tff(3138,plain,
% 1.76/1.92 (~c1_1(a1457)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[245, 3136])).
% 1.76/1.92 tff(3139,plain,
% 1.76/1.92 (~c0_1(a1457)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[251, 3136])).
% 1.76/1.92 tff(3140,plain,
% 1.76/1.92 (c0_1(a1445)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[420, 3129])).
% 1.76/1.92 tff(3141,plain,
% 1.76/1.92 (~c2_1(a1445)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[427, 82, 3140, 3139, 3138, 3137, 3131, 3130, 23])).
% 1.76/1.92 tff(3142,plain,
% 1.76/1.92 (hskp29),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2518, 3129, 3138, 3137, 3139, 11])).
% 1.76/1.92 tff(3143,plain,
% 1.76/1.92 (c3_1(a1483)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[990, 3142])).
% 1.76/1.92 tff(3144,plain,
% 1.76/1.92 (c2_1(a1483)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[998, 3142])).
% 1.76/1.92 tff(3145,plain,
% 1.76/1.92 (c1_1(a1483)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1006, 3142])).
% 1.76/1.92 tff(3146,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3013, 82, 3017, 3145, 3144, 3143, 3131, 3130, 627, 3141])).
% 1.76/1.92 tff(3147,plain,(hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3148,plain,
% 1.76/1.92 (hskp5),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3147, 12])).
% 1.76/1.92 tff(3149,plain,
% 1.76/1.92 (~c2_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[301, 3148])).
% 1.76/1.92 tff(3150,plain,
% 1.76/1.92 (~c3_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[295, 3148])).
% 1.76/1.92 tff(3151,plain,
% 1.76/1.92 (c0_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[363, 3148])).
% 1.76/1.92 tff(3152,plain,
% 1.76/1.92 (~c1_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[721, 82, 647, 698, 692, 704, 196])).
% 1.76/1.92 tff(3153,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3154,plain,
% 1.76/1.92 ((hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1447) | c0_1(a1447) | c1_1(a1447)) <=> (hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3155,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447)))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3154])).
% 1.76/1.92 tff(3156,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1447) | c0_1(a1447) | c1_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.76/1.92 tff(3157,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1447) | c0_1(a1447) | c1_1(a1447))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3158,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | c1_1(a1447)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.76/1.92 tff(3159,plain,
% 1.76/1.92 (hskp0),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3158, 82, 102, 698, 692, 100, 101, 1123, 3152])).
% 1.76/1.92 tff(3160,plain,
% 1.76/1.92 (~c3_1(a1427)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1135, 3159])).
% 1.76/1.92 tff(3161,plain,
% 1.76/1.92 (c0_1(a1427)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1151, 3159])).
% 1.76/1.92 tff(3162,plain,
% 1.76/1.92 (c2_1(a1427)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1143, 3159])).
% 1.76/1.92 tff(3163,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3164,plain,
% 1.76/1.92 (((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447)) <=> (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3165,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447)))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3164])).
% 1.76/1.92 tff(3166,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3165, 3163])).
% 1.76/1.92 tff(3167,plain,
% 1.76/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c1_1(a1435)) | c3_1(a1447) | c2_1(a1447) | c1_1(a1447) | c3_1(a1447) | c1_1(a1447) | c0_1(a1447))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3168,plain,
% 1.76/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | c1_1(a1447)),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3167, 3166])).
% 1.76/1.92 tff(3169,plain,
% 1.76/1.92 (c0_1(a1447) | c2_1(a1447) | (~c1_1(a1435)) | c1_1(a1447)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3168, 82, 706, 100, 101, 2342])).
% 1.76/1.92 tff(3170,plain,
% 1.76/1.92 (~c1_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3169, 2273, 707, 705])).
% 1.76/1.92 tff(3171,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3172,plain,
% 1.76/1.92 ((hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435))) <=> (hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3173,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3172])).
% 1.76/1.92 tff(3174,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3173, 3171])).
% 1.76/1.92 tff(3175,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3176,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 1.76/1.92 tff(3177,plain,
% 1.76/1.92 (hskp21 | c1_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3176, 82, 102, 2398, 2397, 100, 2396, 2437])).
% 1.76/1.92 tff(3178,plain,
% 1.76/1.92 (hskp21),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3177, 3170])).
% 1.76/1.92 tff(3179,plain,
% 1.76/1.92 (~c1_1(a1466)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2450, 3178])).
% 1.76/1.92 tff(3180,plain,
% 1.76/1.92 (c2_1(a1466)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2458, 3178])).
% 1.76/1.92 tff(3181,plain,
% 1.76/1.92 (c0_1(a1466)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[2466, 3178])).
% 1.76/1.92 tff(3182,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3183,plain,
% 1.76/1.92 (((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447)) <=> (c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3184,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3183])).
% 1.76/1.92 tff(3185,plain,
% 1.76/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.76/1.92 tff(3186,plain,
% 1.76/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | c0_1(a1447) | c2_1(a1447))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3187,plain,
% 1.76/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.76/1.92 tff(3188,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3187, 82, 3181, 3180, 102, 3179, 705, 707, 101, 23, 3170, 2273])).
% 1.76/1.92 tff(3189,plain,(c1_1(a1447) | (~c0_1(a1435)) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~c0_1(a1427)) | (~c2_1(a1427)) | c2_1(a1435) | c3_1(a1427) | c3_1(a1447)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3190,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3189, 3162, 3161, 102, 101, 698, 704, 692, 3152, 3160, 100])).
% 1.76/1.92 tff(3191,plain,((~hskp11) | (~c0_1(a1435)) | c3_1(a1435) | c2_1(a1435) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3192,plain,
% 1.76/1.92 (~hskp11),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3191, 647, 3150, 3149, 3151])).
% 1.76/1.92 tff(3193,plain,
% 1.76/1.92 (c2_1(a1427)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1143, 2585])).
% 1.76/1.92 tff(3194,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1385, 82, 647, 1216, 2587, 3193, 2586, 1204])).
% 1.76/1.92 tff(3195,plain,((~hskp0) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3196,plain,
% 1.76/1.92 (~hskp0),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3195, 1216, 647])).
% 1.76/1.92 tff(3197,plain,
% 1.76/1.92 ($false),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[1129, 82, 2631, 102, 37, 24, 100, 101, 1123, 47])).
% 1.76/1.92 tff(3198,plain,(c2_1(a1438) | hskp0 | (~c0_1(a1435)) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.92 tff(3199,plain,
% 1.76/1.92 (c2_1(a1438)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3198, 37, 3151, 2631, 24, 3149, 3150])).
% 1.76/1.92 tff(3200,plain,
% 1.76/1.92 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3201,plain,
% 1.76/1.92 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3202,plain,
% 1.76/1.92 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3201])).
% 1.76/1.92 tff(3203,plain,
% 1.76/1.92 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.76/1.92 tff(3204,plain,
% 1.76/1.92 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3205,plain,
% 1.76/1.92 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.76/1.92 tff(3206,plain,
% 1.76/1.92 (hskp4 | hskp0 | c0_1(a1438) | (~c2_1(a1438))),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3205, 82, 24, 2648])).
% 1.76/1.92 tff(3207,plain,
% 1.76/1.92 (hskp4),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3206, 3199, 2631, 37])).
% 1.76/1.92 tff(3208,plain,
% 1.76/1.92 (~c2_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[125, 3207])).
% 1.76/1.92 tff(3209,plain,
% 1.76/1.92 (c3_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[143, 3207])).
% 1.76/1.92 tff(3210,plain,
% 1.76/1.92 (c1_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[135, 3207])).
% 1.76/1.92 tff(3211,plain,
% 1.76/1.92 (hskp7 | hskp4),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[118, 82, 3151, 3149, 3150, 112])).
% 1.76/1.92 tff(3212,plain,
% 1.76/1.92 (hskp4),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3211, 99])).
% 1.76/1.92 tff(3213,plain,
% 1.76/1.92 (~c2_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[125, 3212])).
% 1.76/1.92 tff(3214,plain,
% 1.76/1.92 (~c1_1(a1435)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[164, 3212, 3149, 99, 3150, 3213])).
% 1.76/1.92 tff(3215,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3216,plain,
% 1.76/1.92 ((hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430))) <=> (hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3217,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435))))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3216])).
% 1.76/1.92 tff(3218,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3217, 3215])).
% 1.76/1.92 tff(3219,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c2_1(a1430)))),
% 1.76/1.92 inference(quant_inst,[status(thm)],[])).
% 1.76/1.92 tff(3220,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c3_1(a1435) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435))),
% 1.76/1.92 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.76/1.92 tff(3221,plain,
% 1.76/1.92 (~c2_1(a1430)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[3220, 82, 647, 3151, 2074, 3150, 12, 1325, 3214])).
% 1.76/1.92 tff(3222,plain,
% 1.76/1.92 (c3_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[143, 3212])).
% 1.76/1.92 tff(3223,plain,
% 1.76/1.92 (c1_1(a1434)),
% 1.76/1.92 inference(unit_resolution,[status(thm)],[135, 3212])).
% 1.76/1.92 tff(3224,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3225,plain,
% 1.76/1.92 ((hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438)) <=> (hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.76/1.92 inference(rewrite,[status(thm)],[])).
% 1.76/1.92 tff(3226,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438)))),
% 1.76/1.92 inference(monotonicity,[status(thm)],[3225])).
% 1.76/1.92 tff(3227,plain,
% 1.76/1.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438))),
% 1.76/1.92 inference(transitivity,[status(thm)],[3226, 3224])).
% 1.76/1.92 tff(3228,plain,
% 1.76/1.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3229,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 1.76/1.93 tff(3230,plain,
% 1.76/1.93 (c2_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3229, 82, 2631, 46, 3223, 3222, 37, 3213, 2323])).
% 1.76/1.93 tff(3231,plain,
% 1.76/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3232,plain,
% 1.76/1.93 (((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430))) <=> (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3233,plain,
% 1.76/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3232])).
% 1.76/1.93 tff(3234,plain,
% 1.76/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3233, 3231])).
% 1.76/1.93 tff(3235,plain,
% 1.76/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3236,plain,
% 1.76/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.76/1.93 tff(3237,plain,
% 1.76/1.93 (c3_1(a1438) | c2_1(a1430) | c1_1(a1435) | (~c2_1(a1438))),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3236, 82, 3151, 2074, 24, 3149, 12, 543])).
% 1.76/1.93 tff(3238,plain,
% 1.76/1.93 ($false),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3237, 3230, 3221, 46, 3214])).
% 1.76/1.93 tff(3239,plain,(c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | hskp0 | c0_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.76/1.93 tff(3240,plain,
% 1.76/1.93 (c3_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3239, 37, 12, 2631, 24, 647])).
% 1.76/1.93 tff(3241,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3242,plain,
% 1.76/1.93 ((hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438))) <=> (hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3243,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3242])).
% 1.76/1.93 tff(3244,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3243, 3241])).
% 1.76/1.93 tff(3245,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c0_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3246,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3245, 3244])).
% 1.76/1.93 tff(3247,plain,
% 1.76/1.93 ($false),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3246, 82, 647, 3240, 3210, 3209, 37, 3208, 1273, 3199])).
% 1.76/1.93 tff(3248,plain,(c0_1(a1438) | hskp12 | hskp0 | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.93 tff(3249,plain,
% 1.76/1.93 (c0_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3248, 3196, 647, 24, 12])).
% 1.76/1.93 tff(3250,plain,
% 1.76/1.93 (~hskp7),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[1021, 3249])).
% 1.76/1.93 tff(3251,plain,
% 1.76/1.93 (hskp4),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3211, 3250])).
% 1.76/1.93 tff(3252,plain,
% 1.76/1.93 (~c2_1(a1434)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[125, 3251])).
% 1.76/1.93 tff(3253,plain,
% 1.76/1.93 (~c1_1(a1435)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[164, 3252, 3149, 3251, 3150, 3250])).
% 1.76/1.93 tff(3254,plain,
% 1.76/1.93 (~c2_1(a1430)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3220, 82, 647, 3151, 2074, 3150, 12, 1325, 3253])).
% 1.76/1.93 tff(3255,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3256,plain,
% 1.76/1.93 ((hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1430) | c0_1(a1430) | c1_1(a1430)) <=> (hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3257,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1430) | c0_1(a1430) | c1_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3256])).
% 1.76/1.93 tff(3258,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1430) | c0_1(a1430) | c1_1(a1430))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3257, 3255])).
% 1.76/1.93 tff(3259,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1430) | c0_1(a1430) | c1_1(a1430))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3260,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3259, 3258])).
% 1.76/1.93 tff(3261,plain,
% 1.76/1.93 (c1_1(a1430)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3260, 82, 3196, 3151, 3149, 3150, 12, 3254, 1123])).
% 1.76/1.93 tff(3262,plain,
% 1.76/1.93 (~c2_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[1710, 3249, 1216, 3196])).
% 1.76/1.93 tff(3263,assumption,(hskp29), introduced(assumption)).
% 1.76/1.93 tff(3264,plain,
% 1.76/1.93 (c3_1(a1483)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[990, 3263])).
% 1.76/1.93 tff(3265,plain,
% 1.76/1.93 (c2_1(a1483)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[998, 3263])).
% 1.76/1.93 tff(3266,plain,
% 1.76/1.93 (c1_1(a1483)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[1006, 3263])).
% 1.76/1.93 tff(3267,plain,
% 1.76/1.93 ($false),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[1634, 82, 99, 3266, 3265, 3264, 46, 24, 627, 47])).
% 1.76/1.93 tff(3268,plain,((~hskp29) | c3_1(a1438) | c1_1(a1438) | c2_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.93 tff(3269,plain,
% 1.76/1.93 (~hskp29),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3268, 46, 24, 47])).
% 1.76/1.93 tff(3270,plain,
% 1.76/1.93 ((hskp29 | hskp26 | hskp0) <=> (hskp29 | hskp26 | hskp0)),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3271,plain,
% 1.76/1.93 (((hskp0 | hskp29) | hskp26) <=> (hskp29 | hskp26 | hskp0)),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3272,axiom,((hskp0 | hskp29) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.76/1.93 tff(3273,plain,
% 1.76/1.93 (hskp29 | hskp26 | hskp0),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.76/1.93 tff(3274,plain,
% 1.76/1.93 (hskp29 | hskp26 | hskp0),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3273, 3270])).
% 1.76/1.93 tff(3275,plain,
% 1.76/1.93 (hskp29 | hskp26 | hskp0),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3274, 3270])).
% 1.76/1.93 tff(3276,plain,
% 1.76/1.93 (hskp29 | hskp26 | hskp0),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3275, 3270])).
% 1.76/1.93 tff(3277,plain,
% 1.76/1.93 (hskp29 | hskp26 | hskp0),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3276, 3270])).
% 1.76/1.93 tff(3278,plain,
% 1.76/1.93 (hskp26),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3277, 3269, 2631])).
% 1.76/1.93 tff(3279,plain,
% 1.76/1.93 (((~hskp26) | (~c0_1(a1517))) <=> ((~hskp26) | (~c0_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3280,plain,
% 1.76/1.93 (((~c0_1(a1517)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3281,axiom,((~c0_1(a1517)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.76/1.93 tff(3282,plain,
% 1.76/1.93 ((~hskp26) | (~c0_1(a1517))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 1.76/1.93 tff(3283,plain,
% 1.76/1.93 ((~hskp26) | (~c0_1(a1517))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3282, 3279])).
% 1.76/1.93 tff(3284,plain,
% 1.76/1.93 (~c0_1(a1517)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3283, 3278])).
% 1.76/1.93 tff(3285,plain,
% 1.76/1.93 (((~hskp26) | c2_1(a1517)) <=> ((~hskp26) | c2_1(a1517))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3286,axiom,((~hskp26) | c2_1(a1517)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.76/1.93 tff(3287,plain,
% 1.76/1.93 ((~hskp26) | c2_1(a1517)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.76/1.93 tff(3288,plain,
% 1.76/1.93 ((~hskp26) | c2_1(a1517)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3287, 3285])).
% 1.76/1.93 tff(3289,plain,
% 1.76/1.93 ((~hskp26) | c2_1(a1517)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3288, 3285])).
% 1.76/1.93 tff(3290,plain,
% 1.76/1.93 ((~hskp26) | c2_1(a1517)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3289, 3285])).
% 1.76/1.93 tff(3291,plain,
% 1.76/1.93 ((~hskp26) | c2_1(a1517)),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3290, 3285])).
% 1.76/1.93 tff(3292,plain,
% 1.76/1.93 (c2_1(a1517)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3291, 3278])).
% 1.76/1.93 tff(3293,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3294,plain,
% 1.76/1.93 ((hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1517) | (~c1_1(a1517)) | (~c2_1(a1517))) <=> (hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3295,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1517) | (~c1_1(a1517)) | (~c2_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3294])).
% 1.76/1.93 tff(3296,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1517) | (~c1_1(a1517)) | (~c2_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3295, 3293])).
% 1.76/1.93 tff(3297,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c0_1(a1438)) | c0_1(a1517) | (~c1_1(a1517)) | (~c2_1(a1517)))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3298,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c3_1(a1438) | c0_1(a1517) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1517)) | (~c1_1(a1517))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3297, 3296])).
% 1.76/1.93 tff(3299,plain,
% 1.76/1.93 (~c1_1(a1517)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3298, 82, 1628, 3292, 46, 3284, 1616, 24, 175])).
% 1.76/1.93 tff(3300,assumption,(c1_1(a1430)), introduced(assumption)).
% 1.76/1.93 tff(3301,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3302,plain,
% 1.76/1.93 ((hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1517) | c1_1(a1517) | (~c2_1(a1517))) <=> (hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3303,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1517) | c1_1(a1517) | (~c2_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3302])).
% 1.76/1.93 tff(3304,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1517) | c1_1(a1517) | (~c2_1(a1517)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3303, 3301])).
% 1.76/1.93 tff(3305,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1517) | c1_1(a1517) | (~c2_1(a1517)))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3306,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 1.76/1.93 tff(3307,plain,
% 1.76/1.93 ($false),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3306, 82, 2631, 3292, 2074, 3284, 12, 2160, 3300, 3299])).
% 1.76/1.93 tff(3308,plain,(c3_1(a1438) | hskp0 | c0_1(a1430) | (~c1_1(a1430)) | (~c0_1(a1438)) | c1_1(a1438) | c2_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.93 tff(3309,plain,
% 1.76/1.93 (c3_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3308, 3196, 12, 3261, 3249, 24, 3262])).
% 1.76/1.93 tff(3310,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3311,plain,
% 1.76/1.93 ((hskp17 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3312,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3311])).
% 1.76/1.93 tff(3313,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3312, 3310])).
% 1.76/1.93 tff(3314,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1438)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3315,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | (~c0_1(a1438)) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1438) | (~c3_1(a1438))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 1.76/1.93 tff(3316,plain,
% 1.76/1.93 (hskp17 | (~c1_1(a1430)) | (~c3_1(a1438))),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3315, 82, 2074, 3249, 12, 312, 3262])).
% 1.76/1.93 tff(3317,plain,
% 1.76/1.93 (hskp17),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3316, 3309, 3261])).
% 1.76/1.93 tff(3318,plain,
% 1.76/1.93 (~c2_1(a1457)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[264, 3317])).
% 1.76/1.93 tff(3319,plain,
% 1.76/1.93 (~c1_1(a1457)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[245, 3317])).
% 1.76/1.93 tff(3320,plain,
% 1.76/1.93 (~c0_1(a1457)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[251, 3317])).
% 1.76/1.93 tff(3321,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3322,plain,
% 1.76/1.93 ((hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457)) <=> (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3323,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))))),
% 1.76/1.93 inference(monotonicity,[status(thm)],[3322])).
% 1.76/1.93 tff(3324,plain,
% 1.76/1.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.76/1.93 inference(transitivity,[status(thm)],[3323, 3321])).
% 1.76/1.93 tff(3325,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c2_1(a1457) | c0_1(a1457) | c1_1(a1457))),
% 1.76/1.93 inference(quant_inst,[status(thm)],[])).
% 1.76/1.93 tff(3326,plain,
% 1.76/1.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3325, 3324])).
% 1.76/1.93 tff(3327,plain,
% 1.76/1.93 ($false),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3326, 82, 3196, 3151, 3320, 3319, 3318, 3149, 3150, 1123])).
% 1.76/1.93 tff(3328,plain,(hskp11 | c0_1(a1430) | c1_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.76/1.93 tff(3329,plain,
% 1.76/1.93 (c1_1(a1438)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3328, 3192, 12, 647])).
% 1.76/1.93 tff(3330,plain,
% 1.76/1.93 (~hskp7),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[1424, 3329])).
% 1.76/1.93 tff(3331,plain,
% 1.76/1.93 (hskp4),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3211, 3330])).
% 1.76/1.93 tff(3332,plain,
% 1.76/1.93 (~c2_1(a1434)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[125, 3331])).
% 1.76/1.93 tff(3333,plain,
% 1.76/1.93 (~c1_1(a1435)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[164, 3332, 3149, 3331, 3150, 3330])).
% 1.76/1.93 tff(3334,plain,
% 1.76/1.93 (~c2_1(a1430)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3220, 82, 647, 3151, 2074, 3150, 12, 1325, 3333])).
% 1.76/1.93 tff(3335,plain,
% 1.76/1.93 (~hskp0),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3195, 3192, 647])).
% 1.76/1.93 tff(3336,plain,
% 1.76/1.93 (c1_1(a1430)),
% 1.76/1.93 inference(unit_resolution,[status(thm)],[3260, 82, 3335, 3151, 3149, 3150, 12, 3334, 1123])).
% 1.76/1.93 tff(3337,plain,
% 1.76/1.93 (^[U: $i] : refl((hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.76/1.93 inference(bind,[status(th)],[])).
% 1.76/1.93 tff(3338,plain,
% 1.76/1.93 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(quant_intro,[status(thm)],[3337])).
% 1.76/1.93 tff(3339,plain,
% 1.76/1.93 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(rewrite,[status(thm)],[])).
% 1.76/1.93 tff(3340,plain,
% 1.76/1.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp19) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.76/1.93 inference(bind,[status(th)],[])).
% 1.76/1.93 tff(3341,plain,
% 1.76/1.93 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp19) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(quant_intro,[status(thm)],[3340])).
% 1.76/1.93 tff(3342,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.76/1.93 tff(3343,plain,
% 1.76/1.93 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 1.76/1.93 tff(3344,plain,
% 1.76/1.93 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3343, 3339])).
% 1.76/1.93 tff(3345,plain,(
% 1.76/1.93 ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(skolemize,[status(sab)],[3344])).
% 1.76/1.93 tff(3346,plain,
% 1.76/1.93 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.76/1.93 inference(modus_ponens,[status(thm)],[3345, 3338])).
% 1.76/1.93 tff(3347,plain,
% 1.76/1.93 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3348,plain,
% 1.76/1.94 ((hskp19 | hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3349,plain,
% 1.76/1.94 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3348])).
% 1.76/1.94 tff(3350,plain,
% 1.76/1.94 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3349, 3347])).
% 1.76/1.94 tff(3351,plain,
% 1.76/1.94 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3352,plain,
% 1.76/1.94 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp3 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.76/1.94 tff(3353,plain,
% 1.76/1.94 (hskp19 | hskp3 | (~c1_1(a1430)) | (~c3_1(a1430))),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3352, 82, 12, 3346])).
% 1.76/1.94 tff(3354,plain,
% 1.76/1.94 (hskp19),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3353, 820, 2074, 3300])).
% 1.76/1.94 tff(3355,plain,
% 1.76/1.94 (~c3_1(a1460)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1165, 3354])).
% 1.76/1.94 tff(3356,plain,
% 1.76/1.94 (~c1_1(a1460)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1184, 3354])).
% 1.76/1.94 tff(3357,plain,
% 1.76/1.94 (~c0_1(a1460)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1171, 3354])).
% 1.76/1.94 tff(3358,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3359,plain,
% 1.76/1.94 ((hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1460) | c0_1(a1460) | c1_1(a1460)) <=> (hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3360,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1460) | c0_1(a1460) | c1_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3359])).
% 1.76/1.94 tff(3361,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1460) | c0_1(a1460) | c1_1(a1460))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3360, 3358])).
% 1.76/1.94 tff(3362,plain,
% 1.76/1.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c3_1(a1460) | c0_1(a1460) | c1_1(a1460))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3363,plain,
% 1.76/1.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.76/1.94 tff(3364,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3363, 82, 820, 851, 843, 835, 3357, 3356, 3355, 819])).
% 1.76/1.94 tff(3365,plain,(hskp3 | hskp17 | (~c1_1(a1430)) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3366,plain,
% 1.76/1.94 (hskp3),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3365, 36, 3336, 12])).
% 1.76/1.94 tff(3367,plain,
% 1.76/1.94 (~c2_1(a1431)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[865, 3366])).
% 1.76/1.94 tff(3368,plain,
% 1.76/1.94 (~c0_1(a1431)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[871, 3366])).
% 1.76/1.94 tff(3369,plain,
% 1.76/1.94 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3370,plain,
% 1.76/1.94 ((hskp11 | hskp0 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441))) <=> (hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3371,plain,
% 1.76/1.94 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3370])).
% 1.76/1.94 tff(3372,plain,
% 1.76/1.94 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3371, 3369])).
% 1.76/1.94 tff(3373,plain,
% 1.76/1.94 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1441) | (~c2_1(a1441)) | (~c0_1(a1441)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3374,plain,
% 1.76/1.94 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 1.76/1.94 tff(3375,plain,
% 1.76/1.94 (~c2_1(a1441)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3374, 82, 1216, 2631, 2754, 2756, 1703])).
% 1.76/1.94 tff(3376,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3377,plain,
% 1.76/1.94 ((hskp17 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3378,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3377])).
% 1.76/1.94 tff(3379,plain,
% 1.76/1.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3378, 3376])).
% 1.76/1.94 tff(3380,plain,
% 1.76/1.94 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c0_1(a1441)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3381,plain,
% 1.76/1.94 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 1.76/1.94 tff(3382,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3381, 82, 36, 2754, 2753, 2074, 12, 312, 3300, 3375])).
% 1.76/1.94 tff(3383,plain,((~hskp8) | hskp17 | c0_1(a1430) | (~c1_1(a1430)) | hskp11 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3384,plain,
% 1.76/1.94 (~hskp8),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3383, 36, 12, 3336, 3192, 3335])).
% 1.76/1.94 tff(3385,plain,
% 1.76/1.94 (hskp14),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[2246, 3384, 647])).
% 1.76/1.94 tff(3386,plain,
% 1.76/1.94 (~c3_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[502, 3385])).
% 1.76/1.94 tff(3387,plain,
% 1.76/1.94 (~c1_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[508, 3385])).
% 1.76/1.94 tff(3388,plain,
% 1.76/1.94 (c2_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[516, 3385])).
% 1.76/1.94 tff(3389,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3390,plain,
% 1.76/1.94 (((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431))) <=> (c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3391,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3390])).
% 1.76/1.94 tff(3392,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3391, 3389])).
% 1.76/1.94 tff(3393,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1431) | c2_1(a1431) | (~c3_1(a1431)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3394,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | (~c3_1(a1431)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3393, 3392])).
% 1.76/1.94 tff(3395,plain,
% 1.76/1.94 (~c3_1(a1431)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3394, 82, 3388, 3151, 3387, 3386, 3149, 3368, 3367, 543, 3333])).
% 1.76/1.94 tff(3396,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3397,plain,
% 1.76/1.94 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | c3_1(a1431)) <=> (hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3398,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | c3_1(a1431))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431)))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3397])).
% 1.76/1.94 tff(3399,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | c3_1(a1431))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3398, 3396])).
% 1.76/1.94 tff(3400,plain,
% 1.76/1.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1431) | c0_1(a1431) | c3_1(a1431))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3401,plain,
% 1.76/1.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431)),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3400, 3399])).
% 1.76/1.94 tff(3402,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3401, 82, 3384, 3330, 3368, 3367, 2212, 3395])).
% 1.76/1.94 tff(3403,plain,(hskp17 | hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3404,plain,
% 1.76/1.94 (hskp17),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3403, 647, 12])).
% 1.76/1.94 tff(3405,plain,
% 1.76/1.94 (~c0_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[251, 3404])).
% 1.76/1.94 tff(3406,plain,
% 1.76/1.94 (~c2_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[264, 3404])).
% 1.76/1.94 tff(3407,plain,
% 1.76/1.94 (c0_1(a1457) | c1_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3326, 82, 3335, 3151, 2514, 3149, 3150, 1123])).
% 1.76/1.94 tff(3408,plain,
% 1.76/1.94 (c1_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3407, 2516])).
% 1.76/1.94 tff(3409,plain,
% 1.76/1.94 (~hskp17),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[245, 3408])).
% 1.76/1.94 tff(3410,plain,
% 1.76/1.94 (~hskp8),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3383, 3409, 12, 3336, 3192, 3335])).
% 1.76/1.94 tff(3411,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3412,plain,
% 1.76/1.94 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | c3_1(a1457)) <=> (hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3413,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | c3_1(a1457))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457)))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3412])).
% 1.76/1.94 tff(3414,plain,
% 1.76/1.94 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | c3_1(a1457))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3413, 3411])).
% 1.76/1.94 tff(3415,plain,
% 1.76/1.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a1457) | c0_1(a1457) | c3_1(a1457))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3416,plain,
% 1.76/1.94 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457)),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 1.76/1.94 tff(3417,plain,
% 1.76/1.94 (hskp8 | c0_1(a1457) | c3_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3416, 82, 3330, 2514, 2212])).
% 1.76/1.94 tff(3418,plain,
% 1.76/1.94 (c3_1(a1457)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3417, 3410, 2516])).
% 1.76/1.94 tff(3419,plain,
% 1.76/1.94 (hskp14),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[2246, 3410, 647])).
% 1.76/1.94 tff(3420,plain,
% 1.76/1.94 (~c3_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[502, 3419])).
% 1.76/1.94 tff(3421,plain,
% 1.76/1.94 (~c1_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[508, 3419])).
% 1.76/1.94 tff(3422,plain,
% 1.76/1.94 (c2_1(a1451)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[516, 3419])).
% 1.76/1.94 tff(3423,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3424,plain,
% 1.76/1.94 (((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457))) <=> (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3425,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3424])).
% 1.76/1.94 tff(3426,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.76/1.94 tff(3427,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1451) | c3_1(a1451) | (~c2_1(a1451)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c2_1(a1457) | (~c3_1(a1457)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3428,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.76/1.94 tff(3429,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3428, 82, 3422, 3151, 2516, 2514, 3421, 3420, 3149, 543, 3333, 3418])).
% 1.76/1.94 tff(3430,plain,(c0_1(a1457) | c2_1(a1457) | hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3431,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3430, 3406, 3405, 647, 12])).
% 1.76/1.94 tff(3432,plain,(hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3433,plain,
% 1.76/1.94 (hskp12),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3432, 12])).
% 1.76/1.94 tff(3434,plain,
% 1.76/1.94 (~c2_1(a1448)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[202, 3433])).
% 1.76/1.94 tff(3435,plain,
% 1.76/1.94 (c2_1(a1438)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3198, 37, 3151, 24, 2631, 3149, 3150])).
% 1.76/1.94 tff(3436,plain,
% 1.76/1.94 (c3_1(a1448)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[218, 3433])).
% 1.76/1.94 tff(3437,plain,
% 1.76/1.94 (c0_1(a1448)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[210, 3433])).
% 1.76/1.94 tff(3438,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3439,plain,
% 1.76/1.94 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3440,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3439])).
% 1.76/1.94 tff(3441,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3440, 3438])).
% 1.76/1.94 tff(3442,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3443,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 1.76/1.94 tff(3444,plain,
% 1.76/1.94 (c0_1(a1438) | (~c1_1(a1430)) | (~c2_1(a1438))),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3443, 82, 3437, 3436, 2074, 3434, 24, 12, 1284])).
% 1.76/1.94 tff(3445,plain,
% 1.76/1.94 (~c1_1(a1430)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3444, 3435, 37])).
% 1.76/1.94 tff(3446,plain,
% 1.76/1.94 (hskp4),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3206, 37, 2631, 3435])).
% 1.76/1.94 tff(3447,plain,
% 1.76/1.94 (~c2_1(a1434)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[125, 128])).
% 1.76/1.94 tff(3448,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3449,plain,
% 1.76/1.94 (((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435)) <=> (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3450,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3449])).
% 1.76/1.94 tff(3451,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438)))),
% 1.76/1.94 inference(transitivity,[status(thm)],[3450, 3448])).
% 1.76/1.94 tff(3452,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))),
% 1.76/1.94 inference(quant_inst,[status(thm)],[])).
% 1.76/1.94 tff(3453,plain,
% 1.76/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438))),
% 1.76/1.94 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 1.76/1.94 tff(3454,plain,
% 1.76/1.94 (c3_1(a1438) | c1_1(a1430) | c1_1(a1435) | (~c2_1(a1438))),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3453, 82, 2074, 24, 3149, 3150, 12, 578])).
% 1.76/1.94 tff(3455,plain,
% 1.76/1.94 (c1_1(a1435)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3454, 46, 544, 768])).
% 1.76/1.94 tff(3456,plain,
% 1.76/1.94 ($false),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[164, 3455, 99, 3149, 128, 3150, 3447])).
% 1.76/1.94 tff(3457,plain,(c3_1(a1438) | (~hskp4) | c1_1(a1430) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.94 tff(3458,plain,
% 1.76/1.94 (c3_1(a1438)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3457, 3446, 3445, 3435, 24, 12])).
% 1.76/1.94 tff(3459,plain,
% 1.76/1.94 (hskp20 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1232, 82, 1216, 24, 1226])).
% 1.76/1.94 tff(3460,plain,
% 1.76/1.94 (hskp20),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[3459, 3458, 3435])).
% 1.76/1.94 tff(3461,plain,
% 1.76/1.94 (~c1_1(a1465)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1239, 3460])).
% 1.76/1.94 tff(3462,plain,
% 1.76/1.94 (c3_1(a1465)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1247, 3460])).
% 1.76/1.94 tff(3463,plain,
% 1.76/1.94 (c2_1(a1465)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1255, 3460])).
% 1.76/1.94 tff(3464,plain,
% 1.76/1.94 (~c0_1(a1465)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[1262, 82, 3463, 3462, 3461, 37, 24, 1214, 3435])).
% 1.76/1.94 tff(3465,plain,
% 1.76/1.94 (c3_1(a1434)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[143, 3446])).
% 1.76/1.94 tff(3466,plain,
% 1.76/1.94 (c1_1(a1434)),
% 1.76/1.94 inference(unit_resolution,[status(thm)],[135, 3446])).
% 1.76/1.94 tff(3467,assumption,(~c0_1(a1434)), introduced(assumption)).
% 1.76/1.94 tff(3468,assumption,(c3_1(a1434)), introduced(assumption)).
% 1.76/1.94 tff(3469,assumption,(c1_1(a1434)), introduced(assumption)).
% 1.76/1.94 tff(3470,assumption,(c3_1(a1448)), introduced(assumption)).
% 1.76/1.94 tff(3471,assumption,(c0_1(a1448)), introduced(assumption)).
% 1.76/1.94 tff(3472,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3473,plain,
% 1.76/1.94 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465))) <=> (c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.76/1.94 inference(rewrite,[status(thm)],[])).
% 1.76/1.94 tff(3474,plain,
% 1.76/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465))))),
% 1.76/1.94 inference(monotonicity,[status(thm)],[3473])).
% 1.76/1.94 tff(3475,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3474, 3472])).
% 1.76/1.95 tff(3476,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3477,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 1.76/1.95 tff(3478,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3477, 82, 1304, 3471, 3470, 3469, 3468, 1285, 230, 1284, 1274, 3467])).
% 1.76/1.95 tff(3479,plain,(c0_1(a1434) | (~c2_1(a1465)) | (~c0_1(a1448)) | (~c3_1(a1448)) | (~c1_1(a1434)) | (~c3_1(a1434)) | c1_1(a1465) | c2_1(a1448) | c0_1(a1465)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3480,plain,
% 1.76/1.95 (c0_1(a1434)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3479, 3463, 3437, 3436, 3466, 3465, 3461, 3434, 3464])).
% 1.76/1.95 tff(3481,plain,
% 1.76/1.95 (^[U: $i] : refl((hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.76/1.95 inference(bind,[status(th)],[])).
% 1.76/1.95 tff(3482,plain,
% 1.76/1.95 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(quant_intro,[status(thm)],[3481])).
% 1.76/1.95 tff(3483,plain,
% 1.76/1.95 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3484,plain,
% 1.76/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp25) <=> ((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp25) <=> (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.76/1.95 inference(bind,[status(th)],[])).
% 1.76/1.95 tff(3485,plain,
% 1.76/1.95 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp25) <=> ![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(quant_intro,[status(thm)],[3484])).
% 1.76/1.95 tff(3486,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.76/1.95 tff(3487,plain,
% 1.76/1.95 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.76/1.95 tff(3488,plain,
% 1.76/1.95 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3487, 3483])).
% 1.76/1.95 tff(3489,plain,(
% 1.76/1.95 ![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(skolemize,[status(sab)],[3488])).
% 1.76/1.95 tff(3490,plain,
% 1.76/1.95 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3489, 3482])).
% 1.76/1.95 tff(3491,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3492,plain,
% 1.76/1.95 ((hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1434)) | (~c1_1(a1434)) | (~c0_1(a1434))) <=> (hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3493,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1434)) | (~c1_1(a1434)) | (~c0_1(a1434)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3492])).
% 1.76/1.95 tff(3494,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1434)) | (~c1_1(a1434)) | (~c0_1(a1434)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3493, 3491])).
% 1.76/1.95 tff(3495,plain,
% 1.76/1.95 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1434)) | (~c1_1(a1434)) | (~c0_1(a1434)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3496,plain,
% 1.76/1.95 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c0_1(a1434)) | (~c1_1(a1434)) | (~c3_1(a1434))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 1.76/1.95 tff(3497,plain,
% 1.76/1.95 (hskp25 | (~c0_1(a1434))),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3496, 82, 2631, 3466, 3465, 3490])).
% 1.76/1.95 tff(3498,plain,
% 1.76/1.95 (hskp25),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3497, 3480])).
% 1.76/1.95 tff(3499,plain,
% 1.76/1.95 (~c0_1(a1504)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[454, 3498])).
% 1.76/1.95 tff(3500,plain,
% 1.76/1.95 (c1_1(a1504)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[464, 3498])).
% 1.76/1.95 tff(3501,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3502,plain,
% 1.76/1.95 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465))) <=> (c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3503,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3502])).
% 1.76/1.95 tff(3504,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3503, 3501])).
% 1.76/1.95 tff(3505,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3506,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 1.76/1.95 tff(3507,plain,
% 1.76/1.95 (~c3_1(a1504)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3506, 82, 3500, 3463, 3437, 3436, 3499, 3461, 3434, 1284, 3464])).
% 1.76/1.95 tff(3508,plain,
% 1.76/1.95 (c2_1(a1504)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[489, 3498])).
% 1.76/1.95 tff(3509,plain,
% 1.76/1.95 (hskp14),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[496, 82, 3500, 3508, 3499, 482, 3507])).
% 1.76/1.95 tff(3510,plain,
% 1.76/1.95 (~c3_1(a1451)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[502, 3509])).
% 1.76/1.95 tff(3511,plain,
% 1.76/1.95 (~c1_1(a1451)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[508, 3509])).
% 1.76/1.95 tff(3512,plain,
% 1.76/1.95 (c2_1(a1451)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[516, 3509])).
% 1.76/1.95 tff(3513,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[523, 82, 3500, 3508, 3512, 3151, 3499, 3511, 3510, 3149, 3150, 185])).
% 1.76/1.95 tff(3514,plain,(c0_1(a1438) | hskp0 | c1_1(a1438) | hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3515,plain,
% 1.76/1.95 (c0_1(a1438)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3514, 2631, 24, 1216, 12])).
% 1.76/1.95 tff(3516,plain,
% 1.76/1.95 (~hskp7),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1021, 3515])).
% 1.76/1.95 tff(3517,plain,
% 1.76/1.95 (hskp4),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3211, 3516])).
% 1.76/1.95 tff(3518,plain,
% 1.76/1.95 (~c2_1(a1434)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[125, 3517])).
% 1.76/1.95 tff(3519,plain,
% 1.76/1.95 (~c1_1(a1435)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[164, 3518, 3149, 3517, 3150, 3516])).
% 1.76/1.95 tff(3520,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3521,plain,
% 1.76/1.95 ((hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504))) <=> (hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3522,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3521])).
% 1.76/1.95 tff(3523,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3522, 3520])).
% 1.76/1.95 tff(3524,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | c0_1(a1504) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3525,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3524, 3523])).
% 1.76/1.95 tff(3526,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3525, 82, 13, 549, 548, 102, 547, 101, 175, 313])).
% 1.76/1.95 tff(3527,plain,((~hskp25) | hskp7 | (~c0_1(a1435)) | c3_1(a1435) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3528,plain,
% 1.76/1.95 (~hskp25),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3527, 3519, 3151, 3150, 3516])).
% 1.76/1.95 tff(3529,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3530,plain,
% 1.76/1.95 ((hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)) | (~c0_1(a1448))) <=> (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3531,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)) | (~c0_1(a1448)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3530])).
% 1.76/1.95 tff(3532,plain,
% 1.76/1.95 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)) | (~c0_1(a1448)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3531, 3529])).
% 1.76/1.95 tff(3533,plain,
% 1.76/1.95 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3534,plain,
% 1.76/1.95 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c1_1(a1448))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 1.76/1.95 tff(3535,plain,
% 1.76/1.95 (hskp25 | hskp0 | (~c1_1(a1448))),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3534, 82, 3437, 3436, 3490])).
% 1.76/1.95 tff(3536,plain,
% 1.76/1.95 (~c1_1(a1448)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3535, 3528, 2631])).
% 1.76/1.95 tff(3537,plain,
% 1.76/1.95 (hskp22 | c1_1(a1448)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2415, 82, 3437, 3436, 3434, 1295])).
% 1.76/1.95 tff(3538,plain,
% 1.76/1.95 (hskp22),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3537, 3536])).
% 1.76/1.95 tff(3539,plain,
% 1.76/1.95 (~c0_1(a1468)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[834, 3538])).
% 1.76/1.95 tff(3540,plain,
% 1.76/1.95 (c3_1(a1468)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[842, 3538])).
% 1.76/1.95 tff(3541,plain,
% 1.76/1.95 (c1_1(a1468)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[850, 3538])).
% 1.76/1.95 tff(3542,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3543,plain,
% 1.76/1.95 ((hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468))) <=> (hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3544,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3543])).
% 1.76/1.95 tff(3545,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3544, 3542])).
% 1.76/1.95 tff(3546,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3547,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.76/1.95 tff(3548,plain,
% 1.76/1.95 (hskp17),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3547, 82, 3541, 3540, 3437, 3436, 3539, 3434, 312])).
% 1.76/1.95 tff(3549,plain,
% 1.76/1.95 (~c2_1(a1457)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[264, 3548])).
% 1.76/1.95 tff(3550,plain,
% 1.76/1.95 (~c1_1(a1457)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[245, 3548])).
% 1.76/1.95 tff(3551,plain,
% 1.76/1.95 (~c0_1(a1457)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[251, 3548])).
% 1.76/1.95 tff(3552,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3326, 82, 2631, 3151, 3551, 3550, 3549, 3149, 3150, 1123])).
% 1.76/1.95 tff(3553,plain,(hskp0 | c1_1(a1438) | hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3554,plain,
% 1.76/1.95 (hskp0),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3553, 24, 1216, 12])).
% 1.76/1.95 tff(3555,plain,
% 1.76/1.95 (~c2_1(a1438)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3457, 3212, 544, 46, 24, 12])).
% 1.76/1.95 tff(3556,plain,
% 1.76/1.95 (~c1_1(a1435)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[164, 3213, 3149, 3212, 3150, 99])).
% 1.76/1.95 tff(3557,assumption,(~hskp21), introduced(assumption)).
% 1.76/1.95 tff(3558,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3176, 82, 3557, 102, 2587, 3193, 100, 2586, 2437, 313])).
% 1.76/1.95 tff(3559,plain,((~hskp0) | hskp21 | (~c0_1(a1435)) | c2_1(a1435) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3560,plain,
% 1.76/1.95 (hskp21),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3559, 3556, 3151, 3149, 2585])).
% 1.76/1.95 tff(3561,plain,
% 1.76/1.95 (~c1_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2450, 3560])).
% 1.76/1.95 tff(3562,plain,
% 1.76/1.95 (c2_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2458, 3560])).
% 1.76/1.95 tff(3563,plain,
% 1.76/1.95 (c0_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2466, 3560])).
% 1.76/1.95 tff(3564,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3565,plain,
% 1.76/1.95 (((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438)) <=> (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3566,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3565])).
% 1.76/1.95 tff(3567,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.76/1.95 tff(3568,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3569,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.76/1.95 tff(3570,plain,
% 1.76/1.95 ($false),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3569, 82, 3563, 3562, 3151, 3561, 37, 24, 3150, 23, 3556, 3555])).
% 1.76/1.95 tff(3571,plain,(c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~hskp0) | c1_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.95 tff(3572,plain,
% 1.76/1.95 (c3_1(a1438)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3571, 544, 24, 3554, 37, 12])).
% 1.76/1.95 tff(3573,plain,
% 1.76/1.95 (~c3_1(a1427)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1135, 3554])).
% 1.76/1.95 tff(3574,plain,
% 1.76/1.95 (c2_1(a1427)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1143, 3554])).
% 1.76/1.95 tff(3575,plain,
% 1.76/1.95 (c0_1(a1427)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1151, 3554])).
% 1.76/1.95 tff(3576,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3577,plain,
% 1.76/1.95 ((hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435))) <=> (hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3578,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3577])).
% 1.76/1.95 tff(3579,plain,
% 1.76/1.95 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3578, 3576])).
% 1.76/1.95 tff(3580,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3581,plain,
% 1.76/1.95 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.76/1.95 tff(3582,plain,
% 1.76/1.95 (hskp19 | c1_1(a1435)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3581, 82, 102, 2587, 3193, 100, 2586, 1113])).
% 1.76/1.95 tff(3583,plain,
% 1.76/1.95 (hskp19),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3582, 313])).
% 1.76/1.95 tff(3584,plain,
% 1.76/1.95 (~c1_1(a1460)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1184, 3583])).
% 1.76/1.95 tff(3585,plain,
% 1.76/1.95 (~c0_1(a1460)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[1171, 3583])).
% 1.76/1.95 tff(3586,plain,
% 1.76/1.95 (hskp21),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[3559, 313, 102, 100, 2585])).
% 1.76/1.95 tff(3587,plain,
% 1.76/1.95 (~c1_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2450, 3586])).
% 1.76/1.95 tff(3588,plain,
% 1.76/1.95 (c2_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2458, 3586])).
% 1.76/1.95 tff(3589,plain,
% 1.76/1.95 (c0_1(a1466)),
% 1.76/1.95 inference(unit_resolution,[status(thm)],[2466, 3586])).
% 1.76/1.95 tff(3590,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3591,plain,
% 1.76/1.95 (((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460)) <=> (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(rewrite,[status(thm)],[])).
% 1.76/1.95 tff(3592,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.76/1.95 inference(monotonicity,[status(thm)],[3591])).
% 1.76/1.95 tff(3593,plain,
% 1.76/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.76/1.95 inference(transitivity,[status(thm)],[3592, 3590])).
% 1.76/1.95 tff(3594,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))),
% 1.76/1.95 inference(quant_inst,[status(thm)],[])).
% 1.76/1.95 tff(3595,plain,
% 1.76/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1460) | c1_1(a1460) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.76/1.95 inference(modus_ponens,[status(thm)],[3594, 3593])).
% 1.76/1.96 tff(3596,plain,
% 1.76/1.96 (c2_1(a1460)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3595, 82, 3589, 3588, 102, 3587, 3585, 3584, 101, 23, 313])).
% 1.76/1.96 tff(3597,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3598,plain,
% 1.76/1.96 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435)) <=> (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3599,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3598])).
% 1.76/1.96 tff(3600,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3599, 3597])).
% 1.76/1.96 tff(3601,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3602,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 1.76/1.96 tff(3603,plain,
% 1.76/1.96 (c3_1(a1466)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3602, 82, 3588, 1215, 3587, 37, 24, 100, 101, 578, 313])).
% 1.76/1.96 tff(3604,plain,
% 1.76/1.96 (c2_1(a1438)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3569, 82, 3589, 3588, 102, 3587, 37, 24, 101, 23, 313])).
% 1.76/1.96 tff(3605,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3606,plain,
% 1.76/1.96 (((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460))) <=> (c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3607,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3606])).
% 1.76/1.96 tff(3608,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3607, 3605])).
% 1.76/1.96 tff(3609,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3610,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3609, 3608])).
% 1.76/1.96 tff(3611,plain,
% 1.76/1.96 ($false),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3610, 82, 3589, 3588, 1215, 3585, 3584, 24, 1214, 3604, 3603, 3596])).
% 1.76/1.96 tff(3612,plain,(c1_1(a1435) | (~c3_1(a1438)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1435)) | (~hskp0)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.96 tff(3613,plain,
% 1.76/1.96 (c1_1(a1435)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3612, 3572, 24, 37, 3149, 3150, 3151, 3554])).
% 1.76/1.96 tff(3614,plain,
% 1.76/1.96 (hskp18 | (~c1_1(a1435))),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[370, 82, 3151, 3149, 3150, 356])).
% 1.76/1.96 tff(3615,plain,
% 1.76/1.96 (hskp18),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3614, 127])).
% 1.76/1.96 tff(3616,plain,
% 1.76/1.96 (~c2_1(a1458)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[376, 3615])).
% 1.76/1.96 tff(3617,plain,
% 1.76/1.96 (c1_1(a1458)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[384, 3615])).
% 1.76/1.96 tff(3618,plain,
% 1.76/1.96 (c0_1(a1458)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[392, 3615])).
% 1.76/1.96 tff(3619,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3620,plain,
% 1.76/1.96 ((hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438))) <=> (hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3621,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3620])).
% 1.76/1.96 tff(3622,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3621, 3619])).
% 1.76/1.96 tff(3623,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3624,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a1458) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1458)) | (~c1_1(a1458))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 1.76/1.96 tff(3625,plain,
% 1.76/1.96 (hskp10),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3624, 82, 3618, 3617, 1215, 3616, 37, 345, 47])).
% 1.76/1.96 tff(3626,plain,
% 1.76/1.96 (~c3_1(a1445)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[406, 3625])).
% 1.76/1.96 tff(3627,plain,
% 1.76/1.96 (~c1_1(a1445)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[412, 3625])).
% 1.76/1.96 tff(3628,plain,
% 1.76/1.96 (c0_1(a1445)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[420, 3625])).
% 1.76/1.96 tff(3629,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3630,plain,
% 1.76/1.96 (((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438)) <=> (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3631,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3630])).
% 1.76/1.96 tff(3632,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3631, 3629])).
% 1.76/1.96 tff(3633,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1445) | (~c2_1(a1445)) | (~c0_1(a1445)) | c3_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c1_1(a1438) | c0_1(a1438) | c2_1(a1438))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3634,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c2_1(a1445)) | (~c0_1(a1445))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 1.76/1.96 tff(3635,plain,
% 1.76/1.96 (~c2_1(a1445)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3634, 82, 3628, 3627, 3626, 37, 24, 23, 47])).
% 1.76/1.96 tff(3636,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3637,plain,
% 1.76/1.96 ((hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445))) <=> (hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3638,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3637])).
% 1.76/1.96 tff(3639,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3638, 3636])).
% 1.76/1.96 tff(3640,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3641,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1445) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1445) | (~c0_1(a1445))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 1.76/1.96 tff(3642,plain,
% 1.76/1.96 (hskp21),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3641, 82, 3628, 2398, 2397, 3627, 2396, 2437, 3635])).
% 1.76/1.96 tff(3643,plain,
% 1.76/1.96 (c2_1(a1466)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[2458, 3642])).
% 1.76/1.96 tff(3644,plain,
% 1.76/1.96 (c0_1(a1466)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[2466, 3642])).
% 1.76/1.96 tff(3645,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3646,plain,
% 1.76/1.96 (((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3647,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3646])).
% 1.76/1.96 tff(3648,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3647, 3645])).
% 1.76/1.96 tff(3649,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3650,plain,
% 1.76/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3649, 3648])).
% 1.76/1.96 tff(3651,plain,
% 1.76/1.96 (~c3_1(a1466)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3650, 82, 3644, 3643, 1215, 3151, 24, 3150, 2491, 127, 47])).
% 1.76/1.96 tff(3652,plain,
% 1.76/1.96 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.76/1.96 inference(bind,[status(th)],[])).
% 1.76/1.96 tff(3653,plain,
% 1.76/1.96 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(quant_intro,[status(thm)],[3652])).
% 1.76/1.96 tff(3654,plain,
% 1.76/1.96 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3655,plain,
% 1.76/1.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | 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))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_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))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.76/1.96 inference(bind,[status(th)],[])).
% 1.76/1.96 tff(3656,plain,
% 1.76/1.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(quant_intro,[status(thm)],[3655])).
% 1.76/1.96 tff(3657,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.76/1.96 tff(3658,plain,
% 1.76/1.96 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3657, 3656])).
% 1.76/1.96 tff(3659,plain,
% 1.76/1.96 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3658, 3654])).
% 1.76/1.96 tff(3660,plain,(
% 1.76/1.96 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(skolemize,[status(sab)],[3659])).
% 1.76/1.96 tff(3661,plain,
% 1.76/1.96 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3660, 3653])).
% 1.76/1.96 tff(3662,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3663,plain,
% 1.76/1.96 ((hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3664,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3663])).
% 1.76/1.96 tff(3665,plain,
% 1.76/1.96 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.96 inference(transitivity,[status(thm)],[3664, 3662])).
% 1.76/1.96 tff(3666,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.96 inference(quant_inst,[status(thm)],[])).
% 1.76/1.96 tff(3667,plain,
% 1.76/1.96 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.76/1.96 inference(modus_ponens,[status(thm)],[3666, 3665])).
% 1.76/1.96 tff(3668,plain,
% 1.76/1.96 (hskp22),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[3667, 82, 3437, 3436, 1215, 3434, 24, 1295, 47])).
% 1.76/1.96 tff(3669,plain,
% 1.76/1.96 (~c0_1(a1468)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[834, 3668])).
% 1.76/1.96 tff(3670,plain,
% 1.76/1.96 (c3_1(a1468)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[842, 3668])).
% 1.76/1.96 tff(3671,plain,
% 1.76/1.96 (c1_1(a1468)),
% 1.76/1.96 inference(unit_resolution,[status(thm)],[850, 3668])).
% 1.76/1.96 tff(3672,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3673,plain,
% 1.76/1.96 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1430) | c0_1(a1430) | (~c2_1(a1430))) <=> (c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.96 inference(rewrite,[status(thm)],[])).
% 1.76/1.96 tff(3674,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.76/1.96 inference(monotonicity,[status(thm)],[3673])).
% 1.76/1.96 tff(3675,plain,
% 1.76/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3674, 3672])).
% 1.76/1.97 tff(3676,plain,
% 1.76/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3677,plain,
% 1.76/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 1.76/1.97 tff(3678,plain,
% 1.76/1.97 (~c2_1(a1430)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3677, 82, 3671, 3670, 3437, 3436, 3669, 3434, 12, 1284, 544])).
% 1.76/1.97 tff(3679,plain,
% 1.76/1.97 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.76/1.97 inference(bind,[status(th)],[])).
% 1.76/1.97 tff(3680,plain,
% 1.76/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(quant_intro,[status(thm)],[3679])).
% 1.76/1.97 tff(3681,plain,
% 1.76/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3682,plain,
% 1.76/1.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~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)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.76/1.97 inference(bind,[status(th)],[])).
% 1.76/1.97 tff(3683,plain,
% 1.76/1.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(quant_intro,[status(thm)],[3682])).
% 1.76/1.97 tff(3684,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.76/1.97 tff(3685,plain,
% 1.76/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 1.76/1.97 tff(3686,plain,
% 1.76/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3685, 3681])).
% 1.76/1.97 tff(3687,plain,(
% 1.76/1.97 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(skolemize,[status(sab)],[3686])).
% 1.76/1.97 tff(3688,plain,
% 1.76/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3687, 3680])).
% 1.76/1.97 tff(3689,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3690,plain,
% 1.76/1.97 ((hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468))) <=> (hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3691,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3690])).
% 1.76/1.97 tff(3692,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3691, 3689])).
% 1.76/1.97 tff(3693,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3694,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c0_1(a1468) | c2_1(a1458) | (~ndr1_0) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 1.76/1.97 tff(3695,plain,
% 1.76/1.97 (hskp28),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3694, 82, 3671, 3670, 3618, 3617, 3669, 3616, 3688])).
% 1.76/1.97 tff(3696,plain,
% 1.76/1.97 (((~hskp28) | c3_1(a1456)) <=> ((~hskp28) | c3_1(a1456))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3697,axiom,((~hskp28) | c3_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.76/1.97 tff(3698,plain,
% 1.76/1.97 ((~hskp28) | c3_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.76/1.97 tff(3699,plain,
% 1.76/1.97 ((~hskp28) | c3_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3698, 3696])).
% 1.76/1.97 tff(3700,plain,
% 1.76/1.97 ((~hskp28) | c3_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3699, 3696])).
% 1.76/1.97 tff(3701,plain,
% 1.76/1.97 ((~hskp28) | c3_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3700, 3696])).
% 1.76/1.97 tff(3702,plain,
% 1.76/1.97 ((~hskp28) | c3_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3701, 3696])).
% 1.76/1.97 tff(3703,plain,
% 1.76/1.97 (c3_1(a1456)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3702, 3695])).
% 1.76/1.97 tff(3704,plain,
% 1.76/1.97 (((~hskp28) | c1_1(a1456)) <=> ((~hskp28) | c1_1(a1456))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3705,axiom,((~hskp28) | c1_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.76/1.97 tff(3706,plain,
% 1.76/1.97 ((~hskp28) | c1_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 1.76/1.97 tff(3707,plain,
% 1.76/1.97 ((~hskp28) | c1_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3706, 3704])).
% 1.76/1.97 tff(3708,plain,
% 1.76/1.97 ((~hskp28) | c1_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3707, 3704])).
% 1.76/1.97 tff(3709,plain,
% 1.76/1.97 ((~hskp28) | c1_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3708, 3704])).
% 1.76/1.97 tff(3710,plain,
% 1.76/1.97 ((~hskp28) | c1_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3709, 3704])).
% 1.76/1.97 tff(3711,plain,
% 1.76/1.97 (c1_1(a1456)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3710, 3695])).
% 1.76/1.97 tff(3712,plain,
% 1.76/1.97 (((~hskp28) | c0_1(a1456)) <=> ((~hskp28) | c0_1(a1456))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3713,axiom,((~hskp28) | c0_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.76/1.97 tff(3714,plain,
% 1.76/1.97 ((~hskp28) | c0_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 1.76/1.97 tff(3715,plain,
% 1.76/1.97 ((~hskp28) | c0_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3714, 3712])).
% 1.76/1.97 tff(3716,plain,
% 1.76/1.97 ((~hskp28) | c0_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3715, 3712])).
% 1.76/1.97 tff(3717,plain,
% 1.76/1.97 ((~hskp28) | c0_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3716, 3712])).
% 1.76/1.97 tff(3718,plain,
% 1.76/1.97 ((~hskp28) | c0_1(a1456)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3717, 3712])).
% 1.76/1.97 tff(3719,plain,
% 1.76/1.97 (c0_1(a1456)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3718, 3695])).
% 1.76/1.97 tff(3720,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3721,plain,
% 1.76/1.97 ((hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1430) | c1_1(a1430) | (~c3_1(a1430))) <=> (hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3722,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3721])).
% 1.76/1.97 tff(3723,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3722, 3720])).
% 1.76/1.97 tff(3724,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1430) | c1_1(a1430) | (~c3_1(a1430)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3725,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3724, 3723])).
% 1.76/1.97 tff(3726,plain,
% 1.76/1.97 (hskp6),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3725, 82, 3719, 3711, 3703, 2074, 3678, 3661, 544])).
% 1.76/1.97 tff(3727,plain,
% 1.76/1.97 (~c2_1(a1437)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[2098, 3726])).
% 1.76/1.97 tff(3728,plain,
% 1.76/1.97 (~c1_1(a1437)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[2119, 3726])).
% 1.76/1.97 tff(3729,plain,
% 1.76/1.97 (~c1_1(a1466)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[2450, 3642])).
% 1.76/1.97 tff(3730,plain,
% 1.76/1.97 (c0_1(a1437)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[2106, 3726])).
% 1.76/1.97 tff(3731,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3732,plain,
% 1.76/1.97 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3733,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3732])).
% 1.76/1.97 tff(3734,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3733, 3731])).
% 1.76/1.97 tff(3735,plain,
% 1.76/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3736,plain,
% 1.76/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 1.76/1.97 tff(3737,plain,
% 1.76/1.97 ($false),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3736, 82, 3643, 1215, 3730, 3729, 37, 3728, 3727, 543, 47, 3651])).
% 1.76/1.97 tff(3738,plain,(c2_1(a1438) | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | (~c1_1(a1435)) | c1_1(a1430) | (~c0_1(a1427)) | (~c2_1(a1427)) | c3_1(a1427) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.76/1.97 tff(3739,plain,
% 1.76/1.97 (c2_1(a1438)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3738, 3572, 37, 24, 3613, 544, 3575, 3574, 3573, 12])).
% 1.76/1.97 tff(3740,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3741,plain,
% 1.76/1.97 ((hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438))) <=> (hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3742,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3741])).
% 1.76/1.97 tff(3743,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3742, 3740])).
% 1.76/1.97 tff(3744,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3745,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a1438) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 1.76/1.97 tff(3746,plain,
% 1.76/1.97 (hskp23 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3745, 82, 3575, 3574, 24, 3573, 1693])).
% 1.76/1.97 tff(3747,plain,
% 1.76/1.97 (hskp23),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3746, 3739, 3572])).
% 1.76/1.97 tff(3748,plain,
% 1.76/1.97 (c2_1(a1477)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1520, 3747])).
% 1.76/1.97 tff(3749,plain,
% 1.76/1.97 (~c0_1(a1477)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1571, 3747])).
% 1.76/1.97 tff(3750,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3751,plain,
% 1.76/1.97 ((hskp8 | (~ndr1_0) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438))) <=> (hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3752,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3751])).
% 1.76/1.97 tff(3753,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3752, 3750])).
% 1.76/1.97 tff(3754,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3755,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp8 | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 1.76/1.97 tff(3756,plain,
% 1.76/1.97 (hskp8 | (~c1_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3755, 82, 3151, 24, 3150, 1537])).
% 1.76/1.97 tff(3757,plain,
% 1.76/1.97 (hskp8),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3756, 3739, 3572, 3613])).
% 1.76/1.97 tff(3758,plain,
% 1.76/1.97 (~c1_1(a1441)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1549, 3757])).
% 1.76/1.97 tff(3759,plain,
% 1.76/1.97 (c3_1(a1441)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1557, 3757])).
% 1.76/1.97 tff(3760,plain,
% 1.76/1.97 (c0_1(a1441)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1565, 3757])).
% 1.76/1.97 tff(3761,plain,
% 1.76/1.97 (~c1_1(a1477)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1526, 3747])).
% 1.76/1.97 tff(3762,plain,
% 1.76/1.97 (~c2_1(a1441)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1587, 3761, 3760, 3759, 3758, 3749, 3748])).
% 1.76/1.97 tff(3763,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3764,plain,
% 1.76/1.97 ((hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441))) <=> (hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3765,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3764])).
% 1.76/1.97 tff(3766,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3765, 3763])).
% 1.76/1.97 tff(3767,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3768,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 1.76/1.97 tff(3769,plain,
% 1.76/1.97 (hskp19),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3768, 82, 3760, 3575, 3574, 3758, 3573, 1113, 3762])).
% 1.76/1.97 tff(3770,plain,
% 1.76/1.97 (~c1_1(a1460)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1184, 3769])).
% 1.76/1.97 tff(3771,plain,
% 1.76/1.97 (~c0_1(a1460)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1171, 3769])).
% 1.76/1.97 tff(3772,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3773,plain,
% 1.76/1.97 ((hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1441) | c1_1(a1441) | (~c3_1(a1441))) <=> (hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3774,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1441) | c1_1(a1441) | (~c3_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3773])).
% 1.76/1.97 tff(3775,plain,
% 1.76/1.97 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1441) | c1_1(a1441) | (~c3_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.76/1.97 tff(3776,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c2_1(a1441) | c1_1(a1441) | (~c3_1(a1441)))),
% 1.76/1.97 inference(quant_inst,[status(thm)],[])).
% 1.76/1.97 tff(3777,plain,
% 1.76/1.97 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a1448) | c1_1(a1441) | (~ndr1_0) | c2_1(a1441) | (~c3_1(a1441)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.76/1.97 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.76/1.97 tff(3778,plain,
% 1.76/1.97 (hskp22),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3777, 82, 3437, 3436, 3759, 3434, 3758, 1295, 3762])).
% 1.76/1.97 tff(3779,plain,
% 1.76/1.97 (~c0_1(a1468)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[834, 3778])).
% 1.76/1.97 tff(3780,plain,
% 1.76/1.97 (c3_1(a1468)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[842, 3778])).
% 1.76/1.97 tff(3781,plain,
% 1.76/1.97 (c1_1(a1468)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[850, 3778])).
% 1.76/1.97 tff(3782,plain,
% 1.76/1.97 (~c2_1(a1460)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[2426, 82, 3781, 3780, 3437, 3436, 3779, 3771, 3770, 3434, 1284])).
% 1.76/1.97 tff(3783,plain,
% 1.76/1.97 (hskp20),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[3459, 3739, 3572])).
% 1.76/1.97 tff(3784,plain,
% 1.76/1.97 (~c1_1(a1465)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1239, 3783])).
% 1.76/1.97 tff(3785,plain,
% 1.76/1.97 (c3_1(a1465)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1247, 3783])).
% 1.76/1.97 tff(3786,plain,
% 1.76/1.97 (c2_1(a1465)),
% 1.76/1.97 inference(unit_resolution,[status(thm)],[1255, 3783])).
% 1.76/1.97 tff(3787,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3788,plain,
% 1.76/1.97 (((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441))) <=> (c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.76/1.97 inference(rewrite,[status(thm)],[])).
% 1.76/1.97 tff(3789,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465))))),
% 1.76/1.97 inference(monotonicity,[status(thm)],[3788])).
% 1.76/1.97 tff(3790,plain,
% 1.76/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465)))),
% 1.76/1.97 inference(transitivity,[status(thm)],[3789, 3787])).
% 1.76/1.97 tff(3791,plain,
% 1.76/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3792,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1465) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c3_1(a1441)) | (~c2_1(a1465)) | (~c3_1(a1465))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 1.82/1.98 tff(3793,plain,
% 1.82/1.98 (~c1_1(a1427)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3792, 82, 3786, 3785, 3759, 3575, 3574, 3784, 3758, 1598, 3762])).
% 1.82/1.98 tff(3794,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3795,plain,
% 1.82/1.98 ((hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441))) <=> (hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3796,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3795])).
% 1.82/1.98 tff(3797,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3796, 3794])).
% 1.82/1.98 tff(3798,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | c1_1(a1441) | (~c0_1(a1441)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3799,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3798, 3797])).
% 1.82/1.98 tff(3800,plain,
% 1.82/1.98 (hskp21),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3799, 82, 3760, 3575, 3574, 3758, 3573, 2437, 3762])).
% 1.82/1.98 tff(3801,plain,
% 1.82/1.98 (~c1_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2450, 3800])).
% 1.82/1.98 tff(3802,plain,
% 1.82/1.98 (c2_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2458, 3800])).
% 1.82/1.98 tff(3803,plain,
% 1.82/1.98 (c0_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2466, 3800])).
% 1.82/1.98 tff(3804,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2473, 82, 3803, 3802, 3575, 3801, 3771, 3770, 3573, 23, 3793, 3782])).
% 1.82/1.98 tff(3805,plain,(c1_1(a1430) | c1_1(a1438) | hskp11 | c0_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(3806,plain,
% 1.82/1.98 (c1_1(a1430)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3805, 37, 1216, 24, 12])).
% 1.82/1.98 tff(3807,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3808,plain,
% 1.82/1.98 ((hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3809,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3808])).
% 1.82/1.98 tff(3810,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3809, 3807])).
% 1.82/1.98 tff(3811,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3812,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3811, 3810])).
% 1.82/1.98 tff(3813,plain,
% 1.82/1.98 (hskp17 | (~c1_1(a1430))),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3812, 82, 3437, 3436, 2074, 3434, 12, 312])).
% 1.82/1.98 tff(3814,plain,
% 1.82/1.98 (hskp17),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3813, 3806])).
% 1.82/1.98 tff(3815,plain,
% 1.82/1.98 (~c2_1(a1457)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[264, 3814])).
% 1.82/1.98 tff(3816,plain,
% 1.82/1.98 (~c1_1(a1457)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[245, 3814])).
% 1.82/1.98 tff(3817,plain,
% 1.82/1.98 (~c0_1(a1457)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[251, 3814])).
% 1.82/1.98 tff(3818,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3819,plain,
% 1.82/1.98 (((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3820,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3819])).
% 1.82/1.98 tff(3821,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3820, 3818])).
% 1.82/1.98 tff(3822,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3823,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3822, 3821])).
% 1.82/1.98 tff(3824,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3823, 82, 3589, 3588, 102, 3587, 2516, 2515, 2514, 101, 23, 313])).
% 1.82/1.98 tff(3825,plain,(c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | c2_1(a1435) | (~hskp0)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(3826,plain,
% 1.82/1.98 (c1_1(a1435)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3825, 3817, 3151, 3816, 3815, 3150, 3149, 3554])).
% 1.82/1.98 tff(3827,plain,
% 1.82/1.98 (hskp7 | hskp4),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[118, 82, 102, 100, 101, 112])).
% 1.82/1.98 tff(3828,plain,
% 1.82/1.98 (hskp4),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3827, 13])).
% 1.82/1.98 tff(3829,plain,
% 1.82/1.98 (~c2_1(a1434)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[125, 3828])).
% 1.82/1.98 tff(3830,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[164, 3829, 3828, 100, 127, 101, 13])).
% 1.82/1.98 tff(3831,plain,(hskp7 | c2_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | (~c0_1(a1435))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(3832,plain,
% 1.82/1.98 (hskp7),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3831, 3826, 3149, 3150, 3151])).
% 1.82/1.98 tff(3833,plain,
% 1.82/1.98 (c3_1(a1438)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[98, 3832])).
% 1.82/1.98 tff(3834,plain,
% 1.82/1.98 (~c2_1(a1438)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3444, 3806, 37])).
% 1.82/1.98 tff(3835,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3836,plain,
% 1.82/1.98 ((hskp10 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438))) <=> (hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3837,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3836])).
% 1.82/1.98 tff(3838,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3837, 3835])).
% 1.82/1.98 tff(3839,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | c0_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3840,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1438) | c2_1(a1435) | (~ndr1_0) | (~c1_1(a1435)) | (~c0_1(a1435)) | c2_1(a1438) | (~c3_1(a1438))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.82/1.98 tff(3841,plain,
% 1.82/1.98 (hskp10 | (~c1_1(a1435)) | (~c3_1(a1438))),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3840, 82, 3151, 37, 3149, 345, 3834])).
% 1.82/1.98 tff(3842,plain,
% 1.82/1.98 (hskp10),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3841, 3833, 3826])).
% 1.82/1.98 tff(3843,plain,
% 1.82/1.98 (~c3_1(a1445)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[406, 3842])).
% 1.82/1.98 tff(3844,plain,
% 1.82/1.98 (~c1_1(a1445)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[412, 3842])).
% 1.82/1.98 tff(3845,plain,
% 1.82/1.98 (c0_1(a1445)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[420, 3842])).
% 1.82/1.98 tff(3846,plain,
% 1.82/1.98 (~c2_1(a1445)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[427, 82, 3845, 3817, 3816, 3815, 3844, 3843, 23])).
% 1.82/1.98 tff(3847,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3848,plain,
% 1.82/1.98 ((hskp28 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3849,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3848])).
% 1.82/1.98 tff(3850,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3849, 3847])).
% 1.82/1.98 tff(3851,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1435) | (~c1_1(a1435)) | (~c0_1(a1435)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3852,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1435) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c1_1(a1435)) | (~c0_1(a1435))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3851, 3850])).
% 1.82/1.98 tff(3853,plain,
% 1.82/1.98 (hskp28 | (~c1_1(a1430)) | (~c1_1(a1435))),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3852, 82, 3151, 2074, 3149, 12, 3688])).
% 1.82/1.98 tff(3854,plain,
% 1.82/1.98 (hskp28),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3853, 3826, 3806])).
% 1.82/1.98 tff(3855,plain,
% 1.82/1.98 (c3_1(a1456)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3702, 3854])).
% 1.82/1.98 tff(3856,plain,
% 1.82/1.98 (c1_1(a1456)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3710, 3854])).
% 1.82/1.98 tff(3857,plain,
% 1.82/1.98 (c0_1(a1456)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3718, 3854])).
% 1.82/1.98 tff(3858,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3859,plain,
% 1.82/1.98 ((hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3860,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3859])).
% 1.82/1.98 tff(3861,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3860, 3858])).
% 1.82/1.98 tff(3862,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3863,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 1.82/1.98 tff(3864,plain,
% 1.82/1.98 (hskp6 | (~c3_1(a1438))),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3863, 82, 3857, 3856, 3855, 24, 3661, 3834])).
% 1.82/1.98 tff(3865,plain,
% 1.82/1.98 (hskp6),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3864, 3833])).
% 1.82/1.98 tff(3866,plain,
% 1.82/1.98 (~c2_1(a1437)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2098, 3865])).
% 1.82/1.98 tff(3867,plain,
% 1.82/1.98 (~c1_1(a1437)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2119, 3865])).
% 1.82/1.98 tff(3868,plain,
% 1.82/1.98 (c0_1(a1437)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2106, 3865])).
% 1.82/1.98 tff(3869,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3870,plain,
% 1.82/1.98 ((hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437))) <=> (hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3871,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3870])).
% 1.82/1.98 tff(3872,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3871, 3869])).
% 1.82/1.98 tff(3873,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3874,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1437) | c2_1(a1437) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | (~c0_1(a1437))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 1.82/1.98 tff(3875,plain,
% 1.82/1.98 (hskp21),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3874, 82, 3868, 3575, 3574, 3867, 3866, 3573, 2437])).
% 1.82/1.98 tff(3876,plain,
% 1.82/1.98 (~c1_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2450, 3875])).
% 1.82/1.98 tff(3877,plain,
% 1.82/1.98 (c2_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2458, 3875])).
% 1.82/1.98 tff(3878,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3879,plain,
% 1.82/1.98 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(3880,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[3879])).
% 1.82/1.98 tff(3881,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.98 inference(transitivity,[status(thm)],[3880, 3878])).
% 1.82/1.98 tff(3882,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1445) | c1_1(a1445) | (~c0_1(a1445)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(3883,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 1.82/1.98 tff(3884,plain,
% 1.82/1.98 (c3_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3883, 82, 3877, 3845, 3833, 3876, 3844, 37, 543, 3834, 3846])).
% 1.82/1.98 tff(3885,plain,
% 1.82/1.98 (c0_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2466, 3875])).
% 1.82/1.98 tff(3886,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3650, 82, 3885, 3877, 3833, 3151, 24, 3150, 2491, 3826, 3834, 3884])).
% 1.82/1.98 tff(3887,plain,(c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(3888,plain,
% 1.82/1.98 (c0_1(a1438)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3887, 24, 12, 1216])).
% 1.82/1.98 tff(3889,plain,
% 1.82/1.98 (~hskp7),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[1021, 3888])).
% 1.82/1.98 tff(3890,plain,
% 1.82/1.98 (~c1_1(a1435)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3831, 3889, 3149, 3150, 3151])).
% 1.82/1.98 tff(3891,plain,
% 1.82/1.98 (hskp19 | c1_1(a1435)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3581, 82, 3151, 3575, 3574, 3149, 3573, 1113])).
% 1.82/1.98 tff(3892,plain,
% 1.82/1.98 (hskp19),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3891, 3890])).
% 1.82/1.98 tff(3893,plain,
% 1.82/1.98 (~c1_1(a1460)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[1184, 3892])).
% 1.82/1.98 tff(3894,plain,
% 1.82/1.98 (~c0_1(a1460)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[1171, 3892])).
% 1.82/1.98 tff(3895,plain,
% 1.82/1.98 (hskp21),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3559, 3890, 3151, 3149, 3554])).
% 1.82/1.98 tff(3896,plain,
% 1.82/1.98 (~c1_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2450, 3895])).
% 1.82/1.98 tff(3897,plain,
% 1.82/1.98 (c2_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2458, 3895])).
% 1.82/1.98 tff(3898,plain,
% 1.82/1.98 (c0_1(a1466)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[2466, 3895])).
% 1.82/1.98 tff(3899,plain,
% 1.82/1.98 (c2_1(a1460)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3595, 82, 3898, 3897, 3151, 3896, 3894, 3893, 3150, 23, 3890])).
% 1.82/1.98 tff(3900,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3901,plain,
% 1.82/1.99 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460))) <=> (c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3902,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3901])).
% 1.82/1.99 tff(3903,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3902, 3900])).
% 1.82/1.99 tff(3904,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3905,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c2_1(a1460))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 1.82/1.99 tff(3906,plain,
% 1.82/1.99 (~c1_1(a1430)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3905, 82, 3437, 3436, 2074, 3894, 3893, 3434, 12, 1284, 3899])).
% 1.82/1.99 tff(3907,plain,
% 1.82/1.99 (~c3_1(a1460)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1165, 3892])).
% 1.82/1.99 tff(3908,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3909,plain,
% 1.82/1.99 (((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435)) <=> (c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3910,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3909])).
% 1.82/1.99 tff(3911,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3910, 3908])).
% 1.82/1.99 tff(3912,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1460) | c3_1(a1460) | (~c2_1(a1460)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3913,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3912, 3911])).
% 1.82/1.99 tff(3914,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3913, 82, 2074, 3893, 3907, 3149, 3150, 12, 578, 3906, 3890, 3899])).
% 1.82/1.99 tff(3915,plain,(c1_1(a1438) | c0_1(a1430) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(3916,plain,
% 1.82/1.99 (c1_1(a1438)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3915, 1216, 12])).
% 1.82/1.99 tff(3917,plain,
% 1.82/1.99 (~hskp7),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1424, 3916])).
% 1.82/1.99 tff(3918,plain,
% 1.82/1.99 (~c1_1(a1435)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3831, 3917, 3149, 3150, 3151])).
% 1.82/1.99 tff(3919,plain,
% 1.82/1.99 (~hskp25),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3527, 3918, 3151, 3150, 3917])).
% 1.82/1.99 tff(3920,plain,
% 1.82/1.99 (hskp4),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3211, 3917])).
% 1.82/1.99 tff(3921,plain,
% 1.82/1.99 (c3_1(a1434)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[143, 3920])).
% 1.82/1.99 tff(3922,plain,
% 1.82/1.99 (c1_1(a1434)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[135, 3920])).
% 1.82/1.99 tff(3923,assumption,(~hskp25), introduced(assumption)).
% 1.82/1.99 tff(3924,plain,
% 1.82/1.99 (hskp0 | (~c0_1(a1434))),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3496, 82, 3923, 3469, 3468, 3490])).
% 1.82/1.99 tff(3925,plain,
% 1.82/1.99 (~c0_1(a1434)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3924, 2631])).
% 1.82/1.99 tff(3926,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3927,plain,
% 1.82/1.99 ((hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434))) <=> (hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3928,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3927])).
% 1.82/1.99 tff(3929,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3928, 3926])).
% 1.82/1.99 tff(3930,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3931,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 1.82/1.99 tff(3932,plain,
% 1.82/1.99 (hskp17),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3931, 82, 3471, 3470, 3469, 3468, 230, 312, 3925])).
% 1.82/1.99 tff(3933,plain,
% 1.82/1.99 (~c2_1(a1457)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[264, 3932])).
% 1.82/1.99 tff(3934,plain,
% 1.82/1.99 (~c1_1(a1457)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[245, 3932])).
% 1.82/1.99 tff(3935,plain,
% 1.82/1.99 (~c0_1(a1457)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[251, 3932])).
% 1.82/1.99 tff(3936,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3326, 82, 2631, 102, 3935, 3934, 3933, 100, 101, 1123])).
% 1.82/1.99 tff(3937,plain,(hskp0 | (~c0_1(a1435)) | c2_1(a1435) | c3_1(a1435) | (~c0_1(a1448)) | (~c3_1(a1448)) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1448) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(3938,plain,
% 1.82/1.99 (hskp0),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3937, 3922, 3149, 3150, 3437, 3436, 3151, 3921, 3434, 3919])).
% 1.82/1.99 tff(3939,plain,
% 1.82/1.99 (hskp21),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3559, 3938, 3151, 3149, 3918])).
% 1.82/1.99 tff(3940,plain,
% 1.82/1.99 (c2_1(a1466)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[2458, 3939])).
% 1.82/1.99 tff(3941,plain,
% 1.82/1.99 (c0_1(a1466)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[2466, 3939])).
% 1.82/1.99 tff(3942,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3943,plain,
% 1.82/1.99 ((hskp11 | (~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435))) <=> (hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3944,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3943])).
% 1.82/1.99 tff(3945,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3944, 3942])).
% 1.82/1.99 tff(3946,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3947,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 1.82/1.99 tff(3948,plain,
% 1.82/1.99 (~c3_1(a1466)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3947, 82, 1216, 3941, 3940, 3151, 3149, 3150, 2933])).
% 1.82/1.99 tff(3949,plain,
% 1.82/1.99 (~c1_1(a1466)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[2450, 3939])).
% 1.82/1.99 tff(3950,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3951,plain,
% 1.82/1.99 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435)) <=> (c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3952,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3951])).
% 1.82/1.99 tff(3953,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3952, 3950])).
% 1.82/1.99 tff(3954,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c0_1(a1430) | c1_1(a1430) | (~c3_1(a1430)) | c3_1(a1435) | c1_1(a1435) | c2_1(a1435))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3955,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1466) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.82/1.99 tff(3956,plain,
% 1.82/1.99 (c1_1(a1430)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3955, 82, 3940, 2074, 3949, 3149, 3150, 12, 578, 3918, 3948])).
% 1.82/1.99 tff(3957,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3958,plain,
% 1.82/1.99 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430))) <=> (c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3959,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3958])).
% 1.82/1.99 tff(3960,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3959, 3957])).
% 1.82/1.99 tff(3961,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3962,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 1.82/1.99 tff(3963,plain,
% 1.82/1.99 (c2_1(a1430)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3962, 82, 3940, 3151, 2074, 3949, 3149, 12, 543, 3918, 3948])).
% 1.82/1.99 tff(3964,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3965,plain,
% 1.82/1.99 ((hskp7 | (~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c0_1(a1466)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430))) <=> (hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3966,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c0_1(a1466)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3965])).
% 1.82/1.99 tff(3967,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c0_1(a1466)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3966, 3964])).
% 1.82/1.99 tff(3968,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c0_1(a1466)) | c0_1(a1430) | (~c1_1(a1430)) | (~c2_1(a1430)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3969,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 1.82/1.99 tff(3970,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3969, 82, 3917, 3941, 3949, 12, 3963, 175, 3956, 3948])).
% 1.82/1.99 tff(3971,plain,(hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(3972,plain,
% 1.82/1.99 (hskp11),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3971, 12])).
% 1.82/1.99 tff(3973,plain,
% 1.82/1.99 (~c3_1(a1447)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[703, 3972])).
% 1.82/1.99 tff(3974,plain,
% 1.82/1.99 (~c2_1(a1447)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[691, 3972])).
% 1.82/1.99 tff(3975,plain,
% 1.82/1.99 (~c0_1(a1447)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[697, 3972])).
% 1.82/1.99 tff(3976,plain,
% 1.82/1.99 (hskp0 | c1_1(a1447)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3158, 82, 102, 705, 707, 100, 101, 1123])).
% 1.82/1.99 tff(3977,plain,
% 1.82/1.99 (c1_1(a1447)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3976, 2631])).
% 1.82/1.99 tff(3978,plain,
% 1.82/1.99 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.82/1.99 inference(bind,[status(th)],[])).
% 1.82/1.99 tff(3979,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(quant_intro,[status(thm)],[3978])).
% 1.82/1.99 tff(3980,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3981,plain,
% 1.82/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.82/1.99 inference(bind,[status(th)],[])).
% 1.82/1.99 tff(3982,plain,
% 1.82/1.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(quant_intro,[status(thm)],[3981])).
% 1.82/1.99 tff(3983,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.82/1.99 tff(3984,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 1.82/1.99 tff(3985,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3984, 3980])).
% 1.82/1.99 tff(3986,plain,(
% 1.82/1.99 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(skolemize,[status(sab)],[3985])).
% 1.82/1.99 tff(3987,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3986, 3979])).
% 1.82/1.99 tff(3988,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3989,plain,
% 1.82/1.99 ((hskp18 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435))) <=> (hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3990,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3989])).
% 1.82/1.99 tff(3991,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[3990, 3988])).
% 1.82/1.99 tff(3992,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1435) | c2_1(a1435) | (~c0_1(a1435)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(3993,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c1_1(a1447))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 1.82/1.99 tff(3994,plain,
% 1.82/1.99 (hskp18 | (~c1_1(a1447))),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3993, 82, 102, 707, 706, 100, 101, 356])).
% 1.82/1.99 tff(3995,plain,
% 1.82/1.99 (hskp18),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3994, 3977])).
% 1.82/1.99 tff(3996,plain,
% 1.82/1.99 (~c2_1(a1458)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[376, 3995])).
% 1.82/1.99 tff(3997,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3998,plain,
% 1.82/1.99 ((hskp0 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(3999,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[3998])).
% 1.82/1.99 tff(4000,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[3999, 3997])).
% 1.82/2.00 tff(4001,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4002,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1448) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c3_1(a1448)) | (~c1_1(a1448))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 1.82/2.00 tff(4003,plain,
% 1.82/2.00 (hskp0 | (~c1_1(a1448))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4002, 82, 3470, 230, 705, 707, 706, 2323])).
% 1.82/2.00 tff(4004,plain,
% 1.82/2.00 (~c1_1(a1448)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4003, 2631])).
% 1.82/2.00 tff(4005,plain,
% 1.82/2.00 (hskp22 | c1_1(a1448)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2415, 82, 3471, 3470, 230, 1295])).
% 1.82/2.00 tff(4006,plain,
% 1.82/2.00 (hskp22),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4005, 4004])).
% 1.82/2.00 tff(4007,plain,
% 1.82/2.00 (~c0_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[834, 4006])).
% 1.82/2.00 tff(4008,plain,
% 1.82/2.00 (c1_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[384, 3995])).
% 1.82/2.00 tff(4009,plain,
% 1.82/2.00 (c0_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[392, 3995])).
% 1.82/2.00 tff(4010,plain,
% 1.82/2.00 (c3_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[842, 4006])).
% 1.82/2.00 tff(4011,plain,
% 1.82/2.00 (c1_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[850, 4006])).
% 1.82/2.00 tff(4012,plain,
% 1.82/2.00 (hskp28),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3694, 82, 4011, 4010, 4009, 4008, 4007, 3996, 3688])).
% 1.82/2.00 tff(4013,plain,
% 1.82/2.00 (c3_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3702, 4012])).
% 1.82/2.00 tff(4014,plain,
% 1.82/2.00 (c1_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3710, 4012])).
% 1.82/2.00 tff(4015,plain,
% 1.82/2.00 (c0_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3718, 4012])).
% 1.82/2.00 tff(4016,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4017,plain,
% 1.82/2.00 ((hskp0 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1447) | c0_1(a1447) | (~c1_1(a1447))) <=> (hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4018,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4017])).
% 1.82/2.00 tff(4019,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4018, 4016])).
% 1.82/2.00 tff(4020,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | c2_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4021,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4020, 4019])).
% 1.82/2.00 tff(4022,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4021, 82, 2631, 4015, 4014, 4013, 705, 707, 3987, 3977])).
% 1.82/2.00 tff(4023,plain,(hskp0 | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1448)) | (~c3_1(a1448)) | c2_1(a1448) | (~c0_1(a1435)) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(4024,plain,
% 1.82/2.00 (hskp0),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4023, 3975, 3974, 3437, 3436, 3434, 3151, 3973, 3149, 3150])).
% 1.82/2.00 tff(4025,plain,
% 1.82/2.00 (~c3_1(a1427)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1135, 4024])).
% 1.82/2.00 tff(4026,plain,
% 1.82/2.00 (c0_1(a1427)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1151, 4024])).
% 1.82/2.00 tff(4027,plain,
% 1.82/2.00 (c2_1(a1427)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1143, 4024])).
% 1.82/2.00 tff(4028,plain,
% 1.82/2.00 (c1_1(a1447)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3189, 4027, 3151, 3150, 3975, 3973, 3974, 4026, 4025, 3149])).
% 1.82/2.00 tff(4029,plain,
% 1.82/2.00 (hskp18 | (~c1_1(a1447))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3993, 82, 3151, 3974, 3973, 3149, 3150, 356])).
% 1.82/2.00 tff(4030,plain,
% 1.82/2.00 (hskp18),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4029, 4028])).
% 1.82/2.00 tff(4031,plain,
% 1.82/2.00 (~c2_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[376, 4030])).
% 1.82/2.00 tff(4032,plain,
% 1.82/2.00 (c1_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[384, 4030])).
% 1.82/2.00 tff(4033,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4034,plain,
% 1.82/2.00 ((hskp7 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447))) <=> (hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4035,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4034])).
% 1.82/2.00 tff(4036,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4035, 4033])).
% 1.82/2.00 tff(4037,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4038,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1458) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1458)) | (~c1_1(a1458))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4037, 4036])).
% 1.82/2.00 tff(4039,plain,
% 1.82/2.00 (hskp7 | (~c3_1(a1458))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4038, 82, 4032, 4031, 3974, 3973, 154, 4028])).
% 1.82/2.00 tff(4040,plain,
% 1.82/2.00 (~c3_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4039, 13])).
% 1.82/2.00 tff(4041,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4042,plain,
% 1.82/2.00 ((hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447))) <=> (hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4043,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4042])).
% 1.82/2.00 tff(4044,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.82/2.00 tff(4045,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1447) | c2_1(a1447) | (~c1_1(a1447)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4046,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1448) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | (~c3_1(a1448)) | (~c1_1(a1448))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.82/2.00 tff(4047,plain,
% 1.82/2.00 (hskp7 | (~c1_1(a1447)) | (~c1_1(a1448))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4046, 82, 3436, 3434, 3974, 3973, 154])).
% 1.82/2.00 tff(4048,plain,
% 1.82/2.00 (~c1_1(a1448)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4047, 13, 4028])).
% 1.82/2.00 tff(4049,plain,
% 1.82/2.00 (c0_1(a1458)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[392, 4030])).
% 1.82/2.00 tff(4050,plain,
% 1.82/2.00 (~c1_1(a1435)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3831, 13, 3149, 3150, 3151])).
% 1.82/2.00 tff(4051,plain,
% 1.82/2.00 (hskp21),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3559, 4050, 3151, 3149, 4024])).
% 1.82/2.00 tff(4052,plain,
% 1.82/2.00 (c2_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2458, 4051])).
% 1.82/2.00 tff(4053,plain,
% 1.82/2.00 (c0_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2466, 4051])).
% 1.82/2.00 tff(4054,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4055,plain,
% 1.82/2.00 (((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448))) <=> (c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4056,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4055])).
% 1.82/2.00 tff(4057,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4056, 4054])).
% 1.82/2.00 tff(4058,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1466)) | (~c3_1(a1466)) | (~c0_1(a1466)) | c3_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c1_1(a1448) | c2_1(a1448) | (~c3_1(a1448)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4059,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | c1_1(a1448) | c3_1(a1458) | (~c0_1(a1458)) | (~c1_1(a1458)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4058, 4057])).
% 1.82/2.00 tff(4060,plain,
% 1.82/2.00 (~c3_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4059, 82, 4053, 4052, 4049, 4032, 3436, 3434, 2491, 4048, 4040])).
% 1.82/2.00 tff(4061,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4062,plain,
% 1.82/2.00 ((hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447)) <=> (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4063,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435)))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4062])).
% 1.82/2.00 tff(4064,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4063, 4061])).
% 1.82/2.00 tff(4065,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1435) | c1_1(a1435) | c3_1(a1435) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4066,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.82/2.00 tff(4067,plain,
% 1.82/2.00 (hskp2 | c1_1(a1435)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4066, 82, 3975, 3974, 3973, 3149, 3150, 57])).
% 1.82/2.00 tff(4068,plain,
% 1.82/2.00 (hskp2),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4067, 4050])).
% 1.82/2.00 tff(4069,plain,
% 1.82/2.00 (~c2_1(a1430)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2182, 4068])).
% 1.82/2.00 tff(4070,plain,
% 1.82/2.00 (~c1_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2450, 4051])).
% 1.82/2.00 tff(4071,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4072,plain,
% 1.82/2.00 (((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430))) <=> (c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4073,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466)))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4072])).
% 1.82/2.00 tff(4074,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4073, 4071])).
% 1.82/2.00 tff(4075,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1466) | c3_1(a1466) | (~c2_1(a1466)) | c2_1(a1448) | c1_1(a1448) | (~c0_1(a1448)) | c0_1(a1430) | c2_1(a1430) | (~c3_1(a1430)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4076,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4075, 4074])).
% 1.82/2.00 tff(4077,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4076, 82, 4052, 3437, 2074, 4070, 3434, 12, 4069, 543, 4048, 4060])).
% 1.82/2.00 tff(4078,plain,(hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(4079,plain,
% 1.82/2.00 (hskp7),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4078, 12])).
% 1.82/2.00 tff(4080,plain,
% 1.82/2.00 (~c0_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1021, 4079])).
% 1.82/2.00 tff(4081,plain,
% 1.82/2.00 (~c1_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1424, 4079])).
% 1.82/2.00 tff(4082,plain,
% 1.82/2.00 (c3_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3571, 544, 24, 4024, 37, 12])).
% 1.82/2.00 tff(4083,plain,
% 1.82/2.00 (c1_1(a1435)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3612, 4082, 24, 37, 3149, 3150, 3151, 4024])).
% 1.82/2.00 tff(4084,plain,
% 1.82/2.00 (c2_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3738, 4082, 37, 24, 544, 4083, 4026, 4027, 4025, 12])).
% 1.82/2.00 tff(4085,plain,
% 1.82/2.00 (hskp23 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3745, 82, 4026, 4027, 24, 4025, 1693])).
% 1.82/2.00 tff(4086,plain,
% 1.82/2.00 (hskp23),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4085, 4082, 4084])).
% 1.82/2.00 tff(4087,plain,
% 1.82/2.00 (c2_1(a1477)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1520, 4086])).
% 1.82/2.00 tff(4088,plain,
% 1.82/2.00 (~c0_1(a1477)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1571, 4086])).
% 1.82/2.00 tff(4089,plain,
% 1.82/2.00 (hskp8),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3756, 4082, 4083, 4084])).
% 1.82/2.00 tff(4090,plain,
% 1.82/2.00 (~c1_1(a1441)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1549, 4089])).
% 1.82/2.00 tff(4091,plain,
% 1.82/2.00 (c3_1(a1441)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1557, 4089])).
% 1.82/2.00 tff(4092,plain,
% 1.82/2.00 (c0_1(a1441)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1565, 4089])).
% 1.82/2.00 tff(4093,plain,
% 1.82/2.00 (~c1_1(a1477)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1526, 4086])).
% 1.82/2.00 tff(4094,plain,
% 1.82/2.00 (~c2_1(a1441)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1587, 4093, 4092, 4091, 4090, 4088, 4087])).
% 1.82/2.00 tff(4095,plain,
% 1.82/2.00 (hskp19),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3768, 82, 4092, 4026, 4027, 4090, 4025, 1113, 4094])).
% 1.82/2.00 tff(4096,plain,
% 1.82/2.00 (~c1_1(a1460)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1184, 4095])).
% 1.82/2.00 tff(4097,plain,
% 1.82/2.00 (~c0_1(a1460)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1171, 4095])).
% 1.82/2.00 tff(4098,plain,
% 1.82/2.00 (hskp22),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3777, 82, 3437, 3436, 4091, 3434, 4090, 1295, 4094])).
% 1.82/2.00 tff(4099,plain,
% 1.82/2.00 (~c0_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[834, 4098])).
% 1.82/2.00 tff(4100,plain,
% 1.82/2.00 (c3_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[842, 4098])).
% 1.82/2.00 tff(4101,plain,
% 1.82/2.00 (c1_1(a1468)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[850, 4098])).
% 1.82/2.00 tff(4102,plain,
% 1.82/2.00 (~c2_1(a1460)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2426, 82, 4101, 4100, 3437, 3436, 4099, 4097, 4096, 3434, 1284])).
% 1.82/2.00 tff(4103,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4104,plain,
% 1.82/2.00 (((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441))) <=> (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4105,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4104])).
% 1.82/2.00 tff(4106,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4105, 4103])).
% 1.82/2.00 tff(4107,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1438)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4108,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 1.82/2.00 tff(4109,plain,
% 1.82/2.00 (~c1_1(a1427)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4108, 82, 4091, 4082, 4026, 4027, 4090, 24, 1598, 4084, 4094])).
% 1.82/2.00 tff(4110,plain,
% 1.82/2.00 (hskp21),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3799, 82, 4092, 4026, 4027, 4090, 4025, 2437, 4094])).
% 1.82/2.00 tff(4111,plain,
% 1.82/2.00 (~c1_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2450, 4110])).
% 1.82/2.00 tff(4112,plain,
% 1.82/2.00 (c2_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2458, 4110])).
% 1.82/2.00 tff(4113,plain,
% 1.82/2.00 (c0_1(a1466)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2466, 4110])).
% 1.82/2.00 tff(4114,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2473, 82, 4113, 4112, 4026, 4111, 4097, 4096, 4025, 23, 4109, 4102])).
% 1.82/2.00 tff(4115,plain,(c1_1(a1430) | c1_1(a1438) | c0_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(4116,plain,
% 1.82/2.00 (c1_1(a1430)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4115, 37, 24, 12])).
% 1.82/2.00 tff(4117,plain,
% 1.82/2.00 (~c2_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3444, 4116, 37])).
% 1.82/2.00 tff(4118,plain,
% 1.82/2.00 (hskp17),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3813, 4116])).
% 1.82/2.00 tff(4119,plain,
% 1.82/2.00 (~c0_1(a1457)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[251, 4118])).
% 1.82/2.00 tff(4120,plain,
% 1.82/2.00 (~c2_1(a1457)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[264, 4118])).
% 1.82/2.00 tff(4121,plain,
% 1.82/2.00 (~c1_1(a1457)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[245, 4118])).
% 1.82/2.00 tff(4122,plain,
% 1.82/2.00 (c1_1(a1435)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3825, 4121, 3151, 4024, 4120, 3150, 3149, 4119])).
% 1.82/2.00 tff(4123,plain,
% 1.82/2.00 (hskp7),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3831, 4122, 3149, 3150, 3151])).
% 1.82/2.00 tff(4124,plain,
% 1.82/2.00 (c3_1(a1438)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[98, 4123])).
% 1.82/2.00 tff(4125,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4126,plain,
% 1.82/2.00 ((hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430))) <=> (hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4127,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[4126])).
% 1.82/2.00 tff(4128,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[4127, 4125])).
% 1.82/2.00 tff(4129,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1458) | (~c1_1(a1458)) | (~c0_1(a1458)) | c0_1(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(4130,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1458) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c0_1(a1458)) | (~c1_1(a1458))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 1.82/2.00 tff(4131,plain,
% 1.82/2.00 (hskp28 | (~c1_1(a1430))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4130, 82, 4049, 4032, 2074, 4031, 12, 3688])).
% 1.82/2.00 tff(4132,plain,
% 1.82/2.00 (hskp28),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4131, 4116])).
% 1.82/2.00 tff(4133,plain,
% 1.82/2.00 (c3_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3702, 4132])).
% 1.82/2.00 tff(4134,plain,
% 1.82/2.00 (c1_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3710, 4132])).
% 1.82/2.00 tff(4135,plain,
% 1.82/2.00 (c0_1(a1456)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3718, 4132])).
% 1.82/2.00 tff(4136,plain,
% 1.82/2.00 (hskp6),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3863, 82, 4135, 4134, 4133, 4124, 24, 3661, 4117])).
% 1.82/2.00 tff(4137,plain,
% 1.82/2.00 (~c2_1(a1437)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2098, 4136])).
% 1.82/2.00 tff(4138,plain,
% 1.82/2.00 (~c1_1(a1437)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2119, 4136])).
% 1.82/2.00 tff(4139,plain,
% 1.82/2.00 (hskp10),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3624, 82, 4049, 4032, 4124, 4031, 37, 345, 4117])).
% 1.82/2.00 tff(4140,plain,
% 1.82/2.00 (~c3_1(a1445)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[406, 4139])).
% 1.82/2.00 tff(4141,plain,
% 1.82/2.00 (~c1_1(a1445)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[412, 4139])).
% 1.82/2.00 tff(4142,plain,
% 1.82/2.00 (c0_1(a1437)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2106, 4136])).
% 1.82/2.00 tff(4143,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4144,plain,
% 1.82/2.01 (((~ndr1_0) | c1_1(a1445) | c3_1(a1445) | (~c2_1(a1445)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438))) <=> (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4145,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1445) | c3_1(a1445) | (~c2_1(a1445)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4144])).
% 1.82/2.01 tff(4146,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1445) | c3_1(a1445) | (~c2_1(a1445)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4145, 4143])).
% 1.82/2.01 tff(4147,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1445) | c3_1(a1445) | (~c2_1(a1445)) | c2_1(a1437) | c1_1(a1437) | (~c0_1(a1437)) | c0_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4148,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4147, 4146])).
% 1.82/2.01 tff(4149,plain,
% 1.82/2.01 (~c2_1(a1445)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4148, 82, 4124, 4142, 4141, 4140, 37, 4138, 4137, 543, 4117])).
% 1.82/2.01 tff(4150,plain,
% 1.82/2.01 (hskp21),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3874, 82, 4142, 4026, 4027, 4138, 4137, 4025, 2437])).
% 1.82/2.01 tff(4151,plain,
% 1.82/2.01 (~c1_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2450, 4150])).
% 1.82/2.01 tff(4152,plain,
% 1.82/2.01 (c0_1(a1445)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[420, 4139])).
% 1.82/2.01 tff(4153,plain,
% 1.82/2.01 (c2_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2458, 4150])).
% 1.82/2.01 tff(4154,plain,
% 1.82/2.01 (c3_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3883, 82, 4153, 4152, 4124, 4151, 4141, 37, 543, 4117, 4149])).
% 1.82/2.01 tff(4155,plain,
% 1.82/2.01 (c0_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2466, 4150])).
% 1.82/2.01 tff(4156,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3650, 82, 4155, 4153, 4124, 3151, 24, 3150, 2491, 4122, 4117, 4154])).
% 1.82/2.01 tff(4157,plain,(c0_1(a1438) | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4158,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4157, 4081, 4080, 12])).
% 1.82/2.01 tff(4159,plain,(c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4160,plain,
% 1.82/2.01 (((~hskp2) | (~c0_1(a1430))) <=> ((~hskp2) | (~c0_1(a1430)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4161,plain,
% 1.82/2.01 (((~c0_1(a1430)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1430)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4162,axiom,((~c0_1(a1430)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.82/2.01 tff(4163,plain,
% 1.82/2.01 ((~hskp2) | (~c0_1(a1430))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 1.82/2.01 tff(4164,plain,
% 1.82/2.01 ((~hskp2) | (~c0_1(a1430))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4163, 4160])).
% 1.82/2.01 tff(4165,plain,
% 1.82/2.01 (~hskp2),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4164, 4159])).
% 1.82/2.01 tff(4166,plain,
% 1.82/2.01 ((~hskp11) | hskp5),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[741, 4165])).
% 1.82/2.01 tff(4167,plain,
% 1.82/2.01 (~hskp11),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4166, 11])).
% 1.82/2.01 tff(4168,plain,
% 1.82/2.01 (hskp5 | (~c3_1(a1487)) | c2_1(a1487)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[951, 4165])).
% 1.82/2.01 tff(4169,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4168, 906, 914, 11])).
% 1.82/2.01 tff(4170,plain,((~hskp24) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4171,plain,
% 1.82/2.01 (~hskp24),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4170, 11])).
% 1.82/2.01 tff(4172,plain,
% 1.82/2.01 (hskp30),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[80, 4171])).
% 1.82/2.01 tff(4173,plain,
% 1.82/2.01 (c1_1(a1507)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1505, 4172])).
% 1.82/2.01 tff(4174,plain,
% 1.82/2.01 (c2_1(a1507)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1435, 4172])).
% 1.82/2.01 tff(4175,plain,
% 1.82/2.01 (c0_1(a1507)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1443, 4172])).
% 1.82/2.01 tff(4176,plain,
% 1.82/2.01 (^[U: $i] : refl((hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(4177,plain,
% 1.82/2.01 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[4176])).
% 1.82/2.01 tff(4178,plain,
% 1.82/2.01 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4179,plain,
% 1.82/2.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) | hskp9) <=> ((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) | hskp9) <=> (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(4180,plain,
% 1.82/2.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) | hskp9) <=> ![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[4179])).
% 1.82/2.01 tff(4181,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.82/2.01 tff(4182,plain,
% 1.82/2.01 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.82/2.01 tff(4183,plain,
% 1.82/2.01 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4182, 4178])).
% 1.82/2.01 tff(4184,plain,(
% 1.82/2.01 ![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[4183])).
% 1.82/2.01 tff(4185,plain,
% 1.82/2.01 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4184, 4177])).
% 1.82/2.01 tff(4186,plain,
% 1.82/2.01 (((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)))) <=> ((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4187,plain,
% 1.82/2.01 ((hskp21 | hskp9 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507))) <=> (hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4188,plain,
% 1.82/2.01 (((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)))) <=> ((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4187])).
% 1.82/2.01 tff(4189,plain,
% 1.82/2.01 (((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)))) <=> ((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4188, 4186])).
% 1.82/2.01 tff(4190,plain,
% 1.82/2.01 ((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4191,plain,
% 1.82/2.01 ((~![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp9 | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 1.82/2.01 tff(4192,plain,
% 1.82/2.01 (hskp21 | hskp9),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4191, 82, 1454, 1870, 1453, 4185])).
% 1.82/2.01 tff(4193,plain,
% 1.82/2.01 (hskp9),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4192, 3557])).
% 1.82/2.01 tff(4194,plain,
% 1.82/2.01 (~c3_1(a1444)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1053, 4193])).
% 1.82/2.01 tff(4195,plain,
% 1.82/2.01 (~c2_1(a1444)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1059, 4193])).
% 1.82/2.01 tff(4196,plain,
% 1.82/2.01 (~c1_1(a1444)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1065, 4193])).
% 1.82/2.01 tff(4197,plain,
% 1.82/2.01 (c0_1(a1444)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1102, 82, 4165, 4196, 4195, 4194, 57])).
% 1.82/2.01 tff(4198,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4199,plain,
% 1.82/2.01 ((hskp11 | (~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c3_1(a1444) | c2_1(a1444) | (~c0_1(a1444))) <=> (hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4200,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c3_1(a1444) | c2_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4199])).
% 1.82/2.01 tff(4201,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c3_1(a1444) | c2_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4200, 4198])).
% 1.82/2.01 tff(4202,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1507)) | (~c3_1(a1507)) | (~c0_1(a1507)) | c3_1(a1444) | c2_1(a1444) | (~c0_1(a1444)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4203,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | (~c3_1(a1507)) | (~c2_1(a1507)) | (~c0_1(a1444))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 1.82/2.01 tff(4204,plain,
% 1.82/2.01 (~c3_1(a1507)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4203, 82, 1216, 1454, 1453, 4195, 4194, 2933, 4197])).
% 1.82/2.01 tff(4205,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4206,plain,
% 1.82/2.01 ((hskp21 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444))) <=> (hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4207,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4206])).
% 1.82/2.01 tff(4208,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4207, 4205])).
% 1.82/2.01 tff(4209,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1507)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4210,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4209, 4208])).
% 1.82/2.01 tff(4211,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4210, 82, 3557, 1454, 1453, 4196, 4195, 2437, 4204, 4197])).
% 1.82/2.01 tff(4212,plain,(hskp21 | (~c0_1(a1507)) | (~c2_1(a1507)) | hskp11 | (~c1_1(a1507))), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4213,plain,
% 1.82/2.01 (hskp21),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4212, 4175, 4174, 4167, 4173])).
% 1.82/2.01 tff(4214,assumption,(hskp21), introduced(assumption)).
% 1.82/2.01 tff(4215,plain,
% 1.82/2.01 (~c1_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2450, 4214])).
% 1.82/2.01 tff(4216,plain,
% 1.82/2.01 (c2_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2458, 4214])).
% 1.82/2.01 tff(4217,plain,
% 1.82/2.01 (c0_1(a1466)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2466, 4214])).
% 1.82/2.01 tff(4218,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4219,plain,
% 1.82/2.01 ((hskp11 | hskp0 | (~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466))) <=> (hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4220,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4219])).
% 1.82/2.01 tff(4221,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4220, 4218])).
% 1.82/2.01 tff(4222,plain,
% 1.82/2.01 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1466) | (~c2_1(a1466)) | (~c0_1(a1466)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4223,plain,
% 1.82/2.01 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4222, 4221])).
% 1.82/2.01 tff(4224,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4223, 82, 1216, 2631, 4217, 4216, 4215, 1703])).
% 1.82/2.01 tff(4225,plain,((~hskp21) | hskp11 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4226,plain,
% 1.82/2.01 (hskp0),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4225, 4213, 4167])).
% 1.82/2.01 tff(4227,plain,
% 1.82/2.01 (hskp12),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3195, 4226, 4167])).
% 1.82/2.01 tff(4228,plain,
% 1.82/2.01 (~c2_1(a1448)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[202, 4227])).
% 1.82/2.01 tff(4229,plain,
% 1.82/2.01 (hskp17),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[239, 4228, 11, 4227])).
% 1.82/2.01 tff(4230,plain,
% 1.82/2.01 (~c1_1(a1457)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[245, 4229])).
% 1.82/2.01 tff(4231,plain,
% 1.82/2.01 (~c0_1(a1457)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[251, 4229])).
% 1.82/2.01 tff(4232,plain,
% 1.82/2.01 (c3_1(a1448)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[218, 4227])).
% 1.82/2.01 tff(4233,plain,
% 1.82/2.01 (c0_1(a1448)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[210, 4227])).
% 1.82/2.01 tff(4234,plain,
% 1.82/2.01 (~c3_1(a1457)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[258, 82, 11, 4233, 4232, 4231, 4230, 4228, 10])).
% 1.82/2.01 tff(4235,plain,
% 1.82/2.01 (~c2_1(a1457)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[264, 4229])).
% 1.82/2.01 tff(4236,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[949, 82, 4165, 4231, 4230, 4235, 57, 4234])).
% 1.82/2.01 tff(4237,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4238,plain,
% 1.82/2.01 (~c3_1(a1435)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[295, 4237])).
% 1.82/2.01 tff(4239,plain,
% 1.82/2.01 (~hskp5),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[363, 646])).
% 1.82/2.01 tff(4240,plain,
% 1.82/2.01 (c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | hskp5),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[681, 4165])).
% 1.82/2.01 tff(4241,plain,
% 1.82/2.01 (c2_1(a1435)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4240, 646, 4239, 101])).
% 1.82/2.01 tff(4242,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4243,plain,
% 1.82/2.01 ((hskp5 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c2_1(a1435)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438))) <=> (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4244,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c2_1(a1435)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4243])).
% 1.82/2.01 tff(4245,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c2_1(a1435)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4244, 4242])).
% 1.82/2.01 tff(4246,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1435) | c3_1(a1435) | (~c2_1(a1435)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4247,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 1.82/2.01 tff(4248,plain,
% 1.82/2.01 (~c3_1(a1438)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4247, 82, 4239, 37, 24, 4241, 101, 794, 313])).
% 1.82/2.01 tff(4249,plain,
% 1.82/2.01 (c2_1(a1438) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[90, 4165])).
% 1.82/2.01 tff(4250,plain,
% 1.82/2.01 (c2_1(a1438)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4249, 4248, 24, 37])).
% 1.82/2.01 tff(4251,plain,
% 1.82/2.01 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4252,plain,
% 1.82/2.01 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a1435) | c0_1(a1435) | (~c2_1(a1435))) <=> (hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4253,plain,
% 1.82/2.01 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435)))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4252])).
% 1.82/2.01 tff(4254,plain,
% 1.82/2.01 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4253, 4251])).
% 1.82/2.01 tff(4255,plain,
% 1.82/2.01 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4256,plain,
% 1.82/2.01 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a1435) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 1.82/2.01 tff(4257,plain,
% 1.82/2.01 (hskp4 | c1_1(a1435)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4256, 82, 2631, 646, 4241, 2648])).
% 1.82/2.01 tff(4258,plain,
% 1.82/2.01 (hskp4),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4257, 313])).
% 1.82/2.01 tff(4259,plain,
% 1.82/2.01 (~c2_1(a1434)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[125, 4258])).
% 1.82/2.01 tff(4260,plain,
% 1.82/2.01 (c3_1(a1434)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[143, 4258])).
% 1.82/2.01 tff(4261,plain,
% 1.82/2.01 (~hskp11),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4166, 4239])).
% 1.82/2.01 tff(4262,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4263,plain,
% 1.82/2.01 ((hskp11 | hskp5 | (~ndr1_0) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434))) <=> (hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4264,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4263])).
% 1.82/2.01 tff(4265,plain,
% 1.82/2.01 (((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))) <=> ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4264, 4262])).
% 1.82/2.01 tff(4266,plain,
% 1.82/2.01 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp5 | (~ndr1_0) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4267,plain,
% 1.82/2.01 ((~![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp5 | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.82/2.01 tff(4268,plain,
% 1.82/2.01 (c0_1(a1434)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4267, 82, 4261, 4239, 4260, 4259, 34])).
% 1.82/2.01 tff(4269,plain,
% 1.82/2.01 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4270,plain,
% 1.82/2.01 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434))) <=> (hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4271,plain,
% 1.82/2.01 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4270])).
% 1.82/2.01 tff(4272,plain,
% 1.82/2.01 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4271, 4269])).
% 1.82/2.01 tff(4273,plain,
% 1.82/2.01 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4274,plain,
% 1.82/2.01 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 1.82/2.01 tff(4275,plain,
% 1.82/2.01 (hskp17 | (~c0_1(a1434))),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4274, 82, 4239, 4260, 4259, 229])).
% 1.82/2.01 tff(4276,plain,
% 1.82/2.01 (hskp17),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4275, 4268])).
% 1.82/2.01 tff(4277,plain,
% 1.82/2.01 ((~hskp17) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp5),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[808, 4165])).
% 1.82/2.01 tff(4278,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4277, 4276, 4250, 24, 4248, 4239])).
% 1.82/2.01 tff(4279,plain,(c1_1(a1435) | c1_1(a1438) | c0_1(a1438) | c3_1(a1435) | hskp0 | c0_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(4280,plain,
% 1.82/2.01 (c1_1(a1435)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4279, 37, 24, 101, 2631, 646])).
% 1.82/2.01 tff(4281,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4282,plain,
% 1.82/2.01 ((hskp14 | (~ndr1_0) | c0_1(a1435) | (~c2_1(a1435)) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435))) <=> (hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(4283,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1435) | (~c2_1(a1435)) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[4282])).
% 1.82/2.01 tff(4284,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1435) | (~c2_1(a1435)) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[4283, 4281])).
% 1.82/2.01 tff(4285,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1435) | (~c2_1(a1435)) | (~c1_1(a1435)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(4286,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4285, 4284])).
% 1.82/2.02 tff(4287,plain,
% 1.82/2.02 (hskp14 | (~c1_1(a1435))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4286, 82, 646, 4241, 101, 482])).
% 1.82/2.02 tff(4288,plain,
% 1.82/2.02 (hskp14),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4287, 4280])).
% 1.82/2.02 tff(4289,plain,
% 1.82/2.02 (~c3_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2777, 4288, 4239, 24, 37])).
% 1.82/2.02 tff(4290,plain,
% 1.82/2.02 (c2_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4249, 4289, 24, 37])).
% 1.82/2.02 tff(4291,plain,
% 1.82/2.02 (hskp4 | c0_1(a1438) | (~c2_1(a1438))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3205, 82, 2631, 24, 2648])).
% 1.82/2.02 tff(4292,plain,
% 1.82/2.02 (hskp4),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4291, 4290, 37])).
% 1.82/2.02 tff(4293,plain,
% 1.82/2.02 (~c2_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[125, 4292])).
% 1.82/2.02 tff(4294,plain,
% 1.82/2.02 (c3_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[143, 4292])).
% 1.82/2.02 tff(4295,plain,
% 1.82/2.02 (~hskp17),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4277, 4290, 24, 4289, 4239])).
% 1.82/2.02 tff(4296,plain,
% 1.82/2.02 (~c0_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4274, 82, 4295, 4239, 4294, 4293, 229])).
% 1.82/2.02 tff(4297,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4267, 82, 4261, 4239, 4294, 4293, 34, 4296])).
% 1.82/2.02 tff(4298,plain,(c0_1(a1438) | hskp0 | c1_1(a1438) | c0_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(4299,plain,
% 1.82/2.02 (c0_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4298, 24, 2631, 646, 101])).
% 1.82/2.02 tff(4300,plain,
% 1.82/2.02 (hskp5 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1649, 4165])).
% 1.82/2.02 tff(4301,plain,
% 1.82/2.02 (c3_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4300, 4299, 4239, 24])).
% 1.82/2.02 tff(4302,plain,
% 1.82/2.02 ((~c0_1(a1438)) | (~c2_1(a1438))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1709, 82, 4261, 2631, 24, 1703])).
% 1.82/2.02 tff(4303,plain,
% 1.82/2.02 (~c2_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4302, 4299])).
% 1.82/2.02 tff(4304,plain,
% 1.82/2.02 (c2_1(a1438) | hskp5 | (~c3_1(a1438)) | (~c0_1(a1438))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1670, 4165])).
% 1.82/2.02 tff(4305,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4304, 4303, 4301, 4239, 4299])).
% 1.82/2.02 tff(4306,plain,(c1_1(a1438) | hskp0 | c0_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(4307,plain,
% 1.82/2.02 (c1_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4306, 646, 2631, 101])).
% 1.82/2.02 tff(4308,plain,
% 1.82/2.02 (~hskp24),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4170, 4239])).
% 1.82/2.02 tff(4309,plain,
% 1.82/2.02 (c3_1(a1438) | hskp5 | (~c1_1(a1438)) | hskp24),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1996, 4165])).
% 1.82/2.02 tff(4310,plain,
% 1.82/2.02 (c3_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4309, 4308, 4239, 4307])).
% 1.82/2.02 tff(4311,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4312,plain,
% 1.82/2.02 ((hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1435) | c1_1(a1435) | (~c2_1(a1435))) <=> (hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4313,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1435) | c1_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4312])).
% 1.82/2.02 tff(4314,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1435) | c1_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4313, 4311])).
% 1.82/2.02 tff(4315,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1435) | c1_1(a1435) | (~c2_1(a1435)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4316,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1435) | c0_1(a1438) | (~c1_1(a1438)) | (~c2_1(a1435)) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1438))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4315, 4314])).
% 1.82/2.02 tff(4317,plain,
% 1.82/2.02 (c1_1(a1435)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4316, 82, 2631, 4310, 646, 37, 4307, 4241, 2160])).
% 1.82/2.02 tff(4318,plain,
% 1.82/2.02 (hskp30),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[80, 4308])).
% 1.82/2.02 tff(4319,plain,
% 1.82/2.02 (c2_1(a1507)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1435, 4318])).
% 1.82/2.02 tff(4320,plain,
% 1.82/2.02 (c1_1(a1507)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1505, 4318])).
% 1.82/2.02 tff(4321,plain,
% 1.82/2.02 (c0_1(a1507)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1443, 4318])).
% 1.82/2.02 tff(4322,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4323,plain,
% 1.82/2.02 ((hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1435) | (~c1_1(a1435)) | (~c2_1(a1435))) <=> (hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4324,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1435) | (~c1_1(a1435)) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4323])).
% 1.82/2.02 tff(4325,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1435) | (~c1_1(a1435)) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4324, 4322])).
% 1.82/2.02 tff(4326,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1435) | (~c1_1(a1435)) | (~c2_1(a1435)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4327,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c1_1(a1435))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 1.82/2.02 tff(4328,plain,
% 1.82/2.02 (hskp23 | (~c1_1(a1435))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4327, 82, 4321, 4320, 4319, 4241, 101, 1498])).
% 1.82/2.02 tff(4329,plain,
% 1.82/2.02 (hskp23),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4328, 4317])).
% 1.82/2.02 tff(4330,plain,
% 1.82/2.02 (~c1_1(a1477)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1526, 4329])).
% 1.82/2.02 tff(4331,plain,
% 1.82/2.02 (~c0_1(a1477)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1571, 4329])).
% 1.82/2.02 tff(4332,plain,
% 1.82/2.02 (c2_1(a1477)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1520, 4329])).
% 1.82/2.02 tff(4333,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4334,plain,
% 1.82/2.02 ((hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1477) | c1_1(a1477) | (~c2_1(a1477))) <=> (hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4335,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1477) | c1_1(a1477) | (~c2_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4334])).
% 1.82/2.02 tff(4336,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1477) | c1_1(a1477) | (~c2_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4335, 4333])).
% 1.82/2.02 tff(4337,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c0_1(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c0_1(a1477) | c1_1(a1477) | (~c2_1(a1477)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4338,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4337, 4336])).
% 1.82/2.02 tff(4339,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4338, 82, 2631, 4332, 4310, 4331, 4330, 37, 4307, 2160])).
% 1.82/2.02 tff(4340,plain,(c0_1(a1438) | hskp0 | c3_1(a1435) | c0_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(4341,plain,
% 1.82/2.02 (c0_1(a1438)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4340, 646, 101, 2631])).
% 1.82/2.02 tff(4342,plain,
% 1.82/2.02 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4343,plain,
% 1.82/2.02 ((hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438))) <=> (hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4344,plain,
% 1.82/2.02 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4343])).
% 1.82/2.02 tff(4345,plain,
% 1.82/2.02 (((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)))) <=> ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4344, 4342])).
% 1.82/2.02 tff(4346,plain,
% 1.82/2.02 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4347,plain,
% 1.82/2.02 ((~![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp0 | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4346, 4345])).
% 1.82/2.02 tff(4348,plain,
% 1.82/2.02 (hskp25 | (~c0_1(a1438)) | (~c3_1(a1438))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4347, 82, 2631, 4307, 3490])).
% 1.82/2.02 tff(4349,plain,
% 1.82/2.02 (hskp25),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4348, 4341, 4310])).
% 1.82/2.02 tff(4350,plain,
% 1.82/2.02 (~c0_1(a1504)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[454, 4349])).
% 1.82/2.02 tff(4351,plain,
% 1.82/2.02 (c2_1(a1504)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[489, 4349])).
% 1.82/2.02 tff(4352,plain,
% 1.82/2.02 (c1_1(a1504)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[464, 4349])).
% 1.82/2.02 tff(4353,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4354,plain,
% 1.82/2.02 ((hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435))) <=> (hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4355,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4354])).
% 1.82/2.02 tff(4356,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4355, 4353])).
% 1.82/2.02 tff(4357,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1435) | c0_1(a1435) | (~c2_1(a1435)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4358,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | c0_1(a1504) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4357, 4356])).
% 1.82/2.02 tff(4359,plain,
% 1.82/2.02 (hskp14),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4358, 82, 4352, 4351, 646, 4350, 4241, 101, 482])).
% 1.82/2.02 tff(4360,plain,
% 1.82/2.02 (~c1_1(a1451)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[508, 4359])).
% 1.82/2.02 tff(4361,plain,
% 1.82/2.02 (c2_1(a1451)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[516, 4359])).
% 1.82/2.02 tff(4362,plain,
% 1.82/2.02 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4363,plain,
% 1.82/2.02 ((hskp11 | hskp0 | (~ndr1_0) | c1_1(a1451) | (~c2_1(a1451)) | (~c0_1(a1451))) <=> (hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4364,plain,
% 1.82/2.02 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1451) | (~c2_1(a1451)) | (~c0_1(a1451)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4363])).
% 1.82/2.02 tff(4365,plain,
% 1.82/2.02 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1451) | (~c2_1(a1451)) | (~c0_1(a1451)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4364, 4362])).
% 1.82/2.02 tff(4366,plain,
% 1.82/2.02 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c1_1(a1451) | (~c2_1(a1451)) | (~c0_1(a1451)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4367,plain,
% 1.82/2.02 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | (~c0_1(a1451))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 1.82/2.02 tff(4368,plain,
% 1.82/2.02 (~c0_1(a1451)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4367, 82, 4261, 2631, 4361, 4360, 1703])).
% 1.82/2.02 tff(4369,plain,
% 1.82/2.02 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4370,plain,
% 1.82/2.02 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a1451) | c0_1(a1451) | (~c2_1(a1451))) <=> (hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4371,plain,
% 1.82/2.02 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1451) | c0_1(a1451) | (~c2_1(a1451)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451)))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4370])).
% 1.82/2.02 tff(4372,plain,
% 1.82/2.02 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1451) | c0_1(a1451) | (~c2_1(a1451)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4371, 4369])).
% 1.82/2.02 tff(4373,plain,
% 1.82/2.02 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a1451) | c0_1(a1451) | (~c2_1(a1451)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4374,plain,
% 1.82/2.02 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c1_1(a1451) | (~ndr1_0) | (~c2_1(a1451)) | c0_1(a1451)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4373, 4372])).
% 1.82/2.02 tff(4375,plain,
% 1.82/2.02 (hskp4),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4374, 82, 2631, 4361, 4360, 2648, 4368])).
% 1.82/2.02 tff(4376,plain,
% 1.82/2.02 (~c2_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[125, 4375])).
% 1.82/2.02 tff(4377,plain,
% 1.82/2.02 (c3_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[143, 4375])).
% 1.82/2.02 tff(4378,plain,
% 1.82/2.02 (c0_1(a1434)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4267, 82, 4261, 4239, 4377, 4376, 34])).
% 1.82/2.02 tff(4379,plain,
% 1.82/2.02 (hskp17 | (~c0_1(a1434))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4274, 82, 4239, 4377, 4376, 229])).
% 1.82/2.02 tff(4380,plain,
% 1.82/2.02 (hskp17),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4379, 4378])).
% 1.82/2.02 tff(4381,plain,
% 1.82/2.02 (~c1_1(a1457)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[245, 4380])).
% 1.82/2.02 tff(4382,plain,
% 1.82/2.02 (~c0_1(a1457)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[251, 4380])).
% 1.82/2.02 tff(4383,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4384,plain,
% 1.82/2.02 ((hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457))) <=> (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4385,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4384])).
% 1.82/2.02 tff(4386,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4385, 4383])).
% 1.82/2.02 tff(4387,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1457) | c1_1(a1457) | (~c3_1(a1457)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4388,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1457))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4387, 4386])).
% 1.82/2.02 tff(4389,plain,
% 1.82/2.02 (~c3_1(a1457)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4388, 82, 4239, 4377, 4382, 4381, 4376, 10, 4378])).
% 1.82/2.02 tff(4390,plain,
% 1.82/2.02 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(4391,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[4390])).
% 1.82/2.02 tff(4392,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4393,plain,
% 1.82/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(4394,plain,
% 1.82/2.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[4393])).
% 1.82/2.02 tff(4395,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.82/2.02 tff(4396,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4395, 4394])).
% 1.82/2.02 tff(4397,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4396, 4392])).
% 1.82/2.02 tff(4398,plain,(
% 1.82/2.02 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(skolemize,[status(sab)],[4397])).
% 1.82/2.02 tff(4399,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4398, 4391])).
% 1.82/2.02 tff(4400,plain,
% 1.82/2.02 (~c3_1(a1451)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[502, 4359])).
% 1.82/2.02 tff(4401,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4402,plain,
% 1.82/2.02 ((hskp13 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451))) <=> (hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4403,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[4402])).
% 1.82/2.02 tff(4404,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[4403, 4401])).
% 1.82/2.02 tff(4405,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a1438)) | (~c1_1(a1438)) | (~c0_1(a1438)) | c3_1(a1451) | c1_1(a1451) | (~c2_1(a1451)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(4406,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a1451) | c3_1(a1451) | (~c0_1(a1438)) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 1.82/2.02 tff(4407,plain,
% 1.82/2.02 (hskp13),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4406, 82, 4361, 4310, 4360, 4400, 4341, 4307, 4399])).
% 1.82/2.02 tff(4408,plain,
% 1.82/2.02 (((~hskp13) | (~c3_1(a1449))) <=> ((~hskp13) | (~c3_1(a1449)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4409,plain,
% 1.82/2.02 (((~c3_1(a1449)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1449)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4410,axiom,((~c3_1(a1449)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.82/2.02 tff(4411,plain,
% 1.82/2.02 ((~hskp13) | (~c3_1(a1449))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 1.82/2.02 tff(4412,plain,
% 1.82/2.02 ((~hskp13) | (~c3_1(a1449))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[4411, 4408])).
% 1.82/2.02 tff(4413,plain,
% 1.82/2.02 (~c3_1(a1449)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4412, 4407])).
% 1.82/2.02 tff(4414,plain,
% 1.82/2.02 (((~hskp13) | c2_1(a1449)) <=> ((~hskp13) | c2_1(a1449))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(4415,axiom,((~hskp13) | c2_1(a1449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.82/2.03 tff(4416,plain,
% 1.82/2.03 ((~hskp13) | c2_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 1.82/2.03 tff(4417,plain,
% 1.82/2.03 ((~hskp13) | c2_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4416, 4414])).
% 1.82/2.03 tff(4418,plain,
% 1.82/2.03 ((~hskp13) | c2_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4417, 4414])).
% 1.82/2.03 tff(4419,plain,
% 1.82/2.03 ((~hskp13) | c2_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4418, 4414])).
% 1.82/2.03 tff(4420,plain,
% 1.82/2.03 ((~hskp13) | c2_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4419, 4414])).
% 1.82/2.03 tff(4421,plain,
% 1.82/2.03 (c2_1(a1449)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4420, 4407])).
% 1.82/2.03 tff(4422,plain,
% 1.82/2.03 (((~hskp13) | c1_1(a1449)) <=> ((~hskp13) | c1_1(a1449))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4423,axiom,((~hskp13) | c1_1(a1449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.82/2.03 tff(4424,plain,
% 1.82/2.03 ((~hskp13) | c1_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4423, 4422])).
% 1.82/2.03 tff(4425,plain,
% 1.82/2.03 ((~hskp13) | c1_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4424, 4422])).
% 1.82/2.03 tff(4426,plain,
% 1.82/2.03 ((~hskp13) | c1_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4425, 4422])).
% 1.82/2.03 tff(4427,plain,
% 1.82/2.03 ((~hskp13) | c1_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4426, 4422])).
% 1.82/2.03 tff(4428,plain,
% 1.82/2.03 ((~hskp13) | c1_1(a1449)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4427, 4422])).
% 1.82/2.03 tff(4429,plain,
% 1.82/2.03 (c1_1(a1449)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4428, 4407])).
% 1.82/2.03 tff(4430,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4431,plain,
% 1.82/2.03 ((hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1449) | (~c1_1(a1449)) | (~c2_1(a1449))) <=> (hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4432,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1449) | (~c1_1(a1449)) | (~c2_1(a1449)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4431])).
% 1.82/2.03 tff(4433,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1449) | (~c1_1(a1449)) | (~c2_1(a1449)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4432, 4430])).
% 1.82/2.03 tff(4434,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | (~c2_1(a1507)) | (~c1_1(a1507)) | (~c0_1(a1507)) | c3_1(a1449) | (~c1_1(a1449)) | (~c2_1(a1449)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4435,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp23 | c3_1(a1449) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1449)) | (~c1_1(a1449))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4434, 4433])).
% 1.82/2.03 tff(4436,plain,
% 1.82/2.03 (hskp23),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4435, 82, 4321, 4320, 4319, 4429, 4421, 4413, 1498])).
% 1.82/2.03 tff(4437,plain,
% 1.82/2.03 (~c1_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1526, 4436])).
% 1.82/2.03 tff(4438,plain,
% 1.82/2.03 (~c0_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1571, 4436])).
% 1.82/2.03 tff(4439,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4440,plain,
% 1.82/2.03 ((hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477))) <=> (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4441,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4440])).
% 1.82/2.03 tff(4442,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4441, 4439])).
% 1.82/2.03 tff(4443,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c0_1(a1434)) | c0_1(a1477) | c1_1(a1477) | (~c3_1(a1477)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4444,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4443, 4442])).
% 1.82/2.03 tff(4445,plain,
% 1.82/2.03 (~c3_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4444, 82, 4239, 4377, 4438, 4437, 4376, 10, 4378])).
% 1.82/2.03 tff(4446,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4380])).
% 1.82/2.03 tff(4447,plain,
% 1.82/2.03 (hskp1),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[595, 82, 4165, 4382, 4381, 4446, 588])).
% 1.82/2.03 tff(4448,plain,
% 1.82/2.03 (~c0_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[601, 4447])).
% 1.82/2.03 tff(4449,plain,
% 1.82/2.03 (c3_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[609, 4447])).
% 1.82/2.03 tff(4450,plain,
% 1.82/2.03 (c2_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1520, 4436])).
% 1.82/2.03 tff(4451,plain,
% 1.82/2.03 (c1_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1932, 82, 4450, 4449, 4437, 4381, 4446, 4448, 578, 4445, 4389])).
% 1.82/2.03 tff(4452,plain,
% 1.82/2.03 (c2_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[634, 4447])).
% 1.82/2.03 tff(4453,plain,
% 1.82/2.03 (~hskp7),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1424, 4307])).
% 1.82/2.03 tff(4454,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[641, 82, 4453, 4452, 4449, 4381, 4446, 627, 4389, 4451])).
% 1.82/2.03 tff(4455,plain,(c0_1(a1435) | hskp0 | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4456,plain,
% 1.82/2.03 (c0_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4455, 101, 2631])).
% 1.82/2.03 tff(4457,assumption,(c2_1(a1435)), introduced(assumption)).
% 1.82/2.03 tff(4458,plain,
% 1.82/2.03 (~hskp5),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[301, 4457])).
% 1.82/2.03 tff(4459,plain,
% 1.82/2.03 (~hskp11),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4166, 4458])).
% 1.82/2.03 tff(4460,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4461,plain,
% 1.82/2.03 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a1435) | (~c2_1(a1435)) | (~c0_1(a1435))) <=> (hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4462,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1435) | (~c2_1(a1435)) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4461])).
% 1.82/2.03 tff(4463,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1435) | (~c2_1(a1435)) | (~c0_1(a1435)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4462, 4460])).
% 1.82/2.03 tff(4464,plain,
% 1.82/2.03 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a1435) | (~c2_1(a1435)) | (~c0_1(a1435)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4465,plain,
% 1.82/2.03 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4464, 4463])).
% 1.82/2.03 tff(4466,plain,
% 1.82/2.03 (hskp12 | hskp11 | (~c2_1(a1435)) | (~c0_1(a1435))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4465, 82, 101, 1204])).
% 1.82/2.03 tff(4467,plain,
% 1.82/2.03 (hskp12),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4466, 4459, 102, 4457])).
% 1.82/2.03 tff(4468,plain,
% 1.82/2.03 (~c2_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[202, 4467])).
% 1.82/2.03 tff(4469,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[239, 4467, 4458, 4468])).
% 1.82/2.03 tff(4470,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4469])).
% 1.82/2.03 tff(4471,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4469])).
% 1.82/2.03 tff(4472,plain,
% 1.82/2.03 (c3_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[218, 4467])).
% 1.82/2.03 tff(4473,plain,
% 1.82/2.03 (c0_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[210, 4467])).
% 1.82/2.03 tff(4474,plain,
% 1.82/2.03 (~c3_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[258, 82, 4458, 4473, 4472, 4471, 4470, 4468, 10])).
% 1.82/2.03 tff(4475,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4469])).
% 1.82/2.03 tff(4476,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[949, 82, 4165, 4471, 4470, 4475, 57, 4474])).
% 1.82/2.03 tff(4477,plain,((~c2_1(a1435)) | (~c0_1(a1435)) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4478,plain,
% 1.82/2.03 (~c2_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4477, 4456, 101])).
% 1.82/2.03 tff(4479,plain,
% 1.82/2.03 (c2_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3198, 37, 2631, 4456, 24, 100, 101])).
% 1.82/2.03 tff(4480,plain,
% 1.82/2.03 (hskp4),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4291, 37, 4479])).
% 1.82/2.03 tff(4481,plain,
% 1.82/2.03 (~c2_1(a1434)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[125, 4480])).
% 1.82/2.03 tff(4482,plain,
% 1.82/2.03 (~c1_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3831, 99, 100, 101, 4456])).
% 1.82/2.03 tff(4483,plain,
% 1.82/2.03 (~hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3527, 4482, 4456, 101, 99])).
% 1.82/2.03 tff(4484,plain,
% 1.82/2.03 (c3_1(a1434)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[143, 4480])).
% 1.82/2.03 tff(4485,plain,
% 1.82/2.03 (c1_1(a1434)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[135, 4480])).
% 1.82/2.03 tff(4486,plain,
% 1.82/2.03 (hskp25 | (~c0_1(a1434))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3496, 82, 2631, 4485, 4484, 3490])).
% 1.82/2.03 tff(4487,plain,
% 1.82/2.03 (~c0_1(a1434)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4486, 4483])).
% 1.82/2.03 tff(4488,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4489,plain,
% 1.82/2.03 ((hskp9 | (~ndr1_0) | c0_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434))) <=> (hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4490,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4489])).
% 1.82/2.03 tff(4491,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4490, 4488])).
% 1.82/2.03 tff(4492,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1434) | c0_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4493,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a1438) | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 1.82/2.03 tff(4494,plain,
% 1.82/2.03 (hskp9 | c3_1(a1438) | c0_1(a1434)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4493, 82, 4484, 37, 4481, 1040, 4479])).
% 1.82/2.03 tff(4495,plain,
% 1.82/2.03 (hskp9),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4494, 4487, 46])).
% 1.82/2.03 tff(4496,plain,
% 1.82/2.03 (~c3_1(a1444)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1053, 4495])).
% 1.82/2.03 tff(4497,plain,
% 1.82/2.03 (~c2_1(a1444)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1059, 4495])).
% 1.82/2.03 tff(4498,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4499,plain,
% 1.82/2.03 ((hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444)) <=> (hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4500,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444)))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4499])).
% 1.82/2.03 tff(4501,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4500, 4498])).
% 1.82/2.03 tff(4502,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4503,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c2_1(a1444) | c3_1(a1444) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c0_1(a1444)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.82/2.03 tff(4504,plain,
% 1.82/2.03 (c0_1(a1444)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4503, 82, 2631, 4485, 4484, 4497, 4496, 4481, 2323])).
% 1.82/2.03 tff(4505,plain,
% 1.82/2.03 (~c1_1(a1444)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1065, 4495])).
% 1.82/2.03 tff(4506,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4507,plain,
% 1.82/2.03 (((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1434) | c2_1(a1434) | (~c3_1(a1434))) <=> (c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4508,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1434) | c2_1(a1434) | (~c3_1(a1434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4507])).
% 1.82/2.03 tff(4509,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1434) | c2_1(a1434) | (~c3_1(a1434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4508, 4506])).
% 1.82/2.03 tff(4510,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1438) | c3_1(a1438) | (~c2_1(a1438)) | c2_1(a1444) | c1_1(a1444) | (~c0_1(a1444)) | c0_1(a1434) | c2_1(a1434) | (~c3_1(a1434)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4511,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 1.82/2.03 tff(4512,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4511, 82, 46, 4484, 4505, 4497, 24, 4481, 543, 4479, 4487, 4504])).
% 1.82/2.03 tff(4513,plain,(c3_1(a1438) | c1_1(a1438) | hskp0 | c0_1(a1438) | c3_1(a1435) | c2_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4514,plain,
% 1.82/2.03 (c3_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4513, 37, 2631, 24, 101, 100])).
% 1.82/2.03 tff(4515,plain,
% 1.82/2.03 (hskp12 | (~c3_1(a1438))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3246, 82, 4485, 4484, 37, 4481, 1273, 4479])).
% 1.82/2.03 tff(4516,plain,
% 1.82/2.03 (hskp12),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4515, 4514])).
% 1.82/2.03 tff(4517,plain,
% 1.82/2.03 (~c2_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[202, 4516])).
% 1.82/2.03 tff(4518,plain,
% 1.82/2.03 (c0_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[210, 4516])).
% 1.82/2.03 tff(4519,plain,
% 1.82/2.03 (c3_1(a1448)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[218, 4516])).
% 1.82/2.03 tff(4520,plain,
% 1.82/2.03 (hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3937, 4519, 2631, 101, 100, 4484, 4456, 4485, 4517, 4518])).
% 1.82/2.03 tff(4521,plain,
% 1.82/2.03 (~c0_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[454, 4520])).
% 1.82/2.03 tff(4522,plain,
% 1.82/2.03 (c1_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[464, 4520])).
% 1.82/2.03 tff(4523,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4524,plain,
% 1.82/2.03 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4525,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4524])).
% 1.82/2.03 tff(4526,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4525, 4523])).
% 1.82/2.03 tff(4527,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1504) | (~c3_1(a1504)) | (~c1_1(a1504)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4528,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4527, 4526])).
% 1.82/2.03 tff(4529,plain,
% 1.82/2.03 (~c3_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4528, 82, 4522, 4518, 4519, 4521, 4517, 37, 24, 1284, 4479])).
% 1.82/2.03 tff(4530,plain,
% 1.82/2.03 (c2_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[489, 4520])).
% 1.82/2.03 tff(4531,plain,
% 1.82/2.03 (hskp14),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[496, 82, 4522, 4530, 4521, 482, 4529])).
% 1.82/2.03 tff(4532,plain,
% 1.82/2.03 (~c3_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[502, 4531])).
% 1.82/2.03 tff(4533,plain,
% 1.82/2.03 (~c1_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[508, 4531])).
% 1.82/2.03 tff(4534,plain,
% 1.82/2.03 (c2_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[516, 4531])).
% 1.82/2.03 tff(4535,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[523, 82, 4522, 4530, 4534, 4456, 4521, 4533, 4532, 100, 101, 185])).
% 1.82/2.03 tff(4536,plain,(c0_1(a1438) | c2_1(a1435) | c3_1(a1435) | c1_1(a1438) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4537,plain,
% 1.82/2.03 (c0_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4536, 100, 101, 24, 2631])).
% 1.82/2.03 tff(4538,plain,
% 1.82/2.03 (~hskp7),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1021, 4537])).
% 1.82/2.03 tff(4539,plain,
% 1.82/2.03 (~c1_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3831, 4538, 100, 101, 4456])).
% 1.82/2.03 tff(4540,plain,
% 1.82/2.03 (~hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3527, 4539, 4456, 101, 4538])).
% 1.82/2.03 tff(4541,plain,
% 1.82/2.03 (hskp25 | hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[448, 4165])).
% 1.82/2.03 tff(4542,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4541, 4540])).
% 1.82/2.03 tff(4543,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4542])).
% 1.82/2.03 tff(4544,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4542])).
% 1.82/2.03 tff(4545,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4542])).
% 1.82/2.03 tff(4546,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3326, 82, 2631, 4456, 4545, 4544, 4543, 100, 101, 1123])).
% 1.82/2.03 tff(4547,plain,(c2_1(a1435) | hskp0 | c3_1(a1435) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4548,plain,
% 1.82/2.03 (c1_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4547, 4478, 101, 2631])).
% 1.82/2.03 tff(4549,plain,
% 1.82/2.03 (~hskp7),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1424, 4548])).
% 1.82/2.03 tff(4550,plain,
% 1.82/2.03 (~c1_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3831, 4549, 4478, 101, 4456])).
% 1.82/2.03 tff(4551,plain,
% 1.82/2.03 (~hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3527, 4550, 4456, 101, 4549])).
% 1.82/2.03 tff(4552,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4541, 4551])).
% 1.82/2.03 tff(4553,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4552])).
% 1.82/2.03 tff(4554,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4552])).
% 1.82/2.03 tff(4555,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4552])).
% 1.82/2.03 tff(4556,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3326, 82, 2631, 4456, 4555, 4554, 4553, 4478, 101, 1123])).
% 1.82/2.03 tff(4557,plain,(c3_1(a1435) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4558,plain,
% 1.82/2.03 (hskp0),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4557, 4238])).
% 1.82/2.03 tff(4559,plain,
% 1.82/2.03 (c0_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[363, 4237])).
% 1.82/2.03 tff(4560,plain,
% 1.82/2.03 (~c2_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[301, 4237])).
% 1.82/2.03 tff(4561,plain,
% 1.82/2.03 (~c1_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3831, 13, 4238, 4560, 4559])).
% 1.82/2.03 tff(4562,plain,
% 1.82/2.03 (~hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3527, 4561, 4559, 4238, 13])).
% 1.82/2.03 tff(4563,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4541, 4562])).
% 1.82/2.03 tff(4564,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4563])).
% 1.82/2.03 tff(4565,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4563])).
% 1.82/2.03 tff(4566,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4563])).
% 1.82/2.03 tff(4567,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3825, 4566, 4565, 4559, 4558, 4561, 4238, 4560, 4564])).
% 1.82/2.03 tff(4568,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4569,plain,
% 1.82/2.03 (~c0_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1021, 4568])).
% 1.82/2.03 tff(4570,plain,
% 1.82/2.03 (~c1_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1424, 4568])).
% 1.82/2.03 tff(4571,plain,
% 1.82/2.03 (c3_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[98, 4568])).
% 1.82/2.03 tff(4572,plain,
% 1.82/2.03 (c1_1(a1435)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3612, 4571, 4558, 4560, 4570, 4238, 4559, 4569])).
% 1.82/2.03 tff(4573,plain,
% 1.82/2.03 (hskp18 | (~c1_1(a1435))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[370, 82, 4559, 4560, 4238, 356])).
% 1.82/2.03 tff(4574,plain,
% 1.82/2.03 (hskp18),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4573, 4572])).
% 1.82/2.03 tff(4575,plain,
% 1.82/2.03 (~c2_1(a1458)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[376, 4574])).
% 1.82/2.03 tff(4576,plain,
% 1.82/2.03 (c1_1(a1458)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[384, 4574])).
% 1.82/2.03 tff(4577,plain,
% 1.82/2.03 (c0_1(a1458)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[392, 4574])).
% 1.82/2.03 tff(4578,plain,
% 1.82/2.03 (hskp10),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3624, 82, 4577, 4576, 4571, 4575, 4569, 345, 47])).
% 1.82/2.03 tff(4579,plain,
% 1.82/2.03 (~c3_1(a1445)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[406, 4578])).
% 1.82/2.03 tff(4580,plain,
% 1.82/2.03 (~c1_1(a1445)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[412, 4578])).
% 1.82/2.03 tff(4581,plain,
% 1.82/2.03 (hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4541, 36])).
% 1.82/2.03 tff(4582,plain,
% 1.82/2.03 (~c0_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[454, 4581])).
% 1.82/2.03 tff(4583,plain,
% 1.82/2.03 (c1_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[464, 4581])).
% 1.82/2.03 tff(4584,plain,
% 1.82/2.03 (~c3_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[471, 82, 36, 4583, 3471, 3470, 4582, 230, 312])).
% 1.82/2.03 tff(4585,plain,
% 1.82/2.03 (c2_1(a1504)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[489, 4581])).
% 1.82/2.03 tff(4586,plain,
% 1.82/2.03 (hskp14),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[496, 82, 4583, 4585, 4582, 482, 4584])).
% 1.82/2.03 tff(4587,plain,
% 1.82/2.03 (~c3_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[502, 4586])).
% 1.82/2.03 tff(4588,plain,
% 1.82/2.03 (~c1_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[508, 4586])).
% 1.82/2.03 tff(4589,plain,
% 1.82/2.03 (c2_1(a1451)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[516, 4586])).
% 1.82/2.03 tff(4590,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[523, 82, 4583, 4585, 4589, 4559, 4582, 4588, 4587, 4560, 4238, 185])).
% 1.82/2.03 tff(4591,plain,(hskp17 | (~c0_1(a1448)) | (~c3_1(a1448)) | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4592,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4591, 3471, 3470, 230])).
% 1.82/2.03 tff(4593,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4592])).
% 1.82/2.03 tff(4594,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4592])).
% 1.82/2.03 tff(4595,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4592])).
% 1.82/2.03 tff(4596,plain,
% 1.82/2.03 (c0_1(a1445)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[420, 4578])).
% 1.82/2.03 tff(4597,plain,
% 1.82/2.03 (~c2_1(a1445)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[427, 82, 4596, 4595, 4594, 4593, 4580, 4579, 23])).
% 1.82/2.03 tff(4598,plain,
% 1.82/2.03 (~c3_1(a1427)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1135, 4558])).
% 1.82/2.03 tff(4599,plain,
% 1.82/2.03 (c2_1(a1427)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1143, 4558])).
% 1.82/2.03 tff(4600,plain,
% 1.82/2.03 (c0_1(a1427)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1151, 4558])).
% 1.82/2.03 tff(4601,plain,
% 1.82/2.03 (hskp21),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3641, 82, 4596, 4600, 4599, 4580, 4598, 2437, 4597])).
% 1.82/2.03 tff(4602,plain,
% 1.82/2.03 (c2_1(a1466)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2458, 4601])).
% 1.82/2.03 tff(4603,plain,
% 1.82/2.03 (c0_1(a1466)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2466, 4601])).
% 1.82/2.03 tff(4604,plain,
% 1.82/2.03 (~c3_1(a1466)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3650, 82, 4603, 4602, 4571, 4559, 4570, 4238, 2491, 4572, 47])).
% 1.82/2.03 tff(4605,plain,
% 1.82/2.03 (hskp22),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3667, 82, 3471, 3470, 4571, 230, 4570, 1295, 47])).
% 1.82/2.03 tff(4606,plain,
% 1.82/2.03 (~c0_1(a1468)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[834, 4605])).
% 1.82/2.03 tff(4607,plain,
% 1.82/2.03 (c3_1(a1468)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[842, 4605])).
% 1.82/2.03 tff(4608,plain,
% 1.82/2.03 (c1_1(a1468)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[850, 4605])).
% 1.82/2.03 tff(4609,plain,
% 1.82/2.03 (hskp28),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3694, 82, 4608, 4607, 4577, 4576, 4606, 4575, 3688])).
% 1.82/2.03 tff(4610,plain,
% 1.82/2.03 (c3_1(a1456)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3702, 4609])).
% 1.82/2.03 tff(4611,plain,
% 1.82/2.03 (c1_1(a1456)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3710, 4609])).
% 1.82/2.03 tff(4612,plain,
% 1.82/2.03 (c0_1(a1456)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3718, 4609])).
% 1.82/2.03 tff(4613,plain,
% 1.82/2.03 (hskp6),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3863, 82, 4612, 4611, 4610, 4571, 4570, 3661, 47])).
% 1.82/2.03 tff(4614,plain,
% 1.82/2.03 (~c2_1(a1437)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2098, 4613])).
% 1.82/2.03 tff(4615,plain,
% 1.82/2.03 (~c1_1(a1437)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2119, 4613])).
% 1.82/2.03 tff(4616,plain,
% 1.82/2.03 (~c1_1(a1466)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2450, 4601])).
% 1.82/2.03 tff(4617,plain,
% 1.82/2.03 (c0_1(a1437)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2106, 4613])).
% 1.82/2.03 tff(4618,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3736, 82, 4602, 4571, 4617, 4616, 4569, 4615, 4614, 543, 47, 4604])).
% 1.82/2.03 tff(4619,plain,(c2_1(a1438) | (~c0_1(a1448)) | (~c3_1(a1448)) | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(4620,plain,
% 1.82/2.03 (c2_1(a1438)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4619, 211, 219, 203])).
% 1.82/2.03 tff(4621,plain,
% 1.82/2.03 (hskp17),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4591, 211, 219, 203])).
% 1.82/2.03 tff(4622,plain,
% 1.82/2.03 (~c2_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[264, 4621])).
% 1.82/2.03 tff(4623,plain,
% 1.82/2.03 (~c1_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[245, 4621])).
% 1.82/2.03 tff(4624,plain,
% 1.82/2.03 (~c0_1(a1457)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[251, 4621])).
% 1.82/2.03 tff(4625,plain,
% 1.82/2.03 (hskp1),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[595, 82, 4165, 4624, 4623, 4622, 588])).
% 1.82/2.03 tff(4626,plain,
% 1.82/2.03 (~c0_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[601, 4625])).
% 1.82/2.03 tff(4627,plain,
% 1.82/2.03 (c3_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[609, 4625])).
% 1.82/2.03 tff(4628,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4629,plain,
% 1.82/2.03 (((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438))) <=> (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(4630,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[4629])).
% 1.82/2.03 tff(4631,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[4630, 4628])).
% 1.82/2.03 tff(4632,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1429) | (~c3_1(a1429)) | (~c1_1(a1429)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(4633,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | (~c1_1(a1429)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[4632, 4631])).
% 1.82/2.03 tff(4634,plain,
% 1.82/2.03 ((~c1_1(a1429)) | (~c2_1(a1438))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4633, 82, 211, 219, 4627, 203, 4569, 4570, 4626, 1284])).
% 1.82/2.03 tff(4635,plain,
% 1.82/2.03 (~c1_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4634, 4620])).
% 1.82/2.03 tff(4636,plain,
% 1.82/2.03 (hskp23 | (~c2_1(a1438))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3745, 82, 4571, 4600, 4599, 4570, 4598, 1693])).
% 1.82/2.03 tff(4637,plain,
% 1.82/2.03 (hskp23),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4636, 4620])).
% 1.82/2.03 tff(4638,plain,
% 1.82/2.03 (c2_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1520, 4637])).
% 1.82/2.03 tff(4639,plain,
% 1.82/2.03 (~c0_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1571, 4637])).
% 1.82/2.03 tff(4640,plain,
% 1.82/2.03 (hskp8 | (~c2_1(a1438))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3755, 82, 4571, 4559, 4570, 4238, 1537, 4572])).
% 1.82/2.03 tff(4641,plain,
% 1.82/2.03 (hskp8),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4640, 4620])).
% 1.82/2.03 tff(4642,plain,
% 1.82/2.03 (~c1_1(a1441)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1549, 4641])).
% 1.82/2.03 tff(4643,plain,
% 1.82/2.03 (c3_1(a1441)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1557, 4641])).
% 1.82/2.03 tff(4644,plain,
% 1.82/2.03 (~c1_1(a1477)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1526, 4637])).
% 1.82/2.03 tff(4645,plain,
% 1.82/2.03 (c0_1(a1441)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1565, 4641])).
% 1.82/2.03 tff(4646,plain,
% 1.82/2.03 (~c2_1(a1441)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1587, 4645, 4644, 4643, 4642, 4639, 4638])).
% 1.82/2.03 tff(4647,plain,
% 1.82/2.03 (c2_1(a1429)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[634, 4625])).
% 1.82/2.03 tff(4648,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(4649,plain,
% 1.82/2.04 (((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441))) <=> (c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(4650,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[4649])).
% 1.82/2.04 tff(4651,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[4650, 4648])).
% 1.82/2.04 tff(4652,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | c1_1(a1429) | (~c3_1(a1429)) | (~c2_1(a1429)) | c1_1(a1441) | c2_1(a1441) | (~c3_1(a1441)))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(4653,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1429)) | (~c3_1(a1429)) | c1_1(a1429) | c2_1(a1441) | (~c3_1(a1441))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[4652, 4651])).
% 1.82/2.04 tff(4654,plain,
% 1.82/2.04 (~c1_1(a1427)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4653, 82, 4643, 4647, 4627, 4600, 4599, 4642, 1598, 4646, 4635])).
% 1.82/2.04 tff(4655,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(4656,plain,
% 1.82/2.04 (((~ndr1_0) | c1_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457)) <=> (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(4657,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[4656])).
% 1.82/2.04 tff(4658,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[4657, 4655])).
% 1.82/2.04 tff(4659,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c3_1(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1457) | c0_1(a1457) | c2_1(a1457))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(4660,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 1.82/2.04 tff(4661,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4660, 82, 4600, 4599, 4624, 4623, 4622, 4598, 23, 4654])).
% 1.82/2.04 tff(4662,plain,(~hskp12), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(4663,plain,
% 1.82/2.04 (~hskp11),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3191, 4662, 4238, 4560, 4559])).
% 1.82/2.04 tff(4664,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3195, 4663, 4662, 4558])).
% 1.82/2.04 % SZS output end Proof
% 1.82/2.04 % E exiting
%------------------------------------------------------------------------------