TSTP Solution File: SYN479-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN479-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:47 EDT 2022
% Result : Unsatisfiable 2.39s 1.75s
% Output : Proof 2.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN479-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 04:28:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.39/1.75 % SZS status Unsatisfiable
% 2.39/1.75 % SZS output start Proof
% 2.39/1.75 tff(hskp0_type, type, (
% 2.39/1.75 hskp0: $o)).
% 2.39/1.75 tff(c3_1_type, type, (
% 2.39/1.75 c3_1: $i > $o)).
% 2.39/1.75 tff(a1435_type, type, (
% 2.39/1.75 a1435: $i)).
% 2.39/1.75 tff(hskp5_type, type, (
% 2.39/1.75 hskp5: $o)).
% 2.39/1.75 tff(a1457_type, type, (
% 2.39/1.75 a1457: $i)).
% 2.39/1.75 tff(c1_1_type, type, (
% 2.39/1.75 c1_1: $i > $o)).
% 2.39/1.75 tff(c0_1_type, type, (
% 2.39/1.75 c0_1: $i > $o)).
% 2.39/1.75 tff(c2_1_type, type, (
% 2.39/1.75 c2_1: $i > $o)).
% 2.39/1.75 tff(ndr1_0_type, type, (
% 2.39/1.75 ndr1_0: $o)).
% 2.39/1.75 tff(a1448_type, type, (
% 2.39/1.75 a1448: $i)).
% 2.39/1.75 tff(hskp12_type, type, (
% 2.39/1.75 hskp12: $o)).
% 2.39/1.75 tff(hskp11_type, type, (
% 2.39/1.75 hskp11: $o)).
% 2.39/1.75 tff(hskp2_type, type, (
% 2.39/1.75 hskp2: $o)).
% 2.39/1.75 tff(a1430_type, type, (
% 2.39/1.75 a1430: $i)).
% 2.39/1.75 tff(a1438_type, type, (
% 2.39/1.75 a1438: $i)).
% 2.39/1.75 tff(hskp7_type, type, (
% 2.39/1.75 hskp7: $o)).
% 2.39/1.75 tff(a1466_type, type, (
% 2.39/1.75 a1466: $i)).
% 2.39/1.75 tff(a1458_type, type, (
% 2.39/1.75 a1458: $i)).
% 2.39/1.75 tff(a1447_type, type, (
% 2.39/1.75 a1447: $i)).
% 2.39/1.75 tff(a1445_type, type, (
% 2.39/1.75 a1445: $i)).
% 2.39/1.75 tff(hskp10_type, type, (
% 2.39/1.75 hskp10: $o)).
% 2.39/1.75 tff(a1431_type, type, (
% 2.39/1.75 a1431: $i)).
% 2.39/1.75 tff(hskp3_type, type, (
% 2.39/1.75 hskp3: $o)).
% 2.39/1.75 tff(hskp17_type, type, (
% 2.39/1.75 hskp17: $o)).
% 2.39/1.75 tff(a1465_type, type, (
% 2.39/1.75 a1465: $i)).
% 2.39/1.75 tff(a1441_type, type, (
% 2.39/1.75 a1441: $i)).
% 2.39/1.75 tff(a1477_type, type, (
% 2.39/1.75 a1477: $i)).
% 2.39/1.75 tff(hskp23_type, type, (
% 2.39/1.75 hskp23: $o)).
% 2.39/1.75 tff(a1507_type, type, (
% 2.39/1.75 a1507: $i)).
% 2.39/1.75 tff(hskp30_type, type, (
% 2.39/1.75 hskp30: $o)).
% 2.39/1.75 tff(hskp24_type, type, (
% 2.39/1.75 hskp24: $o)).
% 2.39/1.75 tff(a1429_type, type, (
% 2.39/1.75 a1429: $i)).
% 2.39/1.75 tff(hskp4_type, type, (
% 2.39/1.75 hskp4: $o)).
% 2.39/1.75 tff(a1434_type, type, (
% 2.39/1.75 a1434: $i)).
% 2.39/1.75 tff(a1451_type, type, (
% 2.39/1.75 a1451: $i)).
% 2.39/1.75 tff(hskp14_type, type, (
% 2.39/1.75 hskp14: $o)).
% 2.39/1.75 tff(a1504_type, type, (
% 2.39/1.75 a1504: $i)).
% 2.39/1.75 tff(hskp25_type, type, (
% 2.39/1.75 hskp25: $o)).
% 2.39/1.75 tff(hskp18_type, type, (
% 2.39/1.75 hskp18: $o)).
% 2.39/1.75 tff(hskp1_type, type, (
% 2.39/1.75 hskp1: $o)).
% 2.39/1.75 tff(a1468_type, type, (
% 2.39/1.75 a1468: $i)).
% 2.39/1.75 tff(hskp22_type, type, (
% 2.39/1.75 hskp22: $o)).
% 2.39/1.75 tff(a1487_type, type, (
% 2.39/1.75 a1487: $i)).
% 2.39/1.75 tff(a1444_type, type, (
% 2.39/1.75 a1444: $i)).
% 2.39/1.75 tff(hskp9_type, type, (
% 2.39/1.75 hskp9: $o)).
% 2.39/1.75 tff(a1483_type, type, (
% 2.39/1.75 a1483: $i)).
% 2.39/1.75 tff(hskp29_type, type, (
% 2.39/1.75 hskp29: $o)).
% 2.39/1.75 tff(a1460_type, type, (
% 2.39/1.75 a1460: $i)).
% 2.39/1.75 tff(hskp19_type, type, (
% 2.39/1.75 hskp19: $o)).
% 2.39/1.75 tff(a1427_type, type, (
% 2.39/1.75 a1427: $i)).
% 2.39/1.75 tff(hskp20_type, type, (
% 2.39/1.75 hskp20: $o)).
% 2.39/1.75 tff(hskp8_type, type, (
% 2.39/1.75 hskp8: $o)).
% 2.39/1.75 tff(a1454_type, type, (
% 2.39/1.75 a1454: $i)).
% 2.39/1.75 tff(hskp16_type, type, (
% 2.39/1.75 hskp16: $o)).
% 2.39/1.75 tff(a1437_type, type, (
% 2.39/1.75 a1437: $i)).
% 2.39/1.75 tff(hskp6_type, type, (
% 2.39/1.75 hskp6: $o)).
% 2.39/1.75 tff(hskp21_type, type, (
% 2.39/1.75 hskp21: $o)).
% 2.39/1.75 tff(a1452_type, type, (
% 2.39/1.75 a1452: $i)).
% 2.39/1.75 tff(hskp15_type, type, (
% 2.39/1.75 hskp15: $o)).
% 2.39/1.75 tff(a1517_type, type, (
% 2.39/1.75 a1517: $i)).
% 2.39/1.75 tff(hskp26_type, type, (
% 2.39/1.75 hskp26: $o)).
% 2.39/1.75 tff(a1456_type, type, (
% 2.39/1.75 a1456: $i)).
% 2.39/1.75 tff(hskp28_type, type, (
% 2.39/1.75 hskp28: $o)).
% 2.39/1.75 tff(a1449_type, type, (
% 2.39/1.75 a1449: $i)).
% 2.39/1.75 tff(hskp13_type, type, (
% 2.39/1.75 hskp13: $o)).
% 2.39/1.75 tff(1,plain,
% 2.39/1.75 (^[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))))),
% 2.39/1.75 inference(bind,[status(th)],[])).
% 2.39/1.75 tff(2,plain,
% 2.39/1.75 (![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))) <=> ![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)))),
% 2.39/1.75 inference(quant_intro,[status(thm)],[1])).
% 2.39/1.75 tff(3,plain,
% 2.39/1.75 (![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))) <=> ![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)))),
% 2.39/1.75 inference(rewrite,[status(thm)],[])).
% 2.39/1.75 tff(4,plain,
% 2.39/1.75 (^[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)))))),
% 2.39/1.75 inference(bind,[status(th)],[])).
% 2.39/1.75 tff(5,plain,
% 2.39/1.75 (![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)))),
% 2.39/1.75 inference(quant_intro,[status(thm)],[4])).
% 2.39/1.75 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')).
% 2.39/1.75 tff(7,plain,
% 2.39/1.75 (![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)))),
% 2.39/1.75 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.39/1.75 tff(8,plain,
% 2.39/1.75 (![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)))),
% 2.39/1.75 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.39/1.75 tff(9,plain,(
% 2.39/1.75 ![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)))),
% 2.39/1.75 inference(skolemize,[status(sab)],[8])).
% 2.39/1.75 tff(10,plain,
% 2.39/1.75 (![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)))),
% 2.39/1.75 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.39/1.75 tff(11,assumption,(~hskp5), introduced(assumption)).
% 2.39/1.75 tff(12,assumption,(~c0_1(a1430)), introduced(assumption)).
% 2.39/1.75 tff(13,assumption,(~hskp7), introduced(assumption)).
% 2.39/1.75 tff(14,plain,
% 2.39/1.75 (^[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)))),
% 2.39/1.75 inference(bind,[status(th)],[])).
% 2.39/1.75 tff(15,plain,
% 2.39/1.75 (![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))),
% 2.39/1.75 inference(quant_intro,[status(thm)],[14])).
% 2.39/1.75 tff(16,plain,
% 2.39/1.75 (![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))),
% 2.39/1.75 inference(rewrite,[status(thm)],[])).
% 2.39/1.75 tff(17,plain,
% 2.39/1.75 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(18,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[17])).
% 2.39/1.76 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')).
% 2.39/1.76 tff(20,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.39/1.76 tff(21,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.39/1.76 tff(22,plain,(
% 2.39/1.76 ![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))),
% 2.39/1.76 inference(skolemize,[status(sab)],[21])).
% 2.39/1.76 tff(23,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.39/1.76 tff(24,assumption,(~c1_1(a1438)), introduced(assumption)).
% 2.39/1.76 tff(25,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(26,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[25])).
% 2.39/1.76 tff(27,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(28,plain,
% 2.39/1.76 (^[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)))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(29,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[28])).
% 2.39/1.76 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')).
% 2.39/1.76 tff(31,plain,
% 2.39/1.76 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.39/1.76 tff(32,plain,
% 2.39/1.76 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[31, 27])).
% 2.39/1.76 tff(33,plain,(
% 2.39/1.76 ![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.39/1.76 inference(skolemize,[status(sab)],[32])).
% 2.39/1.76 tff(34,plain,
% 2.39/1.76 (![U: $i] : (hskp11 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[33, 26])).
% 2.39/1.76 tff(35,assumption,(~c3_1(a1430)), introduced(assumption)).
% 2.39/1.76 tff(36,assumption,(~hskp17), introduced(assumption)).
% 2.39/1.76 tff(37,assumption,(~c0_1(a1438)), introduced(assumption)).
% 2.39/1.76 tff(38,plain,
% 2.39/1.76 (((~hskp2) | c3_1(a1430)) <=> ((~hskp2) | c3_1(a1430))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(39,axiom,((~hskp2) | c3_1(a1430)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 2.39/1.76 tff(40,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.39/1.76 tff(41,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[40, 38])).
% 2.39/1.76 tff(42,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[41, 38])).
% 2.39/1.76 tff(43,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[42, 38])).
% 2.39/1.76 tff(44,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[43, 38])).
% 2.39/1.76 tff(45,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[44, 38])).
% 2.39/1.76 tff(46,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[45, 38])).
% 2.39/1.76 tff(47,plain,
% 2.39/1.76 ((~hskp2) | c3_1(a1430)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[46, 38])).
% 2.39/1.76 tff(48,plain,
% 2.39/1.76 (~hskp2),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[47, 35])).
% 2.39/1.76 tff(49,assumption,(~c3_1(a1438)), introduced(assumption)).
% 2.39/1.76 tff(50,assumption,(~c2_1(a1438)), introduced(assumption)).
% 2.39/1.76 tff(51,plain,
% 2.39/1.76 (^[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)))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(52,plain,
% 2.39/1.76 (![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)) <=> ![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))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[51])).
% 2.39/1.76 tff(53,plain,
% 2.39/1.76 (![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)) <=> ![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))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(54,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(55,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[54])).
% 2.39/1.76 tff(56,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')).
% 2.39/1.76 tff(57,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.39/1.76 tff(58,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[57, 53])).
% 2.39/1.76 tff(59,plain,(
% 2.39/1.76 ![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))),
% 2.39/1.76 inference(skolemize,[status(sab)],[58])).
% 2.39/1.76 tff(60,plain,
% 2.39/1.76 (![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[59, 52])).
% 2.39/1.76 tff(61,assumption,(~hskp2), introduced(assumption)).
% 2.39/1.76 tff(62,assumption,(~ndr1_0), introduced(assumption)).
% 2.39/1.76 tff(63,plain,
% 2.39/1.76 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(64,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 2.39/1.76 tff(65,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.39/1.76 tff(66,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[65, 63])).
% 2.39/1.76 tff(67,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[66, 63])).
% 2.39/1.76 tff(68,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[67, 63])).
% 2.39/1.76 tff(69,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[68, 63])).
% 2.39/1.76 tff(70,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[69, 63])).
% 2.39/1.76 tff(71,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[70, 63])).
% 2.39/1.76 tff(72,plain,
% 2.39/1.76 ((~hskp30) | ndr1_0),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[71, 63])).
% 2.39/1.76 tff(73,plain,
% 2.39/1.76 (~hskp30),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[72, 62])).
% 2.39/1.76 tff(74,plain,
% 2.39/1.76 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(75,plain,
% 2.39/1.76 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(76,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 2.39/1.76 tff(77,plain,
% 2.39/1.76 (ndr1_0 | (~hskp24)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[76, 75])).
% 2.39/1.76 tff(78,plain,
% 2.39/1.76 (ndr1_0 | (~hskp24)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[77, 74])).
% 2.39/1.76 tff(79,plain,
% 2.39/1.76 (~hskp24),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[78, 62])).
% 2.39/1.76 tff(80,plain,
% 2.39/1.76 ((hskp30 | hskp24) <=> (hskp30 | hskp24)),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(81,axiom,(hskp30 | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 2.39/1.76 tff(82,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[81, 80])).
% 2.39/1.76 tff(83,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[82, 80])).
% 2.39/1.76 tff(84,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[83, 80])).
% 2.39/1.76 tff(85,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.39/1.76 tff(86,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[85, 80])).
% 2.39/1.76 tff(87,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[86, 80])).
% 2.39/1.76 tff(88,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[87, 80])).
% 2.39/1.76 tff(89,plain,
% 2.39/1.76 (hskp30 | hskp24),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[88, 80])).
% 2.39/1.76 tff(90,plain,
% 2.39/1.76 ($false),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[89, 79, 73])).
% 2.39/1.76 tff(91,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.39/1.76 tff(92,plain,
% 2.39/1.76 (((~![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 | 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))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(93,plain,
% 2.39/1.76 ((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))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(94,plain,
% 2.39/1.76 (((~![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(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)))),
% 2.39/1.76 inference(monotonicity,[status(thm)],[93])).
% 2.39/1.76 tff(95,plain,
% 2.39/1.76 (((~![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(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))),
% 2.39/1.76 inference(transitivity,[status(thm)],[94, 92])).
% 2.39/1.76 tff(96,plain,
% 2.39/1.76 ((~![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(a1438) | c1_1(a1438) | c3_1(a1438) | c3_1(a1438) | c2_1(a1438) | c0_1(a1438))),
% 2.39/1.76 inference(quant_inst,[status(thm)],[])).
% 2.39/1.76 tff(97,plain,
% 2.39/1.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[96, 95])).
% 2.39/1.76 tff(98,plain,
% 2.39/1.76 ($false),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[97, 91, 61, 49, 37, 24, 60, 50])).
% 2.39/1.76 tff(99,plain,(c2_1(a1438) | hskp2 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.76 tff(100,plain,
% 2.39/1.76 (c2_1(a1438)),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[99, 49, 37, 48, 24])).
% 2.39/1.76 tff(101,plain,
% 2.39/1.76 (((~hskp7) | c3_1(a1438)) <=> ((~hskp7) | c3_1(a1438))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(102,axiom,((~hskp7) | c3_1(a1438)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 2.39/1.76 tff(103,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.39/1.76 tff(104,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[103, 101])).
% 2.39/1.76 tff(105,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[104, 101])).
% 2.39/1.76 tff(106,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[105, 101])).
% 2.39/1.76 tff(107,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[106, 101])).
% 2.39/1.76 tff(108,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[107, 101])).
% 2.39/1.76 tff(109,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[108, 101])).
% 2.39/1.76 tff(110,plain,
% 2.39/1.76 ((~hskp7) | c3_1(a1438)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[109, 101])).
% 2.39/1.76 tff(111,plain,
% 2.39/1.76 (~hskp7),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[110, 49])).
% 2.39/1.76 tff(112,assumption,(~c2_1(a1435)), introduced(assumption)).
% 2.39/1.76 tff(113,assumption,(~c3_1(a1435)), introduced(assumption)).
% 2.39/1.76 tff(114,assumption,(c0_1(a1435)), introduced(assumption)).
% 2.39/1.76 tff(115,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(116,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[115])).
% 2.39/1.76 tff(117,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(118,plain,
% 2.39/1.76 (^[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)))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(119,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[118])).
% 2.39/1.76 tff(120,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 2.39/1.76 tff(121,plain,
% 2.39/1.76 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.39/1.76 tff(122,plain,
% 2.39/1.76 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[121, 117])).
% 2.39/1.76 tff(123,plain,(
% 2.39/1.76 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.39/1.76 inference(skolemize,[status(sab)],[122])).
% 2.39/1.76 tff(124,plain,
% 2.39/1.76 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[123, 116])).
% 2.39/1.76 tff(125,plain,
% 2.39/1.76 (((~![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(126,plain,
% 2.39/1.76 ((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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(127,plain,
% 2.39/1.76 (((~![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))))),
% 2.39/1.76 inference(monotonicity,[status(thm)],[126])).
% 2.39/1.76 tff(128,plain,
% 2.39/1.76 (((~![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)))),
% 2.39/1.76 inference(transitivity,[status(thm)],[127, 125])).
% 2.39/1.76 tff(129,plain,
% 2.39/1.76 ((~![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)))),
% 2.39/1.76 inference(quant_inst,[status(thm)],[])).
% 2.39/1.76 tff(130,plain,
% 2.39/1.76 ((~![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))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.39/1.76 tff(131,plain,
% 2.39/1.76 (hskp7 | hskp4 | c2_1(a1435) | (~c0_1(a1435))),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[130, 91, 113, 124])).
% 2.39/1.76 tff(132,plain,
% 2.39/1.76 (hskp4),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[131, 13, 114, 112])).
% 2.39/1.76 tff(133,plain,
% 2.39/1.76 (((~hskp4) | (~c2_1(a1434))) <=> ((~hskp4) | (~c2_1(a1434)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(134,plain,
% 2.39/1.76 (((~c2_1(a1434)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1434)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(135,axiom,((~c2_1(a1434)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 2.39/1.76 tff(136,plain,
% 2.39/1.76 ((~hskp4) | (~c2_1(a1434))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[135, 134])).
% 2.39/1.76 tff(137,plain,
% 2.39/1.76 ((~hskp4) | (~c2_1(a1434))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[136, 133])).
% 2.39/1.76 tff(138,plain,
% 2.39/1.76 (~c2_1(a1434)),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[137, 132])).
% 2.39/1.76 tff(139,assumption,(c1_1(a1435)), introduced(assumption)).
% 2.39/1.76 tff(140,assumption,(hskp4), introduced(assumption)).
% 2.39/1.76 tff(141,plain,
% 2.39/1.76 (((~hskp4) | c1_1(a1434)) <=> ((~hskp4) | c1_1(a1434))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(142,axiom,((~hskp4) | c1_1(a1434)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 2.39/1.76 tff(143,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[142, 141])).
% 2.39/1.76 tff(144,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[143, 141])).
% 2.39/1.76 tff(145,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[144, 141])).
% 2.39/1.76 tff(146,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[145, 141])).
% 2.39/1.76 tff(147,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[146, 141])).
% 2.39/1.76 tff(148,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[147, 141])).
% 2.39/1.76 tff(149,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[148, 141])).
% 2.39/1.76 tff(150,plain,
% 2.39/1.76 ((~hskp4) | c1_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[149, 141])).
% 2.39/1.76 tff(151,plain,
% 2.39/1.76 (c1_1(a1434)),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[150, 140])).
% 2.39/1.76 tff(152,plain,
% 2.39/1.76 (((~hskp4) | c3_1(a1434)) <=> ((~hskp4) | c3_1(a1434))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(153,axiom,((~hskp4) | c3_1(a1434)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 2.39/1.76 tff(154,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[153, 152])).
% 2.39/1.76 tff(155,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[154, 152])).
% 2.39/1.76 tff(156,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[155, 152])).
% 2.39/1.76 tff(157,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[156, 152])).
% 2.39/1.76 tff(158,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[157, 152])).
% 2.39/1.76 tff(159,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[158, 152])).
% 2.39/1.76 tff(160,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[159, 152])).
% 2.39/1.76 tff(161,plain,
% 2.39/1.76 ((~hskp4) | c3_1(a1434)),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[160, 152])).
% 2.39/1.76 tff(162,plain,
% 2.39/1.76 (c3_1(a1434)),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[161, 140])).
% 2.39/1.76 tff(163,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(164,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[163])).
% 2.39/1.76 tff(165,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(166,plain,
% 2.39/1.76 (^[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)))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(167,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[166])).
% 2.39/1.76 tff(168,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')).
% 2.39/1.76 tff(169,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.39/1.76 tff(170,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[169, 165])).
% 2.39/1.76 tff(171,plain,(
% 2.39/1.76 ![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)))),
% 2.39/1.76 inference(skolemize,[status(sab)],[170])).
% 2.39/1.76 tff(172,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[171, 164])).
% 2.39/1.76 tff(173,assumption,(~c2_1(a1434)), introduced(assumption)).
% 2.39/1.76 tff(174,plain,
% 2.39/1.76 (((~![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(175,plain,
% 2.39/1.76 ((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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(176,plain,
% 2.39/1.76 (((~![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))))),
% 2.39/1.76 inference(monotonicity,[status(thm)],[175])).
% 2.39/1.76 tff(177,plain,
% 2.39/1.76 (((~![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)))),
% 2.39/1.76 inference(transitivity,[status(thm)],[176, 174])).
% 2.39/1.76 tff(178,plain,
% 2.39/1.76 ((~![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)))),
% 2.39/1.76 inference(quant_inst,[status(thm)],[])).
% 2.39/1.76 tff(179,plain,
% 2.39/1.76 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a1435) | c3_1(a1435) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[178, 177])).
% 2.39/1.76 tff(180,plain,
% 2.39/1.76 (hskp7 | c2_1(a1435) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c1_1(a1435))),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[179, 91, 113, 173, 172])).
% 2.39/1.76 tff(181,plain,
% 2.39/1.76 ($false),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[180, 162, 151, 13, 112, 139])).
% 2.39/1.76 tff(182,plain,((~hskp4) | hskp7 | c2_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | c2_1(a1434)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.76 tff(183,plain,
% 2.39/1.76 (~c1_1(a1435)),
% 2.39/1.76 inference(unit_resolution,[status(thm)],[182, 138, 112, 132, 113, 13])).
% 2.39/1.76 tff(184,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(185,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[184])).
% 2.39/1.76 tff(186,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(187,plain,
% 2.39/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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)))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(188,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[187])).
% 2.39/1.76 tff(189,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')).
% 2.39/1.76 tff(190,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.39/1.76 tff(191,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[190, 186])).
% 2.39/1.76 tff(192,plain,(
% 2.39/1.76 ![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)))),
% 2.39/1.76 inference(skolemize,[status(sab)],[191])).
% 2.39/1.76 tff(193,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(modus_ponens,[status(thm)],[192, 185])).
% 2.39/1.76 tff(194,plain,
% 2.39/1.76 (^[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))))),
% 2.39/1.76 inference(bind,[status(th)],[])).
% 2.39/1.76 tff(195,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(quant_intro,[status(thm)],[194])).
% 2.39/1.76 tff(196,plain,
% 2.39/1.76 (![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)))),
% 2.39/1.76 inference(rewrite,[status(thm)],[])).
% 2.39/1.76 tff(197,plain,
% 2.39/1.76 (^[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)))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(198,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[197])).
% 2.39/1.77 tff(199,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')).
% 2.39/1.77 tff(200,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.39/1.77 tff(201,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[200, 196])).
% 2.39/1.77 tff(202,plain,(
% 2.39/1.77 ![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)))),
% 2.39/1.77 inference(skolemize,[status(sab)],[201])).
% 2.39/1.77 tff(203,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[202, 195])).
% 2.39/1.77 tff(204,assumption,(~c2_1(a1430)), introduced(assumption)).
% 2.39/1.77 tff(205,plain,
% 2.39/1.77 (^[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))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(206,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[205])).
% 2.39/1.77 tff(207,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(208,plain,
% 2.39/1.77 (^[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)))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(209,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[208])).
% 2.39/1.77 tff(210,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')).
% 2.39/1.77 tff(211,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.39/1.77 tff(212,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[211, 207])).
% 2.39/1.77 tff(213,plain,(
% 2.39/1.77 ![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)))),
% 2.39/1.77 inference(skolemize,[status(sab)],[212])).
% 2.39/1.77 tff(214,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[213, 206])).
% 2.39/1.77 tff(215,assumption,(hskp12), introduced(assumption)).
% 2.39/1.77 tff(216,plain,
% 2.39/1.77 (((~hskp12) | (~c2_1(a1448))) <=> ((~hskp12) | (~c2_1(a1448)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(217,plain,
% 2.39/1.77 (((~c2_1(a1448)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a1448)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(218,axiom,((~c2_1(a1448)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 2.39/1.77 tff(219,plain,
% 2.39/1.77 ((~hskp12) | (~c2_1(a1448))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.39/1.77 tff(220,plain,
% 2.39/1.77 ((~hskp12) | (~c2_1(a1448))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[219, 216])).
% 2.39/1.77 tff(221,plain,
% 2.39/1.77 (~c2_1(a1448)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[220, 215])).
% 2.39/1.77 tff(222,plain,
% 2.39/1.77 (((~hskp12) | c0_1(a1448)) <=> ((~hskp12) | c0_1(a1448))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(223,axiom,((~hskp12) | c0_1(a1448)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 2.39/1.77 tff(224,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[223, 222])).
% 2.39/1.77 tff(225,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[224, 222])).
% 2.39/1.77 tff(226,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[225, 222])).
% 2.39/1.77 tff(227,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[226, 222])).
% 2.39/1.77 tff(228,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[227, 222])).
% 2.39/1.77 tff(229,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[228, 222])).
% 2.39/1.77 tff(230,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[229, 222])).
% 2.39/1.77 tff(231,plain,
% 2.39/1.77 ((~hskp12) | c0_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[230, 222])).
% 2.39/1.77 tff(232,plain,
% 2.39/1.77 (c0_1(a1448)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[231, 215])).
% 2.39/1.77 tff(233,plain,
% 2.39/1.77 (((~hskp12) | c3_1(a1448)) <=> ((~hskp12) | c3_1(a1448))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(234,axiom,((~hskp12) | c3_1(a1448)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 2.39/1.77 tff(235,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[234, 233])).
% 2.39/1.77 tff(236,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[235, 233])).
% 2.39/1.77 tff(237,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[236, 233])).
% 2.39/1.77 tff(238,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[237, 233])).
% 2.39/1.77 tff(239,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[238, 233])).
% 2.39/1.77 tff(240,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[239, 233])).
% 2.39/1.77 tff(241,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[240, 233])).
% 2.39/1.77 tff(242,plain,
% 2.39/1.77 ((~hskp12) | c3_1(a1448)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[241, 233])).
% 2.39/1.77 tff(243,plain,
% 2.39/1.77 (c3_1(a1448)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[242, 215])).
% 2.39/1.77 tff(244,plain,
% 2.39/1.77 (^[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))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(245,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[244])).
% 2.39/1.77 tff(246,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(247,plain,
% 2.39/1.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(248,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[247])).
% 2.39/1.77 tff(249,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 2.39/1.77 tff(250,plain,
% 2.39/1.77 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.39/1.77 tff(251,plain,
% 2.39/1.77 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[250, 246])).
% 2.39/1.77 tff(252,plain,(
% 2.39/1.77 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.39/1.77 inference(skolemize,[status(sab)],[251])).
% 2.39/1.77 tff(253,plain,
% 2.39/1.77 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[252, 245])).
% 2.39/1.77 tff(254,assumption,(~c2_1(a1448)), introduced(assumption)).
% 2.39/1.77 tff(255,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(256,plain,
% 2.39/1.77 ((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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(257,plain,
% 2.39/1.77 (((~![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))))),
% 2.39/1.77 inference(monotonicity,[status(thm)],[256])).
% 2.39/1.77 tff(258,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(transitivity,[status(thm)],[257, 255])).
% 2.39/1.77 tff(259,plain,
% 2.39/1.77 ((~![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)))),
% 2.39/1.77 inference(quant_inst,[status(thm)],[])).
% 2.39/1.77 tff(260,plain,
% 2.39/1.77 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[259, 258])).
% 2.39/1.77 tff(261,plain,
% 2.39/1.77 (hskp17 | hskp5 | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[260, 91, 254, 253])).
% 2.39/1.77 tff(262,plain,
% 2.39/1.77 ($false),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[261, 243, 232, 36, 11])).
% 2.39/1.77 tff(263,plain,((~hskp12) | hskp17 | hskp5 | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.77 tff(264,plain,
% 2.39/1.77 (hskp17),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[263, 11, 215, 221])).
% 2.39/1.77 tff(265,plain,
% 2.39/1.77 (((~hskp17) | (~c1_1(a1457))) <=> ((~hskp17) | (~c1_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(266,plain,
% 2.39/1.77 (((~c1_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(267,axiom,((~c1_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 2.39/1.77 tff(268,plain,
% 2.39/1.77 ((~hskp17) | (~c1_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[267, 266])).
% 2.39/1.77 tff(269,plain,
% 2.39/1.77 ((~hskp17) | (~c1_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[268, 265])).
% 2.39/1.77 tff(270,plain,
% 2.39/1.77 (~c1_1(a1457)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[269, 264])).
% 2.39/1.77 tff(271,plain,
% 2.39/1.77 (((~hskp17) | (~c0_1(a1457))) <=> ((~hskp17) | (~c0_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(272,plain,
% 2.39/1.77 (((~c0_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(273,axiom,((~c0_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 2.39/1.77 tff(274,plain,
% 2.39/1.77 ((~hskp17) | (~c0_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[273, 272])).
% 2.39/1.77 tff(275,plain,
% 2.39/1.77 ((~hskp17) | (~c0_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[274, 271])).
% 2.39/1.77 tff(276,plain,
% 2.39/1.77 (~c0_1(a1457)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[275, 264])).
% 2.39/1.77 tff(277,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(278,plain,
% 2.39/1.77 ((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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(279,plain,
% 2.39/1.77 (((~![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))))),
% 2.39/1.77 inference(monotonicity,[status(thm)],[278])).
% 2.39/1.77 tff(280,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(transitivity,[status(thm)],[279, 277])).
% 2.39/1.77 tff(281,plain,
% 2.39/1.77 ((~![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)))),
% 2.39/1.77 inference(quant_inst,[status(thm)],[])).
% 2.39/1.77 tff(282,plain,
% 2.39/1.77 ((~![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))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[281, 280])).
% 2.39/1.77 tff(283,plain,
% 2.39/1.77 (~c3_1(a1457)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[282, 91, 11, 232, 243, 276, 270, 221, 10])).
% 2.39/1.77 tff(284,plain,
% 2.39/1.77 (((~hskp17) | (~c2_1(a1457))) <=> ((~hskp17) | (~c2_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(285,plain,
% 2.39/1.77 (((~c2_1(a1457)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1457)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(286,axiom,((~c2_1(a1457)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 2.39/1.77 tff(287,plain,
% 2.39/1.77 ((~hskp17) | (~c2_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[286, 285])).
% 2.39/1.77 tff(288,plain,
% 2.39/1.77 ((~hskp17) | (~c2_1(a1457))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[287, 284])).
% 2.39/1.77 tff(289,plain,
% 2.39/1.77 (~c2_1(a1457)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[288, 264])).
% 2.39/1.77 tff(290,plain,
% 2.39/1.77 (((~![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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(291,plain,
% 2.39/1.77 ((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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(292,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(monotonicity,[status(thm)],[291])).
% 2.39/1.77 tff(293,plain,
% 2.39/1.77 (((~![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))),
% 2.39/1.77 inference(transitivity,[status(thm)],[292, 290])).
% 2.39/1.77 tff(294,plain,
% 2.39/1.77 ((~![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))),
% 2.39/1.77 inference(quant_inst,[status(thm)],[])).
% 2.39/1.77 tff(295,plain,
% 2.39/1.77 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1457) | c2_1(a1457) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c3_1(a1457)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[294, 293])).
% 2.39/1.77 tff(296,plain,
% 2.39/1.77 ($false),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[295, 91, 48, 35, 270, 289, 12, 204, 60, 283])).
% 2.39/1.77 tff(297,plain,(hskp5 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~hskp12)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.77 tff(298,plain,
% 2.39/1.77 (~hskp12),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[297, 35, 12, 204, 11])).
% 2.39/1.77 tff(299,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(300,plain,
% 2.39/1.77 ((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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(301,plain,
% 2.39/1.77 (((~![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))))),
% 2.39/1.77 inference(monotonicity,[status(thm)],[300])).
% 2.39/1.77 tff(302,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(transitivity,[status(thm)],[301, 299])).
% 2.39/1.77 tff(303,plain,
% 2.39/1.77 ((~![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)))),
% 2.39/1.77 inference(quant_inst,[status(thm)],[])).
% 2.39/1.77 tff(304,plain,
% 2.39/1.77 ((~![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))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[303, 302])).
% 2.39/1.77 tff(305,plain,
% 2.39/1.77 (~c1_1(a1430)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[304, 91, 298, 35, 12, 204, 214])).
% 2.39/1.77 tff(306,plain,
% 2.39/1.77 (((~![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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(307,plain,
% 2.39/1.77 ((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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(308,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.77 inference(monotonicity,[status(thm)],[307])).
% 2.39/1.77 tff(309,plain,
% 2.39/1.77 (((~![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))),
% 2.39/1.77 inference(transitivity,[status(thm)],[308, 306])).
% 2.39/1.77 tff(310,plain,
% 2.39/1.77 ((~![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))),
% 2.39/1.77 inference(quant_inst,[status(thm)],[])).
% 2.39/1.77 tff(311,plain,
% 2.39/1.77 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430)),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[310, 309])).
% 2.39/1.77 tff(312,plain,
% 2.39/1.77 ($false),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[311, 91, 48, 35, 12, 204, 60, 305])).
% 2.39/1.77 tff(313,plain,(c3_1(a1430) | c0_1(a1430) | c2_1(a1430) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.39/1.77 tff(314,plain,
% 2.39/1.77 (hskp5),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[313, 204, 35, 12])).
% 2.39/1.77 tff(315,plain,
% 2.39/1.77 (((~hskp5) | (~c3_1(a1435))) <=> ((~hskp5) | (~c3_1(a1435)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(316,plain,
% 2.39/1.77 (((~c3_1(a1435)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1435)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(317,axiom,((~c3_1(a1435)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 2.39/1.77 tff(318,plain,
% 2.39/1.77 ((~hskp5) | (~c3_1(a1435))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[317, 316])).
% 2.39/1.77 tff(319,plain,
% 2.39/1.77 ((~hskp5) | (~c3_1(a1435))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[318, 315])).
% 2.39/1.77 tff(320,plain,
% 2.39/1.77 (~c3_1(a1435)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[319, 314])).
% 2.39/1.77 tff(321,plain,
% 2.39/1.77 (((~hskp5) | (~c2_1(a1435))) <=> ((~hskp5) | (~c2_1(a1435)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(322,plain,
% 2.39/1.77 (((~c2_1(a1435)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1435)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(323,axiom,((~c2_1(a1435)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 2.39/1.77 tff(324,plain,
% 2.39/1.77 ((~hskp5) | (~c2_1(a1435))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[323, 322])).
% 2.39/1.77 tff(325,plain,
% 2.39/1.77 ((~hskp5) | (~c2_1(a1435))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[324, 321])).
% 2.39/1.77 tff(326,plain,
% 2.39/1.77 (~c2_1(a1435)),
% 2.39/1.77 inference(unit_resolution,[status(thm)],[325, 314])).
% 2.39/1.77 tff(327,plain,
% 2.39/1.77 (^[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))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(328,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[327])).
% 2.39/1.77 tff(329,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(330,plain,
% 2.39/1.77 (^[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)) | (~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)))))),
% 2.39/1.77 inference(bind,[status(th)],[])).
% 2.39/1.77 tff(331,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(quant_intro,[status(thm)],[330])).
% 2.39/1.77 tff(332,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')).
% 2.39/1.77 tff(333,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[332, 331])).
% 2.39/1.77 tff(334,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[333, 329])).
% 2.39/1.77 tff(335,plain,(
% 2.39/1.77 ![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)))),
% 2.39/1.77 inference(skolemize,[status(sab)],[334])).
% 2.39/1.77 tff(336,plain,
% 2.39/1.77 (![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)))),
% 2.39/1.77 inference(modus_ponens,[status(thm)],[335, 328])).
% 2.39/1.77 tff(337,assumption,(~c1_1(a1435)), introduced(assumption)).
% 2.39/1.77 tff(338,plain,
% 2.39/1.77 (((~![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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(339,plain,
% 2.39/1.77 ((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))),
% 2.39/1.77 inference(rewrite,[status(thm)],[])).
% 2.39/1.77 tff(340,plain,
% 2.39/1.77 (((~![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)))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[339])).
% 2.39/1.78 tff(341,plain,
% 2.39/1.78 (((~![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))),
% 2.39/1.78 inference(transitivity,[status(thm)],[340, 338])).
% 2.39/1.78 tff(342,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(343,plain,
% 2.39/1.78 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[342, 341])).
% 2.39/1.78 tff(344,plain,
% 2.39/1.78 ($false),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[343, 91, 48, 35, 112, 113, 12, 204, 60, 337])).
% 2.39/1.78 tff(345,plain,(c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.78 tff(346,plain,
% 2.39/1.78 (c1_1(a1435)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[345, 320, 35, 12, 204, 326])).
% 2.39/1.78 tff(347,plain,
% 2.39/1.78 (c1_1(a1430)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[311, 91, 48, 35, 12, 204, 60])).
% 2.39/1.78 tff(348,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(349,plain,
% 2.39/1.78 ((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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(350,plain,
% 2.39/1.78 (((~![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))))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[349])).
% 2.39/1.78 tff(351,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(transitivity,[status(thm)],[350, 348])).
% 2.39/1.78 tff(352,plain,
% 2.39/1.78 ((~![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)))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(353,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[352, 351])).
% 2.39/1.78 tff(354,plain,
% 2.39/1.78 (hskp12),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[353, 91, 35, 326, 320, 12, 214, 347, 346])).
% 2.39/1.78 tff(355,plain,
% 2.39/1.78 (~c2_1(a1448)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[220, 354])).
% 2.39/1.78 tff(356,assumption,(hskp17), introduced(assumption)).
% 2.39/1.78 tff(357,plain,
% 2.39/1.78 (~c2_1(a1457)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[288, 356])).
% 2.39/1.78 tff(358,plain,
% 2.39/1.78 (~c1_1(a1457)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[269, 356])).
% 2.39/1.78 tff(359,plain,
% 2.39/1.78 (c3_1(a1457)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[295, 91, 48, 35, 358, 357, 12, 204, 60])).
% 2.39/1.78 tff(360,plain,
% 2.39/1.78 (^[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))))),
% 2.39/1.78 inference(bind,[status(th)],[])).
% 2.39/1.78 tff(361,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(quant_intro,[status(thm)],[360])).
% 2.39/1.78 tff(362,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(363,plain,
% 2.39/1.78 (^[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)))))),
% 2.39/1.78 inference(bind,[status(th)],[])).
% 2.39/1.78 tff(364,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(quant_intro,[status(thm)],[363])).
% 2.39/1.78 tff(365,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')).
% 2.39/1.78 tff(366,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[365, 364])).
% 2.39/1.78 tff(367,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[366, 362])).
% 2.39/1.78 tff(368,plain,(
% 2.39/1.78 ![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)))),
% 2.39/1.78 inference(skolemize,[status(sab)],[367])).
% 2.39/1.78 tff(369,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[368, 361])).
% 2.39/1.78 tff(370,plain,
% 2.39/1.78 (~c0_1(a1457)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[275, 356])).
% 2.39/1.78 tff(371,plain,
% 2.39/1.78 (^[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))))),
% 2.39/1.78 inference(bind,[status(th)],[])).
% 2.39/1.78 tff(372,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(quant_intro,[status(thm)],[371])).
% 2.39/1.78 tff(373,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(374,plain,
% 2.39/1.78 (^[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)))))),
% 2.39/1.78 inference(bind,[status(th)],[])).
% 2.39/1.78 tff(375,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(quant_intro,[status(thm)],[374])).
% 2.39/1.78 tff(376,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')).
% 2.39/1.78 tff(377,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[376, 375])).
% 2.39/1.78 tff(378,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[377, 373])).
% 2.39/1.78 tff(379,plain,(
% 2.39/1.78 ![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)))),
% 2.39/1.78 inference(skolemize,[status(sab)],[378])).
% 2.39/1.78 tff(380,plain,
% 2.39/1.78 (![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)))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[379, 372])).
% 2.39/1.78 tff(381,plain,
% 2.39/1.78 (((~hskp5) | c0_1(a1435)) <=> ((~hskp5) | c0_1(a1435))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(382,axiom,((~hskp5) | c0_1(a1435)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 2.39/1.78 tff(383,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[382, 381])).
% 2.39/1.78 tff(384,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[383, 381])).
% 2.39/1.78 tff(385,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[384, 381])).
% 2.39/1.78 tff(386,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[385, 381])).
% 2.39/1.78 tff(387,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[386, 381])).
% 2.39/1.78 tff(388,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[387, 381])).
% 2.39/1.78 tff(389,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[388, 381])).
% 2.39/1.78 tff(390,plain,
% 2.39/1.78 ((~hskp5) | c0_1(a1435)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[389, 381])).
% 2.39/1.78 tff(391,plain,
% 2.39/1.78 (c0_1(a1435)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[390, 314])).
% 2.39/1.78 tff(392,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(393,plain,
% 2.39/1.78 ((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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(394,plain,
% 2.39/1.78 (((~![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))))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[393])).
% 2.39/1.78 tff(395,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(transitivity,[status(thm)],[394, 392])).
% 2.39/1.78 tff(396,plain,
% 2.39/1.78 ((~![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)))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(397,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[396, 395])).
% 2.39/1.78 tff(398,plain,
% 2.39/1.78 (hskp18),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[397, 91, 391, 326, 320, 380, 346])).
% 2.39/1.78 tff(399,plain,
% 2.39/1.78 (((~hskp18) | (~c2_1(a1458))) <=> ((~hskp18) | (~c2_1(a1458)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(400,plain,
% 2.39/1.78 (((~c2_1(a1458)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1458)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(401,axiom,((~c2_1(a1458)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 2.39/1.78 tff(402,plain,
% 2.39/1.78 ((~hskp18) | (~c2_1(a1458))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[401, 400])).
% 2.39/1.78 tff(403,plain,
% 2.39/1.78 ((~hskp18) | (~c2_1(a1458))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[402, 399])).
% 2.39/1.78 tff(404,plain,
% 2.39/1.78 (~c2_1(a1458)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[403, 398])).
% 2.39/1.78 tff(405,plain,
% 2.39/1.78 (((~hskp18) | c1_1(a1458)) <=> ((~hskp18) | c1_1(a1458))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(406,axiom,((~hskp18) | c1_1(a1458)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 2.39/1.78 tff(407,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[406, 405])).
% 2.39/1.78 tff(408,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[407, 405])).
% 2.39/1.78 tff(409,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[408, 405])).
% 2.39/1.78 tff(410,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[409, 405])).
% 2.39/1.78 tff(411,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[410, 405])).
% 2.39/1.78 tff(412,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[411, 405])).
% 2.39/1.78 tff(413,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[412, 405])).
% 2.39/1.78 tff(414,plain,
% 2.39/1.78 ((~hskp18) | c1_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[413, 405])).
% 2.39/1.78 tff(415,plain,
% 2.39/1.78 (c1_1(a1458)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[414, 398])).
% 2.39/1.78 tff(416,plain,
% 2.39/1.78 (((~hskp18) | c0_1(a1458)) <=> ((~hskp18) | c0_1(a1458))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(417,axiom,((~hskp18) | c0_1(a1458)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 2.39/1.78 tff(418,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[417, 416])).
% 2.39/1.78 tff(419,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[418, 416])).
% 2.39/1.78 tff(420,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[419, 416])).
% 2.39/1.78 tff(421,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[420, 416])).
% 2.39/1.78 tff(422,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[421, 416])).
% 2.39/1.78 tff(423,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[422, 416])).
% 2.39/1.78 tff(424,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[423, 416])).
% 2.39/1.78 tff(425,plain,
% 2.39/1.78 ((~hskp18) | c0_1(a1458)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[424, 416])).
% 2.39/1.78 tff(426,plain,
% 2.39/1.78 (c0_1(a1458)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[425, 398])).
% 2.39/1.78 tff(427,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(428,plain,
% 2.39/1.78 ((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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(429,plain,
% 2.39/1.78 (((~![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))))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[428])).
% 2.39/1.78 tff(430,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(transitivity,[status(thm)],[429, 427])).
% 2.39/1.78 tff(431,plain,
% 2.39/1.78 ((~![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)))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(432,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[431, 430])).
% 2.39/1.78 tff(433,plain,
% 2.39/1.78 (hskp10 | (~c3_1(a1457))),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[432, 91, 426, 415, 404, 370, 357, 369])).
% 2.39/1.78 tff(434,plain,
% 2.39/1.78 (hskp10),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[433, 359])).
% 2.39/1.78 tff(435,plain,
% 2.39/1.78 (((~hskp10) | (~c3_1(a1445))) <=> ((~hskp10) | (~c3_1(a1445)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(436,plain,
% 2.39/1.78 (((~c3_1(a1445)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1445)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(437,axiom,((~c3_1(a1445)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 2.39/1.78 tff(438,plain,
% 2.39/1.78 ((~hskp10) | (~c3_1(a1445))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[437, 436])).
% 2.39/1.78 tff(439,plain,
% 2.39/1.78 ((~hskp10) | (~c3_1(a1445))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[438, 435])).
% 2.39/1.78 tff(440,plain,
% 2.39/1.78 (~c3_1(a1445)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[439, 434])).
% 2.39/1.78 tff(441,plain,
% 2.39/1.78 (((~hskp10) | (~c1_1(a1445))) <=> ((~hskp10) | (~c1_1(a1445)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(442,plain,
% 2.39/1.78 (((~c1_1(a1445)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1445)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(443,axiom,((~c1_1(a1445)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 2.39/1.78 tff(444,plain,
% 2.39/1.78 ((~hskp10) | (~c1_1(a1445))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[443, 442])).
% 2.39/1.78 tff(445,plain,
% 2.39/1.78 ((~hskp10) | (~c1_1(a1445))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[444, 441])).
% 2.39/1.78 tff(446,plain,
% 2.39/1.78 (~c1_1(a1445)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[445, 434])).
% 2.39/1.78 tff(447,plain,
% 2.39/1.78 (((~hskp10) | c0_1(a1445)) <=> ((~hskp10) | c0_1(a1445))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(448,axiom,((~hskp10) | c0_1(a1445)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 2.39/1.78 tff(449,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[448, 447])).
% 2.39/1.78 tff(450,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[449, 447])).
% 2.39/1.78 tff(451,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[450, 447])).
% 2.39/1.78 tff(452,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[451, 447])).
% 2.39/1.78 tff(453,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[452, 447])).
% 2.39/1.78 tff(454,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[453, 447])).
% 2.39/1.78 tff(455,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[454, 447])).
% 2.39/1.78 tff(456,plain,
% 2.39/1.78 ((~hskp10) | c0_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[455, 447])).
% 2.39/1.78 tff(457,plain,
% 2.39/1.78 (c0_1(a1445)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[456, 434])).
% 2.39/1.78 tff(458,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(459,plain,
% 2.39/1.78 (((~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)))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(460,plain,
% 2.39/1.78 (((~![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))))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[459])).
% 2.39/1.78 tff(461,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(transitivity,[status(thm)],[460, 458])).
% 2.39/1.78 tff(462,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(463,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[462, 461])).
% 2.39/1.78 tff(464,plain,
% 2.39/1.78 (~c2_1(a1445)),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[463, 91, 457, 370, 358, 357, 446, 440, 23])).
% 2.39/1.78 tff(465,plain,
% 2.39/1.78 (((~![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))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(466,plain,
% 2.39/1.78 ((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))),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(467,plain,
% 2.39/1.78 (((~![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)))),
% 2.39/1.78 inference(monotonicity,[status(thm)],[466])).
% 2.39/1.78 tff(468,plain,
% 2.39/1.78 (((~![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))),
% 2.39/1.78 inference(transitivity,[status(thm)],[467, 465])).
% 2.39/1.78 tff(469,plain,
% 2.39/1.78 ((~![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))),
% 2.39/1.78 inference(quant_inst,[status(thm)],[])).
% 2.39/1.78 tff(470,plain,
% 2.39/1.78 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1430) | c1_1(a1445) | c3_1(a1445) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c2_1(a1445)),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[469, 468])).
% 2.39/1.78 tff(471,plain,
% 2.39/1.78 ($false),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[470, 91, 48, 35, 446, 440, 12, 204, 60, 464])).
% 2.39/1.78 tff(472,plain,((~hskp17) | c3_1(a1430) | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.78 tff(473,plain,
% 2.39/1.78 (~hskp17),
% 2.39/1.78 inference(unit_resolution,[status(thm)],[472, 204, 12, 35])).
% 2.39/1.78 tff(474,plain,
% 2.39/1.78 ((hskp25 | hskp17 | hskp2) <=> (hskp25 | hskp17 | hskp2)),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(475,plain,
% 2.39/1.78 (((hskp25 | hskp2) | hskp17) <=> (hskp25 | hskp17 | hskp2)),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(476,plain,
% 2.39/1.78 ((hskp25 | hskp2) <=> (hskp25 | hskp2)),
% 2.39/1.78 inference(rewrite,[status(thm)],[])).
% 2.39/1.78 tff(477,plain,
% 2.39/1.78 (((hskp25 | hskp2) | hskp17) <=> ((hskp25 | hskp2) | hskp17)),
% 2.39/1.78 inference(monotonicity,[status(thm)],[476])).
% 2.39/1.78 tff(478,plain,
% 2.39/1.78 (((hskp25 | hskp2) | hskp17) <=> (hskp25 | hskp17 | hskp2)),
% 2.39/1.78 inference(transitivity,[status(thm)],[477, 475])).
% 2.39/1.78 tff(479,axiom,((hskp25 | hskp2) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 2.39/1.78 tff(480,plain,
% 2.39/1.78 (hskp25 | hskp17 | hskp2),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[479, 478])).
% 2.39/1.78 tff(481,plain,
% 2.39/1.78 (hskp25 | hskp17 | hskp2),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[480, 474])).
% 2.39/1.78 tff(482,plain,
% 2.39/1.78 (hskp25 | hskp17 | hskp2),
% 2.39/1.78 inference(modus_ponens,[status(thm)],[481, 474])).
% 2.39/1.79 tff(483,plain,
% 2.39/1.79 (hskp25 | hskp17 | hskp2),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[482, 474])).
% 2.39/1.79 tff(484,plain,
% 2.39/1.79 (hskp25 | hskp17 | hskp2),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[483, 474])).
% 2.39/1.79 tff(485,plain,
% 2.39/1.79 (hskp25 | hskp17 | hskp2),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[484, 474])).
% 2.39/1.79 tff(486,plain,
% 2.39/1.79 (hskp25 | hskp17 | hskp2),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[485, 474])).
% 2.39/1.79 tff(487,plain,
% 2.39/1.79 (hskp25 | hskp17 | hskp2),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[486, 474])).
% 2.39/1.79 tff(488,plain,
% 2.39/1.79 (hskp25),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[487, 473, 48])).
% 2.39/1.79 tff(489,plain,
% 2.39/1.79 (((~hskp25) | (~c0_1(a1504))) <=> ((~hskp25) | (~c0_1(a1504)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(490,plain,
% 2.39/1.79 (((~c0_1(a1504)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1504)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(491,axiom,((~c0_1(a1504)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 2.39/1.79 tff(492,plain,
% 2.39/1.79 ((~hskp25) | (~c0_1(a1504))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[491, 490])).
% 2.39/1.79 tff(493,plain,
% 2.39/1.79 ((~hskp25) | (~c0_1(a1504))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[492, 489])).
% 2.39/1.79 tff(494,plain,
% 2.39/1.79 (~c0_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[493, 488])).
% 2.39/1.79 tff(495,plain,
% 2.39/1.79 (c3_1(a1448)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[242, 354])).
% 2.39/1.79 tff(496,plain,
% 2.39/1.79 (c0_1(a1448)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[231, 354])).
% 2.39/1.79 tff(497,plain,
% 2.39/1.79 (((~hskp25) | c1_1(a1504)) <=> ((~hskp25) | c1_1(a1504))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(498,axiom,((~hskp25) | c1_1(a1504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 2.39/1.79 tff(499,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[498, 497])).
% 2.39/1.79 tff(500,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[499, 497])).
% 2.39/1.79 tff(501,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[500, 497])).
% 2.39/1.79 tff(502,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[501, 497])).
% 2.39/1.79 tff(503,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[502, 497])).
% 2.39/1.79 tff(504,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[503, 497])).
% 2.39/1.79 tff(505,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[504, 497])).
% 2.39/1.79 tff(506,plain,
% 2.39/1.79 ((~hskp25) | c1_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[505, 497])).
% 2.39/1.79 tff(507,plain,
% 2.39/1.79 (c1_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[506, 488])).
% 2.39/1.79 tff(508,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(509,plain,
% 2.39/1.79 ((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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(510,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[509])).
% 2.39/1.79 tff(511,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[510, 508])).
% 2.39/1.79 tff(512,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(513,plain,
% 2.39/1.79 ((~![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))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[512, 511])).
% 2.39/1.79 tff(514,plain,
% 2.39/1.79 (~c3_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[513, 91, 473, 507, 496, 495, 494, 355, 336])).
% 2.39/1.79 tff(515,plain,
% 2.39/1.79 (^[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))))),
% 2.39/1.79 inference(bind,[status(th)],[])).
% 2.39/1.79 tff(516,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(quant_intro,[status(thm)],[515])).
% 2.39/1.79 tff(517,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(518,plain,
% 2.39/1.79 (^[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)))))),
% 2.39/1.79 inference(bind,[status(th)],[])).
% 2.39/1.79 tff(519,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(quant_intro,[status(thm)],[518])).
% 2.39/1.79 tff(520,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')).
% 2.39/1.79 tff(521,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[520, 519])).
% 2.39/1.79 tff(522,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[521, 517])).
% 2.39/1.79 tff(523,plain,(
% 2.39/1.79 ![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)))),
% 2.39/1.79 inference(skolemize,[status(sab)],[522])).
% 2.39/1.79 tff(524,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[523, 516])).
% 2.39/1.79 tff(525,plain,
% 2.39/1.79 (((~hskp25) | c2_1(a1504)) <=> ((~hskp25) | c2_1(a1504))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(526,axiom,((~hskp25) | c2_1(a1504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 2.39/1.79 tff(527,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[526, 525])).
% 2.39/1.79 tff(528,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[527, 525])).
% 2.39/1.79 tff(529,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[528, 525])).
% 2.39/1.79 tff(530,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[529, 525])).
% 2.39/1.79 tff(531,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[530, 525])).
% 2.39/1.79 tff(532,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[531, 525])).
% 2.39/1.79 tff(533,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[532, 525])).
% 2.39/1.79 tff(534,plain,
% 2.39/1.79 ((~hskp25) | c2_1(a1504)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[533, 525])).
% 2.39/1.79 tff(535,plain,
% 2.39/1.79 (c2_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[534, 488])).
% 2.39/1.79 tff(536,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(537,plain,
% 2.39/1.79 ((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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(538,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[537])).
% 2.39/1.79 tff(539,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[538, 536])).
% 2.39/1.79 tff(540,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(541,plain,
% 2.39/1.79 ((~![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))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[540, 539])).
% 2.39/1.79 tff(542,plain,
% 2.39/1.79 (hskp14),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[541, 91, 507, 535, 494, 524, 514])).
% 2.39/1.79 tff(543,plain,
% 2.39/1.79 (((~hskp14) | (~c3_1(a1451))) <=> ((~hskp14) | (~c3_1(a1451)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(544,plain,
% 2.39/1.79 (((~c3_1(a1451)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1451)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(545,axiom,((~c3_1(a1451)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 2.39/1.79 tff(546,plain,
% 2.39/1.79 ((~hskp14) | (~c3_1(a1451))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[545, 544])).
% 2.39/1.79 tff(547,plain,
% 2.39/1.79 ((~hskp14) | (~c3_1(a1451))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[546, 543])).
% 2.39/1.79 tff(548,plain,
% 2.39/1.79 (~c3_1(a1451)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[547, 542])).
% 2.39/1.79 tff(549,plain,
% 2.39/1.79 (((~hskp14) | (~c1_1(a1451))) <=> ((~hskp14) | (~c1_1(a1451)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(550,plain,
% 2.39/1.79 (((~c1_1(a1451)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1451)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(551,axiom,((~c1_1(a1451)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 2.39/1.79 tff(552,plain,
% 2.39/1.79 ((~hskp14) | (~c1_1(a1451))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[551, 550])).
% 2.39/1.79 tff(553,plain,
% 2.39/1.79 ((~hskp14) | (~c1_1(a1451))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[552, 549])).
% 2.39/1.79 tff(554,plain,
% 2.39/1.79 (~c1_1(a1451)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[553, 542])).
% 2.39/1.79 tff(555,plain,
% 2.39/1.79 (((~hskp14) | c2_1(a1451)) <=> ((~hskp14) | c2_1(a1451))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(556,axiom,((~hskp14) | c2_1(a1451)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 2.39/1.79 tff(557,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[556, 555])).
% 2.39/1.79 tff(558,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[557, 555])).
% 2.39/1.79 tff(559,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[558, 555])).
% 2.39/1.79 tff(560,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[559, 555])).
% 2.39/1.79 tff(561,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[560, 555])).
% 2.39/1.79 tff(562,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[561, 555])).
% 2.39/1.79 tff(563,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[562, 555])).
% 2.39/1.79 tff(564,plain,
% 2.39/1.79 ((~hskp14) | c2_1(a1451)),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[563, 555])).
% 2.39/1.79 tff(565,plain,
% 2.39/1.79 (c2_1(a1451)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[564, 542])).
% 2.39/1.79 tff(566,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(567,plain,
% 2.39/1.79 (((~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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(568,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[567])).
% 2.39/1.79 tff(569,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[568, 566])).
% 2.39/1.79 tff(570,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(571,plain,
% 2.39/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a1504) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[570, 569])).
% 2.39/1.79 tff(572,plain,
% 2.39/1.79 ($false),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[571, 91, 507, 535, 565, 391, 494, 554, 548, 326, 320, 203])).
% 2.39/1.79 tff(573,plain,(c2_1(a1430) | c0_1(a1430) | c3_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.79 tff(574,plain,
% 2.39/1.79 (c2_1(a1430)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[573, 35, 12])).
% 2.39/1.79 tff(575,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(576,plain,
% 2.39/1.79 ((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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(577,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[576])).
% 2.39/1.79 tff(578,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[577, 575])).
% 2.39/1.79 tff(579,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(580,plain,
% 2.39/1.79 ((~![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))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[579, 578])).
% 2.39/1.79 tff(581,plain,
% 2.39/1.79 (~c1_1(a1430)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[580, 91, 13, 114, 113, 12, 574, 193, 183])).
% 2.39/1.79 tff(582,plain,
% 2.39/1.79 (^[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))))),
% 2.39/1.79 inference(bind,[status(th)],[])).
% 2.39/1.79 tff(583,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(quant_intro,[status(thm)],[582])).
% 2.39/1.79 tff(584,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(585,plain,
% 2.39/1.79 (^[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)))))),
% 2.39/1.79 inference(bind,[status(th)],[])).
% 2.39/1.79 tff(586,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(quant_intro,[status(thm)],[585])).
% 2.39/1.79 tff(587,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')).
% 2.39/1.79 tff(588,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[587, 586])).
% 2.39/1.79 tff(589,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[588, 584])).
% 2.39/1.79 tff(590,plain,(
% 2.39/1.79 ![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)))),
% 2.39/1.79 inference(skolemize,[status(sab)],[589])).
% 2.39/1.79 tff(591,plain,
% 2.39/1.79 (![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)))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[590, 583])).
% 2.39/1.79 tff(592,assumption,(~c1_1(a1430)), introduced(assumption)).
% 2.39/1.79 tff(593,assumption,(c2_1(a1430)), introduced(assumption)).
% 2.39/1.79 tff(594,assumption,(hskp25), introduced(assumption)).
% 2.39/1.79 tff(595,plain,
% 2.39/1.79 (~c0_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[493, 594])).
% 2.39/1.79 tff(596,plain,
% 2.39/1.79 (c2_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[534, 594])).
% 2.39/1.79 tff(597,plain,
% 2.39/1.79 (c1_1(a1504)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[506, 594])).
% 2.39/1.79 tff(598,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(599,plain,
% 2.39/1.79 (((~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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(600,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[599])).
% 2.39/1.79 tff(601,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[600, 598])).
% 2.39/1.79 tff(602,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(603,plain,
% 2.39/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1430) | c0_1(a1504) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[602, 601])).
% 2.39/1.79 tff(604,plain,
% 2.39/1.79 ($false),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[603, 91, 597, 596, 114, 35, 595, 112, 113, 593, 203, 592])).
% 2.39/1.79 tff(605,plain,((~hskp25) | (~c0_1(a1435)) | c3_1(a1430) | c2_1(a1435) | c3_1(a1435) | (~c2_1(a1430)) | c1_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.79 tff(606,plain,
% 2.39/1.79 (~hskp25),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[605, 581, 35, 112, 113, 574, 114])).
% 2.39/1.79 tff(607,plain,
% 2.39/1.79 (hskp17),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[487, 606, 48])).
% 2.39/1.79 tff(608,plain,
% 2.39/1.79 (~c2_1(a1457)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[288, 607])).
% 2.39/1.79 tff(609,plain,
% 2.39/1.79 (~c0_1(a1457)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[275, 607])).
% 2.39/1.79 tff(610,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(611,plain,
% 2.39/1.79 (((~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)))),
% 2.39/1.79 inference(rewrite,[status(thm)],[])).
% 2.39/1.79 tff(612,plain,
% 2.39/1.79 (((~![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))))),
% 2.39/1.79 inference(monotonicity,[status(thm)],[611])).
% 2.39/1.79 tff(613,plain,
% 2.39/1.79 (((~![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)))),
% 2.39/1.79 inference(transitivity,[status(thm)],[612, 610])).
% 2.39/1.79 tff(614,plain,
% 2.39/1.79 ((~![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)))),
% 2.39/1.79 inference(quant_inst,[status(thm)],[])).
% 2.39/1.79 tff(615,plain,
% 2.39/1.79 ((~![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))),
% 2.39/1.79 inference(modus_ponens,[status(thm)],[614, 613])).
% 2.39/1.79 tff(616,plain,
% 2.39/1.79 (~c3_1(a1457)),
% 2.39/1.79 inference(unit_resolution,[status(thm)],[615, 91, 114, 35, 609, 608, 112, 574, 591, 581, 183])).
% 2.39/1.79 tff(617,plain,
% 2.39/1.79 (^[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)))),
% 2.39/1.79 inference(bind,[status(th)],[])).
% 2.39/1.79 tff(618,plain,
% 2.39/1.79 (![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[617])).
% 2.39/1.80 tff(619,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(620,plain,
% 2.39/1.80 (^[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))))),
% 2.39/1.80 inference(bind,[status(th)],[])).
% 2.39/1.80 tff(621,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[620])).
% 2.39/1.80 tff(622,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')).
% 2.39/1.80 tff(623,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[622, 621])).
% 2.39/1.80 tff(624,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[623, 619])).
% 2.39/1.80 tff(625,plain,(
% 2.39/1.80 ![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))),
% 2.39/1.80 inference(skolemize,[status(sab)],[624])).
% 2.39/1.80 tff(626,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[625, 618])).
% 2.39/1.80 tff(627,plain,
% 2.39/1.80 (^[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)))),
% 2.39/1.80 inference(bind,[status(th)],[])).
% 2.39/1.80 tff(628,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[627])).
% 2.39/1.80 tff(629,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(630,plain,
% 2.39/1.80 (^[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))))),
% 2.39/1.80 inference(bind,[status(th)],[])).
% 2.39/1.80 tff(631,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[630])).
% 2.39/1.80 tff(632,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 2.39/1.80 tff(633,plain,
% 2.39/1.80 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[632, 631])).
% 2.39/1.80 tff(634,plain,
% 2.39/1.80 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[633, 629])).
% 2.39/1.80 tff(635,plain,(
% 2.39/1.80 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.39/1.80 inference(skolemize,[status(sab)],[634])).
% 2.39/1.80 tff(636,plain,
% 2.39/1.80 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[635, 628])).
% 2.39/1.80 tff(637,plain,
% 2.39/1.80 (~c1_1(a1457)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[269, 607])).
% 2.39/1.80 tff(638,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(639,plain,
% 2.39/1.80 ((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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(640,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[639])).
% 2.39/1.80 tff(641,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(transitivity,[status(thm)],[640, 638])).
% 2.39/1.80 tff(642,plain,
% 2.39/1.80 ((~![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))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(643,plain,
% 2.39/1.80 ((~![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)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[642, 641])).
% 2.39/1.80 tff(644,plain,
% 2.39/1.80 (hskp1),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[643, 91, 48, 609, 637, 608, 636])).
% 2.39/1.80 tff(645,plain,
% 2.39/1.80 (((~hskp1) | (~c0_1(a1429))) <=> ((~hskp1) | (~c0_1(a1429)))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(646,plain,
% 2.39/1.80 (((~c0_1(a1429)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1429)))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(647,axiom,((~c0_1(a1429)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 2.39/1.80 tff(648,plain,
% 2.39/1.80 ((~hskp1) | (~c0_1(a1429))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[647, 646])).
% 2.39/1.80 tff(649,plain,
% 2.39/1.80 ((~hskp1) | (~c0_1(a1429))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[648, 645])).
% 2.39/1.80 tff(650,plain,
% 2.39/1.80 (~c0_1(a1429)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[649, 644])).
% 2.39/1.80 tff(651,plain,
% 2.39/1.80 (((~hskp1) | c3_1(a1429)) <=> ((~hskp1) | c3_1(a1429))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(652,axiom,((~hskp1) | c3_1(a1429)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 2.39/1.80 tff(653,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[652, 651])).
% 2.39/1.80 tff(654,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[653, 651])).
% 2.39/1.80 tff(655,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[654, 651])).
% 2.39/1.80 tff(656,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[655, 651])).
% 2.39/1.80 tff(657,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[656, 651])).
% 2.39/1.80 tff(658,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[657, 651])).
% 2.39/1.80 tff(659,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[658, 651])).
% 2.39/1.80 tff(660,plain,
% 2.39/1.80 ((~hskp1) | c3_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[659, 651])).
% 2.39/1.80 tff(661,plain,
% 2.39/1.80 (c3_1(a1429)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[660, 644])).
% 2.39/1.80 tff(662,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(663,plain,
% 2.39/1.80 (((~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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(664,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[663])).
% 2.39/1.80 tff(665,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(transitivity,[status(thm)],[664, 662])).
% 2.39/1.80 tff(666,plain,
% 2.39/1.80 ((~![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))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(667,plain,
% 2.39/1.80 ((~![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)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[666, 665])).
% 2.39/1.80 tff(668,plain,
% 2.39/1.80 (c1_1(a1429)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[667, 91, 35, 661, 637, 608, 574, 650, 626, 581, 616])).
% 2.39/1.80 tff(669,plain,
% 2.39/1.80 (^[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)))),
% 2.39/1.80 inference(bind,[status(th)],[])).
% 2.39/1.80 tff(670,plain,
% 2.39/1.80 (![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)) <=> ![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[669])).
% 2.39/1.80 tff(671,plain,
% 2.39/1.80 (![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)) <=> ![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(672,plain,
% 2.39/1.80 (^[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))))),
% 2.39/1.80 inference(bind,[status(th)],[])).
% 2.39/1.80 tff(673,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(quant_intro,[status(thm)],[672])).
% 2.39/1.80 tff(674,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')).
% 2.39/1.80 tff(675,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[674, 673])).
% 2.39/1.80 tff(676,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[675, 671])).
% 2.39/1.80 tff(677,plain,(
% 2.39/1.80 ![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))),
% 2.39/1.80 inference(skolemize,[status(sab)],[676])).
% 2.39/1.80 tff(678,plain,
% 2.39/1.80 (![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[677, 670])).
% 2.39/1.80 tff(679,plain,
% 2.39/1.80 (((~hskp1) | c2_1(a1429)) <=> ((~hskp1) | c2_1(a1429))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(680,axiom,((~hskp1) | c2_1(a1429)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 2.39/1.80 tff(681,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[680, 679])).
% 2.39/1.80 tff(682,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[681, 679])).
% 2.39/1.80 tff(683,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[682, 679])).
% 2.39/1.80 tff(684,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[683, 679])).
% 2.39/1.80 tff(685,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[684, 679])).
% 2.39/1.80 tff(686,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[685, 679])).
% 2.39/1.80 tff(687,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[686, 679])).
% 2.39/1.80 tff(688,plain,
% 2.39/1.80 ((~hskp1) | c2_1(a1429)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[687, 679])).
% 2.39/1.80 tff(689,plain,
% 2.39/1.80 (c2_1(a1429)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[688, 644])).
% 2.39/1.80 tff(690,plain,
% 2.39/1.80 (((~![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 | 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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(691,plain,
% 2.39/1.80 ((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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(692,plain,
% 2.39/1.80 (((~![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(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)))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[691])).
% 2.39/1.80 tff(693,plain,
% 2.39/1.80 (((~![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(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))),
% 2.39/1.80 inference(transitivity,[status(thm)],[692, 690])).
% 2.39/1.80 tff(694,plain,
% 2.39/1.80 ((~![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(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457) | c2_1(a1457) | c1_1(a1457))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(695,plain,
% 2.39/1.80 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1429)) | c3_1(a1457)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[694, 693])).
% 2.39/1.80 tff(696,plain,
% 2.39/1.80 ($false),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[695, 91, 13, 689, 661, 637, 608, 678, 616, 668])).
% 2.39/1.80 tff(697,plain,(hskp7 | c3_1(a1430) | (~c0_1(a1435)) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.80 tff(698,plain,
% 2.39/1.80 (~c0_1(a1435)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[697, 113, 35, 13, 112, 12])).
% 2.39/1.80 tff(699,plain,
% 2.39/1.80 (~hskp5),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[390, 698])).
% 2.39/1.80 tff(700,assumption,(~c0_1(a1435)), introduced(assumption)).
% 2.39/1.80 tff(701,assumption,(~hskp12), introduced(assumption)).
% 2.39/1.80 tff(702,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(703,plain,
% 2.39/1.80 ((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)))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(704,plain,
% 2.39/1.80 (((~![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))))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[703])).
% 2.39/1.80 tff(705,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(transitivity,[status(thm)],[704, 702])).
% 2.39/1.80 tff(706,plain,
% 2.39/1.80 ((~![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)))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(707,plain,
% 2.39/1.80 ((~![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))),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[706, 705])).
% 2.39/1.80 tff(708,plain,
% 2.39/1.80 (hskp12 | c0_1(a1435) | (~c1_1(a1435))),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[707, 91, 112, 113, 214])).
% 2.39/1.80 tff(709,plain,
% 2.39/1.80 (~c1_1(a1435)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[708, 700, 701])).
% 2.39/1.80 tff(710,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(711,plain,
% 2.39/1.80 ((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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(712,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[711])).
% 2.39/1.80 tff(713,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(transitivity,[status(thm)],[712, 710])).
% 2.39/1.80 tff(714,plain,
% 2.39/1.80 ((~![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))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(715,plain,
% 2.39/1.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435)),
% 2.39/1.80 inference(modus_ponens,[status(thm)],[714, 713])).
% 2.39/1.80 tff(716,plain,
% 2.39/1.80 (c0_1(a1435) | c1_1(a1435)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[715, 91, 61, 112, 113, 60])).
% 2.39/1.80 tff(717,plain,
% 2.39/1.80 ($false),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[716, 709, 700])).
% 2.39/1.80 tff(718,plain,(c0_1(a1435) | hskp2 | c2_1(a1435) | c3_1(a1435) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.39/1.80 tff(719,plain,
% 2.39/1.80 (hskp12),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[718, 700, 112, 113, 61])).
% 2.39/1.80 tff(720,plain,
% 2.39/1.80 (~c2_1(a1448)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[220, 719])).
% 2.39/1.80 tff(721,plain,
% 2.39/1.80 (hskp17),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[263, 720, 11, 719])).
% 2.39/1.80 tff(722,plain,
% 2.39/1.80 (~c1_1(a1457)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[269, 721])).
% 2.39/1.80 tff(723,plain,
% 2.39/1.80 (~c0_1(a1457)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[275, 721])).
% 2.39/1.80 tff(724,plain,
% 2.39/1.80 (c3_1(a1448)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[242, 719])).
% 2.39/1.80 tff(725,plain,
% 2.39/1.80 (c0_1(a1448)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[231, 719])).
% 2.39/1.80 tff(726,plain,
% 2.39/1.80 (~c3_1(a1457)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[282, 91, 11, 725, 724, 723, 722, 720, 10])).
% 2.39/1.80 tff(727,plain,
% 2.39/1.80 (~c2_1(a1457)),
% 2.39/1.80 inference(unit_resolution,[status(thm)],[288, 721])).
% 2.39/1.80 tff(728,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(729,plain,
% 2.39/1.80 ((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))),
% 2.39/1.80 inference(rewrite,[status(thm)],[])).
% 2.39/1.80 tff(730,plain,
% 2.39/1.80 (((~![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)))),
% 2.39/1.80 inference(monotonicity,[status(thm)],[729])).
% 2.39/1.80 tff(731,plain,
% 2.39/1.80 (((~![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))),
% 2.39/1.80 inference(transitivity,[status(thm)],[730, 728])).
% 2.39/1.80 tff(732,plain,
% 2.39/1.80 ((~![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))),
% 2.39/1.80 inference(quant_inst,[status(thm)],[])).
% 2.39/1.80 tff(733,plain,
% 2.39/1.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1435) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c3_1(a1457)),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[732, 731])).
% 2.39/1.81 tff(734,plain,
% 2.39/1.81 ($false),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[733, 91, 61, 700, 722, 727, 112, 113, 60, 726])).
% 2.39/1.81 tff(735,plain,(c0_1(a1435) | hskp2 | c2_1(a1435) | c3_1(a1435) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.39/1.81 tff(736,plain,
% 2.39/1.81 ($false),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[735, 699, 698, 112, 113, 48])).
% 2.39/1.81 tff(737,plain,(c3_1(a1435) | c2_1(a1435) | c3_1(a1430) | hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.81 tff(738,plain,
% 2.39/1.81 (c3_1(a1435)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[737, 112, 35, 111, 12])).
% 2.39/1.81 tff(739,plain,
% 2.39/1.81 (~hskp5),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[319, 738])).
% 2.39/1.81 tff(740,assumption,(hskp11), introduced(assumption)).
% 2.39/1.81 tff(741,plain,
% 2.39/1.81 (((~hskp11) | (~c2_1(a1447))) <=> ((~hskp11) | (~c2_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(742,plain,
% 2.39/1.81 (((~c2_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(743,axiom,((~c2_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 2.39/1.81 tff(744,plain,
% 2.39/1.81 ((~hskp11) | (~c2_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[743, 742])).
% 2.39/1.81 tff(745,plain,
% 2.39/1.81 ((~hskp11) | (~c2_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[744, 741])).
% 2.39/1.81 tff(746,plain,
% 2.39/1.81 (~c2_1(a1447)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[745, 740])).
% 2.39/1.81 tff(747,plain,
% 2.39/1.81 (((~hskp11) | (~c0_1(a1447))) <=> ((~hskp11) | (~c0_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(748,plain,
% 2.39/1.81 (((~c0_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(749,axiom,((~c0_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 2.39/1.81 tff(750,plain,
% 2.39/1.81 ((~hskp11) | (~c0_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[749, 748])).
% 2.39/1.81 tff(751,plain,
% 2.39/1.81 ((~hskp11) | (~c0_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[750, 747])).
% 2.39/1.81 tff(752,plain,
% 2.39/1.81 (~c0_1(a1447)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[751, 740])).
% 2.39/1.81 tff(753,plain,
% 2.39/1.81 (((~hskp11) | (~c3_1(a1447))) <=> ((~hskp11) | (~c3_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(754,plain,
% 2.39/1.81 (((~c3_1(a1447)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1447)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(755,axiom,((~c3_1(a1447)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 2.39/1.81 tff(756,plain,
% 2.39/1.81 ((~hskp11) | (~c3_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[755, 754])).
% 2.39/1.81 tff(757,plain,
% 2.39/1.81 ((~hskp11) | (~c3_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[756, 753])).
% 2.39/1.81 tff(758,plain,
% 2.39/1.81 (~c3_1(a1447)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[757, 740])).
% 2.39/1.81 tff(759,assumption,(~c0_1(a1447)), introduced(assumption)).
% 2.39/1.81 tff(760,assumption,(~c3_1(a1447)), introduced(assumption)).
% 2.39/1.81 tff(761,assumption,(~c2_1(a1447)), introduced(assumption)).
% 2.39/1.81 tff(762,plain,
% 2.39/1.81 (((~![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 | 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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(763,plain,
% 2.39/1.81 ((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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(764,plain,
% 2.39/1.81 (((~![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(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)))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[763])).
% 2.39/1.81 tff(765,plain,
% 2.39/1.81 (((~![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(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))),
% 2.39/1.81 inference(transitivity,[status(thm)],[764, 762])).
% 2.39/1.81 tff(766,plain,
% 2.39/1.81 ((~![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(a1447) | c1_1(a1447) | c3_1(a1447) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(767,plain,
% 2.39/1.81 ((~![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 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447)),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[766, 765])).
% 2.39/1.81 tff(768,plain,
% 2.39/1.81 (c0_1(a1447) | c1_1(a1447)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[767, 91, 61, 761, 760, 60])).
% 2.39/1.81 tff(769,plain,
% 2.39/1.81 (c1_1(a1447)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[768, 759])).
% 2.39/1.81 tff(770,plain,
% 2.39/1.81 (((~![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(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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(771,plain,
% 2.39/1.81 ((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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(772,plain,
% 2.39/1.81 (((~![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(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))))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[771])).
% 2.39/1.81 tff(773,plain,
% 2.39/1.81 (((~![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(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)))),
% 2.39/1.81 inference(transitivity,[status(thm)],[772, 770])).
% 2.39/1.81 tff(774,plain,
% 2.39/1.81 ((~![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(a1447) | c3_1(a1447) | (~c1_1(a1447)) | c3_1(a1447) | c0_1(a1447) | (~c1_1(a1447)))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(775,plain,
% 2.39/1.81 ((~![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(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[774, 773])).
% 2.39/1.81 tff(776,plain,
% 2.39/1.81 (hskp12 | c0_1(a1447) | (~c1_1(a1447))),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[775, 91, 761, 760, 214])).
% 2.39/1.81 tff(777,plain,
% 2.39/1.81 (hskp12),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[776, 769, 759])).
% 2.39/1.81 tff(778,plain,
% 2.39/1.81 (~c2_1(a1448)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[220, 777])).
% 2.39/1.81 tff(779,plain,
% 2.39/1.81 (hskp17),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[263, 778, 11, 777])).
% 2.39/1.81 tff(780,plain,
% 2.39/1.81 (~c1_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[269, 779])).
% 2.39/1.81 tff(781,plain,
% 2.39/1.81 (~c0_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[275, 779])).
% 2.39/1.81 tff(782,plain,
% 2.39/1.81 (c3_1(a1448)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[242, 777])).
% 2.39/1.81 tff(783,plain,
% 2.39/1.81 (c0_1(a1448)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[231, 777])).
% 2.39/1.81 tff(784,plain,
% 2.39/1.81 (~c3_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[282, 91, 11, 783, 782, 781, 780, 778, 10])).
% 2.39/1.81 tff(785,plain,
% 2.39/1.81 (~c2_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[288, 779])).
% 2.39/1.81 tff(786,plain,
% 2.39/1.81 (((~![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 | 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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(787,plain,
% 2.39/1.81 ((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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(788,plain,
% 2.39/1.81 (((~![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(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)))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[787])).
% 2.39/1.81 tff(789,plain,
% 2.39/1.81 (((~![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(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))),
% 2.39/1.81 inference(transitivity,[status(thm)],[788, 786])).
% 2.39/1.81 tff(790,plain,
% 2.39/1.81 ((~![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(a1447) | c2_1(a1447) | c0_1(a1447))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(791,plain,
% 2.39/1.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c1_1(a1457) | c2_1(a1457) | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c3_1(a1457)),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[790, 789])).
% 2.39/1.81 tff(792,plain,
% 2.39/1.81 ($false),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[791, 91, 61, 780, 785, 759, 761, 760, 60, 784])).
% 2.39/1.81 tff(793,plain,(c0_1(a1447) | hskp2 | c2_1(a1447) | c3_1(a1447) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.39/1.81 tff(794,plain,
% 2.39/1.81 ($false),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[793, 758, 752, 746, 61, 11])).
% 2.39/1.81 tff(795,plain,((~hskp11) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.39/1.81 tff(796,plain,
% 2.39/1.81 (~hskp11),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[795, 739, 48])).
% 2.39/1.81 tff(797,plain,
% 2.39/1.81 (((~![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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(798,plain,
% 2.39/1.81 ((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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(799,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[798])).
% 2.39/1.81 tff(800,plain,
% 2.39/1.81 (((~![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))),
% 2.39/1.81 inference(transitivity,[status(thm)],[799, 797])).
% 2.39/1.81 tff(801,plain,
% 2.39/1.81 ((~![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)))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(802,plain,
% 2.39/1.81 ((~![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)),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[801, 800])).
% 2.39/1.81 tff(803,plain,
% 2.39/1.81 (hskp11 | hskp5 | c0_1(a1435) | (~c3_1(a1435))),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[802, 91, 112, 34])).
% 2.39/1.81 tff(804,plain,
% 2.39/1.81 (c0_1(a1435)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[803, 796, 739, 738])).
% 2.39/1.81 tff(805,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(806,plain,
% 2.39/1.81 ((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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(807,plain,
% 2.39/1.81 (((~![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))))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[806])).
% 2.39/1.81 tff(808,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(transitivity,[status(thm)],[807, 805])).
% 2.39/1.81 tff(809,plain,
% 2.39/1.81 ((~![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)))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(810,plain,
% 2.39/1.81 ((~![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))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[809, 808])).
% 2.39/1.81 tff(811,plain,
% 2.39/1.81 (hskp17 | hskp5 | (~c3_1(a1435)) | (~c0_1(a1435))),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[810, 91, 112, 253])).
% 2.39/1.81 tff(812,plain,
% 2.39/1.81 (hskp17),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[811, 804, 739, 738])).
% 2.39/1.81 tff(813,plain,
% 2.39/1.81 (~c1_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[269, 812])).
% 2.39/1.81 tff(814,plain,
% 2.39/1.81 (~c0_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[275, 812])).
% 2.39/1.81 tff(815,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(816,plain,
% 2.39/1.81 ((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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(817,plain,
% 2.39/1.81 (((~![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))))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[816])).
% 2.39/1.81 tff(818,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(transitivity,[status(thm)],[817, 815])).
% 2.39/1.81 tff(819,plain,
% 2.39/1.81 ((~![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)))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(820,plain,
% 2.39/1.81 ((~![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))),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[819, 818])).
% 2.39/1.81 tff(821,plain,
% 2.39/1.81 (~c3_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[820, 91, 739, 804, 814, 813, 112, 738, 10])).
% 2.39/1.81 tff(822,assumption,(c2_1(a1438)), introduced(assumption)).
% 2.39/1.81 tff(823,plain,
% 2.39/1.81 (~c2_1(a1457)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[288, 812])).
% 2.39/1.81 tff(824,plain,
% 2.39/1.81 (hskp1),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[643, 91, 48, 814, 813, 823, 636])).
% 2.39/1.81 tff(825,plain,
% 2.39/1.81 (~c0_1(a1429)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[649, 824])).
% 2.39/1.81 tff(826,plain,
% 2.39/1.81 (c3_1(a1429)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[660, 824])).
% 2.39/1.81 tff(827,plain,
% 2.39/1.81 (((~![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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(828,plain,
% 2.39/1.81 (((~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))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(829,plain,
% 2.39/1.81 (((~![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)))),
% 2.39/1.81 inference(monotonicity,[status(thm)],[828])).
% 2.39/1.81 tff(830,plain,
% 2.39/1.81 (((~![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))),
% 2.39/1.81 inference(transitivity,[status(thm)],[829, 827])).
% 2.39/1.81 tff(831,plain,
% 2.39/1.81 ((~![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))),
% 2.39/1.81 inference(quant_inst,[status(thm)],[])).
% 2.39/1.81 tff(832,plain,
% 2.39/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c1_1(a1438) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | (~c2_1(a1438)) | c3_1(a1457)),
% 2.39/1.81 inference(modus_ponens,[status(thm)],[831, 830])).
% 2.39/1.81 tff(833,plain,
% 2.39/1.81 (c1_1(a1429)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[832, 91, 49, 826, 813, 823, 24, 825, 626, 822, 821])).
% 2.39/1.81 tff(834,plain,
% 2.39/1.81 (c2_1(a1429)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[688, 824])).
% 2.39/1.81 tff(835,plain,
% 2.39/1.81 ($false),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[695, 91, 111, 834, 826, 813, 823, 678, 821, 833])).
% 2.39/1.81 tff(836,plain,(c2_1(a1435) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.39/1.81 tff(837,plain,
% 2.39/1.81 (c2_1(a1435)),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[836, 49, 24, 100, 35, 12])).
% 2.39/1.81 tff(838,plain,
% 2.39/1.81 (~hskp5),
% 2.39/1.81 inference(unit_resolution,[status(thm)],[325, 837])).
% 2.39/1.81 tff(839,plain,
% 2.39/1.81 (^[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))))),
% 2.39/1.81 inference(bind,[status(th)],[])).
% 2.39/1.81 tff(840,plain,
% 2.39/1.81 (![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)))),
% 2.39/1.81 inference(quant_intro,[status(thm)],[839])).
% 2.39/1.81 tff(841,plain,
% 2.39/1.81 (![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)))),
% 2.39/1.81 inference(rewrite,[status(thm)],[])).
% 2.39/1.81 tff(842,plain,
% 2.39/1.81 (^[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)))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(843,plain,
% 2.45/1.81 (![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)))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[842])).
% 2.45/1.81 tff(844,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')).
% 2.45/1.81 tff(845,plain,
% 2.45/1.81 (![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)))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[844, 843])).
% 2.45/1.81 tff(846,plain,
% 2.45/1.81 (![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)))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[845, 841])).
% 2.45/1.81 tff(847,plain,(
% 2.45/1.81 ![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)))),
% 2.45/1.81 inference(skolemize,[status(sab)],[846])).
% 2.45/1.81 tff(848,plain,
% 2.45/1.81 (![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)))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[847, 840])).
% 2.45/1.81 tff(849,plain,
% 2.45/1.81 (((~![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)))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(850,plain,
% 2.45/1.81 ((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)))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(851,plain,
% 2.45/1.81 (((~![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))))),
% 2.45/1.81 inference(monotonicity,[status(thm)],[850])).
% 2.45/1.81 tff(852,plain,
% 2.45/1.81 (((~![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)))),
% 2.45/1.81 inference(transitivity,[status(thm)],[851, 849])).
% 2.45/1.81 tff(853,plain,
% 2.45/1.81 ((~![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)))),
% 2.45/1.81 inference(quant_inst,[status(thm)],[])).
% 2.45/1.81 tff(854,plain,
% 2.45/1.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c3_1(a1438) | c0_1(a1457) | c1_1(a1457) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1457))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[853, 852])).
% 2.45/1.81 tff(855,plain,
% 2.45/1.81 (~c3_1(a1457)),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[854, 91, 11, 49, 370, 358, 24, 848, 822])).
% 2.45/1.81 tff(856,plain,
% 2.45/1.81 (hskp1),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[643, 91, 61, 370, 358, 357, 636])).
% 2.45/1.81 tff(857,plain,
% 2.45/1.81 (~c0_1(a1429)),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[649, 856])).
% 2.45/1.81 tff(858,plain,
% 2.45/1.81 (c3_1(a1429)),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[660, 856])).
% 2.45/1.81 tff(859,plain,
% 2.45/1.81 (c1_1(a1429)),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[832, 91, 49, 858, 358, 357, 24, 857, 626, 822, 855])).
% 2.45/1.81 tff(860,plain,
% 2.45/1.81 (c2_1(a1429)),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[688, 856])).
% 2.45/1.81 tff(861,plain,
% 2.45/1.81 ($false),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[695, 91, 111, 860, 858, 358, 357, 678, 855, 859])).
% 2.45/1.81 tff(862,plain,((~hskp17) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.45/1.81 tff(863,plain,
% 2.45/1.81 (~hskp17),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[862, 49, 24, 100, 48, 838])).
% 2.45/1.81 tff(864,plain,
% 2.45/1.81 (^[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)))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(865,plain,
% 2.45/1.81 (![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)) <=> ![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))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[864])).
% 2.45/1.81 tff(866,plain,
% 2.45/1.81 (![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)) <=> ![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))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(867,plain,
% 2.45/1.81 (^[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))))),
% 2.45/1.82 inference(bind,[status(th)],[])).
% 2.45/1.82 tff(868,plain,
% 2.45/1.82 (![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))),
% 2.45/1.82 inference(quant_intro,[status(thm)],[867])).
% 2.45/1.82 tff(869,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')).
% 2.45/1.82 tff(870,plain,
% 2.45/1.82 (![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[869, 868])).
% 2.45/1.82 tff(871,plain,
% 2.45/1.82 (![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[870, 866])).
% 2.45/1.82 tff(872,plain,(
% 2.45/1.82 ![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))),
% 2.45/1.82 inference(skolemize,[status(sab)],[871])).
% 2.45/1.82 tff(873,plain,
% 2.45/1.82 (![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[872, 865])).
% 2.45/1.82 tff(874,assumption,(~hskp3), introduced(assumption)).
% 2.45/1.82 tff(875,plain,
% 2.45/1.82 ((hskp22 | hskp17 | hskp3) <=> (hskp22 | hskp17 | hskp3)),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(876,plain,
% 2.45/1.82 (((hskp22 | hskp3) | hskp17) <=> (hskp22 | hskp17 | hskp3)),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(877,axiom,((hskp22 | hskp3) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 2.45/1.82 tff(878,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[877, 876])).
% 2.45/1.82 tff(879,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[878, 875])).
% 2.45/1.82 tff(880,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[879, 875])).
% 2.45/1.82 tff(881,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[880, 875])).
% 2.45/1.82 tff(882,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[881, 875])).
% 2.45/1.82 tff(883,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[882, 875])).
% 2.45/1.82 tff(884,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[883, 875])).
% 2.45/1.82 tff(885,plain,
% 2.45/1.82 (hskp22 | hskp17 | hskp3),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[884, 875])).
% 2.45/1.82 tff(886,plain,
% 2.45/1.82 (hskp22),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[885, 874, 36])).
% 2.45/1.82 tff(887,plain,
% 2.45/1.82 (((~hskp22) | (~c0_1(a1468))) <=> ((~hskp22) | (~c0_1(a1468)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(888,plain,
% 2.45/1.82 (((~c0_1(a1468)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1468)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(889,axiom,((~c0_1(a1468)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 2.45/1.82 tff(890,plain,
% 2.45/1.82 ((~hskp22) | (~c0_1(a1468))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[889, 888])).
% 2.45/1.82 tff(891,plain,
% 2.45/1.82 ((~hskp22) | (~c0_1(a1468))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[890, 887])).
% 2.45/1.82 tff(892,plain,
% 2.45/1.82 (~c0_1(a1468)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[891, 886])).
% 2.45/1.82 tff(893,plain,
% 2.45/1.82 (((~hskp22) | c3_1(a1468)) <=> ((~hskp22) | c3_1(a1468))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(894,axiom,((~hskp22) | c3_1(a1468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 2.45/1.82 tff(895,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[894, 893])).
% 2.45/1.82 tff(896,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[895, 893])).
% 2.45/1.82 tff(897,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[896, 893])).
% 2.45/1.82 tff(898,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[897, 893])).
% 2.45/1.82 tff(899,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[898, 893])).
% 2.45/1.82 tff(900,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[899, 893])).
% 2.45/1.82 tff(901,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[900, 893])).
% 2.45/1.82 tff(902,plain,
% 2.45/1.82 ((~hskp22) | c3_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[901, 893])).
% 2.45/1.82 tff(903,plain,
% 2.45/1.82 (c3_1(a1468)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[902, 886])).
% 2.45/1.82 tff(904,plain,
% 2.45/1.82 (((~hskp22) | c1_1(a1468)) <=> ((~hskp22) | c1_1(a1468))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(905,axiom,((~hskp22) | c1_1(a1468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 2.45/1.82 tff(906,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[905, 904])).
% 2.45/1.82 tff(907,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[906, 904])).
% 2.45/1.82 tff(908,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[907, 904])).
% 2.45/1.82 tff(909,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[908, 904])).
% 2.45/1.82 tff(910,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[909, 904])).
% 2.45/1.82 tff(911,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[910, 904])).
% 2.45/1.82 tff(912,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[911, 904])).
% 2.45/1.82 tff(913,plain,
% 2.45/1.82 ((~hskp22) | c1_1(a1468)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[912, 904])).
% 2.45/1.82 tff(914,plain,
% 2.45/1.82 (c1_1(a1468)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[913, 886])).
% 2.45/1.82 tff(915,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(916,plain,
% 2.45/1.82 ((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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(917,plain,
% 2.45/1.82 (((~![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))))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[916])).
% 2.45/1.82 tff(918,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(transitivity,[status(thm)],[917, 915])).
% 2.45/1.82 tff(919,plain,
% 2.45/1.82 ((~![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))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(920,plain,
% 2.45/1.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c3_1(a1438) | c0_1(a1468) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[919, 918])).
% 2.45/1.82 tff(921,plain,
% 2.45/1.82 ($false),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[920, 91, 874, 914, 903, 49, 892, 37, 24, 873])).
% 2.45/1.82 tff(922,plain,(hskp3 | c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.45/1.82 tff(923,plain,
% 2.45/1.82 (hskp3),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[922, 863, 37, 24, 49])).
% 2.45/1.82 tff(924,plain,
% 2.45/1.82 (((~hskp3) | (~c2_1(a1431))) <=> ((~hskp3) | (~c2_1(a1431)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(925,plain,
% 2.45/1.82 (((~c2_1(a1431)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1431)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(926,axiom,((~c2_1(a1431)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 2.45/1.82 tff(927,plain,
% 2.45/1.82 ((~hskp3) | (~c2_1(a1431))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[926, 925])).
% 2.45/1.82 tff(928,plain,
% 2.45/1.82 ((~hskp3) | (~c2_1(a1431))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[927, 924])).
% 2.45/1.82 tff(929,plain,
% 2.45/1.82 (~c2_1(a1431)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[928, 923])).
% 2.45/1.82 tff(930,plain,
% 2.45/1.82 (((~hskp3) | (~c0_1(a1431))) <=> ((~hskp3) | (~c0_1(a1431)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(931,plain,
% 2.45/1.82 (((~c0_1(a1431)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1431)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(932,axiom,((~c0_1(a1431)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 2.45/1.82 tff(933,plain,
% 2.45/1.82 ((~hskp3) | (~c0_1(a1431))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[932, 931])).
% 2.45/1.82 tff(934,plain,
% 2.45/1.82 ((~hskp3) | (~c0_1(a1431))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[933, 930])).
% 2.45/1.82 tff(935,plain,
% 2.45/1.82 (~c0_1(a1431)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[934, 923])).
% 2.45/1.82 tff(936,plain,
% 2.45/1.82 (~hskp11),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[795, 838, 48])).
% 2.45/1.82 tff(937,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(938,plain,
% 2.45/1.82 ((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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(939,plain,
% 2.45/1.82 (((~![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))))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[938])).
% 2.45/1.82 tff(940,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(transitivity,[status(thm)],[939, 937])).
% 2.45/1.82 tff(941,plain,
% 2.45/1.82 ((~![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)))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(942,plain,
% 2.45/1.82 ((~![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[941, 940])).
% 2.45/1.82 tff(943,plain,
% 2.45/1.82 (~c3_1(a1431)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[942, 91, 936, 838, 935, 929, 34])).
% 2.45/1.82 tff(944,plain,
% 2.45/1.82 (((~hskp3) | c1_1(a1431)) <=> ((~hskp3) | c1_1(a1431))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(945,axiom,((~hskp3) | c1_1(a1431)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 2.45/1.82 tff(946,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[945, 944])).
% 2.45/1.82 tff(947,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[946, 944])).
% 2.45/1.82 tff(948,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[947, 944])).
% 2.45/1.82 tff(949,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[948, 944])).
% 2.45/1.82 tff(950,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[949, 944])).
% 2.45/1.82 tff(951,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[950, 944])).
% 2.45/1.82 tff(952,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[951, 944])).
% 2.45/1.82 tff(953,plain,
% 2.45/1.82 ((~hskp3) | c1_1(a1431)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[952, 944])).
% 2.45/1.82 tff(954,plain,
% 2.45/1.82 (c1_1(a1431)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[953, 923])).
% 2.45/1.82 tff(955,plain,
% 2.45/1.82 (((~![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 | 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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(956,plain,
% 2.45/1.82 ((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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(957,plain,
% 2.45/1.82 (((~![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(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))))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[956])).
% 2.45/1.82 tff(958,plain,
% 2.45/1.82 (((~![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(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)))),
% 2.45/1.82 inference(transitivity,[status(thm)],[957, 955])).
% 2.45/1.82 tff(959,plain,
% 2.45/1.82 ((~![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(a1431) | c0_1(a1431) | (~c1_1(a1431)))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(960,plain,
% 2.45/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[959, 958])).
% 2.45/1.82 tff(961,plain,
% 2.45/1.82 (hskp12),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[960, 91, 954, 935, 929, 214, 943])).
% 2.45/1.82 tff(962,plain,
% 2.45/1.82 (~c2_1(a1448)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[220, 961])).
% 2.45/1.82 tff(963,plain,
% 2.45/1.82 ($false),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[263, 962, 961, 838, 863])).
% 2.45/1.82 tff(964,plain,(c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.45/1.82 tff(965,plain,
% 2.45/1.82 (c3_1(a1438)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[964, 37, 24, 35, 12])).
% 2.45/1.82 tff(966,assumption,(hskp24), introduced(assumption)).
% 2.45/1.82 tff(967,plain,
% 2.45/1.82 (((~hskp24) | (~c2_1(a1487))) <=> ((~hskp24) | (~c2_1(a1487)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(968,plain,
% 2.45/1.82 (((~c2_1(a1487)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1487)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(969,axiom,((~c2_1(a1487)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 2.45/1.82 tff(970,plain,
% 2.45/1.82 ((~hskp24) | (~c2_1(a1487))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[969, 968])).
% 2.45/1.82 tff(971,plain,
% 2.45/1.82 ((~hskp24) | (~c2_1(a1487))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[970, 967])).
% 2.45/1.82 tff(972,plain,
% 2.45/1.82 (~c2_1(a1487)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[971, 966])).
% 2.45/1.82 tff(973,plain,
% 2.45/1.82 (((~hskp24) | c3_1(a1487)) <=> ((~hskp24) | c3_1(a1487))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(974,axiom,((~hskp24) | c3_1(a1487)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 2.45/1.82 tff(975,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[974, 973])).
% 2.45/1.82 tff(976,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[975, 973])).
% 2.45/1.82 tff(977,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[976, 973])).
% 2.45/1.82 tff(978,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[977, 973])).
% 2.45/1.82 tff(979,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[978, 973])).
% 2.45/1.82 tff(980,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[979, 973])).
% 2.45/1.82 tff(981,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[980, 973])).
% 2.45/1.82 tff(982,plain,
% 2.45/1.82 ((~hskp24) | c3_1(a1487)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[981, 973])).
% 2.45/1.82 tff(983,plain,
% 2.45/1.82 (c3_1(a1487)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[982, 966])).
% 2.45/1.82 tff(984,plain,
% 2.45/1.82 (~hskp11),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[795, 11, 61])).
% 2.45/1.82 tff(985,assumption,(~c2_1(a1487)), introduced(assumption)).
% 2.45/1.82 tff(986,assumption,(c3_1(a1487)), introduced(assumption)).
% 2.45/1.82 tff(987,plain,
% 2.45/1.82 (((~![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))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(988,plain,
% 2.45/1.82 ((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))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(989,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[988])).
% 2.45/1.82 tff(990,plain,
% 2.45/1.82 (((~![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))),
% 2.45/1.82 inference(transitivity,[status(thm)],[989, 987])).
% 2.45/1.82 tff(991,plain,
% 2.45/1.82 ((~![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)))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(992,plain,
% 2.45/1.82 ((~![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)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[991, 990])).
% 2.45/1.82 tff(993,plain,
% 2.45/1.82 (hskp11 | hskp5 | c0_1(a1487)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[992, 91, 986, 985, 34])).
% 2.45/1.82 tff(994,plain,
% 2.45/1.82 (c0_1(a1487)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[993, 984, 11])).
% 2.45/1.82 tff(995,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(996,plain,
% 2.45/1.82 ((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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(997,plain,
% 2.45/1.82 (((~![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))))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[996])).
% 2.45/1.82 tff(998,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(transitivity,[status(thm)],[997, 995])).
% 2.45/1.82 tff(999,plain,
% 2.45/1.82 ((~![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)))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(1000,plain,
% 2.45/1.82 ((~![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[999, 998])).
% 2.45/1.82 tff(1001,plain,
% 2.45/1.82 (hskp17 | hskp5 | (~c0_1(a1487))),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1000, 91, 986, 985, 253])).
% 2.45/1.82 tff(1002,plain,
% 2.45/1.82 (hskp17),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1001, 994, 11])).
% 2.45/1.82 tff(1003,plain,
% 2.45/1.82 (~c1_1(a1457)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[269, 1002])).
% 2.45/1.82 tff(1004,plain,
% 2.45/1.82 (~c0_1(a1457)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[275, 1002])).
% 2.45/1.82 tff(1005,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1006,plain,
% 2.45/1.82 ((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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1007,plain,
% 2.45/1.82 (((~![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))))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[1006])).
% 2.45/1.82 tff(1008,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(transitivity,[status(thm)],[1007, 1005])).
% 2.45/1.82 tff(1009,plain,
% 2.45/1.82 ((~![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)))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(1010,plain,
% 2.45/1.82 ((~![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))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 2.45/1.82 tff(1011,plain,
% 2.45/1.82 (~c3_1(a1457)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1010, 91, 11, 986, 985, 1004, 1003, 10, 994])).
% 2.45/1.82 tff(1012,plain,
% 2.45/1.82 (~c2_1(a1457)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[288, 1002])).
% 2.45/1.82 tff(1013,plain,
% 2.45/1.82 (((~![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))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1014,plain,
% 2.45/1.82 ((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))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1015,plain,
% 2.45/1.82 (((~![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)))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[1014])).
% 2.45/1.82 tff(1016,plain,
% 2.45/1.82 (((~![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))),
% 2.45/1.82 inference(transitivity,[status(thm)],[1015, 1013])).
% 2.45/1.82 tff(1017,plain,
% 2.45/1.82 ((~![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))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(1018,plain,
% 2.45/1.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 2.45/1.82 tff(1019,plain,
% 2.45/1.82 ($false),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1018, 91, 61, 1004, 1003, 1012, 60, 1011])).
% 2.45/1.82 tff(1020,plain,(hskp5 | hskp2 | (~c3_1(a1487)) | c2_1(a1487)), inference(lemma,lemma(discharge,[]))).
% 2.45/1.82 tff(1021,plain,
% 2.45/1.82 (hskp5),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1020, 983, 48, 972])).
% 2.45/1.82 tff(1022,plain,
% 2.45/1.82 (~c3_1(a1435)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[319, 1021])).
% 2.45/1.82 tff(1023,plain,
% 2.45/1.82 (((~hskp24) | (~c1_1(a1487))) <=> ((~hskp24) | (~c1_1(a1487)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1024,plain,
% 2.45/1.82 (((~c1_1(a1487)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1487)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1025,axiom,((~c1_1(a1487)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 2.45/1.82 tff(1026,plain,
% 2.45/1.82 ((~hskp24) | (~c1_1(a1487))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 2.45/1.82 tff(1027,plain,
% 2.45/1.82 ((~hskp24) | (~c1_1(a1487))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[1026, 1023])).
% 2.45/1.82 tff(1028,plain,
% 2.45/1.82 (~c1_1(a1487)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[1027, 966])).
% 2.45/1.82 tff(1029,plain,
% 2.45/1.82 (~c2_1(a1435)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[325, 1021])).
% 2.45/1.82 tff(1030,assumption,(~c1_1(a1487)), introduced(assumption)).
% 2.45/1.82 tff(1031,plain,
% 2.45/1.82 (c0_1(a1435)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[735, 11, 112, 113, 48])).
% 2.45/1.82 tff(1032,plain,
% 2.45/1.82 (hskp4),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[131, 114, 13, 112])).
% 2.45/1.82 tff(1033,plain,
% 2.45/1.82 (~c2_1(a1434)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[137, 1032])).
% 2.45/1.82 tff(1034,plain,
% 2.45/1.82 (~c1_1(a1435)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[182, 1033, 112, 1032, 113, 13])).
% 2.45/1.82 tff(1035,plain,
% 2.45/1.82 (^[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))))),
% 2.45/1.82 inference(bind,[status(th)],[])).
% 2.45/1.82 tff(1036,plain,
% 2.45/1.82 (![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)))),
% 2.45/1.82 inference(quant_intro,[status(thm)],[1035])).
% 2.45/1.82 tff(1037,plain,
% 2.45/1.82 (![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)))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(1038,plain,
% 2.45/1.82 (^[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)) | 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)))))),
% 2.45/1.83 inference(bind,[status(th)],[])).
% 2.45/1.83 tff(1039,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(quant_intro,[status(thm)],[1038])).
% 2.45/1.83 tff(1040,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 2.45/1.83 tff(1041,plain,
% 2.45/1.83 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 2.45/1.83 tff(1042,plain,
% 2.45/1.83 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1041, 1037])).
% 2.45/1.83 tff(1043,plain,(
% 2.45/1.83 ![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.45/1.83 inference(skolemize,[status(sab)],[1042])).
% 2.45/1.83 tff(1044,plain,
% 2.45/1.83 (![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1043, 1036])).
% 2.45/1.83 tff(1045,plain,
% 2.45/1.83 (((~![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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1046,plain,
% 2.45/1.83 ((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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1047,plain,
% 2.45/1.83 (((~![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))))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1046])).
% 2.45/1.83 tff(1048,plain,
% 2.45/1.83 (((~![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)))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1047, 1045])).
% 2.45/1.83 tff(1049,plain,
% 2.45/1.83 ((~![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)))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1050,plain,
% 2.45/1.83 ((~![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))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 2.45/1.83 tff(1051,plain,
% 2.45/1.83 (hskp29 | hskp5 | c2_1(a1435) | (~c0_1(a1435))),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1050, 91, 113, 1044])).
% 2.45/1.83 tff(1052,plain,
% 2.45/1.83 (hskp29),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1051, 114, 11, 112])).
% 2.45/1.83 tff(1053,plain,
% 2.45/1.83 (((~hskp29) | c3_1(a1483)) <=> ((~hskp29) | c3_1(a1483))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1054,axiom,((~hskp29) | c3_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 2.45/1.83 tff(1055,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 2.45/1.83 tff(1056,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1055, 1053])).
% 2.45/1.83 tff(1057,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1056, 1053])).
% 2.45/1.83 tff(1058,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 2.45/1.83 tff(1059,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1058, 1053])).
% 2.45/1.83 tff(1060,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1059, 1053])).
% 2.45/1.83 tff(1061,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1060, 1053])).
% 2.45/1.83 tff(1062,plain,
% 2.45/1.83 ((~hskp29) | c3_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1061, 1053])).
% 2.45/1.83 tff(1063,plain,
% 2.45/1.83 (c3_1(a1483)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1062, 1052])).
% 2.45/1.83 tff(1064,plain,
% 2.45/1.83 (((~hskp29) | c2_1(a1483)) <=> ((~hskp29) | c2_1(a1483))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1065,axiom,((~hskp29) | c2_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 2.45/1.83 tff(1066,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 2.45/1.83 tff(1067,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1066, 1064])).
% 2.45/1.83 tff(1068,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1067, 1064])).
% 2.45/1.83 tff(1069,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1068, 1064])).
% 2.45/1.83 tff(1070,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1069, 1064])).
% 2.45/1.83 tff(1071,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1070, 1064])).
% 2.45/1.83 tff(1072,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1071, 1064])).
% 2.45/1.83 tff(1073,plain,
% 2.45/1.83 ((~hskp29) | c2_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1072, 1064])).
% 2.45/1.83 tff(1074,plain,
% 2.45/1.83 (c2_1(a1483)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1073, 1052])).
% 2.45/1.83 tff(1075,plain,
% 2.45/1.83 (((~hskp29) | c1_1(a1483)) <=> ((~hskp29) | c1_1(a1483))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1076,axiom,((~hskp29) | c1_1(a1483)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 2.45/1.83 tff(1077,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 2.45/1.83 tff(1078,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1077, 1075])).
% 2.45/1.83 tff(1079,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1078, 1075])).
% 2.45/1.83 tff(1080,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 2.45/1.83 tff(1081,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1080, 1075])).
% 2.45/1.83 tff(1082,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1081, 1075])).
% 2.45/1.83 tff(1083,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1082, 1075])).
% 2.45/1.83 tff(1084,plain,
% 2.45/1.83 ((~hskp29) | c1_1(a1483)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1083, 1075])).
% 2.45/1.83 tff(1085,plain,
% 2.45/1.83 (c1_1(a1483)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1084, 1052])).
% 2.45/1.83 tff(1086,plain,
% 2.45/1.83 (((~![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(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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1087,plain,
% 2.45/1.83 ((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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1088,plain,
% 2.45/1.83 (((~![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(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))))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1087])).
% 2.45/1.83 tff(1089,plain,
% 2.45/1.83 (((~![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(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)))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1088, 1086])).
% 2.45/1.83 tff(1090,plain,
% 2.45/1.83 ((~![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(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1435) | c2_1(a1435) | c1_1(a1435))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1091,plain,
% 2.45/1.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 2.45/1.83 tff(1092,plain,
% 2.45/1.83 ($false),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1091, 91, 13, 1085, 1074, 1063, 112, 113, 678, 1034])).
% 2.45/1.83 tff(1093,plain,((~c0_1(a1435)) | hskp7 | c2_1(a1435) | c3_1(a1435) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.45/1.83 tff(1094,plain,
% 2.45/1.83 (hskp7),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1093, 1031, 112, 113, 11])).
% 2.45/1.83 tff(1095,plain,
% 2.45/1.83 (((~hskp7) | (~c0_1(a1438))) <=> ((~hskp7) | (~c0_1(a1438)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1096,plain,
% 2.45/1.83 (((~c0_1(a1438)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a1438)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1097,axiom,((~c0_1(a1438)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 2.45/1.83 tff(1098,plain,
% 2.45/1.83 ((~hskp7) | (~c0_1(a1438))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 2.45/1.83 tff(1099,plain,
% 2.45/1.83 ((~hskp7) | (~c0_1(a1438))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1098, 1095])).
% 2.45/1.83 tff(1100,plain,
% 2.45/1.83 (~c0_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1099, 1094])).
% 2.45/1.83 tff(1101,plain,
% 2.45/1.83 (c3_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[110, 1094])).
% 2.45/1.83 tff(1102,plain,
% 2.45/1.83 (((~![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 | 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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1103,plain,
% 2.45/1.83 ((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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1104,plain,
% 2.45/1.83 (((~![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(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))))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1103])).
% 2.45/1.83 tff(1105,plain,
% 2.45/1.83 (((~![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(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)))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1104, 1102])).
% 2.45/1.83 tff(1106,plain,
% 2.45/1.83 ((~![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(a1487) | (~c3_1(a1487)) | (~c0_1(a1487)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1107,plain,
% 2.45/1.83 ((~![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 | c2_1(a1487) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1487)) | (~c0_1(a1487))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 2.45/1.83 tff(1108,plain,
% 2.45/1.83 (~c0_1(a1487)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1107, 91, 11, 986, 1101, 985, 1100, 24, 10])).
% 2.45/1.83 tff(1109,plain,
% 2.45/1.83 (^[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))))),
% 2.45/1.83 inference(bind,[status(th)],[])).
% 2.45/1.83 tff(1110,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(quant_intro,[status(thm)],[1109])).
% 2.45/1.83 tff(1111,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1112,plain,
% 2.45/1.83 (^[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)))))),
% 2.45/1.83 inference(bind,[status(th)],[])).
% 2.45/1.83 tff(1113,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(quant_intro,[status(thm)],[1112])).
% 2.45/1.83 tff(1114,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')).
% 2.45/1.83 tff(1115,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 2.45/1.83 tff(1116,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1115, 1111])).
% 2.45/1.83 tff(1117,plain,(
% 2.45/1.83 ![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)))),
% 2.45/1.83 inference(skolemize,[status(sab)],[1116])).
% 2.45/1.83 tff(1118,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1117, 1110])).
% 2.45/1.83 tff(1119,plain,
% 2.45/1.83 (((~![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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1120,plain,
% 2.45/1.83 ((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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1121,plain,
% 2.45/1.83 (((~![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)))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1120])).
% 2.45/1.83 tff(1122,plain,
% 2.45/1.83 (((~![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))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1121, 1119])).
% 2.45/1.83 tff(1123,plain,
% 2.45/1.83 ((~![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)))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1124,plain,
% 2.45/1.83 ((~![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)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 2.45/1.83 tff(1125,plain,
% 2.45/1.83 (hskp9 | c0_1(a1487)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1124, 91, 986, 35, 985, 12, 574, 1118])).
% 2.45/1.83 tff(1126,plain,
% 2.45/1.83 (hskp9),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1125, 1108])).
% 2.45/1.83 tff(1127,plain,
% 2.45/1.83 (((~hskp9) | (~c3_1(a1444))) <=> ((~hskp9) | (~c3_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1128,plain,
% 2.45/1.83 (((~c3_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1129,axiom,((~c3_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 2.45/1.83 tff(1130,plain,
% 2.45/1.83 ((~hskp9) | (~c3_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 2.45/1.83 tff(1131,plain,
% 2.45/1.83 ((~hskp9) | (~c3_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1130, 1127])).
% 2.45/1.83 tff(1132,plain,
% 2.45/1.83 (~c3_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1131, 1126])).
% 2.45/1.83 tff(1133,plain,
% 2.45/1.83 (((~hskp9) | (~c2_1(a1444))) <=> ((~hskp9) | (~c2_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1134,plain,
% 2.45/1.83 (((~c2_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1135,axiom,((~c2_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 2.45/1.83 tff(1136,plain,
% 2.45/1.83 ((~hskp9) | (~c2_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 2.45/1.83 tff(1137,plain,
% 2.45/1.83 ((~hskp9) | (~c2_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1136, 1133])).
% 2.45/1.83 tff(1138,plain,
% 2.45/1.83 (~c2_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1137, 1126])).
% 2.45/1.83 tff(1139,plain,
% 2.45/1.83 (((~hskp9) | (~c1_1(a1444))) <=> ((~hskp9) | (~c1_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1140,plain,
% 2.45/1.83 (((~c1_1(a1444)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1444)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1141,axiom,((~c1_1(a1444)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 2.45/1.83 tff(1142,plain,
% 2.45/1.83 ((~hskp9) | (~c1_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 2.45/1.83 tff(1143,plain,
% 2.45/1.83 ((~hskp9) | (~c1_1(a1444))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1142, 1139])).
% 2.45/1.83 tff(1144,plain,
% 2.45/1.83 (~c1_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1143, 1126])).
% 2.45/1.83 tff(1145,plain,
% 2.45/1.83 (hskp11),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[993, 1108, 11])).
% 2.45/1.83 tff(1146,plain,
% 2.45/1.83 (~c3_1(a1447)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[757, 1145])).
% 2.45/1.83 tff(1147,plain,
% 2.45/1.83 (~c2_1(a1447)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[745, 1145])).
% 2.45/1.83 tff(1148,plain,
% 2.45/1.83 (~c0_1(a1447)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[751, 1145])).
% 2.45/1.83 tff(1149,plain,
% 2.45/1.83 (((~![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 | 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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1150,plain,
% 2.45/1.83 ((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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1151,plain,
% 2.45/1.83 (((~![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(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)))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1150])).
% 2.45/1.83 tff(1152,plain,
% 2.45/1.83 (((~![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(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))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1151, 1149])).
% 2.45/1.83 tff(1153,plain,
% 2.45/1.83 ((~![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(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1447) | c2_1(a1447) | c0_1(a1447))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1154,plain,
% 2.45/1.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c1_1(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 2.45/1.83 tff(1155,plain,
% 2.45/1.83 ($false),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1154, 91, 48, 1148, 1147, 1146, 1144, 1138, 1132, 60])).
% 2.45/1.83 tff(1156,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,[]))).
% 2.45/1.83 tff(1157,plain,
% 2.45/1.83 (hskp5),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1156, 112, 985, 35, 12, 24, 986, 113])).
% 2.45/1.83 tff(1158,plain,
% 2.45/1.83 (c0_1(a1435)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[390, 1157])).
% 2.45/1.83 tff(1159,plain,
% 2.45/1.83 (hskp7),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[697, 1158, 35, 112, 113, 12])).
% 2.45/1.83 tff(1160,plain,
% 2.45/1.83 (~c0_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1099, 1159])).
% 2.45/1.83 tff(1161,plain,
% 2.45/1.83 (c3_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[110, 1159])).
% 2.45/1.83 tff(1162,plain,
% 2.45/1.83 (hskp7),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[697, 114, 35, 112, 113, 12])).
% 2.45/1.83 tff(1163,plain,
% 2.45/1.83 (~c0_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1099, 1162])).
% 2.45/1.83 tff(1164,plain,
% 2.45/1.83 (c3_1(a1438)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[110, 1162])).
% 2.45/1.83 tff(1165,plain,
% 2.45/1.83 (((~![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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1166,plain,
% 2.45/1.83 ((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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1167,plain,
% 2.45/1.83 (((~![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))))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1166])).
% 2.45/1.83 tff(1168,plain,
% 2.45/1.83 (((~![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)))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1167, 1165])).
% 2.45/1.83 tff(1169,plain,
% 2.45/1.83 ((~![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)))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1170,plain,
% 2.45/1.83 ((~![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))),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 2.45/1.83 tff(1171,plain,
% 2.45/1.83 (hskp9),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1170, 91, 1164, 35, 1163, 12, 574, 1118, 50])).
% 2.45/1.83 tff(1172,plain,
% 2.45/1.83 (~c3_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1131, 1171])).
% 2.45/1.83 tff(1173,plain,
% 2.45/1.83 (~c2_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1137, 1171])).
% 2.45/1.83 tff(1174,plain,
% 2.45/1.83 (~c1_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1143, 1171])).
% 2.45/1.83 tff(1175,plain,
% 2.45/1.83 (((~![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(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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1176,plain,
% 2.45/1.83 ((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))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1177,plain,
% 2.45/1.83 (((~![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(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)))),
% 2.45/1.83 inference(monotonicity,[status(thm)],[1176])).
% 2.45/1.83 tff(1178,plain,
% 2.45/1.83 (((~![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(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))),
% 2.45/1.83 inference(transitivity,[status(thm)],[1177, 1175])).
% 2.45/1.83 tff(1179,plain,
% 2.45/1.83 ((~![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(a1444) | c1_1(a1444) | c3_1(a1444) | c3_1(a1444) | c2_1(a1444) | c0_1(a1444))),
% 2.45/1.83 inference(quant_inst,[status(thm)],[])).
% 2.45/1.83 tff(1180,plain,
% 2.45/1.83 ((~![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(a1444) | c2_1(a1444) | c3_1(a1444) | (~ndr1_0) | c0_1(a1444)),
% 2.45/1.83 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 2.45/1.83 tff(1181,plain,
% 2.45/1.83 (c0_1(a1444)),
% 2.45/1.83 inference(unit_resolution,[status(thm)],[1180, 91, 48, 1174, 1173, 1172, 60])).
% 2.45/1.83 tff(1182,plain,
% 2.45/1.83 (^[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))))),
% 2.45/1.83 inference(bind,[status(th)],[])).
% 2.45/1.83 tff(1183,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(quant_intro,[status(thm)],[1182])).
% 2.45/1.83 tff(1184,plain,
% 2.45/1.83 (![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)))),
% 2.45/1.83 inference(rewrite,[status(thm)],[])).
% 2.45/1.83 tff(1185,plain,
% 2.45/1.83 (^[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)))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1186,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1185])).
% 2.45/1.84 tff(1187,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')).
% 2.45/1.84 tff(1188,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 2.45/1.84 tff(1189,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1188, 1184])).
% 2.45/1.84 tff(1190,plain,(
% 2.45/1.84 ![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)))),
% 2.45/1.84 inference(skolemize,[status(sab)],[1189])).
% 2.45/1.84 tff(1191,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1190, 1183])).
% 2.45/1.84 tff(1192,plain,
% 2.45/1.84 (^[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)))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1193,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1192])).
% 2.45/1.84 tff(1194,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1195,plain,
% 2.45/1.84 (^[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))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1196,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1195])).
% 2.45/1.84 tff(1197,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')).
% 2.45/1.84 tff(1198,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 2.45/1.84 tff(1199,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1198, 1194])).
% 2.45/1.84 tff(1200,plain,(
% 2.45/1.84 ![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))),
% 2.45/1.84 inference(skolemize,[status(sab)],[1199])).
% 2.45/1.84 tff(1201,plain,
% 2.45/1.84 (![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))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1200, 1193])).
% 2.45/1.84 tff(1202,plain,
% 2.45/1.84 (((~![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))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1203,plain,
% 2.45/1.84 ((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))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1204,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(monotonicity,[status(thm)],[1203])).
% 2.45/1.84 tff(1205,plain,
% 2.45/1.84 (((~![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))),
% 2.45/1.84 inference(transitivity,[status(thm)],[1204, 1202])).
% 2.45/1.84 tff(1206,plain,
% 2.45/1.84 ((~![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))),
% 2.45/1.84 inference(quant_inst,[status(thm)],[])).
% 2.45/1.84 tff(1207,plain,
% 2.45/1.84 ((~![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)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 2.45/1.84 tff(1208,plain,
% 2.45/1.84 (hskp0),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1207, 91, 114, 1163, 24, 112, 113, 1201, 50])).
% 2.45/1.84 tff(1209,plain,
% 2.45/1.84 (((~hskp0) | (~c3_1(a1427))) <=> ((~hskp0) | (~c3_1(a1427)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1210,plain,
% 2.45/1.84 (((~c3_1(a1427)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1427)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1211,axiom,((~c3_1(a1427)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 2.45/1.84 tff(1212,plain,
% 2.45/1.84 ((~hskp0) | (~c3_1(a1427))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 2.45/1.84 tff(1213,plain,
% 2.45/1.84 ((~hskp0) | (~c3_1(a1427))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1212, 1209])).
% 2.45/1.84 tff(1214,plain,
% 2.45/1.84 (~c3_1(a1427)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1213, 1208])).
% 2.45/1.84 tff(1215,plain,
% 2.45/1.84 (((~hskp0) | c2_1(a1427)) <=> ((~hskp0) | c2_1(a1427))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1216,axiom,((~hskp0) | c2_1(a1427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 2.45/1.84 tff(1217,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 2.45/1.84 tff(1218,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1217, 1215])).
% 2.45/1.84 tff(1219,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1218, 1215])).
% 2.45/1.84 tff(1220,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 2.45/1.84 tff(1221,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1220, 1215])).
% 2.45/1.84 tff(1222,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1221, 1215])).
% 2.45/1.84 tff(1223,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1222, 1215])).
% 2.45/1.84 tff(1224,plain,
% 2.45/1.84 ((~hskp0) | c2_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1223, 1215])).
% 2.45/1.84 tff(1225,plain,
% 2.45/1.84 (c2_1(a1427)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1224, 1208])).
% 2.45/1.84 tff(1226,plain,
% 2.45/1.84 (((~hskp0) | c0_1(a1427)) <=> ((~hskp0) | c0_1(a1427))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1227,axiom,((~hskp0) | c0_1(a1427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 2.45/1.84 tff(1228,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 2.45/1.84 tff(1229,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1228, 1226])).
% 2.45/1.84 tff(1230,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 2.45/1.84 tff(1231,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 2.45/1.84 tff(1232,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1231, 1226])).
% 2.45/1.84 tff(1233,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1232, 1226])).
% 2.45/1.84 tff(1234,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 2.45/1.84 tff(1235,plain,
% 2.45/1.84 ((~hskp0) | c0_1(a1427)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1234, 1226])).
% 2.45/1.84 tff(1236,plain,
% 2.45/1.84 (c0_1(a1427)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1235, 1208])).
% 2.45/1.84 tff(1237,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1238,plain,
% 2.45/1.84 ((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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1239,plain,
% 2.45/1.84 (((~![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))))),
% 2.45/1.84 inference(monotonicity,[status(thm)],[1238])).
% 2.45/1.84 tff(1240,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(transitivity,[status(thm)],[1239, 1237])).
% 2.45/1.84 tff(1241,plain,
% 2.45/1.84 ((~![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)))),
% 2.45/1.84 inference(quant_inst,[status(thm)],[])).
% 2.45/1.84 tff(1242,plain,
% 2.45/1.84 ((~![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))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 2.45/1.84 tff(1243,plain,
% 2.45/1.84 (hskp19 | (~c0_1(a1444))),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1242, 91, 1236, 1225, 1174, 1173, 1214, 1191])).
% 2.45/1.84 tff(1244,plain,
% 2.45/1.84 (hskp19),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1243, 1181])).
% 2.45/1.84 tff(1245,plain,
% 2.45/1.84 (((~hskp19) | (~c3_1(a1460))) <=> ((~hskp19) | (~c3_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1246,plain,
% 2.45/1.84 (((~c3_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1247,axiom,((~c3_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 2.45/1.84 tff(1248,plain,
% 2.45/1.84 ((~hskp19) | (~c3_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 2.45/1.84 tff(1249,plain,
% 2.45/1.84 ((~hskp19) | (~c3_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1248, 1245])).
% 2.45/1.84 tff(1250,plain,
% 2.45/1.84 (~c3_1(a1460)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1249, 1244])).
% 2.45/1.84 tff(1251,plain,
% 2.45/1.84 (((~hskp19) | (~c0_1(a1460))) <=> ((~hskp19) | (~c0_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1252,plain,
% 2.45/1.84 (((~c0_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1253,axiom,((~c0_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 2.45/1.84 tff(1254,plain,
% 2.45/1.84 ((~hskp19) | (~c0_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 2.45/1.84 tff(1255,plain,
% 2.45/1.84 ((~hskp19) | (~c0_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1254, 1251])).
% 2.45/1.84 tff(1256,plain,
% 2.45/1.84 (~c0_1(a1460)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1255, 1244])).
% 2.45/1.84 tff(1257,plain,
% 2.45/1.84 (((~![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))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1258,plain,
% 2.45/1.84 ((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))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1259,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(monotonicity,[status(thm)],[1258])).
% 2.45/1.84 tff(1260,plain,
% 2.45/1.84 (((~![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))),
% 2.45/1.84 inference(transitivity,[status(thm)],[1259, 1257])).
% 2.45/1.84 tff(1261,plain,
% 2.45/1.84 ((~![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))),
% 2.45/1.84 inference(quant_inst,[status(thm)],[])).
% 2.45/1.84 tff(1262,plain,
% 2.45/1.84 ((~![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)),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 2.45/1.84 tff(1263,plain,
% 2.45/1.84 (c2_1(a1460)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1262, 91, 48, 1256, 1250, 1174, 1173, 1172, 60])).
% 2.45/1.84 tff(1264,plain,
% 2.45/1.84 (((~hskp19) | (~c1_1(a1460))) <=> ((~hskp19) | (~c1_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1265,plain,
% 2.45/1.84 (((~c1_1(a1460)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1460)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1266,axiom,((~c1_1(a1460)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 2.45/1.84 tff(1267,plain,
% 2.45/1.84 ((~hskp19) | (~c1_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 2.45/1.84 tff(1268,plain,
% 2.45/1.84 ((~hskp19) | (~c1_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1267, 1264])).
% 2.45/1.84 tff(1269,plain,
% 2.45/1.84 (~c1_1(a1460)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1268, 1244])).
% 2.45/1.84 tff(1270,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1271,plain,
% 2.45/1.84 (((~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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1272,plain,
% 2.45/1.84 (((~![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))))),
% 2.45/1.84 inference(monotonicity,[status(thm)],[1271])).
% 2.45/1.84 tff(1273,plain,
% 2.45/1.84 (((~![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)))),
% 2.45/1.84 inference(transitivity,[status(thm)],[1272, 1270])).
% 2.45/1.84 tff(1274,plain,
% 2.45/1.84 ((~![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)))),
% 2.45/1.84 inference(quant_inst,[status(thm)],[])).
% 2.45/1.84 tff(1275,plain,
% 2.45/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1460) | c3_1(a1460) | c1_1(a1444) | c2_1(a1444) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c0_1(a1444)) | (~c2_1(a1460))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 2.45/1.84 tff(1276,plain,
% 2.45/1.84 ($false),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1275, 91, 1164, 1269, 1250, 1174, 1173, 1163, 591, 50, 1181, 1263])).
% 2.45/1.84 tff(1277,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,[]))).
% 2.45/1.84 tff(1278,plain,
% 2.45/1.84 (c2_1(a1438)),
% 2.45/1.84 inference(unit_resolution,[status(thm)],[1277, 1158, 24, 112, 113, 35, 12])).
% 2.45/1.84 tff(1279,plain,
% 2.45/1.84 (^[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))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1280,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1279])).
% 2.45/1.84 tff(1281,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1282,plain,
% 2.45/1.84 (^[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)))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1283,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1282])).
% 2.45/1.84 tff(1284,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 2.45/1.84 tff(1285,plain,
% 2.45/1.84 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 2.45/1.84 tff(1286,plain,
% 2.45/1.84 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1285, 1281])).
% 2.45/1.84 tff(1287,plain,(
% 2.45/1.84 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.45/1.84 inference(skolemize,[status(sab)],[1286])).
% 2.45/1.84 tff(1288,plain,
% 2.45/1.84 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1287, 1280])).
% 2.45/1.84 tff(1289,plain,
% 2.45/1.84 (^[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))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1290,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1289])).
% 2.45/1.84 tff(1291,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(rewrite,[status(thm)],[])).
% 2.45/1.84 tff(1292,plain,
% 2.45/1.84 (^[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)))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1293,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1292])).
% 2.45/1.84 tff(1294,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')).
% 2.45/1.84 tff(1295,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 2.45/1.84 tff(1296,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1295, 1291])).
% 2.45/1.84 tff(1297,plain,(
% 2.45/1.84 ![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)))),
% 2.45/1.84 inference(skolemize,[status(sab)],[1296])).
% 2.45/1.84 tff(1298,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(modus_ponens,[status(thm)],[1297, 1290])).
% 2.45/1.84 tff(1299,assumption,(c3_1(a1438)), introduced(assumption)).
% 2.45/1.84 tff(1300,assumption,(~hskp11), introduced(assumption)).
% 2.45/1.84 tff(1301,plain,
% 2.45/1.84 (^[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))))),
% 2.45/1.84 inference(bind,[status(th)],[])).
% 2.45/1.84 tff(1302,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.84 inference(quant_intro,[status(thm)],[1301])).
% 2.45/1.84 tff(1303,plain,
% 2.45/1.84 (![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1304,plain,
% 2.45/1.85 (^[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)))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1305,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1304])).
% 2.45/1.85 tff(1306,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 2.45/1.85 tff(1307,plain,
% 2.45/1.85 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 2.45/1.85 tff(1308,plain,
% 2.45/1.85 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 2.45/1.85 tff(1309,plain,(
% 2.45/1.85 ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.45/1.85 inference(skolemize,[status(sab)],[1308])).
% 2.45/1.85 tff(1310,plain,
% 2.45/1.85 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 2.45/1.85 tff(1311,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1312,plain,
% 2.45/1.85 ((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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1313,plain,
% 2.45/1.85 (((~![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))))),
% 2.45/1.85 inference(monotonicity,[status(thm)],[1312])).
% 2.45/1.85 tff(1314,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(transitivity,[status(thm)],[1313, 1311])).
% 2.45/1.85 tff(1315,plain,
% 2.45/1.85 ((~![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)))),
% 2.45/1.85 inference(quant_inst,[status(thm)],[])).
% 2.45/1.85 tff(1316,plain,
% 2.45/1.85 ((~![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))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 2.45/1.85 tff(1317,plain,
% 2.45/1.85 (hskp20 | hskp11 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1316, 91, 24, 1310])).
% 2.45/1.85 tff(1318,plain,
% 2.45/1.85 (hskp20),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1317, 1300, 1299, 822])).
% 2.45/1.85 tff(1319,plain,
% 2.45/1.85 (((~hskp20) | (~c1_1(a1465))) <=> ((~hskp20) | (~c1_1(a1465)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1320,plain,
% 2.45/1.85 (((~c1_1(a1465)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1465)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1321,axiom,((~c1_1(a1465)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 2.45/1.85 tff(1322,plain,
% 2.45/1.85 ((~hskp20) | (~c1_1(a1465))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 2.45/1.85 tff(1323,plain,
% 2.45/1.85 ((~hskp20) | (~c1_1(a1465))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1322, 1319])).
% 2.45/1.85 tff(1324,plain,
% 2.45/1.85 (~c1_1(a1465)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1323, 1318])).
% 2.45/1.85 tff(1325,plain,
% 2.45/1.85 (((~hskp20) | c3_1(a1465)) <=> ((~hskp20) | c3_1(a1465))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1326,axiom,((~hskp20) | c3_1(a1465)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 2.45/1.85 tff(1327,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 2.45/1.85 tff(1328,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1327, 1325])).
% 2.45/1.85 tff(1329,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1328, 1325])).
% 2.45/1.85 tff(1330,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1329, 1325])).
% 2.45/1.85 tff(1331,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1330, 1325])).
% 2.45/1.85 tff(1332,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1331, 1325])).
% 2.45/1.85 tff(1333,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1332, 1325])).
% 2.45/1.85 tff(1334,plain,
% 2.45/1.85 ((~hskp20) | c3_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1333, 1325])).
% 2.45/1.85 tff(1335,plain,
% 2.45/1.85 (c3_1(a1465)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1334, 1318])).
% 2.45/1.85 tff(1336,plain,
% 2.45/1.85 (((~hskp20) | c2_1(a1465)) <=> ((~hskp20) | c2_1(a1465))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1337,axiom,((~hskp20) | c2_1(a1465)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 2.45/1.85 tff(1338,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 2.45/1.85 tff(1339,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1338, 1336])).
% 2.45/1.85 tff(1340,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1339, 1336])).
% 2.45/1.85 tff(1341,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1340, 1336])).
% 2.45/1.85 tff(1342,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1341, 1336])).
% 2.45/1.85 tff(1343,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1342, 1336])).
% 2.45/1.85 tff(1344,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1343, 1336])).
% 2.45/1.85 tff(1345,plain,
% 2.45/1.85 ((~hskp20) | c2_1(a1465)),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1344, 1336])).
% 2.45/1.85 tff(1346,plain,
% 2.45/1.85 (c2_1(a1465)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1345, 1318])).
% 2.45/1.85 tff(1347,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1348,plain,
% 2.45/1.85 (((~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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1349,plain,
% 2.45/1.85 (((~![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))))),
% 2.45/1.85 inference(monotonicity,[status(thm)],[1348])).
% 2.45/1.85 tff(1350,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(transitivity,[status(thm)],[1349, 1347])).
% 2.45/1.85 tff(1351,plain,
% 2.45/1.85 ((~![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)))),
% 2.45/1.85 inference(quant_inst,[status(thm)],[])).
% 2.45/1.85 tff(1352,plain,
% 2.45/1.85 ((~![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))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 2.45/1.85 tff(1353,plain,
% 2.45/1.85 (~c0_1(a1465)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1352, 91, 1346, 1335, 1324, 37, 24, 1298, 822])).
% 2.45/1.85 tff(1354,plain,
% 2.45/1.85 (^[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))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1355,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1354])).
% 2.45/1.85 tff(1356,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1357,plain,
% 2.45/1.85 (^[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(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)))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1358,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1357])).
% 2.45/1.85 tff(1359,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')).
% 2.45/1.85 tff(1360,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 2.45/1.85 tff(1361,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1360, 1356])).
% 2.45/1.85 tff(1362,plain,(
% 2.45/1.85 ![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)))),
% 2.45/1.85 inference(skolemize,[status(sab)],[1361])).
% 2.45/1.85 tff(1363,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1362, 1355])).
% 2.45/1.85 tff(1364,assumption,(~c0_1(a1465)), introduced(assumption)).
% 2.45/1.85 tff(1365,plain,
% 2.45/1.85 (^[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))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1366,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1365])).
% 2.45/1.85 tff(1367,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1368,plain,
% 2.45/1.85 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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)))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1369,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1368])).
% 2.45/1.85 tff(1370,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')).
% 2.45/1.85 tff(1371,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 2.45/1.85 tff(1372,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1371, 1367])).
% 2.45/1.85 tff(1373,plain,(
% 2.45/1.85 ![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)))),
% 2.45/1.85 inference(skolemize,[status(sab)],[1372])).
% 2.45/1.85 tff(1374,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1373, 1366])).
% 2.45/1.85 tff(1375,assumption,(~c1_1(a1465)), introduced(assumption)).
% 2.45/1.85 tff(1376,plain,
% 2.45/1.85 (^[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))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1377,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1376])).
% 2.45/1.85 tff(1378,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1379,plain,
% 2.45/1.85 (^[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)))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1380,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1379])).
% 2.45/1.85 tff(1381,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')).
% 2.45/1.85 tff(1382,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 2.45/1.85 tff(1383,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1382, 1378])).
% 2.45/1.85 tff(1384,plain,(
% 2.45/1.85 ![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)))),
% 2.45/1.85 inference(skolemize,[status(sab)],[1383])).
% 2.45/1.85 tff(1385,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1384, 1377])).
% 2.45/1.85 tff(1386,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1387,plain,
% 2.45/1.85 ((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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1388,plain,
% 2.45/1.85 (((~![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))))),
% 2.45/1.85 inference(monotonicity,[status(thm)],[1387])).
% 2.45/1.85 tff(1389,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(transitivity,[status(thm)],[1388, 1386])).
% 2.45/1.85 tff(1390,plain,
% 2.45/1.85 ((~![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)))),
% 2.45/1.85 inference(quant_inst,[status(thm)],[])).
% 2.45/1.85 tff(1391,plain,
% 2.45/1.85 ((~![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))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 2.45/1.85 tff(1392,plain,
% 2.45/1.85 (hskp22),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1391, 91, 986, 232, 243, 1030, 985, 221, 1385])).
% 2.45/1.85 tff(1393,plain,
% 2.45/1.85 (~c0_1(a1468)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[891, 1392])).
% 2.45/1.85 tff(1394,assumption,(c2_1(a1465)), introduced(assumption)).
% 2.45/1.85 tff(1395,plain,
% 2.45/1.85 (c3_1(a1468)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[902, 1392])).
% 2.45/1.85 tff(1396,plain,
% 2.45/1.85 (c1_1(a1468)),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[913, 1392])).
% 2.45/1.85 tff(1397,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1398,plain,
% 2.45/1.85 (((~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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1399,plain,
% 2.45/1.85 (((~![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))))),
% 2.45/1.85 inference(monotonicity,[status(thm)],[1398])).
% 2.45/1.85 tff(1400,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(transitivity,[status(thm)],[1399, 1397])).
% 2.45/1.85 tff(1401,plain,
% 2.45/1.85 ((~![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)))),
% 2.45/1.85 inference(quant_inst,[status(thm)],[])).
% 2.45/1.85 tff(1402,plain,
% 2.45/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 2.45/1.85 tff(1403,plain,
% 2.45/1.85 ($false),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1402, 91, 1396, 1395, 1394, 232, 243, 1393, 1375, 221, 1374, 1364])).
% 2.45/1.85 tff(1404,plain,((~hskp12) | (~c2_1(a1465)) | c1_1(a1465) | c0_1(a1465) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487)), inference(lemma,lemma(discharge,[]))).
% 2.45/1.85 tff(1405,plain,
% 2.45/1.85 (~hskp12),
% 2.45/1.85 inference(unit_resolution,[status(thm)],[1404, 1353, 1324, 1346, 986, 1030, 985])).
% 2.45/1.85 tff(1406,plain,
% 2.45/1.85 (^[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))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1407,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1406])).
% 2.45/1.85 tff(1408,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1409,plain,
% 2.45/1.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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)))))),
% 2.45/1.85 inference(bind,[status(th)],[])).
% 2.45/1.85 tff(1410,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(quant_intro,[status(thm)],[1409])).
% 2.45/1.85 tff(1411,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')).
% 2.45/1.85 tff(1412,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 2.45/1.85 tff(1413,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1412, 1408])).
% 2.45/1.85 tff(1414,plain,(
% 2.45/1.85 ![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)))),
% 2.45/1.85 inference(skolemize,[status(sab)],[1413])).
% 2.45/1.85 tff(1415,plain,
% 2.45/1.85 (![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)))),
% 2.45/1.85 inference(modus_ponens,[status(thm)],[1414, 1407])).
% 2.45/1.85 tff(1416,plain,
% 2.45/1.85 (((~![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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1417,plain,
% 2.45/1.85 ((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)))),
% 2.45/1.85 inference(rewrite,[status(thm)],[])).
% 2.45/1.85 tff(1418,plain,
% 2.45/1.85 (((~![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))))),
% 2.45/1.86 inference(monotonicity,[status(thm)],[1417])).
% 2.45/1.86 tff(1419,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(transitivity,[status(thm)],[1418, 1416])).
% 2.45/1.86 tff(1420,plain,
% 2.45/1.86 ((~![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)))),
% 2.45/1.86 inference(quant_inst,[status(thm)],[])).
% 2.45/1.86 tff(1421,plain,
% 2.45/1.86 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 2.45/1.86 tff(1422,plain,
% 2.45/1.86 ($false),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1421, 91, 701, 1299, 114, 37, 113, 1415, 337, 822])).
% 2.45/1.86 tff(1423,plain,(c1_1(a1435) | hskp12 | (~c3_1(a1438)) | (~c0_1(a1435)) | c0_1(a1438) | c3_1(a1435) | (~c2_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.45/1.86 tff(1424,plain,
% 2.45/1.86 (c1_1(a1435)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1423, 1405, 1299, 114, 37, 113, 822])).
% 2.45/1.86 tff(1425,plain,
% 2.45/1.86 (hskp18 | (~c1_1(a1435)) | (~c0_1(a1435))),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[397, 91, 112, 113, 380])).
% 2.45/1.86 tff(1426,plain,
% 2.45/1.86 (hskp18),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1425, 1424, 114])).
% 2.45/1.86 tff(1427,plain,
% 2.45/1.86 (~c2_1(a1458)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[403, 1426])).
% 2.45/1.86 tff(1428,plain,
% 2.45/1.86 (c1_1(a1458)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[414, 1426])).
% 2.45/1.86 tff(1429,plain,
% 2.45/1.86 (((~![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(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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1430,plain,
% 2.45/1.86 ((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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1431,plain,
% 2.45/1.86 (((~![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(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))))),
% 2.45/1.86 inference(monotonicity,[status(thm)],[1430])).
% 2.45/1.86 tff(1432,plain,
% 2.45/1.86 (((~![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(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)))),
% 2.45/1.86 inference(transitivity,[status(thm)],[1431, 1429])).
% 2.45/1.86 tff(1433,plain,
% 2.45/1.86 ((~![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(a1458) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c3_1(a1465)) | (~c2_1(a1465)))),
% 2.45/1.86 inference(quant_inst,[status(thm)],[])).
% 2.45/1.86 tff(1434,plain,
% 2.45/1.86 ((~![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(a1458) | (~ndr1_0) | (~c3_1(a1458)) | (~c1_1(a1458)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1465))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 2.45/1.86 tff(1435,plain,
% 2.45/1.86 (~c3_1(a1458)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1434, 91, 1405, 1346, 1335, 1428, 1427, 1363, 1353])).
% 2.45/1.86 tff(1436,plain,
% 2.45/1.86 (^[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))))),
% 2.45/1.86 inference(bind,[status(th)],[])).
% 2.45/1.86 tff(1437,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(quant_intro,[status(thm)],[1436])).
% 2.45/1.86 tff(1438,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1439,plain,
% 2.45/1.86 (^[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)))))),
% 2.45/1.86 inference(bind,[status(th)],[])).
% 2.45/1.86 tff(1440,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(quant_intro,[status(thm)],[1439])).
% 2.45/1.86 tff(1441,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')).
% 2.45/1.86 tff(1442,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 2.45/1.86 tff(1443,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1442, 1438])).
% 2.45/1.86 tff(1444,plain,(
% 2.45/1.86 ![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)))),
% 2.45/1.86 inference(skolemize,[status(sab)],[1443])).
% 2.45/1.86 tff(1445,plain,
% 2.45/1.86 (![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)))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1444, 1437])).
% 2.45/1.86 tff(1446,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1447,plain,
% 2.45/1.86 ((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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1448,plain,
% 2.45/1.86 (((~![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))))),
% 2.45/1.86 inference(monotonicity,[status(thm)],[1447])).
% 2.45/1.86 tff(1449,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(transitivity,[status(thm)],[1448, 1446])).
% 2.45/1.86 tff(1450,plain,
% 2.45/1.86 ((~![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)))),
% 2.45/1.86 inference(quant_inst,[status(thm)],[])).
% 2.45/1.86 tff(1451,plain,
% 2.45/1.86 ((~![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))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 2.45/1.86 tff(1452,plain,
% 2.45/1.86 (hskp12 | c2_1(a1435) | (~c1_1(a1430)) | (~c1_1(a1435))),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1451, 91, 35, 113, 593, 1445])).
% 2.45/1.86 tff(1453,plain,
% 2.45/1.86 (~c1_1(a1430)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1452, 1424, 112, 1405])).
% 2.45/1.86 tff(1454,plain,
% 2.45/1.86 (~hskp25),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[605, 1453, 35, 112, 113, 593, 114])).
% 2.45/1.86 tff(1455,plain,
% 2.45/1.86 (hskp17),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[487, 1454, 48])).
% 2.45/1.86 tff(1456,plain,
% 2.45/1.86 (~c2_1(a1457)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[288, 1455])).
% 2.45/1.86 tff(1457,plain,
% 2.45/1.86 (~c1_1(a1457)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[269, 1455])).
% 2.45/1.86 tff(1458,plain,
% 2.45/1.86 (~c0_1(a1457)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[275, 1455])).
% 2.45/1.86 tff(1459,plain,
% 2.45/1.86 (c0_1(a1458)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[425, 1426])).
% 2.45/1.86 tff(1460,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1461,plain,
% 2.45/1.86 ((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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1462,plain,
% 2.45/1.86 (((~![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))))),
% 2.45/1.86 inference(monotonicity,[status(thm)],[1461])).
% 2.45/1.86 tff(1463,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(transitivity,[status(thm)],[1462, 1460])).
% 2.45/1.86 tff(1464,plain,
% 2.45/1.86 ((~![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))),
% 2.45/1.86 inference(quant_inst,[status(thm)],[])).
% 2.45/1.86 tff(1465,plain,
% 2.45/1.86 ((~![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))),
% 2.45/1.86 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 2.45/1.86 tff(1466,plain,
% 2.45/1.86 (hskp0),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1465, 91, 1459, 1427, 1458, 1457, 1456, 1201, 1435])).
% 2.45/1.86 tff(1467,plain,
% 2.45/1.86 (~c3_1(a1427)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1213, 1466])).
% 2.45/1.86 tff(1468,plain,
% 2.45/1.86 (c2_1(a1427)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1224, 1466])).
% 2.45/1.86 tff(1469,plain,
% 2.45/1.86 (c0_1(a1427)),
% 2.45/1.86 inference(unit_resolution,[status(thm)],[1235, 1466])).
% 2.45/1.86 tff(1470,plain,
% 2.45/1.86 (((~![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)))),
% 2.45/1.86 inference(rewrite,[status(thm)],[])).
% 2.45/1.86 tff(1471,plain,
% 2.45/1.86 ((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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1472,plain,
% 2.50/1.86 (((~![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))))),
% 2.50/1.86 inference(monotonicity,[status(thm)],[1471])).
% 2.50/1.86 tff(1473,plain,
% 2.50/1.86 (((~![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)))),
% 2.50/1.86 inference(transitivity,[status(thm)],[1472, 1470])).
% 2.50/1.86 tff(1474,plain,
% 2.50/1.86 ((~![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)))),
% 2.50/1.86 inference(quant_inst,[status(thm)],[])).
% 2.50/1.86 tff(1475,plain,
% 2.50/1.86 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 2.50/1.86 tff(1476,plain,
% 2.50/1.86 ($false),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1475, 91, 1405, 1300, 1469, 1468, 1467, 1288])).
% 2.50/1.86 tff(1477,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,[]))).
% 2.50/1.86 tff(1478,plain,
% 2.50/1.86 (hskp11),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1477, 112, 35, 113, 574, 1158, 1161, 1160, 1278, 986, 1030, 985, 24])).
% 2.50/1.86 tff(1479,plain,
% 2.50/1.86 (~c2_1(a1447)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[745, 1478])).
% 2.50/1.86 tff(1480,plain,
% 2.50/1.86 (~c0_1(a1447)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[751, 1478])).
% 2.50/1.86 tff(1481,plain,
% 2.50/1.86 (~c3_1(a1447)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[757, 1478])).
% 2.50/1.86 tff(1482,plain,
% 2.50/1.86 (c0_1(a1447) | c1_1(a1447)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[767, 91, 48, 761, 760, 60])).
% 2.50/1.86 tff(1483,plain,
% 2.50/1.86 (c1_1(a1447)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1482, 759])).
% 2.50/1.86 tff(1484,plain,
% 2.50/1.86 (hskp12),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[776, 1483, 759])).
% 2.50/1.86 tff(1485,plain,
% 2.50/1.86 (~c2_1(a1448)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[220, 1484])).
% 2.50/1.86 tff(1486,plain,
% 2.50/1.86 (c3_1(a1448)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[242, 1484])).
% 2.50/1.86 tff(1487,plain,
% 2.50/1.86 (c0_1(a1448)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[231, 1484])).
% 2.50/1.86 tff(1488,plain,
% 2.50/1.86 (hskp22),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1391, 91, 986, 1487, 1486, 1030, 985, 1485, 1385])).
% 2.50/1.86 tff(1489,plain,
% 2.50/1.86 (~c0_1(a1468)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[891, 1488])).
% 2.50/1.86 tff(1490,plain,
% 2.50/1.86 (c3_1(a1468)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[902, 1488])).
% 2.50/1.86 tff(1491,plain,
% 2.50/1.86 (c1_1(a1468)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[913, 1488])).
% 2.50/1.86 tff(1492,plain,
% 2.50/1.86 (((~![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) | 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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1493,plain,
% 2.50/1.86 (((~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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1494,plain,
% 2.50/1.86 (((~![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(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))))),
% 2.50/1.86 inference(monotonicity,[status(thm)],[1493])).
% 2.50/1.86 tff(1495,plain,
% 2.50/1.86 (((~![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(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)))),
% 2.50/1.86 inference(transitivity,[status(thm)],[1494, 1492])).
% 2.50/1.86 tff(1496,plain,
% 2.50/1.86 ((~![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(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 2.50/1.86 inference(quant_inst,[status(thm)],[])).
% 2.50/1.86 tff(1497,plain,
% 2.50/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1468) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 2.50/1.86 tff(1498,plain,
% 2.50/1.86 (~c2_1(a1438)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1497, 91, 1491, 1490, 1487, 1486, 1489, 1485, 37, 24, 1374])).
% 2.50/1.86 tff(1499,plain,
% 2.50/1.86 (hskp9),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1170, 91, 1299, 35, 37, 12, 574, 1118, 1498])).
% 2.50/1.86 tff(1500,plain,
% 2.50/1.86 (~c3_1(a1444)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1131, 1499])).
% 2.50/1.86 tff(1501,plain,
% 2.50/1.86 (~c2_1(a1444)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1137, 1499])).
% 2.50/1.86 tff(1502,plain,
% 2.50/1.86 (~c1_1(a1444)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1143, 1499])).
% 2.50/1.86 tff(1503,plain,
% 2.50/1.86 ($false),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1154, 91, 48, 759, 761, 760, 1502, 1501, 1500, 60])).
% 2.50/1.86 tff(1504,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,[]))).
% 2.50/1.86 tff(1505,plain,
% 2.50/1.86 ($false),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1504, 1481, 1480, 1479, 1161, 35, 1160, 12, 24, 986, 1030, 985])).
% 2.50/1.86 tff(1506,plain,(c2_1(a1435) | c3_1(a1430) | c0_1(a1430) | c1_1(a1438) | (~c3_1(a1487)) | c1_1(a1487) | c2_1(a1487) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.86 tff(1507,plain,
% 2.50/1.86 (c1_1(a1438)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1506, 1029, 12, 35, 983, 1028, 972, 1022])).
% 2.50/1.86 tff(1508,plain,
% 2.50/1.86 (c0_1(a1435)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[390, 1021])).
% 2.50/1.86 tff(1509,plain,
% 2.50/1.86 (hskp7),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[697, 1029, 35, 1508, 1022, 12])).
% 2.50/1.86 tff(1510,plain,
% 2.50/1.86 (((~hskp7) | (~c1_1(a1438))) <=> ((~hskp7) | (~c1_1(a1438)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1511,plain,
% 2.50/1.86 (((~c1_1(a1438)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1438)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1512,axiom,((~c1_1(a1438)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 2.50/1.86 tff(1513,plain,
% 2.50/1.86 ((~hskp7) | (~c1_1(a1438))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 2.50/1.86 tff(1514,plain,
% 2.50/1.86 ((~hskp7) | (~c1_1(a1438))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1513, 1510])).
% 2.50/1.86 tff(1515,plain,
% 2.50/1.86 ($false),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1514, 1509, 1507])).
% 2.50/1.86 tff(1516,plain,((~hskp24) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.86 tff(1517,plain,
% 2.50/1.86 (~hskp24),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1516, 35, 12])).
% 2.50/1.86 tff(1518,plain,
% 2.50/1.86 (hskp30),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[89, 1517])).
% 2.50/1.86 tff(1519,plain,
% 2.50/1.86 (((~hskp30) | c2_1(a1507)) <=> ((~hskp30) | c2_1(a1507))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1520,axiom,((~hskp30) | c2_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 2.50/1.86 tff(1521,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 2.50/1.86 tff(1522,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1521, 1519])).
% 2.50/1.86 tff(1523,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1522, 1519])).
% 2.50/1.86 tff(1524,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1523, 1519])).
% 2.50/1.86 tff(1525,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1524, 1519])).
% 2.50/1.86 tff(1526,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1525, 1519])).
% 2.50/1.86 tff(1527,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1526, 1519])).
% 2.50/1.86 tff(1528,plain,
% 2.50/1.86 ((~hskp30) | c2_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1527, 1519])).
% 2.50/1.86 tff(1529,plain,
% 2.50/1.86 (c2_1(a1507)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1528, 1518])).
% 2.50/1.86 tff(1530,plain,
% 2.50/1.86 (((~hskp30) | c0_1(a1507)) <=> ((~hskp30) | c0_1(a1507))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1531,axiom,((~hskp30) | c0_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 2.50/1.86 tff(1532,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 2.50/1.86 tff(1533,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1532, 1530])).
% 2.50/1.86 tff(1534,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1533, 1530])).
% 2.50/1.86 tff(1535,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1534, 1530])).
% 2.50/1.86 tff(1536,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1535, 1530])).
% 2.50/1.86 tff(1537,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1536, 1530])).
% 2.50/1.86 tff(1538,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1537, 1530])).
% 2.50/1.86 tff(1539,plain,
% 2.50/1.86 ((~hskp30) | c0_1(a1507)),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1538, 1530])).
% 2.50/1.86 tff(1540,plain,
% 2.50/1.86 (c0_1(a1507)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1539, 1518])).
% 2.50/1.86 tff(1541,plain,
% 2.50/1.86 (((~![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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1542,plain,
% 2.50/1.86 ((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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1543,plain,
% 2.50/1.86 (((~![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))))),
% 2.50/1.86 inference(monotonicity,[status(thm)],[1542])).
% 2.50/1.86 tff(1544,plain,
% 2.50/1.86 (((~![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)))),
% 2.50/1.86 inference(transitivity,[status(thm)],[1543, 1541])).
% 2.50/1.86 tff(1545,plain,
% 2.50/1.86 ((~![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)))),
% 2.50/1.86 inference(quant_inst,[status(thm)],[])).
% 2.50/1.86 tff(1546,plain,
% 2.50/1.86 ((~![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))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 2.50/1.86 tff(1547,plain,
% 2.50/1.86 (hskp11 | hskp5 | c2_1(a1438) | (~c3_1(a1438))),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1546, 91, 37, 34])).
% 2.50/1.86 tff(1548,plain,
% 2.50/1.86 (c2_1(a1438)),
% 2.50/1.86 inference(unit_resolution,[status(thm)],[1547, 984, 1299, 11])).
% 2.50/1.86 tff(1549,assumption,(c2_1(a1507)), introduced(assumption)).
% 2.50/1.86 tff(1550,assumption,(c0_1(a1507)), introduced(assumption)).
% 2.50/1.86 tff(1551,plain,
% 2.50/1.86 (((~![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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1552,plain,
% 2.50/1.86 (((~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)))),
% 2.50/1.86 inference(rewrite,[status(thm)],[])).
% 2.50/1.86 tff(1553,plain,
% 2.50/1.86 (((~![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))))),
% 2.50/1.86 inference(monotonicity,[status(thm)],[1552])).
% 2.50/1.86 tff(1554,plain,
% 2.50/1.86 (((~![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)))),
% 2.50/1.86 inference(transitivity,[status(thm)],[1553, 1551])).
% 2.50/1.86 tff(1555,plain,
% 2.50/1.86 ((~![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)))),
% 2.50/1.86 inference(quant_inst,[status(thm)],[])).
% 2.50/1.86 tff(1556,plain,
% 2.50/1.86 ((~![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))),
% 2.50/1.86 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 2.50/1.87 tff(1557,plain,
% 2.50/1.87 (c0_1(a1438) | (~c3_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1556, 91, 1550, 1549, 24, 1298])).
% 2.50/1.87 tff(1558,plain,
% 2.50/1.87 (~c3_1(a1507)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1557, 1548, 37, 1299])).
% 2.50/1.87 tff(1559,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1560,plain,
% 2.50/1.87 ((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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1561,plain,
% 2.50/1.87 (((~![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))))),
% 2.50/1.87 inference(monotonicity,[status(thm)],[1560])).
% 2.50/1.87 tff(1562,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(transitivity,[status(thm)],[1561, 1559])).
% 2.50/1.87 tff(1563,plain,
% 2.50/1.87 ((~![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)))),
% 2.50/1.87 inference(quant_inst,[status(thm)],[])).
% 2.50/1.87 tff(1564,plain,
% 2.50/1.87 ((~![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))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 2.50/1.87 tff(1565,plain,
% 2.50/1.87 (hskp12 | hskp11 | c3_1(a1507)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1564, 91, 1550, 1549, 1288])).
% 2.50/1.87 tff(1566,plain,
% 2.50/1.87 (hskp12),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1565, 1558, 984])).
% 2.50/1.87 tff(1567,plain,
% 2.50/1.87 (~c2_1(a1448)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[220, 1566])).
% 2.50/1.87 tff(1568,plain,
% 2.50/1.87 (c3_1(a1448)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[242, 1566])).
% 2.50/1.87 tff(1569,plain,
% 2.50/1.87 (c0_1(a1448)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[231, 1566])).
% 2.50/1.87 tff(1570,plain,
% 2.50/1.87 (((~![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 | 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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1571,plain,
% 2.50/1.87 ((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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1572,plain,
% 2.50/1.87 (((~![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(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))))),
% 2.50/1.87 inference(monotonicity,[status(thm)],[1571])).
% 2.50/1.87 tff(1573,plain,
% 2.50/1.87 (((~![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(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)))),
% 2.50/1.87 inference(transitivity,[status(thm)],[1572, 1570])).
% 2.50/1.87 tff(1574,plain,
% 2.50/1.87 ((~![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(a1448) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1438) | c1_1(a1438) | (~c3_1(a1438)))),
% 2.50/1.87 inference(quant_inst,[status(thm)],[])).
% 2.50/1.87 tff(1575,plain,
% 2.50/1.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 2.50/1.87 tff(1576,plain,
% 2.50/1.87 ($false),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1575, 91, 11, 1569, 1568, 1299, 1567, 37, 24, 10])).
% 2.50/1.87 tff(1577,plain,(hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | (~c0_1(a1507)) | (~c2_1(a1507)) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.50/1.87 tff(1578,plain,
% 2.50/1.87 (hskp5),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1577, 965, 37, 24, 1540, 1529, 48])).
% 2.50/1.87 tff(1579,plain,
% 2.50/1.87 (~c3_1(a1435)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[319, 1578])).
% 2.50/1.87 tff(1580,plain,
% 2.50/1.87 (~c2_1(a1435)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[325, 1578])).
% 2.50/1.87 tff(1581,plain,
% 2.50/1.87 (c0_1(a1435)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[390, 1578])).
% 2.50/1.87 tff(1582,plain,
% 2.50/1.87 (c2_1(a1438)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1277, 1581, 24, 1580, 1579, 35, 12])).
% 2.50/1.87 tff(1583,plain,
% 2.50/1.87 (c0_1(a1438) | (~c3_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1556, 91, 1540, 1529, 24, 1298])).
% 2.50/1.87 tff(1584,plain,
% 2.50/1.87 (~c3_1(a1507)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1583, 1582, 37, 965])).
% 2.50/1.87 tff(1585,plain,
% 2.50/1.87 (^[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))))),
% 2.50/1.87 inference(bind,[status(th)],[])).
% 2.50/1.87 tff(1586,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(quant_intro,[status(thm)],[1585])).
% 2.50/1.87 tff(1587,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1588,plain,
% 2.50/1.87 (^[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)))))),
% 2.50/1.87 inference(bind,[status(th)],[])).
% 2.50/1.87 tff(1589,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(quant_intro,[status(thm)],[1588])).
% 2.50/1.87 tff(1590,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')).
% 2.50/1.87 tff(1591,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 2.50/1.87 tff(1592,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1591, 1587])).
% 2.50/1.87 tff(1593,plain,(
% 2.50/1.87 ![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)))),
% 2.50/1.87 inference(skolemize,[status(sab)],[1592])).
% 2.50/1.87 tff(1594,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1593, 1586])).
% 2.50/1.87 tff(1595,plain,
% 2.50/1.87 (((~hskp30) | c1_1(a1507)) <=> ((~hskp30) | c1_1(a1507))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1596,axiom,((~hskp30) | c1_1(a1507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 2.50/1.87 tff(1597,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 2.50/1.87 tff(1598,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1597, 1595])).
% 2.50/1.87 tff(1599,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1598, 1595])).
% 2.50/1.87 tff(1600,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1599, 1595])).
% 2.50/1.87 tff(1601,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1600, 1595])).
% 2.50/1.87 tff(1602,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1601, 1595])).
% 2.50/1.87 tff(1603,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1602, 1595])).
% 2.50/1.87 tff(1604,plain,
% 2.50/1.87 ((~hskp30) | c1_1(a1507)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1603, 1595])).
% 2.50/1.87 tff(1605,plain,
% 2.50/1.87 (c1_1(a1507)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1604, 1518])).
% 2.50/1.87 tff(1606,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1607,plain,
% 2.50/1.87 ((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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1608,plain,
% 2.50/1.87 (((~![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))))),
% 2.50/1.87 inference(monotonicity,[status(thm)],[1607])).
% 2.50/1.87 tff(1609,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(transitivity,[status(thm)],[1608, 1606])).
% 2.50/1.87 tff(1610,plain,
% 2.50/1.87 ((~![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)))),
% 2.50/1.87 inference(quant_inst,[status(thm)],[])).
% 2.50/1.87 tff(1611,plain,
% 2.50/1.87 ((~![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))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 2.50/1.87 tff(1612,plain,
% 2.50/1.87 (hskp23),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1611, 91, 1540, 1605, 1529, 1594, 1584])).
% 2.50/1.87 tff(1613,plain,
% 2.50/1.87 (((~hskp23) | c2_1(a1477)) <=> ((~hskp23) | c2_1(a1477))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1614,axiom,((~hskp23) | c2_1(a1477)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 2.50/1.87 tff(1615,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 2.50/1.87 tff(1616,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1615, 1613])).
% 2.50/1.87 tff(1617,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1616, 1613])).
% 2.50/1.87 tff(1618,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1617, 1613])).
% 2.50/1.87 tff(1619,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1618, 1613])).
% 2.50/1.87 tff(1620,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1619, 1613])).
% 2.50/1.87 tff(1621,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1620, 1613])).
% 2.50/1.87 tff(1622,plain,
% 2.50/1.87 ((~hskp23) | c2_1(a1477)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1621, 1613])).
% 2.50/1.87 tff(1623,plain,
% 2.50/1.87 (c2_1(a1477)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1622, 1612])).
% 2.50/1.87 tff(1624,plain,
% 2.50/1.87 (((~hskp23) | (~c1_1(a1477))) <=> ((~hskp23) | (~c1_1(a1477)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1625,plain,
% 2.50/1.87 (((~c1_1(a1477)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1477)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1626,axiom,((~c1_1(a1477)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 2.50/1.87 tff(1627,plain,
% 2.50/1.87 ((~hskp23) | (~c1_1(a1477))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 2.50/1.87 tff(1628,plain,
% 2.50/1.87 ((~hskp23) | (~c1_1(a1477))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1627, 1624])).
% 2.50/1.87 tff(1629,plain,
% 2.50/1.87 (~c1_1(a1477)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1628, 1612])).
% 2.50/1.87 tff(1630,plain,
% 2.50/1.87 (^[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))))),
% 2.50/1.87 inference(bind,[status(th)],[])).
% 2.50/1.87 tff(1631,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(quant_intro,[status(thm)],[1630])).
% 2.50/1.87 tff(1632,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1633,plain,
% 2.50/1.87 (^[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)))))),
% 2.50/1.87 inference(bind,[status(th)],[])).
% 2.50/1.87 tff(1634,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(quant_intro,[status(thm)],[1633])).
% 2.50/1.87 tff(1635,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')).
% 2.50/1.87 tff(1636,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 2.50/1.87 tff(1637,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1636, 1632])).
% 2.50/1.87 tff(1638,plain,(
% 2.50/1.87 ![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)))),
% 2.50/1.87 inference(skolemize,[status(sab)],[1637])).
% 2.50/1.87 tff(1639,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1638, 1631])).
% 2.50/1.87 tff(1640,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1641,plain,
% 2.50/1.87 ((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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1642,plain,
% 2.50/1.87 (((~![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))))),
% 2.50/1.87 inference(monotonicity,[status(thm)],[1641])).
% 2.50/1.87 tff(1643,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(transitivity,[status(thm)],[1642, 1640])).
% 2.50/1.87 tff(1644,plain,
% 2.50/1.87 ((~![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)))),
% 2.50/1.87 inference(quant_inst,[status(thm)],[])).
% 2.50/1.87 tff(1645,plain,
% 2.50/1.87 ((~![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))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 2.50/1.87 tff(1646,plain,
% 2.50/1.87 (hskp8),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1645, 91, 1540, 1605, 965, 24, 1639, 1584, 1582])).
% 2.50/1.87 tff(1647,plain,
% 2.50/1.87 (((~hskp8) | (~c1_1(a1441))) <=> ((~hskp8) | (~c1_1(a1441)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1648,plain,
% 2.50/1.87 (((~c1_1(a1441)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1441)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1649,axiom,((~c1_1(a1441)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 2.50/1.87 tff(1650,plain,
% 2.50/1.87 ((~hskp8) | (~c1_1(a1441))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 2.50/1.87 tff(1651,plain,
% 2.50/1.87 ((~hskp8) | (~c1_1(a1441))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1650, 1647])).
% 2.50/1.87 tff(1652,plain,
% 2.50/1.87 (~c1_1(a1441)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1651, 1646])).
% 2.50/1.87 tff(1653,plain,
% 2.50/1.87 (((~hskp8) | c3_1(a1441)) <=> ((~hskp8) | c3_1(a1441))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1654,axiom,((~hskp8) | c3_1(a1441)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 2.50/1.87 tff(1655,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 2.50/1.87 tff(1656,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1655, 1653])).
% 2.50/1.87 tff(1657,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1656, 1653])).
% 2.50/1.87 tff(1658,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1657, 1653])).
% 2.50/1.87 tff(1659,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1658, 1653])).
% 2.50/1.87 tff(1660,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1659, 1653])).
% 2.50/1.87 tff(1661,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1660, 1653])).
% 2.50/1.87 tff(1662,plain,
% 2.50/1.87 ((~hskp8) | c3_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1661, 1653])).
% 2.50/1.87 tff(1663,plain,
% 2.50/1.87 (c3_1(a1441)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1662, 1646])).
% 2.50/1.87 tff(1664,plain,
% 2.50/1.87 (((~hskp8) | c0_1(a1441)) <=> ((~hskp8) | c0_1(a1441))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1665,axiom,((~hskp8) | c0_1(a1441)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 2.50/1.87 tff(1666,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 2.50/1.87 tff(1667,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1666, 1664])).
% 2.50/1.87 tff(1668,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1667, 1664])).
% 2.50/1.87 tff(1669,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 2.50/1.87 tff(1670,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1669, 1664])).
% 2.50/1.87 tff(1671,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1670, 1664])).
% 2.50/1.87 tff(1672,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1671, 1664])).
% 2.50/1.87 tff(1673,plain,
% 2.50/1.87 ((~hskp8) | c0_1(a1441)),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1672, 1664])).
% 2.50/1.87 tff(1674,plain,
% 2.50/1.87 (c0_1(a1441)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1673, 1646])).
% 2.50/1.87 tff(1675,plain,
% 2.50/1.87 (((~hskp23) | (~c0_1(a1477))) <=> ((~hskp23) | (~c0_1(a1477)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1676,plain,
% 2.50/1.87 (((~c0_1(a1477)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1477)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1677,axiom,((~c0_1(a1477)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 2.50/1.87 tff(1678,plain,
% 2.50/1.87 ((~hskp23) | (~c0_1(a1477))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 2.50/1.87 tff(1679,plain,
% 2.50/1.87 ((~hskp23) | (~c0_1(a1477))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1678, 1675])).
% 2.50/1.87 tff(1680,plain,
% 2.50/1.87 (~c0_1(a1477)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1679, 1612])).
% 2.50/1.87 tff(1681,assumption,(c2_1(a1441)), introduced(assumption)).
% 2.50/1.87 tff(1682,assumption,(~c1_1(a1441)), introduced(assumption)).
% 2.50/1.87 tff(1683,assumption,(~c1_1(a1477)), introduced(assumption)).
% 2.50/1.87 tff(1684,assumption,(~c0_1(a1477)), introduced(assumption)).
% 2.50/1.87 tff(1685,assumption,(c3_1(a1441)), introduced(assumption)).
% 2.50/1.87 tff(1686,assumption,(c0_1(a1441)), introduced(assumption)).
% 2.50/1.87 tff(1687,assumption,(c2_1(a1477)), introduced(assumption)).
% 2.50/1.87 tff(1688,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1689,plain,
% 2.50/1.87 (((~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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1690,plain,
% 2.50/1.87 (((~![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))))),
% 2.50/1.87 inference(monotonicity,[status(thm)],[1689])).
% 2.50/1.87 tff(1691,plain,
% 2.50/1.87 (((~![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)))),
% 2.50/1.87 inference(transitivity,[status(thm)],[1690, 1688])).
% 2.50/1.87 tff(1692,plain,
% 2.50/1.87 ((~![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)))),
% 2.50/1.87 inference(quant_inst,[status(thm)],[])).
% 2.50/1.87 tff(1693,plain,
% 2.50/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c2_1(a1477))),
% 2.50/1.87 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 2.50/1.87 tff(1694,plain,
% 2.50/1.87 ($false),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1693, 91, 1687, 1686, 1685, 1684, 1683, 1682, 1298, 1681])).
% 2.50/1.87 tff(1695,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,[]))).
% 2.50/1.87 tff(1696,plain,
% 2.50/1.87 (~c2_1(a1441)),
% 2.50/1.87 inference(unit_resolution,[status(thm)],[1695, 1680, 1674, 1663, 1652, 1629, 1623])).
% 2.50/1.87 tff(1697,plain,
% 2.50/1.87 (^[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))))),
% 2.50/1.87 inference(bind,[status(th)],[])).
% 2.50/1.87 tff(1698,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(quant_intro,[status(thm)],[1697])).
% 2.50/1.87 tff(1699,plain,
% 2.50/1.87 (![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)))),
% 2.50/1.87 inference(rewrite,[status(thm)],[])).
% 2.50/1.87 tff(1700,plain,
% 2.50/1.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~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)))))),
% 2.50/1.88 inference(bind,[status(th)],[])).
% 2.50/1.88 tff(1701,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(quant_intro,[status(thm)],[1700])).
% 2.50/1.88 tff(1702,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')).
% 2.50/1.88 tff(1703,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 2.50/1.88 tff(1704,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1703, 1699])).
% 2.50/1.88 tff(1705,plain,(
% 2.50/1.88 ![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)))),
% 2.50/1.88 inference(skolemize,[status(sab)],[1704])).
% 2.50/1.88 tff(1706,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1705, 1698])).
% 2.50/1.88 tff(1707,plain,
% 2.50/1.88 (((~![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) | (~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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1708,plain,
% 2.50/1.88 (((~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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1709,plain,
% 2.50/1.88 (((~![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(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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1708])).
% 2.50/1.88 tff(1710,plain,
% 2.50/1.88 (((~![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(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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1709, 1707])).
% 2.50/1.88 tff(1711,plain,
% 2.50/1.88 ((~![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(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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1712,plain,
% 2.50/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c0_1(a1507)) | (~c1_1(a1507)) | (~c2_1(a1507)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 2.50/1.88 tff(1713,plain,
% 2.50/1.88 ($false),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1712, 91, 1540, 1605, 1529, 1663, 965, 1652, 24, 1706, 1582, 1696])).
% 2.50/1.88 tff(1714,plain,(c0_1(a1438) | c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.88 tff(1715,plain,
% 2.50/1.88 (c0_1(a1438)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1714, 24, 35, 12])).
% 2.50/1.88 tff(1716,plain,
% 2.50/1.88 (~hskp7),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1099, 1715])).
% 2.50/1.88 tff(1717,assumption,(hskp5), introduced(assumption)).
% 2.50/1.88 tff(1718,plain,
% 2.50/1.88 (~c3_1(a1435)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[319, 1717])).
% 2.50/1.88 tff(1719,plain,
% 2.50/1.88 (c0_1(a1435)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[390, 1717])).
% 2.50/1.88 tff(1720,plain,
% 2.50/1.88 (~c2_1(a1435)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[325, 1717])).
% 2.50/1.88 tff(1721,plain,
% 2.50/1.88 ($false),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[697, 1720, 1719, 35, 13, 1718, 12])).
% 2.50/1.88 tff(1722,plain,((~hskp5) | c3_1(a1430) | hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.88 tff(1723,plain,
% 2.50/1.88 (~hskp5),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1722, 1716, 35, 12])).
% 2.50/1.88 tff(1724,assumption,(c0_1(a1438)), introduced(assumption)).
% 2.50/1.88 tff(1725,plain,
% 2.50/1.88 (((~![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))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1726,plain,
% 2.50/1.88 ((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))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1727,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1726])).
% 2.50/1.88 tff(1728,plain,
% 2.50/1.88 (((~![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))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1727, 1725])).
% 2.50/1.88 tff(1729,plain,
% 2.50/1.88 ((~![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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1730,plain,
% 2.50/1.88 ((~![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)),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 2.50/1.88 tff(1731,plain,
% 2.50/1.88 (hskp29 | hskp5 | c3_1(a1438) | c2_1(a1438)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1730, 91, 1724, 1044])).
% 2.50/1.88 tff(1732,plain,
% 2.50/1.88 (hskp29),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1731, 50, 49, 11])).
% 2.50/1.88 tff(1733,plain,
% 2.50/1.88 (c3_1(a1483)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1062, 1732])).
% 2.50/1.88 tff(1734,plain,
% 2.50/1.88 (c2_1(a1483)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1073, 1732])).
% 2.50/1.88 tff(1735,plain,
% 2.50/1.88 (c1_1(a1483)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1084, 1732])).
% 2.50/1.88 tff(1736,plain,
% 2.50/1.88 (~hskp7),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1099, 1724])).
% 2.50/1.88 tff(1737,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1738,plain,
% 2.50/1.88 ((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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1739,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1738])).
% 2.50/1.88 tff(1740,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1739, 1737])).
% 2.50/1.88 tff(1741,plain,
% 2.50/1.88 ((~![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))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1742,plain,
% 2.50/1.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c3_1(a1438) | c1_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 2.50/1.88 tff(1743,plain,
% 2.50/1.88 ($false),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1742, 91, 1736, 1735, 1734, 1733, 49, 24, 678, 50])).
% 2.50/1.88 tff(1744,plain,(c2_1(a1438) | c3_1(a1438) | c1_1(a1438) | hskp5 | (~c0_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.50/1.88 tff(1745,plain,
% 2.50/1.88 (c2_1(a1438)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1744, 11, 24, 49, 1724])).
% 2.50/1.88 tff(1746,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1747,plain,
% 2.50/1.88 ((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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1748,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1747])).
% 2.50/1.88 tff(1749,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1748, 1746])).
% 2.50/1.88 tff(1750,plain,
% 2.50/1.88 ((~![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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1751,plain,
% 2.50/1.88 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | c3_1(a1438) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 2.50/1.88 tff(1752,plain,
% 2.50/1.88 (hskp12 | hskp11 | c3_1(a1438) | (~c2_1(a1438))),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1751, 91, 1724, 1288])).
% 2.50/1.88 tff(1753,plain,
% 2.50/1.88 (hskp12),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1752, 1745, 49, 984])).
% 2.50/1.88 tff(1754,plain,
% 2.50/1.88 (~hskp17),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[862, 1745, 24, 49, 61, 11])).
% 2.50/1.88 tff(1755,plain,
% 2.50/1.88 (c2_1(a1448)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[263, 1754, 11, 1753])).
% 2.50/1.88 tff(1756,plain,
% 2.50/1.88 ($false),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[220, 1755, 1753])).
% 2.50/1.88 tff(1757,plain,(hskp5 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.50/1.88 tff(1758,plain,
% 2.50/1.88 (c3_1(a1438)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1757, 1723, 1715, 24, 48])).
% 2.50/1.88 tff(1759,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1760,plain,
% 2.50/1.88 ((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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1761,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1760])).
% 2.50/1.88 tff(1762,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1761, 1759])).
% 2.50/1.88 tff(1763,plain,
% 2.50/1.88 ((~![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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1764,plain,
% 2.50/1.88 ((~![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))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 2.50/1.88 tff(1765,plain,
% 2.50/1.88 (hskp17 | hskp5 | c2_1(a1438) | (~c3_1(a1438))),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1764, 91, 1724, 253])).
% 2.50/1.88 tff(1766,plain,
% 2.50/1.88 (hskp17),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1765, 50, 11, 1299])).
% 2.50/1.88 tff(1767,plain,
% 2.50/1.88 (~c1_1(a1457)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[269, 1766])).
% 2.50/1.88 tff(1768,plain,
% 2.50/1.88 (~c0_1(a1457)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[275, 1766])).
% 2.50/1.88 tff(1769,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1770,plain,
% 2.50/1.88 ((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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1771,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1770])).
% 2.50/1.88 tff(1772,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1771, 1769])).
% 2.50/1.88 tff(1773,plain,
% 2.50/1.88 ((~![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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1774,plain,
% 2.50/1.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1457) | c1_1(a1457) | (~c0_1(a1438)) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | (~c3_1(a1457))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 2.50/1.88 tff(1775,plain,
% 2.50/1.88 (~c3_1(a1457)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1774, 91, 11, 1299, 1768, 1767, 1724, 10, 50])).
% 2.50/1.88 tff(1776,plain,
% 2.50/1.88 (~c2_1(a1457)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[288, 1766])).
% 2.50/1.88 tff(1777,plain,
% 2.50/1.88 ($false),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1018, 91, 61, 1768, 1767, 1776, 60, 1775])).
% 2.50/1.88 tff(1778,plain,(c2_1(a1438) | hskp2 | hskp5 | (~c3_1(a1438)) | (~c0_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.50/1.88 tff(1779,plain,
% 2.50/1.88 (c2_1(a1438)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1778, 1723, 48, 1758, 1715])).
% 2.50/1.88 tff(1780,plain,
% 2.50/1.88 (~hskp11),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[795, 1723, 48])).
% 2.50/1.88 tff(1781,plain,
% 2.50/1.88 (hskp20),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1317, 1779, 1780, 1758])).
% 2.50/1.88 tff(1782,plain,
% 2.50/1.88 (~c1_1(a1465)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1323, 1781])).
% 2.50/1.88 tff(1783,plain,
% 2.50/1.88 (c3_1(a1465)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1334, 1781])).
% 2.50/1.88 tff(1784,plain,
% 2.50/1.88 (c2_1(a1465)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1345, 1781])).
% 2.50/1.88 tff(1785,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1786,plain,
% 2.50/1.88 (((~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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1787,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.88 inference(monotonicity,[status(thm)],[1786])).
% 2.50/1.88 tff(1788,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(transitivity,[status(thm)],[1787, 1785])).
% 2.50/1.88 tff(1789,plain,
% 2.50/1.88 ((~![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)))),
% 2.50/1.88 inference(quant_inst,[status(thm)],[])).
% 2.50/1.88 tff(1790,plain,
% 2.50/1.88 ((~![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))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 2.50/1.88 tff(1791,plain,
% 2.50/1.88 (c0_1(a1465)),
% 2.50/1.88 inference(unit_resolution,[status(thm)],[1790, 91, 1784, 1783, 1758, 1782, 1715, 1298, 1779])).
% 2.50/1.88 tff(1792,plain,
% 2.50/1.88 (^[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))))),
% 2.50/1.88 inference(bind,[status(th)],[])).
% 2.50/1.88 tff(1793,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(quant_intro,[status(thm)],[1792])).
% 2.50/1.88 tff(1794,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1795,plain,
% 2.50/1.88 (^[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)))))),
% 2.50/1.88 inference(bind,[status(th)],[])).
% 2.50/1.88 tff(1796,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(quant_intro,[status(thm)],[1795])).
% 2.50/1.88 tff(1797,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')).
% 2.50/1.88 tff(1798,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 2.50/1.88 tff(1799,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1798, 1794])).
% 2.50/1.88 tff(1800,plain,(
% 2.50/1.88 ![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)))),
% 2.50/1.88 inference(skolemize,[status(sab)],[1799])).
% 2.50/1.88 tff(1801,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1800, 1793])).
% 2.50/1.88 tff(1802,plain,
% 2.50/1.88 (^[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))))),
% 2.50/1.88 inference(bind,[status(th)],[])).
% 2.50/1.88 tff(1803,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(quant_intro,[status(thm)],[1802])).
% 2.50/1.88 tff(1804,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1805,plain,
% 2.50/1.88 (^[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)))))),
% 2.50/1.88 inference(bind,[status(th)],[])).
% 2.50/1.88 tff(1806,plain,
% 2.50/1.88 (![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)))),
% 2.50/1.88 inference(quant_intro,[status(thm)],[1805])).
% 2.50/1.88 tff(1807,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 2.50/1.88 tff(1808,plain,
% 2.50/1.88 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 2.50/1.88 tff(1809,plain,
% 2.50/1.88 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1808, 1804])).
% 2.50/1.88 tff(1810,plain,(
% 2.50/1.88 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.50/1.88 inference(skolemize,[status(sab)],[1809])).
% 2.50/1.88 tff(1811,plain,
% 2.50/1.88 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.50/1.88 inference(modus_ponens,[status(thm)],[1810, 1803])).
% 2.50/1.88 tff(1812,plain,
% 2.50/1.88 (((~![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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1813,plain,
% 2.50/1.88 ((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)))),
% 2.50/1.88 inference(rewrite,[status(thm)],[])).
% 2.50/1.88 tff(1814,plain,
% 2.50/1.88 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1813])).
% 2.50/1.89 tff(1815,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1814, 1812])).
% 2.50/1.89 tff(1816,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1817,plain,
% 2.50/1.89 ((~![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))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 2.50/1.89 tff(1818,plain,
% 2.50/1.89 (hskp11 | hskp0 | (~c0_1(a1438)) | (~c2_1(a1438))),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1817, 91, 24, 1811])).
% 2.50/1.89 tff(1819,plain,
% 2.50/1.89 (hskp0),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1818, 1779, 1715, 1780])).
% 2.50/1.89 tff(1820,plain,
% 2.50/1.89 (~c3_1(a1427)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1213, 1819])).
% 2.50/1.89 tff(1821,plain,
% 2.50/1.89 (c2_1(a1427)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1224, 1819])).
% 2.50/1.89 tff(1822,plain,
% 2.50/1.89 (c0_1(a1427)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1235, 1819])).
% 2.50/1.89 tff(1823,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1824,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1825,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1824])).
% 2.50/1.89 tff(1826,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1825, 1823])).
% 2.50/1.89 tff(1827,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1828,plain,
% 2.50/1.89 ((~![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))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 2.50/1.89 tff(1829,plain,
% 2.50/1.89 (hskp23),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1828, 91, 1784, 1783, 1822, 1821, 1782, 1820, 1801])).
% 2.50/1.89 tff(1830,plain,
% 2.50/1.89 (~c1_1(a1477)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1628, 1829])).
% 2.50/1.89 tff(1831,plain,
% 2.50/1.89 (~c0_1(a1477)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1679, 1829])).
% 2.50/1.89 tff(1832,plain,
% 2.50/1.89 (c2_1(a1477)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1622, 1829])).
% 2.50/1.89 tff(1833,plain,
% 2.50/1.89 (((~![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)))) | (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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1834,plain,
% 2.50/1.89 (((~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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1835,plain,
% 2.50/1.89 (((~![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(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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1834])).
% 2.50/1.89 tff(1836,plain,
% 2.50/1.89 (((~![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(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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1835, 1833])).
% 2.50/1.89 tff(1837,plain,
% 2.50/1.89 ((~![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(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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1838,plain,
% 2.50/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1477) | c1_1(a1477) | c1_1(a1465) | (~ndr1_0) | (~c2_1(a1465)) | (~c0_1(a1465)) | (~c3_1(a1465)) | (~c2_1(a1477))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 2.50/1.89 tff(1839,plain,
% 2.50/1.89 ($false),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1838, 91, 1832, 1784, 1783, 1831, 1830, 1782, 1298, 1791])).
% 2.50/1.89 tff(1840,plain,(c1_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.89 tff(1841,plain,
% 2.50/1.89 (c1_1(a1438)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1840, 35, 12])).
% 2.50/1.89 tff(1842,plain,
% 2.50/1.89 (~hskp7),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1514, 1841])).
% 2.50/1.89 tff(1843,plain,
% 2.50/1.89 (~hskp5),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1722, 1842, 35, 12])).
% 2.50/1.89 tff(1844,plain,
% 2.50/1.89 (hskp25),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[487, 36, 48])).
% 2.50/1.89 tff(1845,plain,
% 2.50/1.89 (~c0_1(a1504)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[493, 1844])).
% 2.50/1.89 tff(1846,plain,
% 2.50/1.89 (c2_1(a1504)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[534, 1844])).
% 2.50/1.89 tff(1847,plain,
% 2.50/1.89 (c1_1(a1504)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[506, 1844])).
% 2.50/1.89 tff(1848,plain,
% 2.50/1.89 (((~![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 | 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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1849,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1850,plain,
% 2.50/1.89 (((~![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(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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1849])).
% 2.50/1.89 tff(1851,plain,
% 2.50/1.89 (((~![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(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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1850, 1848])).
% 2.50/1.89 tff(1852,plain,
% 2.50/1.89 ((~![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(a1504) | (~c2_1(a1504)) | (~c1_1(a1504)) | c3_1(a1430) | c0_1(a1430) | (~c2_1(a1430)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1853,plain,
% 2.50/1.89 ((~![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 | c3_1(a1430) | c0_1(a1504) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 2.50/1.89 tff(1854,plain,
% 2.50/1.89 (hskp14),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1853, 91, 1847, 1846, 35, 1845, 12, 574, 524])).
% 2.50/1.89 tff(1855,plain,
% 2.50/1.89 (~c1_1(a1451)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[553, 1854])).
% 2.50/1.89 tff(1856,plain,
% 2.50/1.89 (~c3_1(a1451)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[547, 1854])).
% 2.50/1.89 tff(1857,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1858,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1859,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1858])).
% 2.50/1.89 tff(1860,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1859, 1857])).
% 2.50/1.89 tff(1861,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1862,plain,
% 2.50/1.89 ((~![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))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 2.50/1.89 tff(1863,plain,
% 2.50/1.89 (~c0_1(a1451)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1862, 91, 1842, 1847, 1846, 1845, 1855, 1856, 193])).
% 2.50/1.89 tff(1864,assumption,(~c0_1(a1451)), introduced(assumption)).
% 2.50/1.89 tff(1865,assumption,(~c3_1(a1451)), introduced(assumption)).
% 2.50/1.89 tff(1866,assumption,(~c1_1(a1451)), introduced(assumption)).
% 2.50/1.89 tff(1867,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1868,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1869,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1868])).
% 2.50/1.89 tff(1870,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1869, 1867])).
% 2.50/1.89 tff(1871,plain,
% 2.50/1.89 ((~![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))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1872,plain,
% 2.50/1.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c1_1(a1451) | c3_1(a1451) | (~ndr1_0) | c0_1(a1451) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 2.50/1.89 tff(1873,plain,
% 2.50/1.89 ($false),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1872, 91, 874, 914, 903, 892, 1866, 1865, 873, 1864])).
% 2.50/1.89 tff(1874,plain,(hskp3 | c1_1(a1451) | c3_1(a1451) | c0_1(a1451) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.50/1.89 tff(1875,plain,
% 2.50/1.89 (hskp3),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1874, 1863, 36, 1856, 1855])).
% 2.50/1.89 tff(1876,plain,
% 2.50/1.89 (~c2_1(a1431)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[928, 1875])).
% 2.50/1.89 tff(1877,plain,
% 2.50/1.89 (~c0_1(a1431)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[934, 1875])).
% 2.50/1.89 tff(1878,plain,
% 2.50/1.89 (~hskp11),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[795, 1843, 48])).
% 2.50/1.89 tff(1879,plain,
% 2.50/1.89 (~c3_1(a1431)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[942, 91, 1878, 1843, 1877, 1876, 34])).
% 2.50/1.89 tff(1880,plain,
% 2.50/1.89 (^[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))))),
% 2.50/1.89 inference(bind,[status(th)],[])).
% 2.50/1.89 tff(1881,plain,
% 2.50/1.89 (![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)))),
% 2.50/1.89 inference(quant_intro,[status(thm)],[1880])).
% 2.50/1.89 tff(1882,plain,
% 2.50/1.89 (![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1883,plain,
% 2.50/1.89 (^[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)))))),
% 2.50/1.89 inference(bind,[status(th)],[])).
% 2.50/1.89 tff(1884,plain,
% 2.50/1.89 (![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)))),
% 2.50/1.89 inference(quant_intro,[status(thm)],[1883])).
% 2.50/1.89 tff(1885,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 2.50/1.89 tff(1886,plain,
% 2.50/1.89 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 2.50/1.89 tff(1887,plain,
% 2.50/1.89 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1886, 1882])).
% 2.50/1.89 tff(1888,plain,(
% 2.50/1.89 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 2.50/1.89 inference(skolemize,[status(sab)],[1887])).
% 2.50/1.89 tff(1889,plain,
% 2.50/1.89 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1888, 1881])).
% 2.50/1.89 tff(1890,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1891,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1892,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1891])).
% 2.50/1.89 tff(1893,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1892, 1890])).
% 2.50/1.89 tff(1894,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1895,plain,
% 2.50/1.89 ((~![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))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 2.50/1.89 tff(1896,plain,
% 2.50/1.89 (hskp16),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1895, 91, 1842, 1847, 1846, 1845, 1889])).
% 2.50/1.89 tff(1897,plain,
% 2.50/1.89 (((~hskp16) | (~c3_1(a1454))) <=> ((~hskp16) | (~c3_1(a1454)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1898,plain,
% 2.50/1.89 (((~c3_1(a1454)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1454)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1899,axiom,((~c3_1(a1454)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 2.50/1.89 tff(1900,plain,
% 2.50/1.89 ((~hskp16) | (~c3_1(a1454))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 2.50/1.89 tff(1901,plain,
% 2.50/1.89 ((~hskp16) | (~c3_1(a1454))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1900, 1897])).
% 2.50/1.89 tff(1902,plain,
% 2.50/1.89 (~c3_1(a1454)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1901, 1896])).
% 2.50/1.89 tff(1903,plain,
% 2.50/1.89 (((~hskp16) | (~c0_1(a1454))) <=> ((~hskp16) | (~c0_1(a1454)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1904,plain,
% 2.50/1.89 (((~c0_1(a1454)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1454)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1905,axiom,((~c0_1(a1454)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 2.50/1.89 tff(1906,plain,
% 2.50/1.89 ((~hskp16) | (~c0_1(a1454))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 2.50/1.89 tff(1907,plain,
% 2.50/1.89 ((~hskp16) | (~c0_1(a1454))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1906, 1903])).
% 2.50/1.89 tff(1908,plain,
% 2.50/1.89 (~c0_1(a1454)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1907, 1896])).
% 2.50/1.89 tff(1909,plain,
% 2.50/1.89 (c1_1(a1431)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[953, 1875])).
% 2.50/1.89 tff(1910,plain,
% 2.50/1.89 (((~hskp16) | c1_1(a1454)) <=> ((~hskp16) | c1_1(a1454))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1911,axiom,((~hskp16) | c1_1(a1454)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 2.50/1.89 tff(1912,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 2.50/1.89 tff(1913,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1912, 1910])).
% 2.50/1.89 tff(1914,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1913, 1910])).
% 2.50/1.89 tff(1915,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1914, 1910])).
% 2.50/1.89 tff(1916,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1915, 1910])).
% 2.50/1.89 tff(1917,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1916, 1910])).
% 2.50/1.89 tff(1918,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1917, 1910])).
% 2.50/1.89 tff(1919,plain,
% 2.50/1.89 ((~hskp16) | c1_1(a1454)),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1918, 1910])).
% 2.50/1.89 tff(1920,plain,
% 2.50/1.89 (c1_1(a1454)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1919, 1896])).
% 2.50/1.89 tff(1921,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1922,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1923,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1922])).
% 2.50/1.89 tff(1924,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1923, 1921])).
% 2.50/1.89 tff(1925,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.89 inference(quant_inst,[status(thm)],[])).
% 2.50/1.89 tff(1926,plain,
% 2.50/1.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c1_1(a1454))),
% 2.50/1.89 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 2.50/1.89 tff(1927,plain,
% 2.50/1.89 (hskp12),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1926, 91, 1920, 1909, 1908, 1902, 1876, 214, 1879])).
% 2.50/1.89 tff(1928,plain,
% 2.50/1.89 (~c2_1(a1448)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[220, 1927])).
% 2.50/1.89 tff(1929,plain,
% 2.50/1.89 ($false),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[263, 1928, 1927, 1843, 36])).
% 2.50/1.89 tff(1930,plain,(hskp17 | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.89 tff(1931,plain,
% 2.50/1.89 (hskp17),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[1930, 35, 12])).
% 2.50/1.89 tff(1932,plain,
% 2.50/1.89 (~c2_1(a1457)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[288, 1931])).
% 2.50/1.89 tff(1933,plain,
% 2.50/1.89 (~c0_1(a1457)),
% 2.50/1.89 inference(unit_resolution,[status(thm)],[275, 1931])).
% 2.50/1.89 tff(1934,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1935,plain,
% 2.50/1.89 ((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)))),
% 2.50/1.89 inference(rewrite,[status(thm)],[])).
% 2.50/1.89 tff(1936,plain,
% 2.50/1.89 (((~![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))))),
% 2.50/1.89 inference(monotonicity,[status(thm)],[1935])).
% 2.50/1.89 tff(1937,plain,
% 2.50/1.89 (((~![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)))),
% 2.50/1.89 inference(transitivity,[status(thm)],[1936, 1934])).
% 2.50/1.89 tff(1938,plain,
% 2.50/1.89 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1939,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 2.50/1.90 tff(1940,plain,
% 2.50/1.90 (~c3_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1939, 91, 1878, 1843, 1933, 1932, 34])).
% 2.50/1.90 tff(1941,assumption,(~hskp24), introduced(assumption)).
% 2.50/1.90 tff(1942,plain,
% 2.50/1.90 (hskp30),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[89, 1941])).
% 2.50/1.90 tff(1943,plain,
% 2.50/1.90 (c2_1(a1507)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1528, 1942])).
% 2.50/1.90 tff(1944,plain,
% 2.50/1.90 (c1_1(a1507)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1604, 1942])).
% 2.50/1.90 tff(1945,plain,
% 2.50/1.90 (c0_1(a1507)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1539, 1942])).
% 2.50/1.90 tff(1946,assumption,(c1_1(a1438)), introduced(assumption)).
% 2.50/1.90 tff(1947,plain,
% 2.50/1.90 (((~![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 | 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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1948,plain,
% 2.50/1.90 ((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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1949,plain,
% 2.50/1.90 (((~![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(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)))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[1948])).
% 2.50/1.90 tff(1950,plain,
% 2.50/1.90 (((~![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(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))),
% 2.50/1.90 inference(transitivity,[status(thm)],[1949, 1947])).
% 2.50/1.90 tff(1951,plain,
% 2.50/1.90 ((~![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(a1438) | c3_1(a1438) | (~c1_1(a1438)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1952,plain,
% 2.50/1.90 ((~![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 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | c2_1(a1438)),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 2.50/1.90 tff(1953,plain,
% 2.50/1.90 (hskp12),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1952, 91, 49, 37, 1946, 214, 50])).
% 2.50/1.90 tff(1954,plain,
% 2.50/1.90 (~c2_1(a1448)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[220, 1953])).
% 2.50/1.90 tff(1955,plain,
% 2.50/1.90 (hskp17),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[263, 1954, 11, 1953])).
% 2.50/1.90 tff(1956,plain,
% 2.50/1.90 (~c1_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[269, 1955])).
% 2.50/1.90 tff(1957,plain,
% 2.50/1.90 (~c0_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[275, 1955])).
% 2.50/1.90 tff(1958,plain,
% 2.50/1.90 (c3_1(a1448)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[242, 1953])).
% 2.50/1.90 tff(1959,plain,
% 2.50/1.90 (c0_1(a1448)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[231, 1953])).
% 2.50/1.90 tff(1960,plain,
% 2.50/1.90 (~c3_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[282, 91, 11, 1959, 1958, 1957, 1956, 1954, 10])).
% 2.50/1.90 tff(1961,plain,
% 2.50/1.90 (~c2_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[288, 1955])).
% 2.50/1.90 tff(1962,plain,
% 2.50/1.90 (((~![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 | 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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1963,plain,
% 2.50/1.90 ((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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1964,plain,
% 2.50/1.90 (((~![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(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)))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[1963])).
% 2.50/1.90 tff(1965,plain,
% 2.50/1.90 (((~![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(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))),
% 2.50/1.90 inference(transitivity,[status(thm)],[1964, 1962])).
% 2.50/1.90 tff(1966,plain,
% 2.50/1.90 ((~![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(a1438) | c2_1(a1438) | c0_1(a1438))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1967,plain,
% 2.50/1.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c3_1(a1438) | c1_1(a1457) | c2_1(a1457) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | c3_1(a1457)),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 2.50/1.90 tff(1968,plain,
% 2.50/1.90 ($false),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1967, 91, 61, 49, 1956, 1961, 37, 60, 50, 1960])).
% 2.50/1.90 tff(1969,plain,(c2_1(a1438) | hskp2 | c3_1(a1438) | c0_1(a1438) | hskp5 | (~c1_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.50/1.90 tff(1970,plain,
% 2.50/1.90 (c2_1(a1438)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1969, 37, 49, 61, 11, 1946])).
% 2.50/1.90 tff(1971,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1972,plain,
% 2.50/1.90 ((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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1973,plain,
% 2.50/1.90 (((~![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))))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[1972])).
% 2.50/1.90 tff(1974,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(transitivity,[status(thm)],[1973, 1971])).
% 2.50/1.90 tff(1975,plain,
% 2.50/1.90 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1976,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 2.50/1.90 tff(1977,plain,
% 2.50/1.90 (hskp14 | (~c2_1(a1438))),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1976, 91, 49, 37, 1946, 524])).
% 2.50/1.90 tff(1978,plain,
% 2.50/1.90 (hskp14),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1977, 1970])).
% 2.50/1.90 tff(1979,plain,
% 2.50/1.90 (~c3_1(a1451)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[547, 1978])).
% 2.50/1.90 tff(1980,plain,
% 2.50/1.90 (~c1_1(a1451)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[553, 1978])).
% 2.50/1.90 tff(1981,assumption,(c1_1(a1507)), introduced(assumption)).
% 2.50/1.90 tff(1982,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1983,plain,
% 2.50/1.90 ((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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1984,plain,
% 2.50/1.90 (((~![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))))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[1983])).
% 2.50/1.90 tff(1985,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(transitivity,[status(thm)],[1984, 1982])).
% 2.50/1.90 tff(1986,plain,
% 2.50/1.90 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1987,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 2.50/1.90 tff(1988,plain,
% 2.50/1.90 (hskp23 | (~c2_1(a1438))),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1987, 91, 1550, 1981, 1549, 49, 1946, 1594])).
% 2.50/1.90 tff(1989,plain,
% 2.50/1.90 (hskp23),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1988, 1970])).
% 2.50/1.90 tff(1990,plain,
% 2.50/1.90 (~c1_1(a1477)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1628, 1989])).
% 2.50/1.90 tff(1991,plain,
% 2.50/1.90 (~c0_1(a1477)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1679, 1989])).
% 2.50/1.90 tff(1992,plain,
% 2.50/1.90 (c2_1(a1451)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[564, 1978])).
% 2.50/1.90 tff(1993,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1994,plain,
% 2.50/1.90 ((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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(1995,plain,
% 2.50/1.90 (((~![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))))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[1994])).
% 2.50/1.90 tff(1996,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(transitivity,[status(thm)],[1995, 1993])).
% 2.50/1.90 tff(1997,plain,
% 2.50/1.90 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(1998,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 2.50/1.90 tff(1999,plain,
% 2.50/1.90 (~c3_1(a1477)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1998, 91, 11, 1992, 1991, 1990, 1980, 1979, 848])).
% 2.50/1.90 tff(2000,plain,
% 2.50/1.90 (~hskp7),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1514, 1946])).
% 2.50/1.90 tff(2001,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2002,plain,
% 2.50/1.90 ((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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2003,plain,
% 2.50/1.90 (((~![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))))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[2002])).
% 2.50/1.90 tff(2004,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(transitivity,[status(thm)],[2003, 2001])).
% 2.50/1.90 tff(2005,plain,
% 2.50/1.90 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(2006,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 2.50/1.90 tff(2007,plain,
% 2.50/1.90 (~c0_1(a1451)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2006, 91, 2000, 1980, 1979, 37, 1946, 193, 1970])).
% 2.50/1.90 tff(2008,plain,
% 2.50/1.90 (hskp3),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1874, 36, 1865, 1864, 1866])).
% 2.50/1.90 tff(2009,plain,
% 2.50/1.90 (~c2_1(a1431)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[928, 2008])).
% 2.50/1.90 tff(2010,plain,
% 2.50/1.90 (~c0_1(a1431)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[934, 2008])).
% 2.50/1.90 tff(2011,plain,
% 2.50/1.90 (~c3_1(a1431)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[942, 91, 1300, 11, 2010, 2009, 34])).
% 2.50/1.90 tff(2012,plain,
% 2.50/1.90 (c1_1(a1431)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[953, 2008])).
% 2.50/1.90 tff(2013,plain,
% 2.50/1.90 (((~![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 | 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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2014,plain,
% 2.50/1.90 ((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)))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2015,plain,
% 2.50/1.90 (((~![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(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))))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[2014])).
% 2.50/1.90 tff(2016,plain,
% 2.50/1.90 (((~![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(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)))),
% 2.50/1.90 inference(transitivity,[status(thm)],[2015, 2013])).
% 2.50/1.90 tff(2017,plain,
% 2.50/1.90 ((~![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(a1431) | c3_1(a1431) | (~c1_1(a1431)) | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(2018,plain,
% 2.50/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a1438) | c0_1(a1438) | (~c1_1(a1438)) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431))),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 2.50/1.90 tff(2019,plain,
% 2.50/1.90 (hskp12),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2018, 91, 49, 2012, 37, 1946, 2009, 214, 2011])).
% 2.50/1.90 tff(2020,plain,
% 2.50/1.90 (~c2_1(a1448)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[220, 2019])).
% 2.50/1.90 tff(2021,plain,
% 2.50/1.90 ($false),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[263, 2020, 2019, 11, 36])).
% 2.50/1.90 tff(2022,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,[]))).
% 2.50/1.90 tff(2023,plain,
% 2.50/1.90 (hskp17),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2022, 37, 49, 11, 1946, 984, 1979, 2007, 1980])).
% 2.50/1.90 tff(2024,plain,
% 2.50/1.90 (~c1_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[269, 2023])).
% 2.50/1.90 tff(2025,plain,
% 2.50/1.90 (~c0_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[275, 2023])).
% 2.50/1.90 tff(2026,plain,
% 2.50/1.90 (c2_1(a1477)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[1622, 1989])).
% 2.50/1.90 tff(2027,plain,
% 2.50/1.90 (((~![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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2028,plain,
% 2.50/1.90 ((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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2029,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[2028])).
% 2.50/1.90 tff(2030,plain,
% 2.50/1.90 (((~![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))),
% 2.50/1.90 inference(transitivity,[status(thm)],[2029, 2027])).
% 2.50/1.90 tff(2031,plain,
% 2.50/1.90 ((~![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)))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(2032,plain,
% 2.50/1.90 ((~![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)),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 2.50/1.90 tff(2033,plain,
% 2.50/1.90 (~c3_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2032, 91, 11, 2026, 1990, 2025, 2024, 848, 1999])).
% 2.50/1.90 tff(2034,plain,
% 2.50/1.90 (~c2_1(a1457)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[288, 2023])).
% 2.50/1.90 tff(2035,plain,
% 2.50/1.90 (hskp1),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[643, 91, 61, 2025, 2024, 2034, 636])).
% 2.50/1.90 tff(2036,plain,
% 2.50/1.90 (~c0_1(a1429)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[649, 2035])).
% 2.50/1.90 tff(2037,plain,
% 2.50/1.90 (c3_1(a1429)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[660, 2035])).
% 2.50/1.90 tff(2038,plain,
% 2.50/1.90 (((~![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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2039,plain,
% 2.50/1.90 (((~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))),
% 2.50/1.90 inference(rewrite,[status(thm)],[])).
% 2.50/1.90 tff(2040,plain,
% 2.50/1.90 (((~![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)))),
% 2.50/1.90 inference(monotonicity,[status(thm)],[2039])).
% 2.50/1.90 tff(2041,plain,
% 2.50/1.90 (((~![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))),
% 2.50/1.90 inference(transitivity,[status(thm)],[2040, 2038])).
% 2.50/1.90 tff(2042,plain,
% 2.50/1.90 ((~![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))),
% 2.50/1.90 inference(quant_inst,[status(thm)],[])).
% 2.50/1.90 tff(2043,plain,
% 2.50/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1477) | c1_1(a1457) | c2_1(a1457) | c0_1(a1429) | (~ndr1_0) | (~c3_1(a1429)) | c1_1(a1429) | c3_1(a1457) | (~c2_1(a1477)) | c3_1(a1477)),
% 2.50/1.90 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 2.50/1.90 tff(2044,plain,
% 2.50/1.90 (c1_1(a1429)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2043, 91, 2026, 2037, 1990, 2024, 2034, 2036, 626, 1999, 2033])).
% 2.50/1.90 tff(2045,plain,
% 2.50/1.90 (c2_1(a1429)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[688, 2035])).
% 2.50/1.90 tff(2046,plain,
% 2.50/1.90 ($false),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[695, 91, 2000, 2045, 2037, 2024, 2034, 678, 2033, 2044])).
% 2.50/1.90 tff(2047,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,[]))).
% 2.50/1.90 tff(2048,plain,
% 2.50/1.90 (c0_1(a1438)),
% 2.50/1.90 inference(unit_resolution,[status(thm)],[2047, 49, 11, 61, 1946, 1945, 1944, 1943])).
% 2.50/1.90 tff(2049,plain,
% 2.50/1.90 (^[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))))),
% 2.50/1.90 inference(bind,[status(th)],[])).
% 2.50/1.90 tff(2050,plain,
% 2.50/1.90 (![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)))),
% 2.50/1.91 inference(quant_intro,[status(thm)],[2049])).
% 2.50/1.91 tff(2051,plain,
% 2.50/1.91 (![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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2052,plain,
% 2.50/1.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | 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)))))),
% 2.50/1.91 inference(bind,[status(th)],[])).
% 2.50/1.91 tff(2053,plain,
% 2.50/1.91 (![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)))),
% 2.50/1.91 inference(quant_intro,[status(thm)],[2052])).
% 2.50/1.91 tff(2054,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 2.50/1.91 tff(2055,plain,
% 2.50/1.91 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 2.50/1.91 tff(2056,plain,
% 2.50/1.91 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2055, 2051])).
% 2.50/1.91 tff(2057,plain,(
% 2.50/1.91 ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.50/1.91 inference(skolemize,[status(sab)],[2056])).
% 2.50/1.91 tff(2058,plain,
% 2.50/1.91 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2057, 2050])).
% 2.50/1.91 tff(2059,plain,
% 2.50/1.91 (((~![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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2060,plain,
% 2.50/1.91 ((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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2061,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2060])).
% 2.50/1.91 tff(2062,plain,
% 2.50/1.91 (((~![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))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2061, 2059])).
% 2.50/1.91 tff(2063,plain,
% 2.50/1.91 ((~![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)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2064,plain,
% 2.50/1.91 ((~![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)),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 2.50/1.91 tff(2065,plain,
% 2.50/1.91 (hskp4 | (~c0_1(a1438)) | c2_1(a1438)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2064, 1941, 91, 49, 2058])).
% 2.50/1.91 tff(2066,plain,
% 2.50/1.91 (hskp4),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2065, 50, 1724])).
% 2.50/1.91 tff(2067,plain,
% 2.50/1.91 (~c2_1(a1434)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[137, 2066])).
% 2.50/1.91 tff(2068,plain,
% 2.50/1.91 (c3_1(a1434)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[161, 2066])).
% 2.50/1.91 tff(2069,plain,
% 2.50/1.91 (c1_1(a1434)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[150, 2066])).
% 2.50/1.91 tff(2070,plain,
% 2.50/1.91 (((~![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 | 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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2071,plain,
% 2.50/1.91 ((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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2072,plain,
% 2.50/1.91 (((~![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(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)))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2071])).
% 2.50/1.91 tff(2073,plain,
% 2.50/1.91 (((~![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(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))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2072, 2070])).
% 2.50/1.91 tff(2074,plain,
% 2.50/1.91 ((~![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(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c3_1(a1438) | c2_1(a1438) | (~c1_1(a1438)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2075,plain,
% 2.50/1.91 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp7 | c3_1(a1438) | (~c1_1(a1438)) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | c2_1(a1438)),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 2.50/1.91 tff(2076,plain,
% 2.50/1.91 ($false),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2075, 91, 2000, 49, 2069, 2068, 1946, 2067, 172, 50])).
% 2.50/1.91 tff(2077,plain,(c2_1(a1438) | c3_1(a1438) | (~c1_1(a1438)) | (~c0_1(a1438)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.50/1.91 tff(2078,plain,
% 2.50/1.91 (c2_1(a1438)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2077, 49, 1946, 2048, 1941])).
% 2.50/1.91 tff(2079,plain,
% 2.50/1.91 (hskp12 | (~c0_1(a1438)) | (~c2_1(a1438))),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1751, 91, 984, 49, 1288])).
% 2.50/1.91 tff(2080,plain,
% 2.50/1.91 (hskp12),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2079, 2078, 2048])).
% 2.50/1.91 tff(2081,plain,
% 2.50/1.91 (~c2_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[220, 2080])).
% 2.50/1.91 tff(2082,plain,
% 2.50/1.91 (hskp23 | (~c2_1(a1438))),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1987, 91, 1945, 1944, 1943, 49, 1946, 1594])).
% 2.50/1.91 tff(2083,plain,
% 2.50/1.91 (hskp23),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2082, 2078])).
% 2.50/1.91 tff(2084,plain,
% 2.50/1.91 (~c1_1(a1477)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1628, 2083])).
% 2.50/1.91 tff(2085,plain,
% 2.50/1.91 (~c0_1(a1477)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1679, 2083])).
% 2.50/1.91 tff(2086,plain,
% 2.50/1.91 (c3_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[242, 2080])).
% 2.50/1.91 tff(2087,plain,
% 2.50/1.91 (c0_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[231, 2080])).
% 2.50/1.91 tff(2088,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2089,plain,
% 2.50/1.91 ((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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2090,plain,
% 2.50/1.91 (((~![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))))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2089])).
% 2.50/1.91 tff(2091,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2090, 2088])).
% 2.50/1.91 tff(2092,plain,
% 2.50/1.91 ((~![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)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2093,plain,
% 2.50/1.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1477))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 2.50/1.91 tff(2094,plain,
% 2.50/1.91 (~c3_1(a1477)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2093, 91, 11, 2087, 2086, 2085, 2084, 2081, 10])).
% 2.50/1.91 tff(2095,plain,
% 2.50/1.91 (hskp17),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[263, 2081, 11, 2080])).
% 2.50/1.91 tff(2096,plain,
% 2.50/1.91 (~c1_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[269, 2095])).
% 2.50/1.91 tff(2097,plain,
% 2.50/1.91 (~c0_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[275, 2095])).
% 2.50/1.91 tff(2098,plain,
% 2.50/1.91 (~c3_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[282, 91, 11, 2087, 2086, 2097, 2096, 2081, 10])).
% 2.50/1.91 tff(2099,plain,
% 2.50/1.91 (~c2_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[288, 2095])).
% 2.50/1.91 tff(2100,plain,
% 2.50/1.91 (hskp1),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[643, 91, 61, 2097, 2096, 2099, 636])).
% 2.50/1.91 tff(2101,plain,
% 2.50/1.91 (~c0_1(a1429)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[649, 2100])).
% 2.50/1.91 tff(2102,plain,
% 2.50/1.91 (c3_1(a1429)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[660, 2100])).
% 2.50/1.91 tff(2103,plain,
% 2.50/1.91 (c2_1(a1477)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1622, 2083])).
% 2.50/1.91 tff(2104,plain,
% 2.50/1.91 (c1_1(a1429)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2043, 91, 2103, 2102, 2084, 2096, 2099, 2101, 626, 2098, 2094])).
% 2.50/1.91 tff(2105,plain,
% 2.50/1.91 (c2_1(a1429)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[688, 2100])).
% 2.50/1.91 tff(2106,plain,
% 2.50/1.91 ($false),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[695, 91, 2000, 2105, 2102, 2096, 2099, 678, 2098, 2104])).
% 2.50/1.91 tff(2107,plain,(c3_1(a1438) | hskp2 | hskp5 | (~c1_1(a1438)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.50/1.91 tff(2108,plain,
% 2.50/1.91 (c3_1(a1438)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2107, 48, 1843, 1841, 1517])).
% 2.50/1.91 tff(2109,plain,
% 2.50/1.91 (c0_1(a1438) | c2_1(a1438)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1546, 91, 1878, 1843, 2108, 34])).
% 2.50/1.91 tff(2110,plain,
% 2.50/1.91 (c2_1(a1438)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2109, 37])).
% 2.50/1.91 tff(2111,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2112,plain,
% 2.50/1.91 ((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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2113,plain,
% 2.50/1.91 (((~![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))))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2112])).
% 2.50/1.91 tff(2114,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2113, 2111])).
% 2.50/1.91 tff(2115,plain,
% 2.50/1.91 ((~![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)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2116,plain,
% 2.50/1.91 ((~![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))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 2.50/1.91 tff(2117,plain,
% 2.50/1.91 (hskp14),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2116, 91, 35, 37, 1841, 12, 574, 524, 2110])).
% 2.50/1.91 tff(2118,plain,
% 2.50/1.91 (~c3_1(a1451)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[547, 2117])).
% 2.50/1.91 tff(2119,plain,
% 2.50/1.91 (~c1_1(a1451)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[553, 2117])).
% 2.50/1.91 tff(2120,plain,
% 2.50/1.91 (~c0_1(a1451)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2006, 91, 1842, 2119, 2118, 37, 1841, 193, 2110])).
% 2.50/1.91 tff(2121,plain,
% 2.50/1.91 (((~![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 | 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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2122,plain,
% 2.50/1.91 ((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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2123,plain,
% 2.50/1.91 (((~![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(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)))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2122])).
% 2.50/1.91 tff(2124,plain,
% 2.50/1.91 (((~![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(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))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2123, 2121])).
% 2.50/1.91 tff(2125,plain,
% 2.50/1.91 ((~![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(a1438) | (~c3_1(a1438)) | (~c1_1(a1438)) | c3_1(a1451) | c0_1(a1451) | c1_1(a1451))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2126,plain,
% 2.50/1.91 ((~![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 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | c0_1(a1451)),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 2.50/1.91 tff(2127,plain,
% 2.50/1.91 (hskp3),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2126, 91, 2108, 2119, 2118, 37, 1841, 873, 2120])).
% 2.50/1.91 tff(2128,plain,
% 2.50/1.91 (~c2_1(a1431)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[928, 2127])).
% 2.50/1.91 tff(2129,plain,
% 2.50/1.91 (~c0_1(a1431)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[934, 2127])).
% 2.50/1.91 tff(2130,plain,
% 2.50/1.91 (~c3_1(a1431)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[942, 91, 1878, 1843, 2129, 2128, 34])).
% 2.50/1.91 tff(2131,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2132,plain,
% 2.50/1.91 ((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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2133,plain,
% 2.50/1.91 (((~![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))))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2132])).
% 2.50/1.91 tff(2134,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2133, 2131])).
% 2.50/1.91 tff(2135,plain,
% 2.50/1.91 ((~![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)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2136,plain,
% 2.50/1.91 ((~![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))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 2.50/1.91 tff(2137,plain,
% 2.50/1.91 (hskp16 | c0_1(a1438) | (~c2_1(a1438))),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2136, 91, 1842, 1841, 1889])).
% 2.50/1.91 tff(2138,plain,
% 2.50/1.91 (hskp16),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2137, 2110, 37])).
% 2.50/1.91 tff(2139,plain,
% 2.50/1.91 (~c3_1(a1454)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1901, 2138])).
% 2.50/1.91 tff(2140,plain,
% 2.50/1.91 (~c0_1(a1454)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1907, 2138])).
% 2.50/1.91 tff(2141,plain,
% 2.50/1.91 (c1_1(a1431)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[953, 2127])).
% 2.50/1.91 tff(2142,plain,
% 2.50/1.91 (c1_1(a1454)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1919, 2138])).
% 2.50/1.91 tff(2143,plain,
% 2.50/1.91 (hskp12),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[1926, 91, 2142, 2141, 2140, 2139, 2128, 214, 2130])).
% 2.50/1.91 tff(2144,plain,
% 2.50/1.91 (~c2_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[220, 2143])).
% 2.50/1.91 tff(2145,plain,
% 2.50/1.91 (hskp17),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[263, 2144, 1843, 2143])).
% 2.50/1.91 tff(2146,plain,
% 2.50/1.91 (~c2_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[288, 2145])).
% 2.50/1.91 tff(2147,plain,
% 2.50/1.91 (~c1_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[269, 2145])).
% 2.50/1.91 tff(2148,plain,
% 2.50/1.91 (((~![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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2149,plain,
% 2.50/1.91 ((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))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2150,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2149])).
% 2.50/1.91 tff(2151,plain,
% 2.50/1.91 (((~![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))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2150, 2148])).
% 2.50/1.91 tff(2152,plain,
% 2.50/1.91 ((~![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))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2153,plain,
% 2.50/1.91 ((~![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)),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 2.50/1.91 tff(2154,plain,
% 2.50/1.91 (c3_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2153, 91, 48, 2147, 2146, 2129, 2128, 60, 2130])).
% 2.50/1.91 tff(2155,plain,
% 2.50/1.91 (c3_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[242, 2143])).
% 2.50/1.91 tff(2156,plain,
% 2.50/1.91 (((~![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 | 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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2157,plain,
% 2.50/1.91 ((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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2158,plain,
% 2.50/1.91 (((~![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(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))))),
% 2.50/1.91 inference(monotonicity,[status(thm)],[2157])).
% 2.50/1.91 tff(2159,plain,
% 2.50/1.91 (((~![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(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)))),
% 2.50/1.91 inference(transitivity,[status(thm)],[2158, 2156])).
% 2.50/1.91 tff(2160,plain,
% 2.50/1.91 ((~![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(a1448) | (~c3_1(a1448)) | (~c1_1(a1448)) | c3_1(a1431) | c2_1(a1431) | (~c1_1(a1431)))),
% 2.50/1.91 inference(quant_inst,[status(thm)],[])).
% 2.50/1.91 tff(2161,plain,
% 2.50/1.91 ((~![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 | c2_1(a1448) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431) | (~c1_1(a1431)) | (~c3_1(a1448)) | (~c1_1(a1448))),
% 2.50/1.91 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 2.50/1.91 tff(2162,plain,
% 2.50/1.91 (~c1_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[2161, 91, 1842, 2155, 2141, 2144, 2128, 172, 2130])).
% 2.50/1.91 tff(2163,plain,
% 2.50/1.91 (~c0_1(a1457)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[275, 2145])).
% 2.50/1.91 tff(2164,plain,
% 2.50/1.91 (c0_1(a1448)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[231, 2143])).
% 2.50/1.91 tff(2165,plain,
% 2.50/1.91 (c2_1(a1451)),
% 2.50/1.91 inference(unit_resolution,[status(thm)],[564, 2117])).
% 2.50/1.91 tff(2166,plain,
% 2.50/1.91 (((~![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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2167,plain,
% 2.50/1.91 (((~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)))),
% 2.50/1.91 inference(rewrite,[status(thm)],[])).
% 2.50/1.91 tff(2168,plain,
% 2.50/1.91 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2167])).
% 2.50/1.92 tff(2169,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2168, 2166])).
% 2.50/1.92 tff(2170,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2171,plain,
% 2.50/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1448) | (~ndr1_0) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1451)) | (~c3_1(a1457))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 2.50/1.92 tff(2172,plain,
% 2.50/1.92 ($false),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2171, 91, 2165, 2164, 2163, 2146, 2119, 2118, 2144, 591, 2162, 2154])).
% 2.50/1.92 tff(2173,plain,(c0_1(a1438) | c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.92 tff(2174,plain,
% 2.50/1.92 (c0_1(a1438)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2173, 35, 12])).
% 2.50/1.92 tff(2175,plain,
% 2.50/1.92 (c2_1(a1438)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1778, 2174, 48, 1843, 2108])).
% 2.50/1.92 tff(2176,plain,
% 2.50/1.92 (~c1_1(a1457)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[269, 1931])).
% 2.50/1.92 tff(2177,plain,
% 2.50/1.92 (((~![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))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2178,plain,
% 2.50/1.92 ((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))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2179,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2178])).
% 2.50/1.92 tff(2180,plain,
% 2.50/1.92 (((~![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))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2179, 2177])).
% 2.50/1.92 tff(2181,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2182,plain,
% 2.50/1.92 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1457) | c2_1(a1457) | (~c1_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1457)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 2.50/1.92 tff(2183,plain,
% 2.50/1.92 ($false),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2182, 91, 1842, 2108, 2176, 1932, 1841, 678, 2175, 1940])).
% 2.50/1.92 tff(2184,plain,(c3_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.92 tff(2185,plain,
% 2.50/1.92 (c3_1(a1430)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2184, 12])).
% 2.50/1.92 tff(2186,plain,
% 2.50/1.92 (~c1_1(a1447)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[775, 91, 701, 759, 761, 760, 214])).
% 2.50/1.92 tff(2187,plain,
% 2.50/1.92 (^[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))))),
% 2.50/1.92 inference(bind,[status(th)],[])).
% 2.50/1.92 tff(2188,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(quant_intro,[status(thm)],[2187])).
% 2.50/1.92 tff(2189,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2190,plain,
% 2.50/1.92 (^[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)))))),
% 2.50/1.92 inference(bind,[status(th)],[])).
% 2.50/1.92 tff(2191,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(quant_intro,[status(thm)],[2190])).
% 2.50/1.92 tff(2192,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 2.50/1.92 tff(2193,plain,
% 2.50/1.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 2.50/1.92 tff(2194,plain,
% 2.50/1.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2193, 2189])).
% 2.50/1.92 tff(2195,plain,(
% 2.50/1.92 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.50/1.92 inference(skolemize,[status(sab)],[2194])).
% 2.50/1.92 tff(2196,plain,
% 2.50/1.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2195, 2188])).
% 2.50/1.92 tff(2197,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2198,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2199,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2198])).
% 2.50/1.92 tff(2200,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2199, 2197])).
% 2.50/1.92 tff(2201,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2202,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 2.50/1.92 tff(2203,plain,
% 2.50/1.92 (hskp7 | hskp6 | c1_1(a1430) | (~c3_1(a1430))),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2202, 91, 12, 2196])).
% 2.50/1.92 tff(2204,plain,
% 2.50/1.92 (hskp6),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2203, 592, 2185, 13])).
% 2.50/1.92 tff(2205,plain,
% 2.50/1.92 (((~hskp6) | (~c2_1(a1437))) <=> ((~hskp6) | (~c2_1(a1437)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2206,plain,
% 2.50/1.92 (((~c2_1(a1437)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1437)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2207,axiom,((~c2_1(a1437)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 2.50/1.92 tff(2208,plain,
% 2.50/1.92 ((~hskp6) | (~c2_1(a1437))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 2.50/1.92 tff(2209,plain,
% 2.50/1.92 ((~hskp6) | (~c2_1(a1437))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2208, 2205])).
% 2.50/1.92 tff(2210,plain,
% 2.50/1.92 (~c2_1(a1437)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2209, 2204])).
% 2.50/1.92 tff(2211,plain,
% 2.50/1.92 (((~hskp6) | c0_1(a1437)) <=> ((~hskp6) | c0_1(a1437))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2212,axiom,((~hskp6) | c0_1(a1437)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 2.50/1.92 tff(2213,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 2.50/1.92 tff(2214,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2213, 2211])).
% 2.50/1.92 tff(2215,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2214, 2211])).
% 2.50/1.92 tff(2216,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2215, 2211])).
% 2.50/1.92 tff(2217,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2216, 2211])).
% 2.50/1.92 tff(2218,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2217, 2211])).
% 2.50/1.92 tff(2219,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2218, 2211])).
% 2.50/1.92 tff(2220,plain,
% 2.50/1.92 ((~hskp6) | c0_1(a1437)),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2219, 2211])).
% 2.50/1.92 tff(2221,plain,
% 2.50/1.92 (c0_1(a1437)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2220, 2204])).
% 2.50/1.92 tff(2222,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2223,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2224,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2223])).
% 2.50/1.92 tff(2225,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2224, 2222])).
% 2.50/1.92 tff(2226,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2227,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 2.50/1.92 tff(2228,plain,
% 2.50/1.92 (~c3_1(a1437)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2227, 91, 11, 2221, 2185, 2210, 12, 10, 592])).
% 2.50/1.92 tff(2229,plain,
% 2.50/1.92 (((~hskp6) | (~c1_1(a1437))) <=> ((~hskp6) | (~c1_1(a1437)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2230,plain,
% 2.50/1.92 (((~c1_1(a1437)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a1437)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2231,axiom,((~c1_1(a1437)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 2.50/1.92 tff(2232,plain,
% 2.50/1.92 ((~hskp6) | (~c1_1(a1437))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 2.50/1.92 tff(2233,plain,
% 2.50/1.92 ((~hskp6) | (~c1_1(a1437))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2232, 2229])).
% 2.50/1.92 tff(2234,plain,
% 2.50/1.92 (~c1_1(a1437)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2233, 2204])).
% 2.50/1.92 tff(2235,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2236,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2237,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2236])).
% 2.50/1.92 tff(2238,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2237, 2235])).
% 2.50/1.92 tff(2239,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2240,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 2.50/1.92 tff(2241,plain,
% 2.50/1.92 (hskp29 | c3_1(a1437)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2240, 91, 11, 2221, 2210, 1044])).
% 2.50/1.92 tff(2242,plain,
% 2.50/1.92 (hskp29),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2241, 2228])).
% 2.50/1.92 tff(2243,plain,
% 2.50/1.92 (c3_1(a1483)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1062, 2242])).
% 2.50/1.92 tff(2244,plain,
% 2.50/1.92 (c2_1(a1483)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1073, 2242])).
% 2.50/1.92 tff(2245,plain,
% 2.50/1.92 (c1_1(a1483)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1084, 2242])).
% 2.50/1.92 tff(2246,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2247,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2248,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2247])).
% 2.50/1.92 tff(2249,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2248, 2246])).
% 2.50/1.92 tff(2250,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2251,plain,
% 2.50/1.92 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | c3_1(a1437) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 2.50/1.92 tff(2252,plain,
% 2.50/1.92 ($false),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2251, 91, 13, 2245, 2244, 2243, 2234, 2210, 678, 2228])).
% 2.50/1.92 tff(2253,plain,(c1_1(a1430) | hskp7 | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.92 tff(2254,plain,
% 2.50/1.92 (c1_1(a1430)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2253, 111, 11, 12])).
% 2.50/1.92 tff(2255,plain,
% 2.50/1.92 (c2_1(a1438)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[99, 61, 24, 49, 37])).
% 2.50/1.92 tff(2256,plain,
% 2.50/1.92 (~hskp17),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[862, 2255, 24, 49, 61, 11])).
% 2.50/1.92 tff(2257,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2258,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2259,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2258])).
% 2.50/1.92 tff(2260,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2259, 2257])).
% 2.50/1.92 tff(2261,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2262,plain,
% 2.50/1.92 ((~![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))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 2.50/1.92 tff(2263,plain,
% 2.50/1.92 (c3_1(a1438) | c1_1(a1430) | (~c2_1(a1438))),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2262, 91, 11, 2185, 24, 12, 848])).
% 2.50/1.92 tff(2264,plain,
% 2.50/1.92 (c1_1(a1430)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2263, 2255, 49])).
% 2.50/1.92 tff(2265,plain,
% 2.50/1.92 (^[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))))),
% 2.50/1.92 inference(bind,[status(th)],[])).
% 2.50/1.92 tff(2266,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(quant_intro,[status(thm)],[2265])).
% 2.50/1.92 tff(2267,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2268,plain,
% 2.50/1.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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)))))),
% 2.50/1.92 inference(bind,[status(th)],[])).
% 2.50/1.92 tff(2269,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(quant_intro,[status(thm)],[2268])).
% 2.50/1.92 tff(2270,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')).
% 2.50/1.92 tff(2271,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 2.50/1.92 tff(2272,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2271, 2267])).
% 2.50/1.92 tff(2273,plain,(
% 2.50/1.92 ![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)))),
% 2.50/1.92 inference(skolemize,[status(sab)],[2272])).
% 2.50/1.92 tff(2274,plain,
% 2.50/1.92 (![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)))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2273, 2266])).
% 2.50/1.92 tff(2275,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2276,plain,
% 2.50/1.92 ((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)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2277,plain,
% 2.50/1.92 (((~![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))))),
% 2.50/1.92 inference(monotonicity,[status(thm)],[2276])).
% 2.50/1.92 tff(2278,plain,
% 2.50/1.92 (((~![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)))),
% 2.50/1.92 inference(transitivity,[status(thm)],[2277, 2275])).
% 2.50/1.92 tff(2279,plain,
% 2.50/1.92 ((~![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)))),
% 2.50/1.92 inference(quant_inst,[status(thm)],[])).
% 2.50/1.92 tff(2280,plain,
% 2.50/1.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 2.50/1.92 tff(2281,plain,
% 2.50/1.92 (hskp0 | (~c1_1(a1430)) | (~c2_1(a1438))),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2280, 91, 2185, 37, 24, 12, 2274])).
% 2.50/1.92 tff(2282,plain,
% 2.50/1.92 (hskp0),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2281, 2264, 2255])).
% 2.50/1.92 tff(2283,plain,
% 2.50/1.92 (~c3_1(a1427)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1213, 2282])).
% 2.50/1.92 tff(2284,plain,
% 2.50/1.92 (c2_1(a1427)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1224, 2282])).
% 2.50/1.92 tff(2285,plain,
% 2.50/1.92 (c0_1(a1427)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1235, 2282])).
% 2.50/1.92 tff(2286,plain,
% 2.50/1.92 (~hskp11),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[795, 61, 11])).
% 2.50/1.92 tff(2287,plain,
% 2.50/1.92 (hskp12),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[1475, 91, 2286, 2285, 2284, 2283, 1288])).
% 2.50/1.92 tff(2288,plain,
% 2.50/1.92 (~c2_1(a1448)),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[220, 2287])).
% 2.50/1.92 tff(2289,plain,
% 2.50/1.92 ($false),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[263, 2288, 2287, 11, 2256])).
% 2.50/1.92 tff(2290,plain,(hskp2 | hskp5 | c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | c3_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.92 tff(2291,plain,
% 2.50/1.92 (hskp2),
% 2.50/1.92 inference(unit_resolution,[status(thm)],[2290, 37, 11, 24, 12, 49])).
% 2.50/1.92 tff(2292,plain,
% 2.50/1.92 (((~hskp2) | (~c2_1(a1430))) <=> ((~hskp2) | (~c2_1(a1430)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2293,plain,
% 2.50/1.92 (((~c2_1(a1430)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1430)))),
% 2.50/1.92 inference(rewrite,[status(thm)],[])).
% 2.50/1.92 tff(2294,axiom,((~c2_1(a1430)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 2.50/1.92 tff(2295,plain,
% 2.50/1.92 ((~hskp2) | (~c2_1(a1430))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 2.50/1.92 tff(2296,plain,
% 2.50/1.92 ((~hskp2) | (~c2_1(a1430))),
% 2.50/1.92 inference(modus_ponens,[status(thm)],[2295, 2292])).
% 2.50/1.93 tff(2297,plain,
% 2.50/1.93 (~c2_1(a1430)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2296, 2291])).
% 2.50/1.93 tff(2298,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2299,plain,
% 2.50/1.93 ((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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2300,plain,
% 2.50/1.93 (((~![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))))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2299])).
% 2.50/1.93 tff(2301,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2300, 2298])).
% 2.50/1.93 tff(2302,plain,
% 2.50/1.93 ((~![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)))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2303,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 2.50/1.93 tff(2304,plain,
% 2.50/1.93 (hskp11 | hskp5 | c2_1(a1430) | (~c3_1(a1430))),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2303, 91, 12, 34])).
% 2.50/1.93 tff(2305,plain,
% 2.50/1.93 (hskp11),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2304, 2297, 2185, 11])).
% 2.50/1.93 tff(2306,plain,
% 2.50/1.93 (~c3_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[757, 2305])).
% 2.50/1.93 tff(2307,plain,
% 2.50/1.93 (~c2_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[745, 2305])).
% 2.50/1.93 tff(2308,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2309,plain,
% 2.50/1.93 ((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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2310,plain,
% 2.50/1.93 (((~![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))))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2309])).
% 2.50/1.93 tff(2311,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2310, 2308])).
% 2.50/1.93 tff(2312,plain,
% 2.50/1.93 ((~![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)))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2313,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 2.50/1.93 tff(2314,plain,
% 2.50/1.93 (~c1_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2313, 91, 111, 2185, 2307, 2306, 2297, 172, 2254])).
% 2.50/1.93 tff(2315,plain,
% 2.50/1.93 (c3_1(a1430)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[313, 11, 204, 12])).
% 2.50/1.93 tff(2316,assumption,(~hskp8), introduced(assumption)).
% 2.50/1.93 tff(2317,plain,
% 2.50/1.93 (^[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)))),
% 2.50/1.93 inference(bind,[status(th)],[])).
% 2.50/1.93 tff(2318,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(quant_intro,[status(thm)],[2317])).
% 2.50/1.93 tff(2319,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2320,plain,
% 2.50/1.93 (^[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))))),
% 2.50/1.93 inference(bind,[status(th)],[])).
% 2.50/1.93 tff(2321,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(quant_intro,[status(thm)],[2320])).
% 2.50/1.93 tff(2322,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 2.50/1.93 tff(2323,plain,
% 2.50/1.93 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 2.50/1.93 tff(2324,plain,
% 2.50/1.93 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2323, 2319])).
% 2.50/1.93 tff(2325,plain,(
% 2.50/1.93 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.50/1.93 inference(skolemize,[status(sab)],[2324])).
% 2.50/1.93 tff(2326,plain,
% 2.50/1.93 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2325, 2318])).
% 2.50/1.93 tff(2327,plain,
% 2.50/1.93 (hskp11 | hskp5 | c0_1(a1430) | (~c3_1(a1430))),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2303, 91, 204, 34])).
% 2.50/1.93 tff(2328,plain,
% 2.50/1.93 (hskp11),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2327, 2315, 11, 12])).
% 2.50/1.93 tff(2329,plain,
% 2.50/1.93 (~c3_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[757, 2328])).
% 2.50/1.93 tff(2330,plain,
% 2.50/1.93 (~c2_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[745, 2328])).
% 2.50/1.93 tff(2331,plain,
% 2.50/1.93 (~c0_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[751, 2328])).
% 2.50/1.93 tff(2332,plain,
% 2.50/1.93 (((~![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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2333,plain,
% 2.50/1.93 ((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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2334,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2333])).
% 2.50/1.93 tff(2335,plain,
% 2.50/1.93 (((~![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))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2334, 2332])).
% 2.50/1.93 tff(2336,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2337,plain,
% 2.50/1.93 ((~![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)),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 2.50/1.93 tff(2338,plain,
% 2.50/1.93 (hskp8 | hskp7),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2337, 91, 2331, 2330, 2329, 2326])).
% 2.50/1.93 tff(2339,plain,
% 2.50/1.93 (hskp7),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2338, 2316])).
% 2.50/1.93 tff(2340,plain,
% 2.50/1.93 (c3_1(a1438)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[110, 2339])).
% 2.50/1.93 tff(2341,plain,
% 2.50/1.93 (~c0_1(a1438)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1099, 2339])).
% 2.50/1.93 tff(2342,plain,
% 2.50/1.93 (~c1_1(a1438)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1514, 2339])).
% 2.50/1.93 tff(2343,assumption,(c3_1(a1430)), introduced(assumption)).
% 2.50/1.93 tff(2344,plain,
% 2.50/1.93 (hskp11),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2327, 11, 2343, 12])).
% 2.50/1.93 tff(2345,plain,
% 2.50/1.93 (~c0_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[751, 2344])).
% 2.50/1.93 tff(2346,plain,
% 2.50/1.93 (~c3_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[757, 2344])).
% 2.50/1.93 tff(2347,plain,
% 2.50/1.93 (~c2_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[745, 2344])).
% 2.50/1.93 tff(2348,plain,
% 2.50/1.93 (hskp12 | (~c1_1(a1447))),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[775, 91, 759, 761, 760, 214])).
% 2.50/1.93 tff(2349,plain,
% 2.50/1.93 (~c1_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2348, 701])).
% 2.50/1.93 tff(2350,plain,
% 2.50/1.93 ((hskp14 | hskp12 | hskp8) <=> (hskp14 | hskp12 | hskp8)),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2351,plain,
% 2.50/1.93 (((hskp12 | hskp8) | hskp14) <=> (hskp14 | hskp12 | hskp8)),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2352,plain,
% 2.50/1.93 ((hskp8 | hskp12) <=> (hskp12 | hskp8)),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2353,plain,
% 2.50/1.93 (((hskp8 | hskp12) | hskp14) <=> ((hskp12 | hskp8) | hskp14)),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2352])).
% 2.50/1.93 tff(2354,plain,
% 2.50/1.93 (((hskp8 | hskp12) | hskp14) <=> (hskp14 | hskp12 | hskp8)),
% 2.50/1.93 inference(transitivity,[status(thm)],[2353, 2351])).
% 2.50/1.93 tff(2355,axiom,((hskp8 | hskp12) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 2.50/1.93 tff(2356,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 2.50/1.93 tff(2357,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2356, 2350])).
% 2.50/1.93 tff(2358,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2357, 2350])).
% 2.50/1.93 tff(2359,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2358, 2350])).
% 2.50/1.93 tff(2360,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2359, 2350])).
% 2.50/1.93 tff(2361,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2360, 2350])).
% 2.50/1.93 tff(2362,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2361, 2350])).
% 2.50/1.93 tff(2363,plain,
% 2.50/1.93 (hskp14 | hskp12 | hskp8),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2362, 2350])).
% 2.50/1.93 tff(2364,plain,
% 2.50/1.93 (hskp14),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2363, 701, 2316])).
% 2.50/1.93 tff(2365,plain,
% 2.50/1.93 (~c3_1(a1451)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[547, 2364])).
% 2.50/1.93 tff(2366,plain,
% 2.50/1.93 (~c1_1(a1451)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[553, 2364])).
% 2.50/1.93 tff(2367,plain,
% 2.50/1.93 (hskp7),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2337, 91, 2316, 759, 761, 760, 2326])).
% 2.50/1.93 tff(2368,plain,
% 2.50/1.93 (c3_1(a1438)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[110, 2367])).
% 2.50/1.93 tff(2369,plain,
% 2.50/1.93 (c2_1(a1451)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[564, 2364])).
% 2.50/1.93 tff(2370,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2371,plain,
% 2.50/1.93 (((~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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2372,plain,
% 2.50/1.93 (((~![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))))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2371])).
% 2.50/1.93 tff(2373,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2372, 2370])).
% 2.50/1.93 tff(2374,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2375,plain,
% 2.50/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1451) | c3_1(a1451) | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c1_1(a1447) | (~c2_1(a1451))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 2.50/1.93 tff(2376,plain,
% 2.50/1.93 ($false),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2375, 91, 2369, 2368, 2366, 2365, 761, 760, 37, 24, 626, 2349])).
% 2.50/1.93 tff(2377,plain,(hskp12 | c2_1(a1447) | c3_1(a1447) | c0_1(a1438) | c1_1(a1438) | c0_1(a1447) | hskp8), inference(lemma,lemma(discharge,[]))).
% 2.50/1.93 tff(2378,plain,
% 2.50/1.93 (hskp12),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2377, 2347, 37, 2346, 24, 2345, 2316])).
% 2.50/1.93 tff(2379,plain,
% 2.50/1.93 (~c2_1(a1448)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[220, 2378])).
% 2.50/1.93 tff(2380,plain,
% 2.50/1.93 (c3_1(a1448)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[242, 2378])).
% 2.50/1.93 tff(2381,plain,
% 2.50/1.93 (c0_1(a1448)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[231, 2378])).
% 2.50/1.93 tff(2382,plain,
% 2.50/1.93 ($false),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1575, 91, 11, 2381, 2380, 1299, 2379, 37, 24, 10])).
% 2.50/1.93 tff(2383,plain,(hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438) | hskp8 | (~c3_1(a1430)) | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.93 tff(2384,plain,
% 2.50/1.93 ($false),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2383, 2342, 2341, 11, 2316, 2340, 2315, 12, 204])).
% 2.50/1.93 tff(2385,plain,(hskp8 | hskp5 | c0_1(a1430) | c2_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.50/1.93 tff(2386,plain,
% 2.50/1.93 (hskp8),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2385, 2297, 12, 11])).
% 2.50/1.93 tff(2387,plain,
% 2.50/1.93 (c3_1(a1441)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1662, 2386])).
% 2.50/1.93 tff(2388,plain,
% 2.50/1.93 (~c1_1(a1441)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1651, 2386])).
% 2.50/1.93 tff(2389,plain,
% 2.50/1.93 (c0_1(a1441)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[1673, 2386])).
% 2.50/1.93 tff(2390,assumption,(~c1_1(a1447)), introduced(assumption)).
% 2.50/1.93 tff(2391,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2392,plain,
% 2.50/1.93 ((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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2393,plain,
% 2.50/1.93 (((~![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))))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2392])).
% 2.50/1.93 tff(2394,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2393, 2391])).
% 2.50/1.93 tff(2395,plain,
% 2.50/1.93 ((~![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)))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2396,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 2.50/1.93 tff(2397,plain,
% 2.50/1.93 (hskp17 | c2_1(a1441)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2396, 91, 11, 1686, 1685, 253])).
% 2.50/1.93 tff(2398,plain,
% 2.50/1.93 (c2_1(a1441)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2397, 36])).
% 2.50/1.93 tff(2399,plain,
% 2.50/1.93 (^[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)))),
% 2.50/1.93 inference(bind,[status(th)],[])).
% 2.50/1.93 tff(2400,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(quant_intro,[status(thm)],[2399])).
% 2.50/1.93 tff(2401,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2402,plain,
% 2.50/1.93 (^[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))))),
% 2.50/1.93 inference(bind,[status(th)],[])).
% 2.50/1.93 tff(2403,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(quant_intro,[status(thm)],[2402])).
% 2.50/1.93 tff(2404,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')).
% 2.50/1.93 tff(2405,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 2.50/1.93 tff(2406,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2405, 2401])).
% 2.50/1.93 tff(2407,plain,(
% 2.50/1.93 ![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))),
% 2.50/1.93 inference(skolemize,[status(sab)],[2406])).
% 2.50/1.93 tff(2408,plain,
% 2.50/1.93 (![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2407, 2400])).
% 2.50/1.93 tff(2409,plain,
% 2.50/1.93 (((~![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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2410,plain,
% 2.50/1.93 ((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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2411,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2410])).
% 2.50/1.93 tff(2412,plain,
% 2.50/1.93 (((~![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))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2411, 2409])).
% 2.50/1.93 tff(2413,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2414,plain,
% 2.50/1.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a1447) | c3_1(a1447) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | c1_1(a1447)),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 2.50/1.93 tff(2415,plain,
% 2.50/1.93 (hskp17 | (~c2_1(a1441)) | c1_1(a1447)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2414, 91, 1686, 761, 760, 1682, 2408])).
% 2.50/1.93 tff(2416,plain,
% 2.50/1.93 ($false),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2415, 2398, 36, 2390])).
% 2.50/1.93 tff(2417,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,[]))).
% 2.50/1.93 tff(2418,plain,
% 2.50/1.93 (hskp17),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2417, 2314, 2389, 2307, 2306, 2388, 11, 2387])).
% 2.50/1.93 tff(2419,plain,
% 2.50/1.93 (~c0_1(a1457)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[275, 2418])).
% 2.50/1.93 tff(2420,plain,
% 2.50/1.93 (~c2_1(a1457)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[288, 2418])).
% 2.50/1.93 tff(2421,plain,
% 2.50/1.93 (~c1_1(a1457)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[269, 2418])).
% 2.50/1.93 tff(2422,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2423,plain,
% 2.50/1.93 ((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)))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2424,plain,
% 2.50/1.93 (((~![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))))),
% 2.50/1.93 inference(monotonicity,[status(thm)],[2423])).
% 2.50/1.93 tff(2425,plain,
% 2.50/1.93 (((~![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)))),
% 2.50/1.93 inference(transitivity,[status(thm)],[2424, 2422])).
% 2.50/1.93 tff(2426,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(quant_inst,[status(thm)],[])).
% 2.50/1.93 tff(2427,plain,
% 2.50/1.93 ((~![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))),
% 2.50/1.93 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 2.50/1.93 tff(2428,plain,
% 2.50/1.93 (hskp3 | c0_1(a1438) | (~c1_1(a1430))),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2427, 91, 49, 2185, 24, 12, 873])).
% 2.50/1.93 tff(2429,plain,
% 2.50/1.93 (hskp3),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[2428, 37, 2254])).
% 2.50/1.93 tff(2430,plain,
% 2.50/1.93 (c1_1(a1431)),
% 2.50/1.93 inference(unit_resolution,[status(thm)],[953, 2429])).
% 2.50/1.93 tff(2431,plain,
% 2.50/1.93 (^[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)))),
% 2.50/1.93 inference(bind,[status(th)],[])).
% 2.50/1.93 tff(2432,plain,
% 2.50/1.93 (![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)) <=> ![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))),
% 2.50/1.93 inference(quant_intro,[status(thm)],[2431])).
% 2.50/1.93 tff(2433,plain,
% 2.50/1.93 (![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)) <=> ![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))),
% 2.50/1.93 inference(rewrite,[status(thm)],[])).
% 2.50/1.93 tff(2434,plain,
% 2.50/1.93 (^[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))))),
% 2.50/1.94 inference(bind,[status(th)],[])).
% 2.50/1.94 tff(2435,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(quant_intro,[status(thm)],[2434])).
% 2.50/1.94 tff(2436,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')).
% 2.50/1.94 tff(2437,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 2.50/1.94 tff(2438,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2437, 2433])).
% 2.50/1.94 tff(2439,plain,(
% 2.50/1.94 ![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))),
% 2.50/1.94 inference(skolemize,[status(sab)],[2438])).
% 2.50/1.94 tff(2440,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2439, 2432])).
% 2.50/1.94 tff(2441,plain,
% 2.50/1.94 (~c0_1(a1447)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[751, 2305])).
% 2.50/1.94 tff(2442,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2443,plain,
% 2.50/1.94 ((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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2444,plain,
% 2.50/1.94 (((~![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))))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2443])).
% 2.50/1.94 tff(2445,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(transitivity,[status(thm)],[2444, 2442])).
% 2.50/1.94 tff(2446,plain,
% 2.50/1.94 ((~![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))),
% 2.50/1.94 inference(quant_inst,[status(thm)],[])).
% 2.50/1.94 tff(2447,plain,
% 2.50/1.94 ((~![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 2.50/1.94 tff(2448,plain,
% 2.50/1.94 (hskp0),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2447, 91, 2185, 2441, 2307, 2306, 2297, 2440, 2254])).
% 2.50/1.94 tff(2449,plain,
% 2.50/1.94 (c2_1(a1427)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[1224, 2448])).
% 2.50/1.94 tff(2450,plain,
% 2.50/1.94 (^[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)))),
% 2.50/1.94 inference(bind,[status(th)],[])).
% 2.50/1.94 tff(2451,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(quant_intro,[status(thm)],[2450])).
% 2.50/1.94 tff(2452,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2453,plain,
% 2.50/1.94 (^[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))))),
% 2.50/1.94 inference(bind,[status(th)],[])).
% 2.50/1.94 tff(2454,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(quant_intro,[status(thm)],[2453])).
% 2.50/1.94 tff(2455,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')).
% 2.50/1.94 tff(2456,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 2.50/1.94 tff(2457,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2456, 2452])).
% 2.50/1.94 tff(2458,plain,(
% 2.50/1.94 ![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))),
% 2.50/1.94 inference(skolemize,[status(sab)],[2457])).
% 2.50/1.94 tff(2459,plain,
% 2.50/1.94 (![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2458, 2451])).
% 2.50/1.94 tff(2460,plain,
% 2.50/1.94 (~c2_1(a1431)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[928, 2429])).
% 2.50/1.94 tff(2461,plain,
% 2.50/1.94 (((~![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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2462,plain,
% 2.50/1.94 (((~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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2463,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2462])).
% 2.50/1.94 tff(2464,plain,
% 2.50/1.94 (((~![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))),
% 2.50/1.94 inference(transitivity,[status(thm)],[2463, 2461])).
% 2.50/1.94 tff(2465,plain,
% 2.50/1.94 ((~![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))),
% 2.50/1.94 inference(quant_inst,[status(thm)],[])).
% 2.50/1.94 tff(2466,plain,
% 2.50/1.94 ((~![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)),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 2.50/1.94 tff(2467,plain,
% 2.50/1.94 (c3_1(a1431) | c1_1(a1447)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2466, 91, 2430, 2441, 2307, 2306, 2460, 2459])).
% 2.50/1.94 tff(2468,plain,
% 2.50/1.94 (c3_1(a1431)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2467, 2314])).
% 2.50/1.94 tff(2469,plain,
% 2.50/1.94 (~c0_1(a1431)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[934, 2429])).
% 2.50/1.94 tff(2470,plain,
% 2.50/1.94 (~c3_1(a1427)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[1213, 2448])).
% 2.50/1.94 tff(2471,plain,
% 2.50/1.94 (c0_1(a1427)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[1235, 2448])).
% 2.50/1.94 tff(2472,assumption,(c3_1(a1431)), introduced(assumption)).
% 2.50/1.94 tff(2473,assumption,(~c2_1(a1431)), introduced(assumption)).
% 2.50/1.94 tff(2474,assumption,(c1_1(a1431)), introduced(assumption)).
% 2.50/1.94 tff(2475,assumption,(~hskp10), introduced(assumption)).
% 2.50/1.94 tff(2476,assumption,(hskp1), introduced(assumption)).
% 2.50/1.94 tff(2477,plain,
% 2.50/1.94 (~c0_1(a1429)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[649, 2476])).
% 2.50/1.94 tff(2478,plain,
% 2.50/1.94 (c3_1(a1429)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[660, 2476])).
% 2.50/1.94 tff(2479,plain,
% 2.50/1.94 (c2_1(a1429)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[688, 2476])).
% 2.50/1.94 tff(2480,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2481,plain,
% 2.50/1.94 ((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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2482,plain,
% 2.50/1.94 (((~![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))))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2481])).
% 2.50/1.94 tff(2483,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(transitivity,[status(thm)],[2482, 2480])).
% 2.50/1.94 tff(2484,plain,
% 2.50/1.94 ((~![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)))),
% 2.50/1.94 inference(quant_inst,[status(thm)],[])).
% 2.50/1.94 tff(2485,plain,
% 2.50/1.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1431) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1431)) | (~c3_1(a1431))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 2.50/1.94 tff(2486,plain,
% 2.50/1.94 ($false),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2485, 91, 701, 2474, 2479, 2478, 2473, 2477, 1363, 2472])).
% 2.50/1.94 tff(2487,plain,((~hskp1) | hskp12 | (~c1_1(a1431)) | c2_1(a1431) | (~c3_1(a1431))), inference(lemma,lemma(discharge,[]))).
% 2.50/1.94 tff(2488,plain,
% 2.50/1.94 (~hskp1),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2487, 701, 2474, 2473, 2472])).
% 2.50/1.94 tff(2489,plain,
% 2.50/1.94 ((hskp12 | hskp10 | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2490,plain,
% 2.50/1.94 (((hskp12 | hskp10) | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2491,plain,
% 2.50/1.94 ((hskp12 | hskp10) <=> (hskp12 | hskp10)),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2492,plain,
% 2.50/1.94 (((hskp12 | hskp10) | hskp1) <=> ((hskp12 | hskp10) | hskp1)),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2491])).
% 2.50/1.94 tff(2493,plain,
% 2.50/1.94 (((hskp12 | hskp10) | hskp1) <=> (hskp12 | hskp10 | hskp1)),
% 2.50/1.94 inference(transitivity,[status(thm)],[2492, 2490])).
% 2.50/1.94 tff(2494,axiom,((hskp12 | hskp10) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 2.50/1.94 tff(2495,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 2.50/1.94 tff(2496,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2495, 2489])).
% 2.50/1.94 tff(2497,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2496, 2489])).
% 2.50/1.94 tff(2498,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2497, 2489])).
% 2.50/1.94 tff(2499,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2498, 2489])).
% 2.50/1.94 tff(2500,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2499, 2489])).
% 2.50/1.94 tff(2501,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2500, 2489])).
% 2.50/1.94 tff(2502,plain,
% 2.50/1.94 (hskp12 | hskp10 | hskp1),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2501, 2489])).
% 2.50/1.94 tff(2503,plain,
% 2.50/1.94 ($false),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2502, 2488, 701, 2475])).
% 2.50/1.94 tff(2504,plain,(hskp12 | hskp10 | (~c1_1(a1431)) | c2_1(a1431) | (~c3_1(a1431))), inference(lemma,lemma(discharge,[]))).
% 2.50/1.94 tff(2505,plain,
% 2.50/1.94 (hskp12),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2504, 2475, 2474, 2473, 2472])).
% 2.50/1.94 tff(2506,plain,
% 2.50/1.94 (~c2_1(a1448)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[220, 2505])).
% 2.50/1.94 tff(2507,assumption,(~c0_1(a1431)), introduced(assumption)).
% 2.50/1.94 tff(2508,plain,
% 2.50/1.94 (c0_1(a1448)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[231, 2505])).
% 2.50/1.94 tff(2509,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2510,plain,
% 2.50/1.94 ((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)))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2511,plain,
% 2.50/1.94 (((~![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))))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2510])).
% 2.50/1.94 tff(2512,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(transitivity,[status(thm)],[2511, 2509])).
% 2.50/1.94 tff(2513,plain,
% 2.50/1.94 ((~![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)))),
% 2.50/1.94 inference(quant_inst,[status(thm)],[])).
% 2.50/1.94 tff(2514,plain,
% 2.50/1.94 ((~![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))),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 2.50/1.94 tff(2515,plain,
% 2.50/1.94 (~c1_1(a1448)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2514, 91, 2475, 2508, 2506, 2507, 2473, 369, 2472])).
% 2.50/1.94 tff(2516,assumption,(~c3_1(a1427)), introduced(assumption)).
% 2.50/1.94 tff(2517,assumption,(c2_1(a1427)), introduced(assumption)).
% 2.50/1.94 tff(2518,assumption,(c0_1(a1427)), introduced(assumption)).
% 2.50/1.94 tff(2519,plain,
% 2.50/1.94 (((~![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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2520,plain,
% 2.50/1.94 ((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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2521,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2520])).
% 2.50/1.94 tff(2522,plain,
% 2.50/1.94 (((~![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))),
% 2.50/1.94 inference(transitivity,[status(thm)],[2521, 2519])).
% 2.50/1.94 tff(2523,plain,
% 2.50/1.94 ((~![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)))),
% 2.50/1.94 inference(quant_inst,[status(thm)],[])).
% 2.50/1.94 tff(2524,plain,
% 2.50/1.94 ((~![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)),
% 2.50/1.94 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 2.50/1.94 tff(2525,plain,
% 2.50/1.94 (hskp19 | c1_1(a1448)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2524, 91, 2508, 2518, 2517, 2506, 2516, 1191])).
% 2.50/1.94 tff(2526,plain,
% 2.50/1.94 (hskp19),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[2525, 2515])).
% 2.50/1.94 tff(2527,plain,
% 2.50/1.94 (~c1_1(a1460)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[1268, 2526])).
% 2.50/1.94 tff(2528,plain,
% 2.50/1.94 (~c0_1(a1460)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[1255, 2526])).
% 2.50/1.94 tff(2529,plain,
% 2.50/1.94 (c3_1(a1448)),
% 2.50/1.94 inference(unit_resolution,[status(thm)],[242, 2505])).
% 2.50/1.94 tff(2530,plain,
% 2.50/1.94 (((~![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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2531,plain,
% 2.50/1.94 ((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))),
% 2.50/1.94 inference(rewrite,[status(thm)],[])).
% 2.50/1.94 tff(2532,plain,
% 2.50/1.94 (((~![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)))),
% 2.50/1.94 inference(monotonicity,[status(thm)],[2531])).
% 2.50/1.94 tff(2533,plain,
% 2.50/1.94 (((~![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))),
% 2.58/1.94 inference(transitivity,[status(thm)],[2532, 2530])).
% 2.58/1.94 tff(2534,plain,
% 2.58/1.94 ((~![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)))),
% 2.58/1.94 inference(quant_inst,[status(thm)],[])).
% 2.58/1.94 tff(2535,plain,
% 2.58/1.94 ((~![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)),
% 2.58/1.94 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 2.58/1.94 tff(2536,plain,
% 2.58/1.94 (hskp22 | c1_1(a1448)),
% 2.58/1.94 inference(unit_resolution,[status(thm)],[2535, 91, 2508, 2529, 2506, 1385])).
% 2.58/1.94 tff(2537,plain,
% 2.58/1.94 (hskp22),
% 2.58/1.94 inference(unit_resolution,[status(thm)],[2536, 2515])).
% 2.58/1.94 tff(2538,plain,
% 2.58/1.94 (~c0_1(a1468)),
% 2.58/1.94 inference(unit_resolution,[status(thm)],[891, 2537])).
% 2.58/1.94 tff(2539,plain,
% 2.58/1.94 (c3_1(a1468)),
% 2.58/1.94 inference(unit_resolution,[status(thm)],[902, 2537])).
% 2.58/1.94 tff(2540,plain,
% 2.58/1.94 (c1_1(a1468)),
% 2.58/1.94 inference(unit_resolution,[status(thm)],[913, 2537])).
% 2.58/1.94 tff(2541,plain,
% 2.58/1.94 (((~![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)))) | (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)))),
% 2.58/1.94 inference(rewrite,[status(thm)],[])).
% 2.58/1.94 tff(2542,plain,
% 2.58/1.94 (((~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)))),
% 2.58/1.94 inference(rewrite,[status(thm)],[])).
% 2.58/1.94 tff(2543,plain,
% 2.58/1.94 (((~![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(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))))),
% 2.58/1.94 inference(monotonicity,[status(thm)],[2542])).
% 2.58/1.94 tff(2544,plain,
% 2.58/1.94 (((~![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(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)))),
% 2.58/1.94 inference(transitivity,[status(thm)],[2543, 2541])).
% 2.58/1.94 tff(2545,plain,
% 2.58/1.94 ((~![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(a1468) | (~c3_1(a1468)) | (~c1_1(a1468)) | c1_1(a1460) | c0_1(a1460) | (~c2_1(a1460)))),
% 2.58/1.94 inference(quant_inst,[status(thm)],[])).
% 2.58/1.94 tff(2546,plain,
% 2.58/1.94 ((~![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)))) | 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))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 2.58/1.95 tff(2547,plain,
% 2.58/1.95 (~c2_1(a1460)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2546, 91, 2540, 2539, 2508, 2529, 2538, 2528, 2527, 2506, 1374])).
% 2.58/1.95 tff(2548,plain,
% 2.58/1.95 (^[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))))),
% 2.58/1.95 inference(bind,[status(th)],[])).
% 2.58/1.95 tff(2549,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(quant_intro,[status(thm)],[2548])).
% 2.58/1.95 tff(2550,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2551,plain,
% 2.58/1.95 (^[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)))))),
% 2.58/1.95 inference(bind,[status(th)],[])).
% 2.58/1.95 tff(2552,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(quant_intro,[status(thm)],[2551])).
% 2.58/1.95 tff(2553,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')).
% 2.58/1.95 tff(2554,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 2.58/1.95 tff(2555,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2554, 2550])).
% 2.58/1.95 tff(2556,plain,(
% 2.58/1.95 ![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)))),
% 2.58/1.95 inference(skolemize,[status(sab)],[2555])).
% 2.58/1.95 tff(2557,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2556, 2549])).
% 2.58/1.95 tff(2558,plain,
% 2.58/1.95 (((~![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))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2559,plain,
% 2.58/1.95 ((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))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2560,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2559])).
% 2.58/1.95 tff(2561,plain,
% 2.58/1.95 (((~![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))),
% 2.58/1.95 inference(transitivity,[status(thm)],[2560, 2558])).
% 2.58/1.95 tff(2562,plain,
% 2.58/1.95 ((~![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)))),
% 2.58/1.95 inference(quant_inst,[status(thm)],[])).
% 2.58/1.95 tff(2563,plain,
% 2.58/1.95 ((~![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)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 2.58/1.95 tff(2564,plain,
% 2.58/1.95 (hskp21 | c1_1(a1448)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2563, 91, 2508, 2518, 2517, 2506, 2516, 2557])).
% 2.58/1.95 tff(2565,plain,
% 2.58/1.95 (hskp21),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2564, 2515])).
% 2.58/1.95 tff(2566,plain,
% 2.58/1.95 (((~hskp21) | (~c1_1(a1466))) <=> ((~hskp21) | (~c1_1(a1466)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2567,plain,
% 2.58/1.95 (((~c1_1(a1466)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1466)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2568,axiom,((~c1_1(a1466)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 2.58/1.95 tff(2569,plain,
% 2.58/1.95 ((~hskp21) | (~c1_1(a1466))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 2.58/1.95 tff(2570,plain,
% 2.58/1.95 ((~hskp21) | (~c1_1(a1466))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2569, 2566])).
% 2.58/1.95 tff(2571,plain,
% 2.58/1.95 (~c1_1(a1466)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2570, 2565])).
% 2.58/1.95 tff(2572,plain,
% 2.58/1.95 (((~hskp21) | c2_1(a1466)) <=> ((~hskp21) | c2_1(a1466))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2573,axiom,((~hskp21) | c2_1(a1466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 2.58/1.95 tff(2574,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 2.58/1.95 tff(2575,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2574, 2572])).
% 2.58/1.95 tff(2576,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2575, 2572])).
% 2.58/1.95 tff(2577,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2576, 2572])).
% 2.58/1.95 tff(2578,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2577, 2572])).
% 2.58/1.95 tff(2579,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2578, 2572])).
% 2.58/1.95 tff(2580,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2579, 2572])).
% 2.58/1.95 tff(2581,plain,
% 2.58/1.95 ((~hskp21) | c2_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2580, 2572])).
% 2.58/1.95 tff(2582,plain,
% 2.58/1.95 (c2_1(a1466)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2581, 2565])).
% 2.58/1.95 tff(2583,plain,
% 2.58/1.95 (((~hskp21) | c0_1(a1466)) <=> ((~hskp21) | c0_1(a1466))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2584,axiom,((~hskp21) | c0_1(a1466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 2.58/1.95 tff(2585,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 2.58/1.95 tff(2586,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2585, 2583])).
% 2.58/1.95 tff(2587,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2586, 2583])).
% 2.58/1.95 tff(2588,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2587, 2583])).
% 2.58/1.95 tff(2589,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2588, 2583])).
% 2.58/1.95 tff(2590,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2589, 2583])).
% 2.58/1.95 tff(2591,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2590, 2583])).
% 2.58/1.95 tff(2592,plain,
% 2.58/1.95 ((~hskp21) | c0_1(a1466)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2591, 2583])).
% 2.58/1.95 tff(2593,plain,
% 2.58/1.95 (c0_1(a1466)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2592, 2565])).
% 2.58/1.95 tff(2594,plain,
% 2.58/1.95 (((~![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(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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2595,plain,
% 2.58/1.95 (((~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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2596,plain,
% 2.58/1.95 (((~![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(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))))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2595])).
% 2.58/1.95 tff(2597,plain,
% 2.58/1.95 (((~![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(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)))),
% 2.58/1.95 inference(transitivity,[status(thm)],[2596, 2594])).
% 2.58/1.95 tff(2598,plain,
% 2.58/1.95 ((~![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(a1427) | c1_1(a1427) | (~c0_1(a1427)) | c1_1(a1460) | c0_1(a1460) | c2_1(a1460))),
% 2.58/1.95 inference(quant_inst,[status(thm)],[])).
% 2.58/1.95 tff(2599,plain,
% 2.58/1.95 ((~![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(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | c2_1(a1460) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 2.58/1.95 tff(2600,plain,
% 2.58/1.95 (c1_1(a1427)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2599, 91, 2593, 2582, 2518, 2571, 2528, 2527, 2516, 23, 2547])).
% 2.58/1.95 tff(2601,plain,
% 2.58/1.95 (((~![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))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2602,plain,
% 2.58/1.95 (((~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))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2603,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2602])).
% 2.58/1.95 tff(2604,plain,
% 2.58/1.95 (((~![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))),
% 2.58/1.95 inference(transitivity,[status(thm)],[2603, 2601])).
% 2.58/1.95 tff(2605,plain,
% 2.58/1.95 ((~![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)))),
% 2.58/1.95 inference(quant_inst,[status(thm)],[])).
% 2.58/1.95 tff(2606,plain,
% 2.58/1.95 ((~![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)),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 2.58/1.95 tff(2607,plain,
% 2.58/1.95 (c3_1(a1466)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2606, 91, 2582, 2508, 2571, 2506, 2507, 2473, 591, 2472, 2515])).
% 2.58/1.95 tff(2608,plain,
% 2.58/1.95 (^[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))))),
% 2.58/1.95 inference(bind,[status(th)],[])).
% 2.58/1.95 tff(2609,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(quant_intro,[status(thm)],[2608])).
% 2.58/1.95 tff(2610,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2611,plain,
% 2.58/1.95 (^[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)))))),
% 2.58/1.95 inference(bind,[status(th)],[])).
% 2.58/1.95 tff(2612,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(quant_intro,[status(thm)],[2611])).
% 2.58/1.95 tff(2613,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')).
% 2.58/1.95 tff(2614,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 2.58/1.95 tff(2615,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2614, 2610])).
% 2.58/1.95 tff(2616,plain,(
% 2.58/1.95 ![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)))),
% 2.58/1.95 inference(skolemize,[status(sab)],[2615])).
% 2.58/1.95 tff(2617,plain,
% 2.58/1.95 (![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)))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2616, 2609])).
% 2.58/1.95 tff(2618,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2619,plain,
% 2.58/1.95 (((~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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2620,plain,
% 2.58/1.95 (((~![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))))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2619])).
% 2.58/1.95 tff(2621,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(transitivity,[status(thm)],[2620, 2618])).
% 2.58/1.95 tff(2622,plain,
% 2.58/1.95 ((~![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)))),
% 2.58/1.95 inference(quant_inst,[status(thm)],[])).
% 2.58/1.95 tff(2623,plain,
% 2.58/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1448) | c3_1(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c3_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 2.58/1.95 tff(2624,plain,
% 2.58/1.95 ((~c1_1(a1427)) | (~c3_1(a1466))),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2623, 91, 2593, 2582, 2529, 2518, 2506, 2516, 2617, 2515])).
% 2.58/1.95 tff(2625,plain,
% 2.58/1.95 ($false),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2624, 2607, 2600])).
% 2.58/1.95 tff(2626,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,[]))).
% 2.58/1.95 tff(2627,plain,
% 2.58/1.95 (hskp10),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2626, 2471, 2470, 2469, 2460, 2468, 2449, 2430])).
% 2.58/1.95 tff(2628,assumption,(hskp10), introduced(assumption)).
% 2.58/1.95 tff(2629,plain,
% 2.58/1.95 (~c3_1(a1445)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[439, 2628])).
% 2.58/1.95 tff(2630,plain,
% 2.58/1.95 (c0_1(a1445)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[456, 2628])).
% 2.58/1.95 tff(2631,assumption,(~hskp29), introduced(assumption)).
% 2.58/1.95 tff(2632,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2633,plain,
% 2.58/1.95 ((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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2634,plain,
% 2.58/1.95 (((~![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))))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2633])).
% 2.58/1.95 tff(2635,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(transitivity,[status(thm)],[2634, 2632])).
% 2.58/1.95 tff(2636,plain,
% 2.58/1.95 ((~![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)))),
% 2.58/1.95 inference(quant_inst,[status(thm)],[])).
% 2.58/1.95 tff(2637,plain,
% 2.58/1.95 ((~![U: $i] : (hskp29 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | hskp5 | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))),
% 2.58/1.95 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 2.58/1.95 tff(2638,plain,
% 2.58/1.95 (c2_1(a1445)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2637, 91, 2631, 11, 2630, 2629, 1044])).
% 2.58/1.95 tff(2639,plain,
% 2.58/1.95 (~c1_1(a1445)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[445, 2628])).
% 2.58/1.95 tff(2640,assumption,(~c2_1(a1457)), introduced(assumption)).
% 2.58/1.95 tff(2641,assumption,(~c1_1(a1457)), introduced(assumption)).
% 2.58/1.95 tff(2642,assumption,(~c0_1(a1457)), introduced(assumption)).
% 2.58/1.95 tff(2643,plain,
% 2.58/1.95 ($false),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[463, 91, 2630, 2642, 2641, 2640, 2639, 2629, 23, 2638])).
% 2.58/1.95 tff(2644,plain,((~hskp10) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | hskp29 | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.58/1.95 tff(2645,plain,
% 2.58/1.95 (hskp29),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[2644, 2627, 2421, 2420, 2419, 11])).
% 2.58/1.95 tff(2646,plain,
% 2.58/1.95 (c3_1(a1483)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[1062, 2645])).
% 2.58/1.95 tff(2647,plain,
% 2.58/1.95 (c2_1(a1483)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[1073, 2645])).
% 2.58/1.95 tff(2648,plain,
% 2.58/1.95 (c1_1(a1483)),
% 2.58/1.95 inference(unit_resolution,[status(thm)],[1084, 2645])).
% 2.58/1.95 tff(2649,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2650,plain,
% 2.58/1.95 ((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)))),
% 2.58/1.95 inference(rewrite,[status(thm)],[])).
% 2.58/1.95 tff(2651,plain,
% 2.58/1.95 (((~![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))))),
% 2.58/1.95 inference(monotonicity,[status(thm)],[2650])).
% 2.58/1.95 tff(2652,plain,
% 2.58/1.95 (((~![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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2651, 2649])).
% 2.58/1.96 tff(2653,plain,
% 2.58/1.96 ((~![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))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2654,plain,
% 2.58/1.96 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c2_1(a1447) | c3_1(a1447) | (~ndr1_0) | c1_1(a1447) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 2.58/1.96 tff(2655,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2654, 91, 111, 2648, 2647, 2646, 2307, 2306, 678, 2314])).
% 2.58/1.96 tff(2656,plain,(c0_1(a1438) | hskp5 | c0_1(a1430) | c3_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.96 tff(2657,plain,
% 2.58/1.96 (c0_1(a1438)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2656, 49, 12, 11, 24])).
% 2.58/1.96 tff(2658,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2659,plain,
% 2.58/1.96 ((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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2660,plain,
% 2.58/1.96 (((~![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))))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2659])).
% 2.58/1.96 tff(2661,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2660, 2658])).
% 2.58/1.96 tff(2662,plain,
% 2.58/1.96 ((~![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)))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2663,plain,
% 2.58/1.96 ((~![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))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2662, 2661])).
% 2.58/1.96 tff(2664,plain,
% 2.58/1.96 (hskp7 | c3_1(a1438) | (~c0_1(a1438)) | (~c2_1(a1430)) | (~c1_1(a1430))),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2663, 91, 24, 12, 193])).
% 2.58/1.96 tff(2665,plain,
% 2.58/1.96 (~c2_1(a1430)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2664, 2657, 49, 111, 2254])).
% 2.58/1.96 tff(2666,plain,
% 2.58/1.96 (hskp11),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2304, 2665, 2185, 11])).
% 2.58/1.96 tff(2667,plain,
% 2.58/1.96 (~c3_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[757, 2666])).
% 2.58/1.96 tff(2668,plain,
% 2.58/1.96 (~c2_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[745, 2666])).
% 2.58/1.96 tff(2669,plain,
% 2.58/1.96 (~c1_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2313, 91, 111, 2185, 2668, 2667, 2665, 172, 2254])).
% 2.58/1.96 tff(2670,plain,
% 2.58/1.96 (c2_1(a1438)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1744, 2657, 24, 11, 49])).
% 2.58/1.96 tff(2671,plain,
% 2.58/1.96 (~c0_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[751, 2666])).
% 2.58/1.96 tff(2672,plain,
% 2.58/1.96 (((~![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))) | (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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2673,plain,
% 2.58/1.96 (((~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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2674,plain,
% 2.58/1.96 (((~![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(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)))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2673])).
% 2.58/1.96 tff(2675,plain,
% 2.58/1.96 (((~![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(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))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2674, 2672])).
% 2.58/1.96 tff(2676,plain,
% 2.58/1.96 ((~![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(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))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2677,plain,
% 2.58/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a1438) | c0_1(a1447) | c2_1(a1447) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | c1_1(a1447)),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 2.58/1.96 tff(2678,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2677, 91, 49, 2671, 2668, 2657, 24, 23, 2670, 2669])).
% 2.58/1.96 tff(2679,plain,(c3_1(a1438) | c1_1(a1438) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.96 tff(2680,plain,
% 2.58/1.96 (c3_1(a1438)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2679, 24, 11, 12])).
% 2.58/1.96 tff(2681,plain,
% 2.58/1.96 (hskp11 | c0_1(a1438) | c2_1(a1438)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1546, 91, 11, 2680, 34])).
% 2.58/1.96 tff(2682,plain,
% 2.58/1.96 (hskp11),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2681, 50, 37])).
% 2.58/1.96 tff(2683,plain,
% 2.58/1.96 (hskp2),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[795, 2682, 11])).
% 2.58/1.96 tff(2684,plain,
% 2.58/1.96 (~c2_1(a1430)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2296, 2683])).
% 2.58/1.96 tff(2685,plain,
% 2.58/1.96 (hskp8),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2385, 2684, 12, 11])).
% 2.58/1.96 tff(2686,plain,
% 2.58/1.96 (c3_1(a1441)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1662, 2685])).
% 2.58/1.96 tff(2687,plain,
% 2.58/1.96 (c0_1(a1441)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1673, 2685])).
% 2.58/1.96 tff(2688,assumption,(~c2_1(a1441)), introduced(assumption)).
% 2.58/1.96 tff(2689,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2690,plain,
% 2.58/1.96 ((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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2691,plain,
% 2.58/1.96 (((~![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))))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2690])).
% 2.58/1.96 tff(2692,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2691, 2689])).
% 2.58/1.96 tff(2693,plain,
% 2.58/1.96 ((~![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)))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2694,plain,
% 2.58/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 2.58/1.96 tff(2695,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2694, 91, 11, 1686, 1685, 1299, 37, 24, 10, 2688])).
% 2.58/1.96 tff(2696,plain,(c2_1(a1441) | hskp5 | (~c0_1(a1441)) | (~c3_1(a1441)) | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.96 tff(2697,plain,
% 2.58/1.96 (c2_1(a1441)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2696, 2687, 11, 2686, 2680, 37, 24])).
% 2.58/1.96 tff(2698,plain,
% 2.58/1.96 (~c1_1(a1441)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1651, 2685])).
% 2.58/1.96 tff(2699,plain,
% 2.58/1.96 (~c3_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[757, 2682])).
% 2.58/1.96 tff(2700,plain,
% 2.58/1.96 (~c2_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[745, 2682])).
% 2.58/1.96 tff(2701,plain,
% 2.58/1.96 (~c0_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[751, 2682])).
% 2.58/1.96 tff(2702,plain,
% 2.58/1.96 (c1_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2417, 36, 1686, 761, 760, 1682, 11, 1685])).
% 2.58/1.96 tff(2703,plain,
% 2.58/1.96 (hskp12),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2348, 2702])).
% 2.58/1.96 tff(2704,plain,
% 2.58/1.96 (~c2_1(a1448)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[220, 2703])).
% 2.58/1.96 tff(2705,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[263, 2704, 2703, 11, 36])).
% 2.58/1.96 tff(2706,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,[]))).
% 2.58/1.96 tff(2707,plain,
% 2.58/1.96 (hskp17),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2706, 2701, 11, 2700, 2699, 2687, 2698, 2686])).
% 2.58/1.96 tff(2708,plain,
% 2.58/1.96 (~c2_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[288, 2707])).
% 2.58/1.96 tff(2709,plain,
% 2.58/1.96 (~c1_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[269, 2707])).
% 2.58/1.96 tff(2710,plain,
% 2.58/1.96 (~c0_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[275, 2707])).
% 2.58/1.96 tff(2711,assumption,(hskp0), introduced(assumption)).
% 2.58/1.96 tff(2712,plain,
% 2.58/1.96 (~c3_1(a1427)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1213, 2711])).
% 2.58/1.96 tff(2713,plain,
% 2.58/1.96 (c0_1(a1427)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1235, 2711])).
% 2.58/1.96 tff(2714,plain,
% 2.58/1.96 (((~![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(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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2715,plain,
% 2.58/1.96 (((~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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2716,plain,
% 2.58/1.96 (((~![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(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))))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2715])).
% 2.58/1.96 tff(2717,plain,
% 2.58/1.96 (((~![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(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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2716, 2714])).
% 2.58/1.96 tff(2718,plain,
% 2.58/1.96 ((~![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(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)))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2719,plain,
% 2.58/1.96 ((~![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(a1427) | (~ndr1_0) | (~c1_1(a1427)) | (~c0_1(a1427)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 2.58/1.96 tff(2720,plain,
% 2.58/1.96 (~c1_1(a1427)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2719, 91, 1686, 1685, 1299, 2713, 24, 2712, 2617, 50, 1681])).
% 2.58/1.96 tff(2721,plain,
% 2.58/1.96 (((~![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))) | (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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2722,plain,
% 2.58/1.96 (((~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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2723,plain,
% 2.58/1.96 (((~![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(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))))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2722])).
% 2.58/1.96 tff(2724,plain,
% 2.58/1.96 (((~![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(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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2723, 2721])).
% 2.58/1.96 tff(2725,plain,
% 2.58/1.96 ((~![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(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))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2726,plain,
% 2.58/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 2.58/1.96 tff(2727,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2726, 91, 1686, 2713, 2642, 2641, 2640, 1682, 2712, 23, 1681, 2720])).
% 2.58/1.96 tff(2728,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,[]))).
% 2.58/1.96 tff(2729,plain,
% 2.58/1.96 (~hskp0),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2728, 2687, 2710, 2709, 2708, 2698, 2697, 2686, 2680, 24, 50])).
% 2.58/1.96 tff(2730,plain,
% 2.58/1.96 (hskp0 | (~c1_1(a1430))),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2447, 91, 2185, 2701, 2700, 2699, 2684, 2440])).
% 2.58/1.96 tff(2731,plain,
% 2.58/1.96 (~c1_1(a1430)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2730, 2729])).
% 2.58/1.96 tff(2732,plain,
% 2.58/1.96 (hskp11 | c0_1(a1438) | c2_1(a1438)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[1546, 91, 11, 1299, 34])).
% 2.58/1.96 tff(2733,plain,
% 2.58/1.96 (hskp11),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2732, 50, 37])).
% 2.58/1.96 tff(2734,plain,
% 2.58/1.96 (~c3_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[757, 2733])).
% 2.58/1.96 tff(2735,plain,
% 2.58/1.96 (~c2_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[745, 2733])).
% 2.58/1.96 tff(2736,plain,
% 2.58/1.96 (~c0_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[751, 2733])).
% 2.58/1.96 tff(2737,plain,
% 2.58/1.96 (hskp12 | (~c1_1(a1447))),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[775, 91, 2736, 2735, 2734, 214])).
% 2.58/1.96 tff(2738,plain,
% 2.58/1.96 (~c1_1(a1447)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2737, 701])).
% 2.58/1.96 tff(2739,plain,
% 2.58/1.96 (c2_1(a1441)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2696, 1686, 11, 1685, 1299, 37, 24])).
% 2.58/1.96 tff(2740,plain,
% 2.58/1.96 (hskp17),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2706, 2736, 11, 2735, 2734, 1686, 1682, 1685])).
% 2.58/1.96 tff(2741,plain,
% 2.58/1.96 (~c2_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[288, 2740])).
% 2.58/1.96 tff(2742,plain,
% 2.58/1.96 (~c1_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[269, 2740])).
% 2.58/1.96 tff(2743,plain,
% 2.58/1.96 (~c0_1(a1457)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[275, 2740])).
% 2.58/1.96 tff(2744,plain,
% 2.58/1.96 (~hskp0),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2728, 1686, 2743, 2742, 2741, 1682, 2739, 1685, 1299, 24, 50])).
% 2.58/1.96 tff(2745,plain,
% 2.58/1.96 (((~![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))) | (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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2746,plain,
% 2.58/1.96 (((~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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2747,plain,
% 2.58/1.96 (((~![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(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))))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2746])).
% 2.58/1.96 tff(2748,plain,
% 2.58/1.96 (((~![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(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)))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2747, 2745])).
% 2.58/1.96 tff(2749,plain,
% 2.58/1.96 ((~![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(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))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2750,plain,
% 2.58/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1445) | c3_1(a1445) | c1_1(a1441) | (~ndr1_0) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c0_1(a1445))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 2.58/1.96 tff(2751,plain,
% 2.58/1.96 ($false),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2750, 91, 2630, 1686, 2642, 2641, 2640, 2639, 2629, 1682, 23, 1681])).
% 2.58/1.96 tff(2752,plain,((~hskp10) | (~c0_1(a1441)) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c2_1(a1441))), inference(lemma,lemma(discharge,[]))).
% 2.58/1.96 tff(2753,plain,
% 2.58/1.96 (~hskp10),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2752, 1686, 2743, 2742, 2741, 1682, 2739])).
% 2.58/1.96 tff(2754,plain,
% 2.58/1.96 (hskp1),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2502, 701, 2753])).
% 2.58/1.96 tff(2755,assumption,(~c1_1(a1431)), introduced(assumption)).
% 2.58/1.96 tff(2756,plain,
% 2.58/1.96 (~hskp3),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[953, 2755])).
% 2.58/1.96 tff(2757,assumption,(~hskp0), introduced(assumption)).
% 2.58/1.96 tff(2758,plain,
% 2.58/1.96 (((~![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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2759,plain,
% 2.58/1.96 ((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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2760,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2759])).
% 2.58/1.96 tff(2761,plain,
% 2.58/1.96 (((~![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))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2760, 2758])).
% 2.58/1.96 tff(2762,plain,
% 2.58/1.96 ((~![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))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2763,plain,
% 2.58/1.96 ((~![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)),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 2.58/1.96 tff(2764,plain,
% 2.58/1.96 (~c1_1(a1429)),
% 2.58/1.96 inference(unit_resolution,[status(thm)],[2763, 91, 874, 2478, 759, 760, 2477, 873, 2390])).
% 2.58/1.96 tff(2765,plain,
% 2.58/1.96 (^[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))))),
% 2.58/1.96 inference(bind,[status(th)],[])).
% 2.58/1.96 tff(2766,plain,
% 2.58/1.96 (![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)))),
% 2.58/1.96 inference(quant_intro,[status(thm)],[2765])).
% 2.58/1.96 tff(2767,plain,
% 2.58/1.96 (![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)))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2768,plain,
% 2.58/1.96 (^[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)))))),
% 2.58/1.96 inference(bind,[status(th)],[])).
% 2.58/1.96 tff(2769,plain,
% 2.58/1.96 (![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)))),
% 2.58/1.96 inference(quant_intro,[status(thm)],[2768])).
% 2.58/1.96 tff(2770,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 2.58/1.96 tff(2771,plain,
% 2.58/1.96 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 2.58/1.96 tff(2772,plain,
% 2.58/1.96 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2771, 2767])).
% 2.58/1.96 tff(2773,plain,(
% 2.58/1.96 ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.58/1.96 inference(skolemize,[status(sab)],[2772])).
% 2.58/1.96 tff(2774,plain,
% 2.58/1.96 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.58/1.96 inference(modus_ponens,[status(thm)],[2773, 2766])).
% 2.58/1.96 tff(2775,plain,
% 2.58/1.96 (((~![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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2776,plain,
% 2.58/1.96 ((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))),
% 2.58/1.96 inference(rewrite,[status(thm)],[])).
% 2.58/1.96 tff(2777,plain,
% 2.58/1.96 (((~![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)))),
% 2.58/1.96 inference(monotonicity,[status(thm)],[2776])).
% 2.58/1.96 tff(2778,plain,
% 2.58/1.96 (((~![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))),
% 2.58/1.96 inference(transitivity,[status(thm)],[2777, 2775])).
% 2.58/1.96 tff(2779,plain,
% 2.58/1.96 ((~![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)))),
% 2.58/1.96 inference(quant_inst,[status(thm)],[])).
% 2.58/1.96 tff(2780,plain,
% 2.58/1.96 ((~![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)),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 2.58/1.97 tff(2781,plain,
% 2.58/1.97 (hskp4 | c1_1(a1429)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2780, 91, 2757, 2479, 2477, 2774])).
% 2.58/1.97 tff(2782,plain,
% 2.58/1.97 (hskp4),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2781, 2764])).
% 2.58/1.97 tff(2783,plain,
% 2.58/1.97 (~c2_1(a1434)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[137, 2782])).
% 2.58/1.97 tff(2784,plain,
% 2.58/1.97 (c3_1(a1434)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[161, 2782])).
% 2.58/1.97 tff(2785,plain,
% 2.58/1.97 (c1_1(a1434)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[150, 2782])).
% 2.58/1.97 tff(2786,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2787,plain,
% 2.58/1.97 ((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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2788,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2787])).
% 2.58/1.97 tff(2789,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2788, 2786])).
% 2.58/1.97 tff(2790,plain,
% 2.58/1.97 ((~![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)))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2791,plain,
% 2.58/1.97 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1434) | c0_1(a1429) | (~ndr1_0) | (~c2_1(a1429)) | (~c3_1(a1429)) | (~c1_1(a1434)) | (~c3_1(a1434))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 2.58/1.97 tff(2792,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2791, 91, 701, 2785, 2784, 2479, 2478, 2783, 2477, 1363])).
% 2.58/1.97 tff(2793,plain,((~hskp1) | hskp12 | hskp0 | hskp3 | c0_1(a1447) | c3_1(a1447) | c1_1(a1447)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.97 tff(2794,plain,
% 2.58/1.97 (~hskp1),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2793, 2757, 701, 2756, 759, 760, 2390])).
% 2.58/1.97 tff(2795,plain,
% 2.58/1.97 (hskp10),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2502, 2794, 701])).
% 2.58/1.97 tff(2796,plain,
% 2.58/1.97 (~c3_1(a1445)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[439, 2795])).
% 2.58/1.97 tff(2797,plain,
% 2.58/1.97 (~c1_1(a1445)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[445, 2795])).
% 2.58/1.97 tff(2798,plain,
% 2.58/1.97 (c0_1(a1445)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[456, 2795])).
% 2.58/1.97 tff(2799,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2800,plain,
% 2.58/1.97 (((~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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2801,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2800])).
% 2.58/1.97 tff(2802,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2801, 2799])).
% 2.58/1.97 tff(2803,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2804,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 2.58/1.97 tff(2805,plain,
% 2.58/1.97 (~c2_1(a1445)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2804, 91, 2798, 2755, 2797, 2796, 2507, 2473, 23])).
% 2.58/1.97 tff(2806,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2807,plain,
% 2.58/1.97 ((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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2808,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2807])).
% 2.58/1.97 tff(2809,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2808, 2806])).
% 2.58/1.97 tff(2810,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2811,plain,
% 2.58/1.97 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c0_1(a1445))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 2.58/1.97 tff(2812,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2811, 91, 2757, 2798, 2642, 2641, 2640, 2796, 1201, 2805])).
% 2.58/1.97 tff(2813,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,[]))).
% 2.58/1.97 tff(2814,plain,
% 2.58/1.97 (hskp0),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2813, 2507, 2641, 2640, 2755, 2642, 2473, 701, 759, 760, 2390])).
% 2.58/1.97 tff(2815,plain,
% 2.58/1.97 (c2_1(a1427)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[1224, 2814])).
% 2.58/1.97 tff(2816,plain,
% 2.58/1.97 (c0_1(a1427)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[1235, 2814])).
% 2.58/1.97 tff(2817,plain,
% 2.58/1.97 (((~![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(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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2818,plain,
% 2.58/1.97 (((~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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2819,plain,
% 2.58/1.97 (((~![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(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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2818])).
% 2.58/1.97 tff(2820,plain,
% 2.58/1.97 (((~![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(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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2819, 2817])).
% 2.58/1.97 tff(2821,plain,
% 2.58/1.97 ((~![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(a1441) | (~c3_1(a1441)) | (~c2_1(a1441)) | c1_1(a1438) | c2_1(a1438) | (~c3_1(a1438)))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2822,plain,
% 2.58/1.97 ((~![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(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))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 2.58/1.97 tff(2823,plain,
% 2.58/1.97 (~c1_1(a1427)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2822, 91, 1685, 1299, 2816, 2815, 1682, 24, 1706, 50, 1681])).
% 2.58/1.97 tff(2824,plain,
% 2.58/1.97 (~c3_1(a1427)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[1213, 2814])).
% 2.58/1.97 tff(2825,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2826,plain,
% 2.58/1.97 (((~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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2827,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2826])).
% 2.58/1.97 tff(2828,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2827, 2825])).
% 2.58/1.97 tff(2829,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2830,plain,
% 2.58/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c1_1(a1441) | c0_1(a1431) | c2_1(a1431) | c3_1(a1427) | (~ndr1_0) | c1_1(a1427) | (~c0_1(a1427)) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 2.58/1.97 tff(2831,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2830, 91, 1686, 2755, 2816, 1682, 2507, 2473, 2824, 23, 1681, 2823])).
% 2.58/1.97 tff(2832,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,[]))).
% 2.58/1.97 tff(2833,plain,
% 2.58/1.97 (c0_1(a1431)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2832, 2755, 1686, 1682, 2473, 2739, 1685, 1299, 24, 50, 2742, 2741, 2743, 701, 2736, 2734, 2738])).
% 2.58/1.97 tff(2834,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2835,plain,
% 2.58/1.97 ((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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2836,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2835])).
% 2.58/1.97 tff(2837,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2836, 2834])).
% 2.58/1.97 tff(2838,plain,
% 2.58/1.97 ((~![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)))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2839,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 2.58/1.97 tff(2840,plain,
% 2.58/1.97 ((~c0_1(a1431)) | (~c3_1(a1431))),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2839, 91, 11, 1299, 37, 24, 2473, 10])).
% 2.58/1.97 tff(2841,plain,
% 2.58/1.97 (~c3_1(a1431)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2840, 2833])).
% 2.58/1.97 tff(2842,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2843,plain,
% 2.58/1.97 (((~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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2844,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2843])).
% 2.58/1.97 tff(2845,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2844, 2842])).
% 2.58/1.97 tff(2846,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2847,plain,
% 2.58/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1431) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c1_1(a1441) | (~c0_1(a1431)) | (~ndr1_0) | c3_1(a1431) | (~c2_1(a1441)) | (~c0_1(a1441))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 2.58/1.97 tff(2848,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2847, 91, 1686, 2755, 2743, 2742, 2741, 1682, 2833, 23, 2841, 2739])).
% 2.58/1.97 tff(2849,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,[]))).
% 2.58/1.97 tff(2850,plain,
% 2.58/1.97 (c1_1(a1431)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2849, 2473, 1682, 11, 1299, 37, 24, 1686, 1685, 50, 701])).
% 2.58/1.97 tff(2851,plain,
% 2.58/1.97 (c3_1(a1431)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2466, 91, 2850, 2736, 2735, 2734, 2473, 2459, 2738])).
% 2.58/1.97 tff(2852,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2853,plain,
% 2.58/1.97 ((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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2854,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2853])).
% 2.58/1.97 tff(2855,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(transitivity,[status(thm)],[2854, 2852])).
% 2.58/1.97 tff(2856,plain,
% 2.58/1.97 ((~![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))),
% 2.58/1.97 inference(quant_inst,[status(thm)],[])).
% 2.58/1.97 tff(2857,plain,
% 2.58/1.97 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a1447) | c2_1(a1447) | c3_1(a1447) | c2_1(a1431) | (~ndr1_0) | (~c1_1(a1431)) | (~c3_1(a1431))),
% 2.58/1.97 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 2.58/1.97 tff(2858,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2857, 91, 2744, 2850, 2736, 2735, 2734, 2473, 2440, 2851])).
% 2.58/1.97 tff(2859,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,[]))).
% 2.58/1.97 tff(2860,plain,
% 2.58/1.97 (c2_1(a1431)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2859, 701, 11, 1299, 37, 24, 1686, 1685, 50, 1682])).
% 2.58/1.97 tff(2861,plain,
% 2.58/1.97 (~hskp3),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[928, 2860])).
% 2.58/1.97 tff(2862,plain,
% 2.58/1.97 ($false),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2793, 2861, 2754, 2744, 701, 2736, 2734, 2738])).
% 2.58/1.97 tff(2863,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,[]))).
% 2.58/1.97 tff(2864,plain,
% 2.58/1.97 (hskp12),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[2863, 2687, 2680, 37, 24, 11, 2686, 50, 2698])).
% 2.58/1.97 tff(2865,plain,
% 2.58/1.97 (~c2_1(a1448)),
% 2.58/1.97 inference(unit_resolution,[status(thm)],[220, 2864])).
% 2.58/1.97 tff(2866,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2867,plain,
% 2.58/1.97 ((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)))),
% 2.58/1.97 inference(rewrite,[status(thm)],[])).
% 2.58/1.97 tff(2868,plain,
% 2.58/1.97 (((~![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))))),
% 2.58/1.97 inference(monotonicity,[status(thm)],[2867])).
% 2.58/1.97 tff(2869,plain,
% 2.58/1.97 (((~![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)))),
% 2.58/1.98 inference(transitivity,[status(thm)],[2868, 2866])).
% 2.58/1.98 tff(2870,plain,
% 2.58/1.98 ((~![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)))),
% 2.58/1.98 inference(quant_inst,[status(thm)],[])).
% 2.58/1.98 tff(2871,plain,
% 2.58/1.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a1448) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.58/1.98 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 2.58/1.98 tff(2872,plain,
% 2.58/1.98 (hskp5 | c1_1(a1430) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2871, 91, 2343, 254, 12, 10])).
% 2.58/1.98 tff(2873,plain,
% 2.58/1.98 ($false),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2872, 243, 232, 11, 592])).
% 2.58/1.98 tff(2874,plain,((~hskp12) | hskp5 | c1_1(a1430) | (~c3_1(a1430)) | c2_1(a1448) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.98 tff(2875,plain,
% 2.58/1.98 ($false),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2874, 2865, 2864, 12, 2185, 2731, 11])).
% 2.58/1.98 tff(2876,plain,(c2_1(a1438) | c0_1(a1430) | hskp5 | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.98 tff(2877,plain,
% 2.58/1.98 (c2_1(a1438)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2876, 37, 11, 12, 24])).
% 2.58/1.98 tff(2878,assumption,(hskp8), introduced(assumption)).
% 2.58/1.98 tff(2879,plain,
% 2.58/1.98 (c3_1(a1441)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[1662, 2878])).
% 2.58/1.98 tff(2880,plain,
% 2.58/1.98 (c0_1(a1441)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[1673, 2878])).
% 2.58/1.98 tff(2881,plain,
% 2.58/1.98 (c2_1(a1441)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2696, 2880, 11, 2879, 1299, 37, 24])).
% 2.58/1.98 tff(2882,plain,
% 2.58/1.98 (~c1_1(a1441)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[1651, 2878])).
% 2.58/1.98 tff(2883,plain,
% 2.58/1.98 (((~![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)))),
% 2.58/1.98 inference(rewrite,[status(thm)],[])).
% 2.58/1.98 tff(2884,plain,
% 2.58/1.98 (((~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)))),
% 2.58/1.98 inference(rewrite,[status(thm)],[])).
% 2.58/1.98 tff(2885,plain,
% 2.58/1.98 (((~![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))))),
% 2.58/1.98 inference(monotonicity,[status(thm)],[2884])).
% 2.58/1.98 tff(2886,plain,
% 2.58/1.98 (((~![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)))),
% 2.58/1.98 inference(transitivity,[status(thm)],[2885, 2883])).
% 2.58/1.98 tff(2887,plain,
% 2.58/1.98 ((~![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)))),
% 2.58/1.98 inference(quant_inst,[status(thm)],[])).
% 2.58/1.98 tff(2888,plain,
% 2.58/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1441) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c2_1(a1441)) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 2.58/1.98 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 2.58/1.98 tff(2889,plain,
% 2.58/1.98 ($false),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2888, 91, 2880, 2879, 2882, 37, 24, 1298, 822, 2881])).
% 2.58/1.98 tff(2890,plain,((~hskp8) | c0_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp5 | (~c3_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.58/1.98 tff(2891,plain,
% 2.58/1.98 (~hskp8),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[2890, 37, 24, 2877, 11, 2680])).
% 2.58/1.98 tff(2892,assumption,(hskp14), introduced(assumption)).
% 2.58/1.98 tff(2893,plain,
% 2.58/1.98 (~c3_1(a1451)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[547, 2892])).
% 2.58/1.98 tff(2894,plain,
% 2.58/1.98 (~c1_1(a1451)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[553, 2892])).
% 2.58/1.98 tff(2895,plain,
% 2.58/1.98 (c2_1(a1451)),
% 2.58/1.98 inference(unit_resolution,[status(thm)],[564, 2892])).
% 2.58/1.98 tff(2896,plain,
% 2.58/1.98 (((~![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)))),
% 2.58/1.98 inference(rewrite,[status(thm)],[])).
% 2.58/1.98 tff(2897,plain,
% 2.58/1.98 ((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)))),
% 2.58/1.98 inference(rewrite,[status(thm)],[])).
% 2.58/1.98 tff(2898,plain,
% 2.58/1.98 (((~![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))))),
% 2.58/1.98 inference(monotonicity,[status(thm)],[2897])).
% 2.58/1.98 tff(2899,plain,
% 2.58/1.98 (((~![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)))),
% 2.58/1.98 inference(transitivity,[status(thm)],[2898, 2896])).
% 2.58/1.98 tff(2900,plain,
% 2.58/1.98 ((~![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)))),
% 2.58/1.98 inference(quant_inst,[status(thm)],[])).
% 2.58/1.98 tff(2901,plain,
% 2.58/1.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a1451) | c3_1(a1451) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1451))),
% 2.58/1.98 inference(modus_ponens,[status(thm)],[2900, 2899])).
% 2.58/1.98 tff(2902,plain,
% 2.58/1.98 ($false),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2901, 91, 11, 2895, 1299, 2894, 2893, 37, 24, 848])).
% 2.62/1.98 tff(2903,plain,((~hskp14) | hskp5 | (~c3_1(a1438)) | c0_1(a1438) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/1.98 tff(2904,plain,
% 2.62/1.98 (~hskp14),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2903, 37, 2680, 11, 24])).
% 2.62/1.98 tff(2905,plain,
% 2.62/1.98 (hskp12),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2363, 2904, 2891])).
% 2.62/1.98 tff(2906,plain,
% 2.62/1.98 (~c2_1(a1448)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[220, 2905])).
% 2.62/1.98 tff(2907,plain,
% 2.62/1.98 (c1_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2874, 2906, 12, 2185, 2905, 11])).
% 2.62/1.98 tff(2908,plain,
% 2.62/1.98 (c2_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2385, 2891, 12, 11])).
% 2.62/1.98 tff(2909,plain,
% 2.62/1.98 ((hskp19 | hskp14 | hskp8) <=> (hskp19 | hskp14 | hskp8)),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2910,plain,
% 2.62/1.98 (((hskp14 | hskp8) | hskp19) <=> (hskp19 | hskp14 | hskp8)),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2911,plain,
% 2.62/1.98 ((hskp8 | hskp14) <=> (hskp14 | hskp8)),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2912,plain,
% 2.62/1.98 (((hskp8 | hskp14) | hskp19) <=> ((hskp14 | hskp8) | hskp19)),
% 2.62/1.98 inference(monotonicity,[status(thm)],[2911])).
% 2.62/1.98 tff(2913,plain,
% 2.62/1.98 (((hskp8 | hskp14) | hskp19) <=> (hskp19 | hskp14 | hskp8)),
% 2.62/1.98 inference(transitivity,[status(thm)],[2912, 2910])).
% 2.62/1.98 tff(2914,axiom,((hskp8 | hskp14) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 2.62/1.98 tff(2915,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 2.62/1.98 tff(2916,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2915, 2909])).
% 2.62/1.98 tff(2917,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2916, 2909])).
% 2.62/1.98 tff(2918,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2917, 2909])).
% 2.62/1.98 tff(2919,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2918, 2909])).
% 2.62/1.98 tff(2920,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2919, 2909])).
% 2.62/1.98 tff(2921,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2920, 2909])).
% 2.62/1.98 tff(2922,plain,
% 2.62/1.98 (hskp19 | hskp14 | hskp8),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2921, 2909])).
% 2.62/1.98 tff(2923,plain,
% 2.62/1.98 (hskp19),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2922, 2904, 2891])).
% 2.62/1.98 tff(2924,plain,
% 2.62/1.98 (~c3_1(a1460)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1249, 2923])).
% 2.62/1.98 tff(2925,plain,
% 2.62/1.98 (~c0_1(a1460)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1255, 2923])).
% 2.62/1.98 tff(2926,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2927,plain,
% 2.62/1.98 ((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)))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2928,plain,
% 2.62/1.98 (((~![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))))),
% 2.62/1.98 inference(monotonicity,[status(thm)],[2927])).
% 2.62/1.98 tff(2929,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(transitivity,[status(thm)],[2928, 2926])).
% 2.62/1.98 tff(2930,plain,
% 2.62/1.98 ((~![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)))),
% 2.62/1.98 inference(quant_inst,[status(thm)],[])).
% 2.62/1.98 tff(2931,plain,
% 2.62/1.98 ((~![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))),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 2.62/1.98 tff(2932,plain,
% 2.62/1.98 (~c2_1(a1460)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2931, 91, 2904, 2925, 2924, 12, 2908, 524, 2907])).
% 2.62/1.98 tff(2933,plain,
% 2.62/1.98 (hskp17),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[263, 2906, 11, 2905])).
% 2.62/1.98 tff(2934,plain,
% 2.62/1.98 (~c1_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[269, 2933])).
% 2.62/1.98 tff(2935,plain,
% 2.62/1.98 (~c0_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[275, 2933])).
% 2.62/1.98 tff(2936,plain,
% 2.62/1.98 (c3_1(a1448)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[242, 2905])).
% 2.62/1.98 tff(2937,plain,
% 2.62/1.98 (c0_1(a1448)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[231, 2905])).
% 2.62/1.98 tff(2938,plain,
% 2.62/1.98 (~c3_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[282, 91, 11, 2937, 2936, 2935, 2934, 2906, 10])).
% 2.62/1.98 tff(2939,plain,
% 2.62/1.98 (~c2_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[288, 2933])).
% 2.62/1.98 tff(2940,plain,
% 2.62/1.98 (~hskp2),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2296, 2908])).
% 2.62/1.98 tff(2941,plain,
% 2.62/1.98 (((~![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))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2942,plain,
% 2.62/1.98 ((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))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2943,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(monotonicity,[status(thm)],[2942])).
% 2.62/1.98 tff(2944,plain,
% 2.62/1.98 (((~![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))),
% 2.62/1.98 inference(transitivity,[status(thm)],[2943, 2941])).
% 2.62/1.98 tff(2945,plain,
% 2.62/1.98 ((~![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))),
% 2.62/1.98 inference(quant_inst,[status(thm)],[])).
% 2.62/1.98 tff(2946,plain,
% 2.62/1.98 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp2 | c0_1(a1460) | c3_1(a1460) | c1_1(a1457) | c2_1(a1457) | (~ndr1_0) | c3_1(a1457) | c2_1(a1460)),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 2.62/1.98 tff(2947,plain,
% 2.62/1.98 ($false),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2946, 91, 2940, 2925, 2924, 2934, 2939, 60, 2938, 2932])).
% 2.62/1.98 tff(2948,plain,(c0_1(a1438) | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/1.98 tff(2949,plain,
% 2.62/1.98 (c0_1(a1438)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2948, 24, 11, 12])).
% 2.62/1.98 tff(2950,plain,
% 2.62/1.98 (c1_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2253, 1736, 11, 12])).
% 2.62/1.98 tff(2951,plain,
% 2.62/1.98 (hskp2),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1778, 50, 1724, 11, 1299])).
% 2.62/1.98 tff(2952,plain,
% 2.62/1.98 (~c2_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2296, 2951])).
% 2.62/1.98 tff(2953,plain,
% 2.62/1.98 (hskp11),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2304, 2952, 2185, 11])).
% 2.62/1.98 tff(2954,plain,
% 2.62/1.98 (~c3_1(a1447)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[757, 2953])).
% 2.62/1.98 tff(2955,plain,
% 2.62/1.98 (~c2_1(a1447)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[745, 2953])).
% 2.62/1.98 tff(2956,plain,
% 2.62/1.98 (~c1_1(a1447)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2313, 91, 1736, 2185, 2955, 2954, 2952, 172, 2950])).
% 2.62/1.98 tff(2957,plain,
% 2.62/1.98 (hskp17 | (~c0_1(a1438)) | c2_1(a1438)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1764, 91, 11, 1299, 253])).
% 2.62/1.98 tff(2958,plain,
% 2.62/1.98 (hskp17),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2957, 50, 1724])).
% 2.62/1.98 tff(2959,plain,
% 2.62/1.98 (~c0_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[275, 2958])).
% 2.62/1.98 tff(2960,plain,
% 2.62/1.98 (~c2_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[288, 2958])).
% 2.62/1.98 tff(2961,plain,
% 2.62/1.98 (~c1_1(a1457)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[269, 2958])).
% 2.62/1.98 tff(2962,plain,
% 2.62/1.98 (~c0_1(a1447)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[751, 2953])).
% 2.62/1.98 tff(2963,plain,
% 2.62/1.98 (((~![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))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2964,plain,
% 2.62/1.98 ((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))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2965,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(monotonicity,[status(thm)],[2964])).
% 2.62/1.98 tff(2966,plain,
% 2.62/1.98 (((~![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))),
% 2.62/1.98 inference(transitivity,[status(thm)],[2965, 2963])).
% 2.62/1.98 tff(2967,plain,
% 2.62/1.98 ((~![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))),
% 2.62/1.98 inference(quant_inst,[status(thm)],[])).
% 2.62/1.98 tff(2968,plain,
% 2.62/1.98 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1447) | c3_1(a1447) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1447)),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 2.62/1.98 tff(2969,plain,
% 2.62/1.98 (hskp3),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2968, 91, 2185, 2962, 2954, 12, 873, 2950, 2956])).
% 2.62/1.98 tff(2970,plain,
% 2.62/1.98 (c1_1(a1431)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[953, 2969])).
% 2.62/1.98 tff(2971,plain,
% 2.62/1.98 (~c2_1(a1431)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[928, 2969])).
% 2.62/1.98 tff(2972,plain,
% 2.62/1.98 (c3_1(a1431)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2466, 91, 2970, 2962, 2955, 2954, 2971, 2459, 2956])).
% 2.62/1.98 tff(2973,plain,
% 2.62/1.98 (hskp10),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2504, 2972, 2971, 701, 2970])).
% 2.62/1.98 tff(2974,plain,
% 2.62/1.98 (hskp29),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2644, 2973, 2961, 2960, 2959, 11])).
% 2.62/1.98 tff(2975,plain,
% 2.62/1.98 (c3_1(a1483)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1062, 2974])).
% 2.62/1.98 tff(2976,plain,
% 2.62/1.98 (c2_1(a1483)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1073, 2974])).
% 2.62/1.98 tff(2977,plain,
% 2.62/1.98 (c1_1(a1483)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1084, 2974])).
% 2.62/1.98 tff(2978,plain,
% 2.62/1.98 ($false),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2654, 91, 1736, 2977, 2976, 2975, 2955, 2954, 678, 2956])).
% 2.62/1.98 tff(2979,plain,(c2_1(a1438) | hskp5 | hskp12 | c0_1(a1430) | (~c0_1(a1438)) | (~c3_1(a1438))), inference(lemma,lemma(discharge,[]))).
% 2.62/1.98 tff(2980,plain,
% 2.62/1.98 (c2_1(a1438)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2979, 701, 11, 12, 2949, 2680])).
% 2.62/1.98 tff(2981,plain,
% 2.62/1.98 (hskp2),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[793, 761, 760, 759, 11])).
% 2.62/1.98 tff(2982,plain,
% 2.62/1.98 (~c2_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2296, 2981])).
% 2.62/1.98 tff(2983,plain,
% 2.62/1.98 (~hskp7),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[1099, 2949])).
% 2.62/1.98 tff(2984,plain,
% 2.62/1.98 (c1_1(a1430)),
% 2.62/1.98 inference(unit_resolution,[status(thm)],[2253, 2983, 11, 12])).
% 2.62/1.98 tff(2985,plain,
% 2.62/1.98 (^[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))))),
% 2.62/1.98 inference(bind,[status(th)],[])).
% 2.62/1.98 tff(2986,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(quant_intro,[status(thm)],[2985])).
% 2.62/1.98 tff(2987,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2988,plain,
% 2.62/1.98 (^[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)))))),
% 2.62/1.98 inference(bind,[status(th)],[])).
% 2.62/1.98 tff(2989,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(quant_intro,[status(thm)],[2988])).
% 2.62/1.98 tff(2990,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')).
% 2.62/1.98 tff(2991,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 2.62/1.98 tff(2992,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2991, 2987])).
% 2.62/1.98 tff(2993,plain,(
% 2.62/1.98 ![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)))),
% 2.62/1.98 inference(skolemize,[status(sab)],[2992])).
% 2.62/1.98 tff(2994,plain,
% 2.62/1.98 (![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)))),
% 2.62/1.98 inference(modus_ponens,[status(thm)],[2993, 2986])).
% 2.62/1.98 tff(2995,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2996,plain,
% 2.62/1.98 ((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)))),
% 2.62/1.98 inference(rewrite,[status(thm)],[])).
% 2.62/1.98 tff(2997,plain,
% 2.62/1.98 (((~![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))))),
% 2.62/1.98 inference(monotonicity,[status(thm)],[2996])).
% 2.62/1.98 tff(2998,plain,
% 2.62/1.98 (((~![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)))),
% 2.62/1.98 inference(transitivity,[status(thm)],[2997, 2995])).
% 2.62/1.98 tff(2999,plain,
% 2.62/1.98 ((~![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)))),
% 2.62/1.98 inference(quant_inst,[status(thm)],[])).
% 2.62/1.98 tff(3000,plain,
% 2.62/1.98 ((~![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))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 2.62/1.99 tff(3001,plain,
% 2.62/1.99 (hskp18),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3000, 91, 2680, 2185, 2949, 12, 2994, 2984, 2980])).
% 2.62/1.99 tff(3002,plain,
% 2.62/1.99 (~c2_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[403, 3001])).
% 2.62/1.99 tff(3003,plain,
% 2.62/1.99 (c1_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[414, 3001])).
% 2.62/1.99 tff(3004,plain,
% 2.62/1.99 (c0_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[425, 3001])).
% 2.62/1.99 tff(3005,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3006,plain,
% 2.62/1.99 ((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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3007,plain,
% 2.62/1.99 (((~![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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3006])).
% 2.62/1.99 tff(3008,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3007, 3005])).
% 2.62/1.99 tff(3009,plain,
% 2.62/1.99 ((~![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)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3010,plain,
% 2.62/1.99 ((~![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))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 2.62/1.99 tff(3011,plain,
% 2.62/1.99 (hskp10),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3010, 91, 3004, 3003, 2185, 3002, 12, 2982, 369])).
% 2.62/1.99 tff(3012,plain,
% 2.62/1.99 (~c3_1(a1445)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[439, 3011])).
% 2.62/1.99 tff(3013,plain,
% 2.62/1.99 (~c1_1(a1445)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[445, 3011])).
% 2.62/1.99 tff(3014,plain,
% 2.62/1.99 (c0_1(a1445)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[456, 3011])).
% 2.62/1.99 tff(3015,plain,
% 2.62/1.99 (((~![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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3016,plain,
% 2.62/1.99 (((~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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3017,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3016])).
% 2.62/1.99 tff(3018,plain,
% 2.62/1.99 (((~![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))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3017, 3015])).
% 2.62/1.99 tff(3019,plain,
% 2.62/1.99 ((~![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))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3020,plain,
% 2.62/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1447) | c2_1(a1447) | c1_1(a1445) | c3_1(a1445) | (~c0_1(a1438)) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c0_1(a1445)) | c1_1(a1447)),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 2.62/1.99 tff(3021,plain,
% 2.62/1.99 ($false),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3020, 91, 3014, 759, 761, 3013, 3012, 2949, 24, 23, 2980, 2186])).
% 2.62/1.99 tff(3022,plain,(c2_1(a1447) | c0_1(a1447) | c1_1(a1438) | c0_1(a1430) | hskp12 | c3_1(a1447) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.62/1.99 tff(3023,plain,
% 2.62/1.99 (c2_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3022, 759, 24, 12, 701, 760, 11])).
% 2.62/1.99 tff(3024,plain,
% 2.62/1.99 (~hskp11),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[745, 3023])).
% 2.62/1.99 tff(3025,plain,
% 2.62/1.99 (c2_1(a1430)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[2304, 3024, 2185, 11])).
% 2.62/1.99 tff(3026,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3027,plain,
% 2.62/1.99 ((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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3028,plain,
% 2.62/1.99 (((~![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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3027])).
% 2.62/1.99 tff(3029,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3028, 3026])).
% 2.62/1.99 tff(3030,plain,
% 2.62/1.99 ((~![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)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3031,plain,
% 2.62/1.99 ((~![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))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 2.62/1.99 tff(3032,plain,
% 2.62/1.99 ((~c2_1(a1430)) | (~c3_1(a1458))),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3031, 91, 701, 3003, 2185, 3002, 12, 1363])).
% 2.62/1.99 tff(3033,plain,
% 2.62/1.99 (~c3_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3032, 3025])).
% 2.62/1.99 tff(3034,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3035,plain,
% 2.62/1.99 (((~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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3036,plain,
% 2.62/1.99 (((~![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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3035])).
% 2.62/1.99 tff(3037,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3036, 3034])).
% 2.62/1.99 tff(3038,plain,
% 2.62/1.99 ((~![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)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3039,plain,
% 2.62/1.99 ((~![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))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3038, 3037])).
% 2.62/1.99 tff(3040,plain,
% 2.62/1.99 ((~c2_1(a1447)) | (~c2_1(a1430)) | c1_1(a1447) | c3_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3039, 91, 3004, 3002, 760, 12, 203, 2984])).
% 2.62/1.99 tff(3041,plain,
% 2.62/1.99 (c1_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3040, 3025, 3023, 3033])).
% 2.62/1.99 tff(3042,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3043,plain,
% 2.62/1.99 ((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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3044,plain,
% 2.62/1.99 (((~![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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3043])).
% 2.62/1.99 tff(3045,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3044, 3042])).
% 2.62/1.99 tff(3046,plain,
% 2.62/1.99 ((~![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)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3047,plain,
% 2.62/1.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a1458) | c0_1(a1447) | c3_1(a1447) | (~ndr1_0) | (~c1_1(a1447)) | c3_1(a1458) | (~c1_1(a1458))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 2.62/1.99 tff(3048,plain,
% 2.62/1.99 (c0_1(a1447) | (~c1_1(a1447)) | c3_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3047, 91, 701, 3003, 3002, 760, 214])).
% 2.62/1.99 tff(3049,plain,
% 2.62/1.99 ($false),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3048, 3041, 3033, 759])).
% 2.62/1.99 tff(3050,plain,(c0_1(a1447) | hskp12 | c3_1(a1447) | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/1.99 tff(3051,plain,
% 2.62/1.99 (c0_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3050, 760, 701, 12, 11, 24])).
% 2.62/1.99 tff(3052,plain,
% 2.62/1.99 (~hskp11),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[751, 3051])).
% 2.62/1.99 tff(3053,plain,
% 2.62/1.99 (^[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))))),
% 2.62/1.99 inference(bind,[status(th)],[])).
% 2.62/1.99 tff(3054,plain,
% 2.62/1.99 (![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))) <=> ![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)))),
% 2.62/1.99 inference(quant_intro,[status(thm)],[3053])).
% 2.62/1.99 tff(3055,plain,
% 2.62/1.99 (![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))) <=> ![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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3056,plain,
% 2.62/1.99 (^[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)))))),
% 2.62/1.99 inference(bind,[status(th)],[])).
% 2.62/1.99 tff(3057,plain,
% 2.62/1.99 (![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)))),
% 2.62/1.99 inference(quant_intro,[status(thm)],[3056])).
% 2.62/1.99 tff(3058,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')).
% 2.62/1.99 tff(3059,plain,
% 2.62/1.99 (![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)))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 2.62/1.99 tff(3060,plain,
% 2.62/1.99 (![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)))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3059, 3055])).
% 2.62/1.99 tff(3061,plain,(
% 2.62/1.99 ![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)))),
% 2.62/1.99 inference(skolemize,[status(sab)],[3060])).
% 2.62/1.99 tff(3062,plain,
% 2.62/1.99 (![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)))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3061, 3054])).
% 2.62/1.99 tff(3063,plain,
% 2.62/1.99 (((~![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 | (~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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3064,plain,
% 2.62/1.99 ((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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3065,plain,
% 2.62/1.99 (((~![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(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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3064])).
% 2.62/1.99 tff(3066,plain,
% 2.62/1.99 (((~![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(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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3065, 3063])).
% 2.62/1.99 tff(3067,plain,
% 2.62/1.99 ((~![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(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1447) | c2_1(a1447) | (~c0_1(a1447)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3068,plain,
% 2.62/1.99 ((~![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 | (~c0_1(a1447)) | c2_1(a1447) | c3_1(a1447) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 2.62/1.99 tff(3069,plain,
% 2.62/1.99 (hskp11 | (~c0_1(a1447)) | c2_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3068, 91, 2680, 760, 2949, 3062, 2980])).
% 2.62/1.99 tff(3070,plain,
% 2.62/1.99 (c2_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3069, 3052, 3051])).
% 2.62/1.99 tff(3071,plain,
% 2.62/1.99 (((~![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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3072,plain,
% 2.62/1.99 ((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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3073,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3072])).
% 2.62/1.99 tff(3074,plain,
% 2.62/1.99 (((~![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))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3073, 3071])).
% 2.62/1.99 tff(3075,plain,
% 2.62/1.99 ((~![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)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3076,plain,
% 2.62/1.99 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c0_1(a1447)) | (~c2_1(a1447)) | c3_1(a1447) | (~ndr1_0)),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 2.62/1.99 tff(3077,plain,
% 2.62/1.99 (hskp11 | (~c0_1(a1447)) | (~c2_1(a1447))),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3076, 91, 701, 760, 1288])).
% 2.62/1.99 tff(3078,plain,
% 2.62/1.99 ($false),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3077, 3070, 3052, 3051])).
% 2.62/1.99 tff(3079,plain,(c3_1(a1447) | hskp12 | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/1.99 tff(3080,plain,
% 2.62/1.99 (c3_1(a1447)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3079, 701, 12, 11, 24])).
% 2.62/1.99 tff(3081,plain,
% 2.62/1.99 (~hskp11),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[757, 3080])).
% 2.62/1.99 tff(3082,plain,
% 2.62/1.99 (c2_1(a1430)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[2304, 3081, 2185, 11])).
% 2.62/1.99 tff(3083,plain,
% 2.62/1.99 (~c3_1(a1458)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3032, 3082])).
% 2.62/1.99 tff(3084,plain,
% 2.62/1.99 (((~![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(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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3085,plain,
% 2.62/1.99 ((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)))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3086,plain,
% 2.62/1.99 (((~![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(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))))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3085])).
% 2.62/1.99 tff(3087,plain,
% 2.62/1.99 (((~![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(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)))),
% 2.62/1.99 inference(transitivity,[status(thm)],[3086, 3084])).
% 2.62/1.99 tff(3088,plain,
% 2.62/1.99 ((~![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(a1438)) | (~c3_1(a1438)) | (~c0_1(a1438)) | c3_1(a1458) | c2_1(a1458) | (~c0_1(a1458)))),
% 2.62/1.99 inference(quant_inst,[status(thm)],[])).
% 2.62/1.99 tff(3089,plain,
% 2.62/1.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a1458) | (~c0_1(a1438)) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | c3_1(a1458) | (~c0_1(a1458))),
% 2.62/1.99 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 2.62/1.99 tff(3090,plain,
% 2.62/1.99 ($false),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3089, 91, 3081, 3004, 2680, 3002, 2949, 3062, 2980, 3083])).
% 2.62/1.99 tff(3091,plain,(hskp12 | c0_1(a1430) | hskp5 | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/1.99 tff(3092,plain,
% 2.62/1.99 (hskp12),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[3091, 24, 11, 12])).
% 2.62/1.99 tff(3093,plain,
% 2.62/1.99 (~c2_1(a1448)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[220, 3092])).
% 2.62/1.99 tff(3094,plain,
% 2.62/1.99 (hskp17),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[263, 3093, 11, 3092])).
% 2.62/1.99 tff(3095,plain,
% 2.62/1.99 (~c1_1(a1457)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[269, 3094])).
% 2.62/1.99 tff(3096,plain,
% 2.62/1.99 (~c0_1(a1457)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[275, 3094])).
% 2.62/1.99 tff(3097,plain,
% 2.62/1.99 (c3_1(a1448)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[242, 3092])).
% 2.62/1.99 tff(3098,plain,
% 2.62/1.99 (c0_1(a1448)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[231, 3092])).
% 2.62/1.99 tff(3099,plain,
% 2.62/1.99 (~c3_1(a1457)),
% 2.62/1.99 inference(unit_resolution,[status(thm)],[282, 91, 11, 3098, 3097, 3096, 3095, 3093, 10])).
% 2.62/1.99 tff(3100,plain,
% 2.62/1.99 (((~![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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3101,plain,
% 2.62/1.99 ((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))),
% 2.62/1.99 inference(rewrite,[status(thm)],[])).
% 2.62/1.99 tff(3102,plain,
% 2.62/1.99 (((~![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)))),
% 2.62/1.99 inference(monotonicity,[status(thm)],[3101])).
% 2.62/1.99 tff(3103,plain,
% 2.62/1.99 (((~![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))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3102, 3100])).
% 2.62/2.00 tff(3104,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3105,plain,
% 2.62/2.00 ((~![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)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3104, 3103])).
% 2.62/2.00 tff(3106,plain,
% 2.62/2.00 (hskp3),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3105, 91, 2185, 3096, 3095, 12, 873, 2984, 3099])).
% 2.62/2.00 tff(3107,plain,
% 2.62/2.00 (c1_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[953, 3106])).
% 2.62/2.00 tff(3108,plain,
% 2.62/2.00 (~c2_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[928, 3106])).
% 2.62/2.00 tff(3109,plain,
% 2.62/2.00 (~c2_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[288, 3094])).
% 2.62/2.00 tff(3110,plain,
% 2.62/2.00 (((~![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))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3111,plain,
% 2.62/2.00 (((~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))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3112,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3111])).
% 2.62/2.00 tff(3113,plain,
% 2.62/2.00 (((~![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))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3112, 3110])).
% 2.62/2.00 tff(3114,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3115,plain,
% 2.62/2.00 ((~![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)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 2.62/2.00 tff(3116,plain,
% 2.62/2.00 (c3_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3115, 91, 3107, 3096, 3095, 3109, 3108, 2459, 3099])).
% 2.62/2.00 tff(3117,plain,
% 2.62/2.00 (hskp2),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1018, 91, 3096, 3095, 3109, 60, 3099])).
% 2.62/2.00 tff(3118,plain,
% 2.62/2.00 (~c2_1(a1430)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2296, 3117])).
% 2.62/2.00 tff(3119,plain,
% 2.62/2.00 (hskp11),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2304, 3118, 2185, 11])).
% 2.62/2.00 tff(3120,plain,
% 2.62/2.00 (~c3_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[757, 3119])).
% 2.62/2.00 tff(3121,plain,
% 2.62/2.00 (~c2_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[745, 3119])).
% 2.62/2.00 tff(3122,plain,
% 2.62/2.00 (~c0_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[751, 3119])).
% 2.62/2.00 tff(3123,plain,
% 2.62/2.00 (hskp0),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2857, 91, 3107, 3122, 3121, 3120, 3108, 2440, 3116])).
% 2.62/2.00 tff(3124,plain,
% 2.62/2.00 (c2_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1224, 3123])).
% 2.62/2.00 tff(3125,plain,
% 2.62/2.00 (c0_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1235, 3123])).
% 2.62/2.00 tff(3126,plain,
% 2.62/2.00 (~c0_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[934, 3106])).
% 2.62/2.00 tff(3127,plain,
% 2.62/2.00 (~c3_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1213, 3123])).
% 2.62/2.00 tff(3128,plain,
% 2.62/2.00 (hskp10),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2626, 3127, 3116, 3126, 3108, 3125, 3124, 3107])).
% 2.62/2.00 tff(3129,plain,
% 2.62/2.00 (~c3_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[439, 3128])).
% 2.62/2.00 tff(3130,plain,
% 2.62/2.00 (~c1_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[445, 3128])).
% 2.62/2.00 tff(3131,plain,
% 2.62/2.00 (c0_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[456, 3128])).
% 2.62/2.00 tff(3132,plain,
% 2.62/2.00 (~c2_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[463, 91, 3131, 3096, 3095, 3109, 3130, 3129, 23])).
% 2.62/2.00 tff(3133,plain,
% 2.62/2.00 (hskp29),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2644, 3128, 3095, 3109, 3096, 11])).
% 2.62/2.00 tff(3134,plain,
% 2.62/2.00 (c3_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1062, 3133])).
% 2.62/2.00 tff(3135,plain,
% 2.62/2.00 (c2_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1073, 3133])).
% 2.62/2.00 tff(3136,plain,
% 2.62/2.00 (c1_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1084, 3133])).
% 2.62/2.00 tff(3137,plain,
% 2.62/2.00 (((~![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 | 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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3138,plain,
% 2.62/2.00 ((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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3139,plain,
% 2.62/2.00 (((~![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(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))))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3138])).
% 2.62/2.00 tff(3140,plain,
% 2.62/2.00 (((~![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(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)))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3139, 3137])).
% 2.62/2.00 tff(3141,plain,
% 2.62/2.00 ((~![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(a1483)) | (~c3_1(a1483)) | (~c1_1(a1483)) | c3_1(a1445) | c2_1(a1445) | c1_1(a1445))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3142,plain,
% 2.62/2.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp7 | c1_1(a1445) | c3_1(a1445) | (~ndr1_0) | c2_1(a1445) | (~c3_1(a1483)) | (~c2_1(a1483)) | (~c1_1(a1483))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3141, 3140])).
% 2.62/2.00 tff(3143,plain,
% 2.62/2.00 ($false),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3142, 91, 2983, 3136, 3135, 3134, 3130, 3129, 678, 3132])).
% 2.62/2.00 tff(3144,plain,(c1_1(a1438) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.00 tff(3145,plain,
% 2.62/2.00 (c1_1(a1438)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3144, 11, 12])).
% 2.62/2.00 tff(3146,plain,
% 2.62/2.00 (~hskp7),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1514, 3145])).
% 2.62/2.00 tff(3147,plain,
% 2.62/2.00 (c1_1(a1430)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2253, 3146, 11, 12])).
% 2.62/2.00 tff(3148,plain,
% 2.62/2.00 (hskp17),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[263, 221, 11, 215])).
% 2.62/2.00 tff(3149,plain,
% 2.62/2.00 (~c1_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[269, 3148])).
% 2.62/2.00 tff(3150,plain,
% 2.62/2.00 (~c0_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[275, 3148])).
% 2.62/2.00 tff(3151,plain,
% 2.62/2.00 (~c3_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[282, 91, 11, 232, 243, 3150, 3149, 221, 10])).
% 2.62/2.00 tff(3152,plain,
% 2.62/2.00 (hskp3),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3105, 91, 2185, 3150, 3149, 12, 873, 3147, 3151])).
% 2.62/2.00 tff(3153,plain,
% 2.62/2.00 (c1_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[953, 3152])).
% 2.62/2.00 tff(3154,plain,
% 2.62/2.00 (~c2_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[928, 3152])).
% 2.62/2.00 tff(3155,plain,
% 2.62/2.00 (~c2_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[288, 3148])).
% 2.62/2.00 tff(3156,plain,
% 2.62/2.00 (c3_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3115, 91, 3153, 3150, 3149, 3155, 3154, 2459, 3151])).
% 2.62/2.00 tff(3157,plain,
% 2.62/2.00 (hskp2),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1018, 91, 3150, 3149, 3155, 60, 3151])).
% 2.62/2.00 tff(3158,plain,
% 2.62/2.00 (~c2_1(a1430)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2296, 3157])).
% 2.62/2.00 tff(3159,plain,
% 2.62/2.00 (hskp11),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2304, 3158, 2185, 11])).
% 2.62/2.00 tff(3160,plain,
% 2.62/2.00 (~c3_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[757, 3159])).
% 2.62/2.00 tff(3161,plain,
% 2.62/2.00 (~c2_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[745, 3159])).
% 2.62/2.00 tff(3162,plain,
% 2.62/2.00 (~c0_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[751, 3159])).
% 2.62/2.00 tff(3163,plain,
% 2.62/2.00 (hskp0),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2857, 91, 3153, 3162, 3161, 3160, 3154, 2440, 3156])).
% 2.62/2.00 tff(3164,plain,
% 2.62/2.00 (c2_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1224, 3163])).
% 2.62/2.00 tff(3165,plain,
% 2.62/2.00 (c0_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1235, 3163])).
% 2.62/2.00 tff(3166,plain,
% 2.62/2.00 (~c0_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[934, 3152])).
% 2.62/2.00 tff(3167,plain,
% 2.62/2.00 (~c3_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1213, 3163])).
% 2.62/2.00 tff(3168,plain,
% 2.62/2.00 (hskp10),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2626, 3167, 3156, 3166, 3154, 3165, 3164, 3153])).
% 2.62/2.00 tff(3169,plain,
% 2.62/2.00 (~c3_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[439, 3168])).
% 2.62/2.00 tff(3170,plain,
% 2.62/2.00 (~c1_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[445, 3168])).
% 2.62/2.00 tff(3171,plain,
% 2.62/2.00 (c0_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[456, 3168])).
% 2.62/2.00 tff(3172,plain,
% 2.62/2.00 (~c2_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[463, 91, 3171, 3150, 3149, 3155, 3170, 3169, 23])).
% 2.62/2.00 tff(3173,plain,
% 2.62/2.00 (hskp29),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2644, 3168, 3149, 3155, 3150, 11])).
% 2.62/2.00 tff(3174,plain,
% 2.62/2.00 (c3_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1062, 3173])).
% 2.62/2.00 tff(3175,plain,
% 2.62/2.00 (c2_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1073, 3173])).
% 2.62/2.00 tff(3176,plain,
% 2.62/2.00 (c1_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1084, 3173])).
% 2.62/2.00 tff(3177,plain,
% 2.62/2.00 ($false),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3142, 91, 3146, 3176, 3175, 3174, 3170, 3169, 678, 3172])).
% 2.62/2.00 tff(3178,plain,((~hskp12) | hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.00 tff(3179,plain,
% 2.62/2.00 (~hskp12),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3178, 11, 12])).
% 2.62/2.00 tff(3180,plain,
% 2.62/2.00 (c2_1(a1430)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2304, 1300, 2185, 11])).
% 2.62/2.00 tff(3181,plain,
% 2.62/2.00 (^[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))))),
% 2.62/2.00 inference(bind,[status(th)],[])).
% 2.62/2.00 tff(3182,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(quant_intro,[status(thm)],[3181])).
% 2.62/2.00 tff(3183,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3184,plain,
% 2.62/2.00 (^[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)))))),
% 2.62/2.00 inference(bind,[status(th)],[])).
% 2.62/2.00 tff(3185,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(quant_intro,[status(thm)],[3184])).
% 2.62/2.00 tff(3186,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')).
% 2.62/2.00 tff(3187,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 2.62/2.00 tff(3188,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3187, 3183])).
% 2.62/2.00 tff(3189,plain,(
% 2.62/2.00 ![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)))),
% 2.62/2.00 inference(skolemize,[status(sab)],[3188])).
% 2.62/2.00 tff(3190,plain,
% 2.62/2.00 (![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)))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3189, 3182])).
% 2.62/2.00 tff(3191,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3192,plain,
% 2.62/2.00 ((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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3193,plain,
% 2.62/2.00 (((~![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))))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3192])).
% 2.62/2.00 tff(3194,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3193, 3191])).
% 2.62/2.00 tff(3195,plain,
% 2.62/2.00 ((~![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)))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3196,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 2.62/2.00 tff(3197,plain,
% 2.62/2.00 (hskp15 | (~c2_1(a1430)) | (~c1_1(a1430)) | (~c3_1(a1430))),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3196, 91, 12, 3190])).
% 2.62/2.00 tff(3198,plain,
% 2.62/2.00 (hskp15),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3197, 3180, 2185, 3147])).
% 2.62/2.00 tff(3199,plain,
% 2.62/2.00 (((~hskp15) | (~c3_1(a1452))) <=> ((~hskp15) | (~c3_1(a1452)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3200,plain,
% 2.62/2.00 (((~c3_1(a1452)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1452)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3201,axiom,((~c3_1(a1452)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 2.62/2.00 tff(3202,plain,
% 2.62/2.00 ((~hskp15) | (~c3_1(a1452))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 2.62/2.00 tff(3203,plain,
% 2.62/2.00 ((~hskp15) | (~c3_1(a1452))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3202, 3199])).
% 2.62/2.00 tff(3204,plain,
% 2.62/2.00 (~c3_1(a1452)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3203, 3198])).
% 2.62/2.00 tff(3205,plain,
% 2.62/2.00 (((~hskp15) | c0_1(a1452)) <=> ((~hskp15) | c0_1(a1452))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3206,axiom,((~hskp15) | c0_1(a1452)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 2.62/2.00 tff(3207,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 2.62/2.00 tff(3208,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3207, 3205])).
% 2.62/2.00 tff(3209,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3208, 3205])).
% 2.62/2.00 tff(3210,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3209, 3205])).
% 2.62/2.00 tff(3211,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3210, 3205])).
% 2.62/2.00 tff(3212,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3211, 3205])).
% 2.62/2.00 tff(3213,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3212, 3205])).
% 2.62/2.00 tff(3214,plain,
% 2.62/2.00 ((~hskp15) | c0_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3213, 3205])).
% 2.62/2.00 tff(3215,plain,
% 2.62/2.00 (c0_1(a1452)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3214, 3198])).
% 2.62/2.00 tff(3216,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3217,plain,
% 2.62/2.00 ((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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3218,plain,
% 2.62/2.00 (((~![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))))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3217])).
% 2.62/2.00 tff(3219,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3218, 3216])).
% 2.62/2.00 tff(3220,plain,
% 2.62/2.00 ((~![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)))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3221,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 2.62/2.00 tff(3222,plain,
% 2.62/2.00 (~c2_1(a1452)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3221, 91, 701, 1300, 3215, 3204, 1288])).
% 2.62/2.00 tff(3223,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3224,plain,
% 2.62/2.00 ((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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3225,plain,
% 2.62/2.00 (((~![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))))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3224])).
% 2.62/2.00 tff(3226,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3225, 3223])).
% 2.62/2.00 tff(3227,plain,
% 2.62/2.00 ((~![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)))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3228,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 2.62/2.00 tff(3229,plain,
% 2.62/2.00 (hskp16 | hskp7 | (~c2_1(a1430)) | (~c1_1(a1430))),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3228, 91, 12, 1889])).
% 2.62/2.00 tff(3230,plain,
% 2.62/2.00 (hskp16),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3229, 3180, 3146, 3147])).
% 2.62/2.00 tff(3231,plain,
% 2.62/2.00 (~c3_1(a1454)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1901, 3230])).
% 2.62/2.00 tff(3232,plain,
% 2.62/2.00 (~c0_1(a1454)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1907, 3230])).
% 2.62/2.00 tff(3233,plain,
% 2.62/2.00 (((~hskp15) | c1_1(a1452)) <=> ((~hskp15) | c1_1(a1452))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3234,axiom,((~hskp15) | c1_1(a1452)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 2.62/2.00 tff(3235,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 2.62/2.00 tff(3236,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3235, 3233])).
% 2.62/2.00 tff(3237,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3236, 3233])).
% 2.62/2.00 tff(3238,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3237, 3233])).
% 2.62/2.00 tff(3239,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3238, 3233])).
% 2.62/2.00 tff(3240,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3239, 3233])).
% 2.62/2.00 tff(3241,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3240, 3233])).
% 2.62/2.00 tff(3242,plain,
% 2.62/2.00 ((~hskp15) | c1_1(a1452)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3241, 3233])).
% 2.62/2.00 tff(3243,plain,
% 2.62/2.00 (c1_1(a1452)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3242, 3198])).
% 2.62/2.00 tff(3244,plain,
% 2.62/2.00 (c1_1(a1454)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1919, 3230])).
% 2.62/2.00 tff(3245,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3246,plain,
% 2.62/2.00 ((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)))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3247,plain,
% 2.62/2.00 (((~![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))))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3246])).
% 2.62/2.00 tff(3248,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3247, 3245])).
% 2.62/2.00 tff(3249,plain,
% 2.62/2.00 ((~![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)))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3250,plain,
% 2.62/2.00 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a1454) | c3_1(a1454) | c3_1(a1452) | (~ndr1_0) | c2_1(a1452) | (~c1_1(a1452)) | (~c1_1(a1454))),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 2.62/2.00 tff(3251,plain,
% 2.62/2.00 ($false),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3250, 91, 701, 3244, 3243, 3232, 3231, 3204, 214, 3222])).
% 2.62/2.00 tff(3252,plain,(hskp11 | hskp12 | c0_1(a1430) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.62/2.00 tff(3253,plain,
% 2.62/2.00 (hskp11),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3252, 3179, 12, 11])).
% 2.62/2.00 tff(3254,plain,
% 2.62/2.00 (hskp2),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[795, 3253, 11])).
% 2.62/2.00 tff(3255,plain,
% 2.62/2.00 (~c2_1(a1430)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2296, 3254])).
% 2.62/2.00 tff(3256,plain,
% 2.62/2.00 (~c3_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[757, 3253])).
% 2.62/2.00 tff(3257,plain,
% 2.62/2.00 (~c2_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[745, 3253])).
% 2.62/2.00 tff(3258,plain,
% 2.62/2.00 (~c1_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2313, 91, 3146, 2185, 3257, 3256, 3255, 172, 3147])).
% 2.62/2.00 tff(3259,plain,
% 2.62/2.00 (~c0_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[751, 3253])).
% 2.62/2.00 tff(3260,plain,
% 2.62/2.00 (hskp3),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2968, 91, 2185, 3259, 3256, 12, 873, 3147, 3258])).
% 2.62/2.00 tff(3261,plain,
% 2.62/2.00 (c1_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[953, 3260])).
% 2.62/2.00 tff(3262,plain,
% 2.62/2.00 (~c2_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[928, 3260])).
% 2.62/2.00 tff(3263,plain,
% 2.62/2.00 (c3_1(a1431)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2466, 91, 3261, 3259, 3257, 3256, 3262, 2459, 3258])).
% 2.62/2.00 tff(3264,plain,
% 2.62/2.00 (hskp10),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2504, 3263, 3179, 3262, 3261])).
% 2.62/2.00 tff(3265,plain,
% 2.62/2.00 (~c3_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[439, 3264])).
% 2.62/2.00 tff(3266,plain,
% 2.62/2.00 (~c1_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[445, 3264])).
% 2.62/2.00 tff(3267,plain,
% 2.62/2.00 (hskp8),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2385, 3255, 12, 11])).
% 2.62/2.00 tff(3268,plain,
% 2.62/2.00 (c3_1(a1441)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1662, 3267])).
% 2.62/2.00 tff(3269,plain,
% 2.62/2.00 (~c1_1(a1441)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1651, 3267])).
% 2.62/2.00 tff(3270,plain,
% 2.62/2.00 (c0_1(a1441)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1673, 3267])).
% 2.62/2.00 tff(3271,plain,
% 2.62/2.00 (hskp17),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2706, 3270, 11, 3259, 3256, 3257, 3269, 3268])).
% 2.62/2.00 tff(3272,plain,
% 2.62/2.00 (~c2_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[288, 3271])).
% 2.62/2.00 tff(3273,plain,
% 2.62/2.00 (~c1_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[269, 3271])).
% 2.62/2.00 tff(3274,plain,
% 2.62/2.00 (~c0_1(a1457)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[275, 3271])).
% 2.62/2.00 tff(3275,plain,
% 2.62/2.00 (c0_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[456, 3264])).
% 2.62/2.00 tff(3276,plain,
% 2.62/2.00 (~c2_1(a1445)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[463, 91, 3275, 3274, 3273, 3272, 3266, 3265, 23])).
% 2.62/2.00 tff(3277,plain,
% 2.62/2.00 (hskp29),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[2644, 3264, 3273, 3272, 3274, 11])).
% 2.62/2.00 tff(3278,plain,
% 2.62/2.00 (c3_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1062, 3277])).
% 2.62/2.00 tff(3279,plain,
% 2.62/2.00 (c2_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1073, 3277])).
% 2.62/2.00 tff(3280,plain,
% 2.62/2.00 (c1_1(a1483)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1084, 3277])).
% 2.62/2.00 tff(3281,plain,
% 2.62/2.00 ($false),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3142, 91, 3146, 3280, 3279, 3278, 3266, 3265, 678, 3276])).
% 2.62/2.00 tff(3282,plain,(hskp5 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.00 tff(3283,plain,
% 2.62/2.00 (hskp5),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3282, 12])).
% 2.62/2.00 tff(3284,plain,
% 2.62/2.00 (~c2_1(a1435)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[325, 3283])).
% 2.62/2.00 tff(3285,plain,
% 2.62/2.00 (~c3_1(a1435)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[319, 3283])).
% 2.62/2.00 tff(3286,plain,
% 2.62/2.00 (c0_1(a1435)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[390, 3283])).
% 2.62/2.00 tff(3287,plain,
% 2.62/2.00 (~c1_1(a1447)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[775, 91, 701, 752, 746, 758, 214])).
% 2.62/2.00 tff(3288,plain,
% 2.62/2.00 (((~![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))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3289,plain,
% 2.62/2.00 ((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))),
% 2.62/2.00 inference(rewrite,[status(thm)],[])).
% 2.62/2.00 tff(3290,plain,
% 2.62/2.00 (((~![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)))),
% 2.62/2.00 inference(monotonicity,[status(thm)],[3289])).
% 2.62/2.00 tff(3291,plain,
% 2.62/2.00 (((~![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))),
% 2.62/2.00 inference(transitivity,[status(thm)],[3290, 3288])).
% 2.62/2.00 tff(3292,plain,
% 2.62/2.00 ((~![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))),
% 2.62/2.00 inference(quant_inst,[status(thm)],[])).
% 2.62/2.00 tff(3293,plain,
% 2.62/2.00 ((~![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)),
% 2.62/2.00 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 2.62/2.00 tff(3294,plain,
% 2.62/2.00 (hskp0),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[3293, 91, 114, 752, 746, 112, 113, 1201, 3287])).
% 2.62/2.00 tff(3295,plain,
% 2.62/2.00 (~c3_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1213, 3294])).
% 2.62/2.00 tff(3296,plain,
% 2.62/2.00 (c0_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1235, 3294])).
% 2.62/2.00 tff(3297,plain,
% 2.62/2.00 (c2_1(a1427)),
% 2.62/2.00 inference(unit_resolution,[status(thm)],[1224, 3294])).
% 2.62/2.00 tff(3298,plain,
% 2.62/2.00 (((~![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))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3299,plain,
% 2.62/2.01 (((~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))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3300,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3299])).
% 2.62/2.01 tff(3301,plain,
% 2.62/2.01 (((~![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))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3300, 3298])).
% 2.62/2.01 tff(3302,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3303,plain,
% 2.62/2.01 ((~![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)),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 2.62/2.01 tff(3304,plain,
% 2.62/2.01 (c0_1(a1447) | c2_1(a1447) | (~c1_1(a1435)) | c1_1(a1447)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3303, 91, 760, 112, 113, 2459])).
% 2.62/2.01 tff(3305,plain,
% 2.62/2.01 (~c1_1(a1435)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3304, 2390, 761, 759])).
% 2.62/2.01 tff(3306,plain,
% 2.62/2.01 (((~![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 | 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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3307,plain,
% 2.62/2.01 ((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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3308,plain,
% 2.62/2.01 (((~![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(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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3307])).
% 2.62/2.01 tff(3309,plain,
% 2.62/2.01 (((~![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(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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3308, 3306])).
% 2.62/2.01 tff(3310,plain,
% 2.62/2.01 ((~![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(a1427) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1435) | c1_1(a1435) | (~c0_1(a1435)))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3311,plain,
% 2.62/2.01 ((~![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 | c2_1(a1435) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c1_1(a1435) | (~c0_1(a1435))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 2.62/2.01 tff(3312,plain,
% 2.62/2.01 (hskp21 | c1_1(a1435)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3311, 91, 114, 2518, 2517, 112, 2516, 2557])).
% 2.62/2.01 tff(3313,plain,
% 2.62/2.01 (hskp21),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3312, 3305])).
% 2.62/2.01 tff(3314,plain,
% 2.62/2.01 (~c1_1(a1466)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[2570, 3313])).
% 2.62/2.01 tff(3315,plain,
% 2.62/2.01 (c2_1(a1466)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[2581, 3313])).
% 2.62/2.01 tff(3316,plain,
% 2.62/2.01 (c0_1(a1466)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[2592, 3313])).
% 2.62/2.01 tff(3317,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3318,plain,
% 2.62/2.01 (((~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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3319,plain,
% 2.62/2.01 (((~![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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3318])).
% 2.62/2.01 tff(3320,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3319, 3317])).
% 2.62/2.01 tff(3321,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3322,plain,
% 2.62/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1447) | c2_1(a1447) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c1_1(a1447) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 2.62/2.01 tff(3323,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3322, 91, 3316, 3315, 114, 3314, 759, 761, 113, 23, 3305, 2390])).
% 2.62/2.01 tff(3324,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,[]))).
% 2.62/2.01 tff(3325,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3324, 3297, 3296, 114, 113, 752, 758, 746, 3287, 3295, 112])).
% 2.62/2.01 tff(3326,plain,((~hskp11) | (~c0_1(a1435)) | c3_1(a1435) | c2_1(a1435) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.62/2.01 tff(3327,plain,
% 2.62/2.01 (~hskp11),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3326, 701, 3285, 3284, 3286])).
% 2.62/2.01 tff(3328,plain,
% 2.62/2.01 (c2_1(a1427)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1224, 2711])).
% 2.62/2.01 tff(3329,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1475, 91, 701, 1300, 2713, 3328, 2712, 1288])).
% 2.62/2.01 tff(3330,plain,((~hskp0) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 2.62/2.01 tff(3331,plain,
% 2.62/2.01 (~hskp0),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3330, 1300, 701])).
% 2.62/2.01 tff(3332,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1207, 91, 2757, 114, 37, 24, 112, 113, 1201, 50])).
% 2.62/2.01 tff(3333,plain,(c2_1(a1438) | hskp0 | (~c0_1(a1435)) | c0_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.01 tff(3334,plain,
% 2.62/2.01 (c2_1(a1438)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3333, 37, 3286, 2757, 24, 3284, 3285])).
% 2.62/2.01 tff(3335,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3336,plain,
% 2.62/2.01 ((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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3337,plain,
% 2.62/2.01 (((~![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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3336])).
% 2.62/2.01 tff(3338,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3337, 3335])).
% 2.62/2.01 tff(3339,plain,
% 2.62/2.01 ((~![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)))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3340,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 2.62/2.01 tff(3341,plain,
% 2.62/2.01 (hskp4 | hskp0 | c0_1(a1438) | (~c2_1(a1438))),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3340, 91, 24, 2774])).
% 2.62/2.01 tff(3342,plain,
% 2.62/2.01 (hskp4),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3341, 3334, 2757, 37])).
% 2.62/2.01 tff(3343,plain,
% 2.62/2.01 (~c2_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[137, 3342])).
% 2.62/2.01 tff(3344,plain,
% 2.62/2.01 (c3_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[161, 3342])).
% 2.62/2.01 tff(3345,plain,
% 2.62/2.01 (c1_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[150, 3342])).
% 2.62/2.01 tff(3346,plain,
% 2.62/2.01 (hskp7 | hskp4),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[130, 91, 3286, 3284, 3285, 124])).
% 2.62/2.01 tff(3347,plain,
% 2.62/2.01 (hskp4),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3346, 111])).
% 2.62/2.01 tff(3348,plain,
% 2.62/2.01 (~c2_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[137, 3347])).
% 2.62/2.01 tff(3349,plain,
% 2.62/2.01 (~c1_1(a1435)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[182, 3347, 3284, 111, 3285, 3348])).
% 2.62/2.01 tff(3350,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3351,plain,
% 2.62/2.01 ((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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3352,plain,
% 2.62/2.01 (((~![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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3351])).
% 2.62/2.01 tff(3353,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3352, 3350])).
% 2.62/2.01 tff(3354,plain,
% 2.62/2.01 ((~![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)))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3355,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 2.62/2.01 tff(3356,plain,
% 2.62/2.01 (~c2_1(a1430)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3355, 91, 701, 3286, 2185, 3285, 12, 1415, 3349])).
% 2.62/2.01 tff(3357,plain,
% 2.62/2.01 (c3_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[161, 3347])).
% 2.62/2.01 tff(3358,plain,
% 2.62/2.01 (c1_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[150, 3347])).
% 2.62/2.01 tff(3359,plain,
% 2.62/2.01 (((~![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))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3360,plain,
% 2.62/2.01 ((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))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3361,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3360])).
% 2.62/2.01 tff(3362,plain,
% 2.62/2.01 (((~![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))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3361, 3359])).
% 2.62/2.01 tff(3363,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3364,plain,
% 2.62/2.01 ((~![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)),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 2.62/2.01 tff(3365,plain,
% 2.62/2.01 (c2_1(a1438)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3364, 91, 2757, 49, 3358, 3357, 37, 3348, 2440])).
% 2.62/2.01 tff(3366,plain,
% 2.62/2.01 (((~![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)))) | (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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3367,plain,
% 2.62/2.01 (((~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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3368,plain,
% 2.62/2.01 (((~![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(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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3367])).
% 2.62/2.01 tff(3369,plain,
% 2.62/2.01 (((~![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(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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3368, 3366])).
% 2.62/2.01 tff(3370,plain,
% 2.62/2.01 ((~![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(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)))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3371,plain,
% 2.62/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1438))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 2.62/2.01 tff(3372,plain,
% 2.62/2.01 (c3_1(a1438) | c2_1(a1430) | c1_1(a1435) | (~c2_1(a1438))),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3371, 91, 3286, 2185, 24, 3284, 12, 591])).
% 2.62/2.01 tff(3373,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3372, 3365, 3356, 49, 3349])).
% 2.62/2.01 tff(3374,plain,(c3_1(a1438) | c1_1(a1438) | c0_1(a1430) | hskp0 | c0_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.62/2.01 tff(3375,plain,
% 2.62/2.01 (c3_1(a1438)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3374, 37, 12, 2757, 24, 701])).
% 2.62/2.01 tff(3376,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3377,plain,
% 2.62/2.01 ((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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3378,plain,
% 2.62/2.01 (((~![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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3377])).
% 2.62/2.01 tff(3379,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3378, 3376])).
% 2.62/2.01 tff(3380,plain,
% 2.62/2.01 ((~![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)))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3381,plain,
% 2.62/2.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a1438) | c2_1(a1434) | (~ndr1_0) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 2.62/2.01 tff(3382,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3381, 91, 701, 3375, 3345, 3344, 37, 3343, 1363, 3334])).
% 2.62/2.01 tff(3383,plain,(c0_1(a1438) | hskp12 | hskp0 | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.01 tff(3384,plain,
% 2.62/2.01 (c0_1(a1438)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3383, 3331, 701, 24, 12])).
% 2.62/2.01 tff(3385,plain,
% 2.62/2.01 (~hskp7),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1099, 3384])).
% 2.62/2.01 tff(3386,plain,
% 2.62/2.01 (hskp4),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3346, 3385])).
% 2.62/2.01 tff(3387,plain,
% 2.62/2.01 (~c2_1(a1434)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[137, 3386])).
% 2.62/2.01 tff(3388,plain,
% 2.62/2.01 (~c1_1(a1435)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[182, 3387, 3284, 3386, 3285, 3385])).
% 2.62/2.01 tff(3389,plain,
% 2.62/2.01 (~c2_1(a1430)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3355, 91, 701, 3286, 2185, 3285, 12, 1415, 3388])).
% 2.62/2.01 tff(3390,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3391,plain,
% 2.62/2.01 ((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)))),
% 2.62/2.01 inference(rewrite,[status(thm)],[])).
% 2.62/2.01 tff(3392,plain,
% 2.62/2.01 (((~![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))))),
% 2.62/2.01 inference(monotonicity,[status(thm)],[3391])).
% 2.62/2.01 tff(3393,plain,
% 2.62/2.01 (((~![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)))),
% 2.62/2.01 inference(transitivity,[status(thm)],[3392, 3390])).
% 2.62/2.01 tff(3394,plain,
% 2.62/2.01 ((~![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))),
% 2.62/2.01 inference(quant_inst,[status(thm)],[])).
% 2.62/2.01 tff(3395,plain,
% 2.62/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c0_1(a1435))),
% 2.62/2.01 inference(modus_ponens,[status(thm)],[3394, 3393])).
% 2.62/2.01 tff(3396,plain,
% 2.62/2.01 (c1_1(a1430)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[3395, 91, 3331, 3286, 3284, 3285, 12, 3389, 1201])).
% 2.62/2.01 tff(3397,plain,
% 2.62/2.01 (~c2_1(a1438)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1818, 3384, 1300, 3331])).
% 2.62/2.01 tff(3398,assumption,(hskp29), introduced(assumption)).
% 2.62/2.01 tff(3399,plain,
% 2.62/2.01 (c3_1(a1483)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1062, 3398])).
% 2.62/2.01 tff(3400,plain,
% 2.62/2.01 (c2_1(a1483)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1073, 3398])).
% 2.62/2.01 tff(3401,plain,
% 2.62/2.01 (c1_1(a1483)),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1084, 3398])).
% 2.62/2.01 tff(3402,plain,
% 2.62/2.01 ($false),
% 2.62/2.01 inference(unit_resolution,[status(thm)],[1742, 91, 111, 3401, 3400, 3399, 49, 24, 678, 50])).
% 2.62/2.01 tff(3403,plain,((~hskp29) | c3_1(a1438) | c1_1(a1438) | c2_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.02 tff(3404,plain,
% 2.62/2.02 (~hskp29),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3403, 49, 24, 50])).
% 2.62/2.02 tff(3405,plain,
% 2.62/2.02 ((hskp29 | hskp26 | hskp0) <=> (hskp29 | hskp26 | hskp0)),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3406,plain,
% 2.62/2.02 (((hskp0 | hskp29) | hskp26) <=> (hskp29 | hskp26 | hskp0)),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3407,axiom,((hskp0 | hskp29) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 2.62/2.02 tff(3408,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 2.62/2.02 tff(3409,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3408, 3405])).
% 2.62/2.02 tff(3410,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3409, 3405])).
% 2.62/2.02 tff(3411,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3410, 3405])).
% 2.62/2.02 tff(3412,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3411, 3405])).
% 2.62/2.02 tff(3413,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3412, 3405])).
% 2.62/2.02 tff(3414,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3413, 3405])).
% 2.62/2.02 tff(3415,plain,
% 2.62/2.02 (hskp29 | hskp26 | hskp0),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3414, 3405])).
% 2.62/2.02 tff(3416,plain,
% 2.62/2.02 (hskp26),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3415, 3404, 2757])).
% 2.62/2.02 tff(3417,plain,
% 2.62/2.02 (((~hskp26) | (~c0_1(a1517))) <=> ((~hskp26) | (~c0_1(a1517)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3418,plain,
% 2.62/2.02 (((~c0_1(a1517)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1517)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3419,axiom,((~c0_1(a1517)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 2.62/2.02 tff(3420,plain,
% 2.62/2.02 ((~hskp26) | (~c0_1(a1517))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 2.62/2.02 tff(3421,plain,
% 2.62/2.02 ((~hskp26) | (~c0_1(a1517))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3420, 3417])).
% 2.62/2.02 tff(3422,plain,
% 2.62/2.02 (~c0_1(a1517)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3421, 3416])).
% 2.62/2.02 tff(3423,plain,
% 2.62/2.02 (((~hskp26) | c2_1(a1517)) <=> ((~hskp26) | c2_1(a1517))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3424,axiom,((~hskp26) | c2_1(a1517)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 2.62/2.02 tff(3425,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 2.62/2.02 tff(3426,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3425, 3423])).
% 2.62/2.02 tff(3427,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3426, 3423])).
% 2.62/2.02 tff(3428,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3427, 3423])).
% 2.62/2.02 tff(3429,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3428, 3423])).
% 2.62/2.02 tff(3430,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3429, 3423])).
% 2.62/2.02 tff(3431,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3430, 3423])).
% 2.62/2.02 tff(3432,plain,
% 2.62/2.02 ((~hskp26) | c2_1(a1517)),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3431, 3423])).
% 2.62/2.02 tff(3433,plain,
% 2.62/2.02 (c2_1(a1517)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3432, 3416])).
% 2.62/2.02 tff(3434,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3435,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3436,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3435])).
% 2.62/2.02 tff(3437,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3436, 3434])).
% 2.62/2.02 tff(3438,plain,
% 2.62/2.02 ((~![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)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3439,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 2.62/2.02 tff(3440,plain,
% 2.62/2.02 (~c1_1(a1517)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3439, 91, 1736, 3433, 49, 3422, 1724, 24, 193])).
% 2.62/2.02 tff(3441,assumption,(c1_1(a1430)), introduced(assumption)).
% 2.62/2.02 tff(3442,plain,
% 2.62/2.02 (((~![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(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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3443,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3444,plain,
% 2.62/2.02 (((~![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(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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3443])).
% 2.62/2.02 tff(3445,plain,
% 2.62/2.02 (((~![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(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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3444, 3442])).
% 2.62/2.02 tff(3446,plain,
% 2.62/2.02 ((~![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(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c0_1(a1517) | c1_1(a1517) | (~c2_1(a1517)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3447,plain,
% 2.62/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1517) | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c1_1(a1517) | (~c2_1(a1517))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 2.62/2.02 tff(3448,plain,
% 2.62/2.02 ($false),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3447, 91, 2757, 3433, 2185, 3422, 12, 2274, 3441, 3440])).
% 2.62/2.02 tff(3449,plain,(c3_1(a1438) | hskp0 | c0_1(a1430) | (~c1_1(a1430)) | (~c0_1(a1438)) | c1_1(a1438) | c2_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.02 tff(3450,plain,
% 2.62/2.02 (c3_1(a1438)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3449, 3331, 12, 3396, 3384, 24, 3397])).
% 2.62/2.02 tff(3451,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3452,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3453,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3452])).
% 2.62/2.02 tff(3454,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3453, 3451])).
% 2.62/2.02 tff(3455,plain,
% 2.62/2.02 ((~![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)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3456,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3455, 3454])).
% 2.62/2.02 tff(3457,plain,
% 2.62/2.02 (hskp17 | (~c1_1(a1430)) | (~c3_1(a1438))),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3456, 91, 2185, 3384, 12, 336, 3397])).
% 2.62/2.02 tff(3458,plain,
% 2.62/2.02 (hskp17),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3457, 3450, 3396])).
% 2.62/2.02 tff(3459,plain,
% 2.62/2.02 (~c2_1(a1457)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[288, 3458])).
% 2.62/2.02 tff(3460,plain,
% 2.62/2.02 (~c1_1(a1457)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[269, 3458])).
% 2.62/2.02 tff(3461,plain,
% 2.62/2.02 (~c0_1(a1457)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[275, 3458])).
% 2.62/2.02 tff(3462,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3463,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3464,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3463])).
% 2.62/2.02 tff(3465,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3464, 3462])).
% 2.62/2.02 tff(3466,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3467,plain,
% 2.62/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c2_1(a1435) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 2.62/2.02 tff(3468,plain,
% 2.62/2.02 ($false),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3467, 91, 3331, 3286, 3461, 3460, 3459, 3284, 3285, 1201])).
% 2.62/2.02 tff(3469,plain,(hskp11 | c0_1(a1430) | c1_1(a1438) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.62/2.02 tff(3470,plain,
% 2.62/2.02 (c1_1(a1438)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3469, 3327, 12, 701])).
% 2.62/2.02 tff(3471,plain,
% 2.62/2.02 (~hskp7),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[1514, 3470])).
% 2.62/2.02 tff(3472,plain,
% 2.62/2.02 (hskp4),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3346, 3471])).
% 2.62/2.02 tff(3473,plain,
% 2.62/2.02 (~c2_1(a1434)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[137, 3472])).
% 2.62/2.02 tff(3474,plain,
% 2.62/2.02 (~c1_1(a1435)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[182, 3473, 3284, 3472, 3285, 3471])).
% 2.62/2.02 tff(3475,plain,
% 2.62/2.02 (~c2_1(a1430)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3355, 91, 701, 3286, 2185, 3285, 12, 1415, 3474])).
% 2.62/2.02 tff(3476,plain,
% 2.62/2.02 (~hskp0),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3330, 3327, 701])).
% 2.62/2.02 tff(3477,plain,
% 2.62/2.02 (c1_1(a1430)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3395, 91, 3476, 3286, 3284, 3285, 12, 3475, 1201])).
% 2.62/2.02 tff(3478,plain,
% 2.62/2.02 (^[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))))),
% 2.62/2.02 inference(bind,[status(th)],[])).
% 2.62/2.02 tff(3479,plain,
% 2.62/2.02 (![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)))),
% 2.62/2.02 inference(quant_intro,[status(thm)],[3478])).
% 2.62/2.02 tff(3480,plain,
% 2.62/2.02 (![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3481,plain,
% 2.62/2.02 (^[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)))))),
% 2.62/2.02 inference(bind,[status(th)],[])).
% 2.62/2.02 tff(3482,plain,
% 2.62/2.02 (![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)))),
% 2.62/2.02 inference(quant_intro,[status(thm)],[3481])).
% 2.62/2.02 tff(3483,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 2.62/2.02 tff(3484,plain,
% 2.62/2.02 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 2.62/2.02 tff(3485,plain,
% 2.62/2.02 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3484, 3480])).
% 2.62/2.02 tff(3486,plain,(
% 2.62/2.02 ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.62/2.02 inference(skolemize,[status(sab)],[3485])).
% 2.62/2.02 tff(3487,plain,
% 2.62/2.02 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3486, 3479])).
% 2.62/2.02 tff(3488,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3489,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3490,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3489])).
% 2.62/2.02 tff(3491,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3490, 3488])).
% 2.62/2.02 tff(3492,plain,
% 2.62/2.02 ((~![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)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3493,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 2.62/2.02 tff(3494,plain,
% 2.62/2.02 (hskp19 | hskp3 | (~c1_1(a1430)) | (~c3_1(a1430))),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3493, 91, 12, 3487])).
% 2.62/2.02 tff(3495,plain,
% 2.62/2.02 (hskp19),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3494, 874, 2185, 3441])).
% 2.62/2.02 tff(3496,plain,
% 2.62/2.02 (~c3_1(a1460)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[1249, 3495])).
% 2.62/2.02 tff(3497,plain,
% 2.62/2.02 (~c1_1(a1460)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[1268, 3495])).
% 2.62/2.02 tff(3498,plain,
% 2.62/2.02 (~c0_1(a1460)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[1255, 3495])).
% 2.62/2.02 tff(3499,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3500,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3501,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3500])).
% 2.62/2.02 tff(3502,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3501, 3499])).
% 2.62/2.02 tff(3503,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3504,plain,
% 2.62/2.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp3 | c0_1(a1468) | c0_1(a1460) | c1_1(a1460) | c3_1(a1460) | (~ndr1_0) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3503, 3502])).
% 2.62/2.02 tff(3505,plain,
% 2.62/2.02 ($false),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3504, 91, 874, 914, 903, 892, 3498, 3497, 3496, 873])).
% 2.62/2.02 tff(3506,plain,(hskp3 | hskp17 | (~c1_1(a1430)) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.02 tff(3507,plain,
% 2.62/2.02 (hskp3),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3506, 36, 3477, 12])).
% 2.62/2.02 tff(3508,plain,
% 2.62/2.02 (~c2_1(a1431)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[928, 3507])).
% 2.62/2.02 tff(3509,plain,
% 2.62/2.02 (~c0_1(a1431)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[934, 3507])).
% 2.62/2.02 tff(3510,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3511,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3512,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3511])).
% 2.62/2.02 tff(3513,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3512, 3510])).
% 2.62/2.02 tff(3514,plain,
% 2.62/2.02 ((~![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)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3515,plain,
% 2.62/2.02 ((~![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))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 2.62/2.02 tff(3516,plain,
% 2.62/2.02 (~c2_1(a1441)),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3515, 91, 1300, 2757, 2880, 2882, 1811])).
% 2.62/2.02 tff(3517,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3518,plain,
% 2.62/2.02 ((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)))),
% 2.62/2.02 inference(rewrite,[status(thm)],[])).
% 2.62/2.02 tff(3519,plain,
% 2.62/2.02 (((~![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))))),
% 2.62/2.02 inference(monotonicity,[status(thm)],[3518])).
% 2.62/2.02 tff(3520,plain,
% 2.62/2.02 (((~![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)))),
% 2.62/2.02 inference(transitivity,[status(thm)],[3519, 3517])).
% 2.62/2.02 tff(3521,plain,
% 2.62/2.02 ((~![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)))),
% 2.62/2.02 inference(quant_inst,[status(thm)],[])).
% 2.62/2.02 tff(3522,plain,
% 2.62/2.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | c2_1(a1441) | (~c0_1(a1441)) | (~c3_1(a1441))),
% 2.62/2.02 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 2.62/2.02 tff(3523,plain,
% 2.62/2.02 ($false),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3522, 91, 36, 2880, 2879, 2185, 12, 336, 3441, 3516])).
% 2.62/2.02 tff(3524,plain,((~hskp8) | hskp17 | c0_1(a1430) | (~c1_1(a1430)) | hskp11 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.62/2.02 tff(3525,plain,
% 2.62/2.02 (~hskp8),
% 2.62/2.02 inference(unit_resolution,[status(thm)],[3524, 36, 12, 3477, 3327, 3476])).
% 2.62/2.03 tff(3526,plain,
% 2.62/2.03 (hskp14),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[2363, 3525, 701])).
% 2.62/2.03 tff(3527,plain,
% 2.62/2.03 (~c3_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[547, 3526])).
% 2.62/2.03 tff(3528,plain,
% 2.62/2.03 (~c1_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[553, 3526])).
% 2.62/2.03 tff(3529,plain,
% 2.62/2.03 (c2_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[564, 3526])).
% 2.62/2.03 tff(3530,plain,
% 2.62/2.03 (((~![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)))) | (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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3531,plain,
% 2.62/2.03 (((~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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3532,plain,
% 2.62/2.03 (((~![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(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))))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3531])).
% 2.62/2.03 tff(3533,plain,
% 2.62/2.03 (((~![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(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)))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3532, 3530])).
% 2.62/2.03 tff(3534,plain,
% 2.62/2.03 ((~![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(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)))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3535,plain,
% 2.62/2.03 ((~![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)))) | 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))),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 2.62/2.03 tff(3536,plain,
% 2.62/2.03 (~c3_1(a1431)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3535, 91, 3529, 3286, 3528, 3527, 3284, 3509, 3508, 591, 3474])).
% 2.62/2.03 tff(3537,plain,
% 2.62/2.03 (((~![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))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3538,plain,
% 2.62/2.03 ((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))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3539,plain,
% 2.62/2.03 (((~![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)))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3538])).
% 2.62/2.03 tff(3540,plain,
% 2.62/2.03 (((~![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))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3539, 3537])).
% 2.62/2.03 tff(3541,plain,
% 2.62/2.03 ((~![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))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3542,plain,
% 2.62/2.03 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a1431) | c2_1(a1431) | (~ndr1_0) | c3_1(a1431)),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 2.62/2.03 tff(3543,plain,
% 2.62/2.03 ($false),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3542, 91, 3525, 3471, 3509, 3508, 2326, 3536])).
% 2.62/2.03 tff(3544,plain,(hskp17 | hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.03 tff(3545,plain,
% 2.62/2.03 (hskp17),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3544, 701, 12])).
% 2.62/2.03 tff(3546,plain,
% 2.62/2.03 (~c0_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[275, 3545])).
% 2.62/2.03 tff(3547,plain,
% 2.62/2.03 (~c2_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[288, 3545])).
% 2.62/2.03 tff(3548,plain,
% 2.62/2.03 (c0_1(a1457) | c1_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3467, 91, 3476, 3286, 2640, 3284, 3285, 1201])).
% 2.62/2.03 tff(3549,plain,
% 2.62/2.03 (c1_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3548, 2642])).
% 2.62/2.03 tff(3550,plain,
% 2.62/2.03 (~hskp17),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[269, 3549])).
% 2.62/2.03 tff(3551,plain,
% 2.62/2.03 (~hskp8),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3524, 3550, 12, 3477, 3327, 3476])).
% 2.62/2.03 tff(3552,plain,
% 2.62/2.03 (((~![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))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3553,plain,
% 2.62/2.03 ((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))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3554,plain,
% 2.62/2.03 (((~![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)))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3553])).
% 2.62/2.03 tff(3555,plain,
% 2.62/2.03 (((~![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))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3554, 3552])).
% 2.62/2.03 tff(3556,plain,
% 2.62/2.03 ((~![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))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3557,plain,
% 2.62/2.03 ((~![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)),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3556, 3555])).
% 2.62/2.03 tff(3558,plain,
% 2.62/2.03 (hskp8 | c0_1(a1457) | c3_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3557, 91, 3471, 2640, 2326])).
% 2.62/2.03 tff(3559,plain,
% 2.62/2.03 (c3_1(a1457)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3558, 3551, 2642])).
% 2.62/2.03 tff(3560,plain,
% 2.62/2.03 (hskp14),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[2363, 3551, 701])).
% 2.62/2.03 tff(3561,plain,
% 2.62/2.03 (~c3_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[547, 3560])).
% 2.62/2.03 tff(3562,plain,
% 2.62/2.03 (~c1_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[553, 3560])).
% 2.62/2.03 tff(3563,plain,
% 2.62/2.03 (c2_1(a1451)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[564, 3560])).
% 2.62/2.03 tff(3564,plain,
% 2.62/2.03 (((~![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)))) | (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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3565,plain,
% 2.62/2.03 (((~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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3566,plain,
% 2.62/2.03 (((~![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(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))))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3565])).
% 2.62/2.03 tff(3567,plain,
% 2.62/2.03 (((~![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(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)))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3566, 3564])).
% 2.62/2.03 tff(3568,plain,
% 2.62/2.03 ((~![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(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)))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3569,plain,
% 2.62/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a1457) | c2_1(a1457) | c1_1(a1451) | c3_1(a1451) | c2_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1451)) | (~c3_1(a1457))),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 2.62/2.03 tff(3570,plain,
% 2.62/2.03 ($false),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3569, 91, 3563, 3286, 2642, 2640, 3562, 3561, 3284, 591, 3474, 3559])).
% 2.62/2.03 tff(3571,plain,(c0_1(a1457) | c2_1(a1457) | hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.03 tff(3572,plain,
% 2.62/2.03 ($false),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3571, 3547, 3546, 701, 12])).
% 2.62/2.03 tff(3573,plain,(hskp12 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.03 tff(3574,plain,
% 2.62/2.03 (hskp12),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3573, 12])).
% 2.62/2.03 tff(3575,plain,
% 2.62/2.03 (~c2_1(a1448)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[220, 3574])).
% 2.62/2.03 tff(3576,plain,
% 2.62/2.03 (c2_1(a1438)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3333, 37, 3286, 24, 2757, 3284, 3285])).
% 2.62/2.03 tff(3577,plain,
% 2.62/2.03 (c3_1(a1448)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[242, 3574])).
% 2.62/2.03 tff(3578,plain,
% 2.62/2.03 (c0_1(a1448)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[231, 3574])).
% 2.62/2.03 tff(3579,plain,
% 2.62/2.03 (((~![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(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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3580,plain,
% 2.62/2.03 (((~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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3581,plain,
% 2.62/2.03 (((~![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(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))))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3580])).
% 2.62/2.03 tff(3582,plain,
% 2.62/2.03 (((~![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(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)))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3581, 3579])).
% 2.62/2.03 tff(3583,plain,
% 2.62/2.03 ((~![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(a1430) | (~c3_1(a1430)) | (~c1_1(a1430)) | c1_1(a1438) | c0_1(a1438) | (~c2_1(a1438)))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3584,plain,
% 2.62/2.03 ((~![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(a1430) | (~ndr1_0) | (~c1_1(a1430)) | (~c3_1(a1430)) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3583, 3582])).
% 2.62/2.03 tff(3585,plain,
% 2.62/2.03 (c0_1(a1438) | (~c1_1(a1430)) | (~c2_1(a1438))),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3584, 91, 3578, 3577, 2185, 3575, 24, 12, 1374])).
% 2.62/2.03 tff(3586,plain,
% 2.62/2.03 (~c1_1(a1430)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3585, 3576, 37])).
% 2.62/2.03 tff(3587,plain,
% 2.62/2.03 (hskp4),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3341, 37, 2757, 3576])).
% 2.62/2.03 tff(3588,plain,
% 2.62/2.03 (~c2_1(a1434)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[137, 140])).
% 2.62/2.03 tff(3589,plain,
% 2.62/2.03 (((~![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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3590,plain,
% 2.62/2.03 (((~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)))),
% 2.62/2.03 inference(rewrite,[status(thm)],[])).
% 2.62/2.03 tff(3591,plain,
% 2.62/2.03 (((~![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))))),
% 2.62/2.03 inference(monotonicity,[status(thm)],[3590])).
% 2.62/2.03 tff(3592,plain,
% 2.62/2.03 (((~![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)))),
% 2.62/2.03 inference(transitivity,[status(thm)],[3591, 3589])).
% 2.62/2.03 tff(3593,plain,
% 2.62/2.03 ((~![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))),
% 2.62/2.03 inference(quant_inst,[status(thm)],[])).
% 2.62/2.03 tff(3594,plain,
% 2.62/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1438) | c1_1(a1438) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1438))),
% 2.62/2.03 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 2.62/2.03 tff(3595,plain,
% 2.62/2.03 (c3_1(a1438) | c1_1(a1430) | c1_1(a1435) | (~c2_1(a1438))),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3594, 91, 2185, 24, 3284, 3285, 12, 626])).
% 2.62/2.03 tff(3596,plain,
% 2.62/2.03 (c1_1(a1435)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3595, 49, 592, 822])).
% 2.62/2.03 tff(3597,plain,
% 2.62/2.03 ($false),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[182, 3596, 111, 3284, 140, 3285, 3588])).
% 2.62/2.03 tff(3598,plain,(c3_1(a1438) | (~hskp4) | c1_1(a1430) | (~c2_1(a1438)) | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.03 tff(3599,plain,
% 2.62/2.03 (c3_1(a1438)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3598, 3587, 3586, 3576, 24, 12])).
% 2.62/2.03 tff(3600,plain,
% 2.62/2.03 (hskp20 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[1316, 91, 1300, 24, 1310])).
% 2.62/2.03 tff(3601,plain,
% 2.62/2.03 (hskp20),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[3600, 3599, 3576])).
% 2.62/2.03 tff(3602,plain,
% 2.62/2.03 (~c1_1(a1465)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[1323, 3601])).
% 2.62/2.03 tff(3603,plain,
% 2.62/2.03 (c3_1(a1465)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[1334, 3601])).
% 2.62/2.03 tff(3604,plain,
% 2.62/2.03 (c2_1(a1465)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[1345, 3601])).
% 2.62/2.03 tff(3605,plain,
% 2.62/2.03 (~c0_1(a1465)),
% 2.62/2.03 inference(unit_resolution,[status(thm)],[1352, 91, 3604, 3603, 3602, 37, 24, 1298, 3576])).
% 2.67/2.03 tff(3606,plain,
% 2.67/2.03 (c3_1(a1434)),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[161, 3587])).
% 2.67/2.03 tff(3607,plain,
% 2.67/2.03 (c1_1(a1434)),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[150, 3587])).
% 2.67/2.03 tff(3608,assumption,(~c0_1(a1434)), introduced(assumption)).
% 2.67/2.03 tff(3609,assumption,(c3_1(a1434)), introduced(assumption)).
% 2.67/2.03 tff(3610,assumption,(c1_1(a1434)), introduced(assumption)).
% 2.67/2.03 tff(3611,assumption,(c3_1(a1448)), introduced(assumption)).
% 2.67/2.03 tff(3612,assumption,(c0_1(a1448)), introduced(assumption)).
% 2.67/2.03 tff(3613,plain,
% 2.67/2.03 (((~![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)))) | (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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3614,plain,
% 2.67/2.03 (((~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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3615,plain,
% 2.67/2.03 (((~![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(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))))),
% 2.67/2.03 inference(monotonicity,[status(thm)],[3614])).
% 2.67/2.03 tff(3616,plain,
% 2.67/2.03 (((~![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(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)))),
% 2.67/2.03 inference(transitivity,[status(thm)],[3615, 3613])).
% 2.67/2.03 tff(3617,plain,
% 2.67/2.03 ((~![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(a1434) | (~c3_1(a1434)) | (~c1_1(a1434)) | c1_1(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 2.67/2.03 inference(quant_inst,[status(thm)],[])).
% 2.67/2.03 tff(3618,plain,
% 2.67/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465))),
% 2.67/2.03 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 2.67/2.03 tff(3619,plain,
% 2.67/2.03 ($false),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[3618, 91, 1394, 3612, 3611, 3610, 3609, 1375, 254, 1374, 1364, 3608])).
% 2.67/2.03 tff(3620,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,[]))).
% 2.67/2.03 tff(3621,plain,
% 2.67/2.03 (c0_1(a1434)),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[3620, 3604, 3578, 3577, 3607, 3606, 3602, 3575, 3605])).
% 2.67/2.03 tff(3622,plain,
% 2.67/2.03 (^[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))))),
% 2.67/2.03 inference(bind,[status(th)],[])).
% 2.67/2.03 tff(3623,plain,
% 2.67/2.03 (![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)))),
% 2.67/2.03 inference(quant_intro,[status(thm)],[3622])).
% 2.67/2.03 tff(3624,plain,
% 2.67/2.03 (![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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3625,plain,
% 2.67/2.03 (^[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)))))),
% 2.67/2.03 inference(bind,[status(th)],[])).
% 2.67/2.03 tff(3626,plain,
% 2.67/2.03 (![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)))),
% 2.67/2.03 inference(quant_intro,[status(thm)],[3625])).
% 2.67/2.03 tff(3627,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 2.67/2.03 tff(3628,plain,
% 2.67/2.03 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.67/2.03 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 2.67/2.03 tff(3629,plain,
% 2.67/2.03 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.67/2.03 inference(modus_ponens,[status(thm)],[3628, 3624])).
% 2.67/2.03 tff(3630,plain,(
% 2.67/2.03 ![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.67/2.03 inference(skolemize,[status(sab)],[3629])).
% 2.67/2.03 tff(3631,plain,
% 2.67/2.03 (![U: $i] : (hskp25 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.67/2.03 inference(modus_ponens,[status(thm)],[3630, 3623])).
% 2.67/2.03 tff(3632,plain,
% 2.67/2.03 (((~![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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3633,plain,
% 2.67/2.03 ((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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3634,plain,
% 2.67/2.03 (((~![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))))),
% 2.67/2.03 inference(monotonicity,[status(thm)],[3633])).
% 2.67/2.03 tff(3635,plain,
% 2.67/2.03 (((~![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)))),
% 2.67/2.03 inference(transitivity,[status(thm)],[3634, 3632])).
% 2.67/2.03 tff(3636,plain,
% 2.67/2.03 ((~![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)))),
% 2.67/2.03 inference(quant_inst,[status(thm)],[])).
% 2.67/2.03 tff(3637,plain,
% 2.67/2.03 ((~![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))),
% 2.67/2.03 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 2.67/2.03 tff(3638,plain,
% 2.67/2.03 (hskp25 | (~c0_1(a1434))),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[3637, 91, 2757, 3607, 3606, 3631])).
% 2.67/2.03 tff(3639,plain,
% 2.67/2.03 (hskp25),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[3638, 3621])).
% 2.67/2.03 tff(3640,plain,
% 2.67/2.03 (~c0_1(a1504)),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[493, 3639])).
% 2.67/2.03 tff(3641,plain,
% 2.67/2.03 (c1_1(a1504)),
% 2.67/2.03 inference(unit_resolution,[status(thm)],[506, 3639])).
% 2.67/2.03 tff(3642,plain,
% 2.67/2.03 (((~![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) | 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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3643,plain,
% 2.67/2.03 (((~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)))),
% 2.67/2.03 inference(rewrite,[status(thm)],[])).
% 2.67/2.03 tff(3644,plain,
% 2.67/2.03 (((~![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(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))))),
% 2.67/2.03 inference(monotonicity,[status(thm)],[3643])).
% 2.67/2.03 tff(3645,plain,
% 2.67/2.03 (((~![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(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)))),
% 2.67/2.03 inference(transitivity,[status(thm)],[3644, 3642])).
% 2.67/2.03 tff(3646,plain,
% 2.67/2.03 ((~![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(a1465) | c0_1(a1465) | (~c2_1(a1465)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3647,plain,
% 2.67/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c1_1(a1465) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | c0_1(a1465) | (~c2_1(a1465)) | (~c3_1(a1504)) | (~c1_1(a1504))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 2.67/2.04 tff(3648,plain,
% 2.67/2.04 (~c3_1(a1504)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3647, 91, 3641, 3604, 3578, 3577, 3640, 3602, 3575, 1374, 3605])).
% 2.67/2.04 tff(3649,plain,
% 2.67/2.04 (c2_1(a1504)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[534, 3639])).
% 2.67/2.04 tff(3650,plain,
% 2.67/2.04 (hskp14),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[541, 91, 3641, 3649, 3640, 524, 3648])).
% 2.67/2.04 tff(3651,plain,
% 2.67/2.04 (~c3_1(a1451)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[547, 3650])).
% 2.67/2.04 tff(3652,plain,
% 2.67/2.04 (~c1_1(a1451)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[553, 3650])).
% 2.67/2.04 tff(3653,plain,
% 2.67/2.04 (c2_1(a1451)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[564, 3650])).
% 2.67/2.04 tff(3654,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[571, 91, 3641, 3649, 3653, 3286, 3640, 3652, 3651, 3284, 3285, 203])).
% 2.67/2.04 tff(3655,plain,(c0_1(a1438) | hskp0 | c1_1(a1438) | hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.04 tff(3656,plain,
% 2.67/2.04 (c0_1(a1438)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3655, 2757, 24, 1300, 12])).
% 2.67/2.04 tff(3657,plain,
% 2.67/2.04 (~hskp7),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1099, 3656])).
% 2.67/2.04 tff(3658,plain,
% 2.67/2.04 (hskp4),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3346, 3657])).
% 2.67/2.04 tff(3659,plain,
% 2.67/2.04 (~c2_1(a1434)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[137, 3658])).
% 2.67/2.04 tff(3660,plain,
% 2.67/2.04 (~c1_1(a1435)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[182, 3659, 3284, 3658, 3285, 3657])).
% 2.67/2.04 tff(3661,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3662,plain,
% 2.67/2.04 ((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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3663,plain,
% 2.67/2.04 (((~![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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3662])).
% 2.67/2.04 tff(3664,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3663, 3661])).
% 2.67/2.04 tff(3665,plain,
% 2.67/2.04 ((~![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)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3666,plain,
% 2.67/2.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1504) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c1_1(a1504)) | (~c2_1(a1504))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 2.67/2.04 tff(3667,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3666, 91, 13, 597, 596, 114, 595, 113, 193, 337])).
% 2.67/2.04 tff(3668,plain,((~hskp25) | hskp7 | (~c0_1(a1435)) | c3_1(a1435) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.04 tff(3669,plain,
% 2.67/2.04 (~hskp25),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3668, 3660, 3286, 3285, 3657])).
% 2.67/2.04 tff(3670,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3671,plain,
% 2.67/2.04 ((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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3672,plain,
% 2.67/2.04 (((~![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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3671])).
% 2.67/2.04 tff(3673,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3672, 3670])).
% 2.67/2.04 tff(3674,plain,
% 2.67/2.04 ((~![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)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3675,plain,
% 2.67/2.04 ((~![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))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3674, 3673])).
% 2.67/2.04 tff(3676,plain,
% 2.67/2.04 (hskp25 | hskp0 | (~c1_1(a1448))),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3675, 91, 3578, 3577, 3631])).
% 2.67/2.04 tff(3677,plain,
% 2.67/2.04 (~c1_1(a1448)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3676, 3669, 2757])).
% 2.67/2.04 tff(3678,plain,
% 2.67/2.04 (hskp22 | c1_1(a1448)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2535, 91, 3578, 3577, 3575, 1385])).
% 2.67/2.04 tff(3679,plain,
% 2.67/2.04 (hskp22),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3678, 3677])).
% 2.67/2.04 tff(3680,plain,
% 2.67/2.04 (~c0_1(a1468)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[891, 3679])).
% 2.67/2.04 tff(3681,plain,
% 2.67/2.04 (c3_1(a1468)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[902, 3679])).
% 2.67/2.04 tff(3682,plain,
% 2.67/2.04 (c1_1(a1468)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[913, 3679])).
% 2.67/2.04 tff(3683,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3684,plain,
% 2.67/2.04 ((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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3685,plain,
% 2.67/2.04 (((~![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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3684])).
% 2.67/2.04 tff(3686,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3685, 3683])).
% 2.67/2.04 tff(3687,plain,
% 2.67/2.04 ((~![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)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3688,plain,
% 2.67/2.04 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1468) | c2_1(a1448) | (~ndr1_0) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1468)) | (~c1_1(a1468))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3687, 3686])).
% 2.67/2.04 tff(3689,plain,
% 2.67/2.04 (hskp17),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3688, 91, 3682, 3681, 3578, 3577, 3680, 3575, 336])).
% 2.67/2.04 tff(3690,plain,
% 2.67/2.04 (~c2_1(a1457)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[288, 3689])).
% 2.67/2.04 tff(3691,plain,
% 2.67/2.04 (~c1_1(a1457)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[269, 3689])).
% 2.67/2.04 tff(3692,plain,
% 2.67/2.04 (~c0_1(a1457)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[275, 3689])).
% 2.67/2.04 tff(3693,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3467, 91, 2757, 3286, 3692, 3691, 3690, 3284, 3285, 1201])).
% 2.67/2.04 tff(3694,plain,(hskp0 | c1_1(a1438) | hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.04 tff(3695,plain,
% 2.67/2.04 (hskp0),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3694, 24, 1300, 12])).
% 2.67/2.04 tff(3696,plain,
% 2.67/2.04 (~c2_1(a1438)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3598, 3347, 592, 49, 24, 12])).
% 2.67/2.04 tff(3697,plain,
% 2.67/2.04 (~c1_1(a1435)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[182, 3348, 3284, 3347, 3285, 111])).
% 2.67/2.04 tff(3698,assumption,(~hskp21), introduced(assumption)).
% 2.67/2.04 tff(3699,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3311, 91, 3698, 114, 2713, 3328, 112, 2712, 2557, 337])).
% 2.67/2.04 tff(3700,plain,((~hskp0) | hskp21 | (~c0_1(a1435)) | c2_1(a1435) | c1_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.04 tff(3701,plain,
% 2.67/2.04 (hskp21),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3700, 3697, 3286, 3284, 2711])).
% 2.67/2.04 tff(3702,plain,
% 2.67/2.04 (~c1_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2570, 3701])).
% 2.67/2.04 tff(3703,plain,
% 2.67/2.04 (c2_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2581, 3701])).
% 2.67/2.04 tff(3704,plain,
% 2.67/2.04 (c0_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2592, 3701])).
% 2.67/2.04 tff(3705,plain,
% 2.67/2.04 (((~![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))) | (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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3706,plain,
% 2.67/2.04 (((~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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3707,plain,
% 2.67/2.04 (((~![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(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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3706])).
% 2.67/2.04 tff(3708,plain,
% 2.67/2.04 (((~![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(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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3707, 3705])).
% 2.67/2.04 tff(3709,plain,
% 2.67/2.04 ((~![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(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))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3710,plain,
% 2.67/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1438) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | c2_1(a1438) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3709, 3708])).
% 2.67/2.04 tff(3711,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3710, 91, 3704, 3703, 3286, 3702, 37, 24, 3285, 23, 3697, 3696])).
% 2.67/2.04 tff(3712,plain,(c3_1(a1438) | c0_1(a1438) | c1_1(a1438) | (~hskp0) | c1_1(a1430) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.04 tff(3713,plain,
% 2.67/2.04 (c3_1(a1438)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3712, 592, 24, 3695, 37, 12])).
% 2.67/2.04 tff(3714,plain,
% 2.67/2.04 (~c3_1(a1427)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1213, 3695])).
% 2.67/2.04 tff(3715,plain,
% 2.67/2.04 (c2_1(a1427)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1224, 3695])).
% 2.67/2.04 tff(3716,plain,
% 2.67/2.04 (c0_1(a1427)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1235, 3695])).
% 2.67/2.04 tff(3717,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3718,plain,
% 2.67/2.04 ((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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3719,plain,
% 2.67/2.04 (((~![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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3718])).
% 2.67/2.04 tff(3720,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3719, 3717])).
% 2.67/2.04 tff(3721,plain,
% 2.67/2.04 ((~![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)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3722,plain,
% 2.67/2.04 ((~![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))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 2.67/2.04 tff(3723,plain,
% 2.67/2.04 (hskp19 | c1_1(a1435)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3722, 91, 114, 2713, 3328, 112, 2712, 1191])).
% 2.67/2.04 tff(3724,plain,
% 2.67/2.04 (hskp19),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3723, 337])).
% 2.67/2.04 tff(3725,plain,
% 2.67/2.04 (~c1_1(a1460)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1268, 3724])).
% 2.67/2.04 tff(3726,plain,
% 2.67/2.04 (~c0_1(a1460)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[1255, 3724])).
% 2.67/2.04 tff(3727,plain,
% 2.67/2.04 (hskp21),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3700, 337, 114, 112, 2711])).
% 2.67/2.04 tff(3728,plain,
% 2.67/2.04 (~c1_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2570, 3727])).
% 2.67/2.04 tff(3729,plain,
% 2.67/2.04 (c2_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2581, 3727])).
% 2.67/2.04 tff(3730,plain,
% 2.67/2.04 (c0_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[2592, 3727])).
% 2.67/2.04 tff(3731,plain,
% 2.67/2.04 (((~![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))) | (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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3732,plain,
% 2.67/2.04 (((~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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3733,plain,
% 2.67/2.04 (((~![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(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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3732])).
% 2.67/2.04 tff(3734,plain,
% 2.67/2.04 (((~![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(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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3733, 3731])).
% 2.67/2.04 tff(3735,plain,
% 2.67/2.04 ((~![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(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))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3736,plain,
% 2.67/2.04 ((~![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))) | 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))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 2.67/2.04 tff(3737,plain,
% 2.67/2.04 (c2_1(a1460)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3736, 91, 3730, 3729, 114, 3728, 3726, 3725, 113, 23, 337])).
% 2.67/2.04 tff(3738,plain,
% 2.67/2.04 (((~![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))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3739,plain,
% 2.67/2.04 (((~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))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3740,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3739])).
% 2.67/2.04 tff(3741,plain,
% 2.67/2.04 (((~![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))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3740, 3738])).
% 2.67/2.04 tff(3742,plain,
% 2.67/2.04 ((~![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))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3743,plain,
% 2.67/2.04 ((~![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)),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3742, 3741])).
% 2.67/2.04 tff(3744,plain,
% 2.67/2.04 (c3_1(a1466)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3743, 91, 3729, 1299, 3728, 37, 24, 112, 113, 626, 337])).
% 2.67/2.04 tff(3745,plain,
% 2.67/2.04 (c2_1(a1438)),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3710, 91, 3730, 3729, 114, 3728, 37, 24, 113, 23, 337])).
% 2.67/2.04 tff(3746,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3747,plain,
% 2.67/2.04 (((~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)))),
% 2.67/2.04 inference(rewrite,[status(thm)],[])).
% 2.67/2.04 tff(3748,plain,
% 2.67/2.04 (((~![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))))),
% 2.67/2.04 inference(monotonicity,[status(thm)],[3747])).
% 2.67/2.04 tff(3749,plain,
% 2.67/2.04 (((~![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)))),
% 2.67/2.04 inference(transitivity,[status(thm)],[3748, 3746])).
% 2.67/2.04 tff(3750,plain,
% 2.67/2.04 ((~![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)))),
% 2.67/2.04 inference(quant_inst,[status(thm)],[])).
% 2.67/2.04 tff(3751,plain,
% 2.67/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1460) | c1_1(a1460) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1438)) | (~c2_1(a1460)) | (~c2_1(a1466)) | (~c0_1(a1466)) | (~c3_1(a1466))),
% 2.67/2.04 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 2.67/2.04 tff(3752,plain,
% 2.67/2.04 ($false),
% 2.67/2.04 inference(unit_resolution,[status(thm)],[3751, 91, 3730, 3729, 1299, 3726, 3725, 24, 1298, 3745, 3744, 3737])).
% 2.67/2.04 tff(3753,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,[]))).
% 2.67/2.05 tff(3754,plain,
% 2.67/2.05 (c1_1(a1435)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[3753, 3713, 24, 37, 3284, 3285, 3286, 3695])).
% 2.67/2.05 tff(3755,plain,
% 2.67/2.05 (hskp18 | (~c1_1(a1435))),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[397, 91, 3286, 3284, 3285, 380])).
% 2.67/2.05 tff(3756,plain,
% 2.67/2.05 (hskp18),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[3755, 139])).
% 2.67/2.05 tff(3757,plain,
% 2.67/2.05 (~c2_1(a1458)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[403, 3756])).
% 2.67/2.05 tff(3758,plain,
% 2.67/2.05 (c1_1(a1458)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[414, 3756])).
% 2.67/2.05 tff(3759,plain,
% 2.67/2.05 (c0_1(a1458)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[425, 3756])).
% 2.67/2.05 tff(3760,plain,
% 2.67/2.05 (((~![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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3761,plain,
% 2.67/2.05 ((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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3762,plain,
% 2.67/2.05 (((~![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))))),
% 2.67/2.05 inference(monotonicity,[status(thm)],[3761])).
% 2.67/2.05 tff(3763,plain,
% 2.67/2.05 (((~![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)))),
% 2.67/2.05 inference(transitivity,[status(thm)],[3762, 3760])).
% 2.67/2.05 tff(3764,plain,
% 2.67/2.05 ((~![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)))),
% 2.67/2.05 inference(quant_inst,[status(thm)],[])).
% 2.67/2.05 tff(3765,plain,
% 2.67/2.05 ((~![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))),
% 2.67/2.05 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 2.67/2.05 tff(3766,plain,
% 2.67/2.05 (hskp10),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[3765, 91, 3759, 3758, 1299, 3757, 37, 369, 50])).
% 2.67/2.05 tff(3767,plain,
% 2.67/2.05 (~c3_1(a1445)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[439, 3766])).
% 2.67/2.05 tff(3768,plain,
% 2.67/2.05 (~c1_1(a1445)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[445, 3766])).
% 2.67/2.05 tff(3769,plain,
% 2.67/2.05 (c0_1(a1445)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[456, 3766])).
% 2.67/2.05 tff(3770,plain,
% 2.67/2.05 (((~![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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3771,plain,
% 2.67/2.05 (((~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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3772,plain,
% 2.67/2.05 (((~![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))))),
% 2.67/2.05 inference(monotonicity,[status(thm)],[3771])).
% 2.67/2.05 tff(3773,plain,
% 2.67/2.05 (((~![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)))),
% 2.67/2.05 inference(transitivity,[status(thm)],[3772, 3770])).
% 2.67/2.05 tff(3774,plain,
% 2.67/2.05 ((~![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))),
% 2.67/2.05 inference(quant_inst,[status(thm)],[])).
% 2.67/2.05 tff(3775,plain,
% 2.67/2.05 ((~![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))),
% 2.67/2.05 inference(modus_ponens,[status(thm)],[3774, 3773])).
% 2.67/2.05 tff(3776,plain,
% 2.67/2.05 (~c2_1(a1445)),
% 2.67/2.05 inference(unit_resolution,[status(thm)],[3775, 91, 3769, 3768, 3767, 37, 24, 23, 50])).
% 2.67/2.05 tff(3777,plain,
% 2.67/2.05 (((~![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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3778,plain,
% 2.67/2.05 ((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)))),
% 2.67/2.05 inference(rewrite,[status(thm)],[])).
% 2.67/2.05 tff(3779,plain,
% 2.67/2.05 (((~![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))))),
% 2.67/2.05 inference(monotonicity,[status(thm)],[3778])).
% 2.67/2.05 tff(3780,plain,
% 2.67/2.05 (((~![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)))),
% 2.69/2.05 inference(transitivity,[status(thm)],[3779, 3777])).
% 2.69/2.05 tff(3781,plain,
% 2.69/2.05 ((~![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)))),
% 2.69/2.05 inference(quant_inst,[status(thm)],[])).
% 2.69/2.05 tff(3782,plain,
% 2.69/2.05 ((~![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))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 2.69/2.05 tff(3783,plain,
% 2.69/2.05 (hskp21),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[3782, 91, 3769, 2518, 2517, 3768, 2516, 2557, 3776])).
% 2.69/2.05 tff(3784,plain,
% 2.69/2.05 (c2_1(a1466)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[2581, 3783])).
% 2.69/2.05 tff(3785,plain,
% 2.69/2.05 (c0_1(a1466)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[2592, 3783])).
% 2.69/2.05 tff(3786,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3787,plain,
% 2.69/2.05 (((~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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3788,plain,
% 2.69/2.05 (((~![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))))),
% 2.69/2.05 inference(monotonicity,[status(thm)],[3787])).
% 2.69/2.05 tff(3789,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(transitivity,[status(thm)],[3788, 3786])).
% 2.69/2.05 tff(3790,plain,
% 2.69/2.05 ((~![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)))),
% 2.69/2.05 inference(quant_inst,[status(thm)],[])).
% 2.69/2.05 tff(3791,plain,
% 2.69/2.05 ((~![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))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 2.69/2.05 tff(3792,plain,
% 2.69/2.05 (~c3_1(a1466)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[3791, 91, 3785, 3784, 1299, 3286, 24, 3285, 2617, 139, 50])).
% 2.69/2.05 tff(3793,plain,
% 2.69/2.05 (^[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))))),
% 2.69/2.05 inference(bind,[status(th)],[])).
% 2.69/2.05 tff(3794,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(quant_intro,[status(thm)],[3793])).
% 2.69/2.05 tff(3795,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3796,plain,
% 2.69/2.05 (^[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)))))),
% 2.69/2.05 inference(bind,[status(th)],[])).
% 2.69/2.05 tff(3797,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(quant_intro,[status(thm)],[3796])).
% 2.69/2.05 tff(3798,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')).
% 2.69/2.05 tff(3799,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3798, 3797])).
% 2.69/2.05 tff(3800,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3799, 3795])).
% 2.69/2.05 tff(3801,plain,(
% 2.69/2.05 ![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)))),
% 2.69/2.05 inference(skolemize,[status(sab)],[3800])).
% 2.69/2.05 tff(3802,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3801, 3794])).
% 2.69/2.05 tff(3803,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3804,plain,
% 2.69/2.05 ((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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3805,plain,
% 2.69/2.05 (((~![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))))),
% 2.69/2.05 inference(monotonicity,[status(thm)],[3804])).
% 2.69/2.05 tff(3806,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(transitivity,[status(thm)],[3805, 3803])).
% 2.69/2.05 tff(3807,plain,
% 2.69/2.05 ((~![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)))),
% 2.69/2.05 inference(quant_inst,[status(thm)],[])).
% 2.69/2.05 tff(3808,plain,
% 2.69/2.05 ((~![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))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 2.69/2.05 tff(3809,plain,
% 2.69/2.05 (hskp22),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[3808, 91, 3578, 3577, 1299, 3575, 24, 1385, 50])).
% 2.69/2.05 tff(3810,plain,
% 2.69/2.05 (~c0_1(a1468)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[891, 3809])).
% 2.69/2.05 tff(3811,plain,
% 2.69/2.05 (c3_1(a1468)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[902, 3809])).
% 2.69/2.05 tff(3812,plain,
% 2.69/2.05 (c1_1(a1468)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[913, 3809])).
% 2.69/2.05 tff(3813,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3814,plain,
% 2.69/2.05 (((~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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3815,plain,
% 2.69/2.05 (((~![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))))),
% 2.69/2.05 inference(monotonicity,[status(thm)],[3814])).
% 2.69/2.05 tff(3816,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.05 inference(transitivity,[status(thm)],[3815, 3813])).
% 2.69/2.05 tff(3817,plain,
% 2.69/2.05 ((~![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)))),
% 2.69/2.05 inference(quant_inst,[status(thm)],[])).
% 2.69/2.05 tff(3818,plain,
% 2.69/2.05 ((~![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))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 2.69/2.05 tff(3819,plain,
% 2.69/2.05 (~c2_1(a1430)),
% 2.69/2.05 inference(unit_resolution,[status(thm)],[3818, 91, 3812, 3811, 3578, 3577, 3810, 3575, 12, 1374, 592])).
% 2.69/2.05 tff(3820,plain,
% 2.69/2.05 (^[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))))),
% 2.69/2.05 inference(bind,[status(th)],[])).
% 2.69/2.05 tff(3821,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(quant_intro,[status(thm)],[3820])).
% 2.69/2.05 tff(3822,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(3823,plain,
% 2.69/2.05 (^[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)))))),
% 2.69/2.05 inference(bind,[status(th)],[])).
% 2.69/2.05 tff(3824,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(quant_intro,[status(thm)],[3823])).
% 2.69/2.05 tff(3825,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')).
% 2.69/2.05 tff(3826,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3825, 3824])).
% 2.69/2.05 tff(3827,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3826, 3822])).
% 2.69/2.05 tff(3828,plain,(
% 2.69/2.05 ![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)))),
% 2.69/2.05 inference(skolemize,[status(sab)],[3827])).
% 2.69/2.05 tff(3829,plain,
% 2.69/2.05 (![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)))),
% 2.69/2.05 inference(modus_ponens,[status(thm)],[3828, 3821])).
% 2.69/2.05 tff(3830,plain,
% 2.69/2.05 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3831,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3832,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3831])).
% 2.69/2.06 tff(3833,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3832, 3830])).
% 2.69/2.06 tff(3834,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3835,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3834, 3833])).
% 2.69/2.06 tff(3836,plain,
% 2.69/2.06 (hskp28),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3835, 91, 3812, 3811, 3759, 3758, 3810, 3757, 3829])).
% 2.69/2.06 tff(3837,plain,
% 2.69/2.06 (((~hskp28) | c3_1(a1456)) <=> ((~hskp28) | c3_1(a1456))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3838,axiom,((~hskp28) | c3_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 2.69/2.06 tff(3839,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 2.69/2.06 tff(3840,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3839, 3837])).
% 2.69/2.06 tff(3841,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3840, 3837])).
% 2.69/2.06 tff(3842,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3841, 3837])).
% 2.69/2.06 tff(3843,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3842, 3837])).
% 2.69/2.06 tff(3844,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3843, 3837])).
% 2.69/2.06 tff(3845,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3844, 3837])).
% 2.69/2.06 tff(3846,plain,
% 2.69/2.06 ((~hskp28) | c3_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3845, 3837])).
% 2.69/2.06 tff(3847,plain,
% 2.69/2.06 (c3_1(a1456)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3846, 3836])).
% 2.69/2.06 tff(3848,plain,
% 2.69/2.06 (((~hskp28) | c1_1(a1456)) <=> ((~hskp28) | c1_1(a1456))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3849,axiom,((~hskp28) | c1_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.69/2.06 tff(3850,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 2.69/2.06 tff(3851,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3850, 3848])).
% 2.69/2.06 tff(3852,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3851, 3848])).
% 2.69/2.06 tff(3853,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3852, 3848])).
% 2.69/2.06 tff(3854,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3853, 3848])).
% 2.69/2.06 tff(3855,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3854, 3848])).
% 2.69/2.06 tff(3856,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3855, 3848])).
% 2.69/2.06 tff(3857,plain,
% 2.69/2.06 ((~hskp28) | c1_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3856, 3848])).
% 2.69/2.06 tff(3858,plain,
% 2.69/2.06 (c1_1(a1456)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3857, 3836])).
% 2.69/2.06 tff(3859,plain,
% 2.69/2.06 (((~hskp28) | c0_1(a1456)) <=> ((~hskp28) | c0_1(a1456))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3860,axiom,((~hskp28) | c0_1(a1456)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 2.69/2.06 tff(3861,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3860, 3859])).
% 2.69/2.06 tff(3862,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3861, 3859])).
% 2.69/2.06 tff(3863,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3862, 3859])).
% 2.69/2.06 tff(3864,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3863, 3859])).
% 2.69/2.06 tff(3865,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3864, 3859])).
% 2.69/2.06 tff(3866,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3865, 3859])).
% 2.69/2.06 tff(3867,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3866, 3859])).
% 2.69/2.06 tff(3868,plain,
% 2.69/2.06 ((~hskp28) | c0_1(a1456)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3867, 3859])).
% 2.69/2.06 tff(3869,plain,
% 2.69/2.06 (c0_1(a1456)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3868, 3836])).
% 2.69/2.06 tff(3870,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3871,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3872,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3871])).
% 2.69/2.06 tff(3873,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3872, 3870])).
% 2.69/2.06 tff(3874,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3875,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 2.69/2.06 tff(3876,plain,
% 2.69/2.06 (hskp6),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3875, 91, 3869, 3858, 3847, 2185, 3819, 3802, 592])).
% 2.69/2.06 tff(3877,plain,
% 2.69/2.06 (~c2_1(a1437)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2209, 3876])).
% 2.69/2.06 tff(3878,plain,
% 2.69/2.06 (~c1_1(a1437)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2233, 3876])).
% 2.69/2.06 tff(3879,plain,
% 2.69/2.06 (~c1_1(a1466)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2570, 3783])).
% 2.69/2.06 tff(3880,plain,
% 2.69/2.06 (c0_1(a1437)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2220, 3876])).
% 2.69/2.06 tff(3881,plain,
% 2.69/2.06 (((~![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))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3882,plain,
% 2.69/2.06 (((~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))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3883,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3882])).
% 2.69/2.06 tff(3884,plain,
% 2.69/2.06 (((~![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))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3883, 3881])).
% 2.69/2.06 tff(3885,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3886,plain,
% 2.69/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1466)) | c3_1(a1466)),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 2.69/2.06 tff(3887,plain,
% 2.69/2.06 ($false),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3886, 91, 3784, 1299, 3880, 3879, 37, 3878, 3877, 591, 50, 3792])).
% 2.69/2.06 tff(3888,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,[]))).
% 2.69/2.06 tff(3889,plain,
% 2.69/2.06 (c2_1(a1438)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3888, 3713, 37, 24, 3754, 592, 3716, 3715, 3714, 12])).
% 2.69/2.06 tff(3890,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3891,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3892,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3891])).
% 2.69/2.06 tff(3893,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3892, 3890])).
% 2.69/2.06 tff(3894,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3895,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 2.69/2.06 tff(3896,plain,
% 2.69/2.06 (hskp23 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3895, 91, 3716, 3715, 24, 3714, 1801])).
% 2.69/2.06 tff(3897,plain,
% 2.69/2.06 (hskp23),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3896, 3889, 3713])).
% 2.69/2.06 tff(3898,plain,
% 2.69/2.06 (c2_1(a1477)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1622, 3897])).
% 2.69/2.06 tff(3899,plain,
% 2.69/2.06 (~c0_1(a1477)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1679, 3897])).
% 2.69/2.06 tff(3900,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3901,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3902,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3901])).
% 2.69/2.06 tff(3903,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3902, 3900])).
% 2.69/2.06 tff(3904,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3905,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 2.69/2.06 tff(3906,plain,
% 2.69/2.06 (hskp8 | (~c1_1(a1435)) | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3905, 91, 3286, 24, 3285, 1639])).
% 2.69/2.06 tff(3907,plain,
% 2.69/2.06 (hskp8),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3906, 3889, 3713, 3754])).
% 2.69/2.06 tff(3908,plain,
% 2.69/2.06 (~c1_1(a1441)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1651, 3907])).
% 2.69/2.06 tff(3909,plain,
% 2.69/2.06 (c3_1(a1441)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1662, 3907])).
% 2.69/2.06 tff(3910,plain,
% 2.69/2.06 (c0_1(a1441)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1673, 3907])).
% 2.69/2.06 tff(3911,plain,
% 2.69/2.06 (~c1_1(a1477)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1628, 3897])).
% 2.69/2.06 tff(3912,plain,
% 2.69/2.06 (~c2_1(a1441)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1695, 3911, 3910, 3909, 3908, 3899, 3898])).
% 2.69/2.06 tff(3913,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3914,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3915,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3914])).
% 2.69/2.06 tff(3916,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3915, 3913])).
% 2.69/2.06 tff(3917,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3918,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 2.69/2.06 tff(3919,plain,
% 2.69/2.06 (hskp19),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3918, 91, 3910, 3716, 3715, 3908, 3714, 1191, 3912])).
% 2.69/2.06 tff(3920,plain,
% 2.69/2.06 (~c1_1(a1460)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1268, 3919])).
% 2.69/2.06 tff(3921,plain,
% 2.69/2.06 (~c0_1(a1460)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1255, 3919])).
% 2.69/2.06 tff(3922,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3923,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3924,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3923])).
% 2.69/2.06 tff(3925,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3924, 3922])).
% 2.69/2.06 tff(3926,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3927,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 2.69/2.06 tff(3928,plain,
% 2.69/2.06 (hskp22),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3927, 91, 3578, 3577, 3909, 3575, 3908, 1385, 3912])).
% 2.69/2.06 tff(3929,plain,
% 2.69/2.06 (~c0_1(a1468)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[891, 3928])).
% 2.69/2.06 tff(3930,plain,
% 2.69/2.06 (c3_1(a1468)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[902, 3928])).
% 2.69/2.06 tff(3931,plain,
% 2.69/2.06 (c1_1(a1468)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[913, 3928])).
% 2.69/2.06 tff(3932,plain,
% 2.69/2.06 (~c2_1(a1460)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2546, 91, 3931, 3930, 3578, 3577, 3929, 3921, 3920, 3575, 1374])).
% 2.69/2.06 tff(3933,plain,
% 2.69/2.06 (hskp20),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3600, 3889, 3713])).
% 2.69/2.06 tff(3934,plain,
% 2.69/2.06 (~c1_1(a1465)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1323, 3933])).
% 2.69/2.06 tff(3935,plain,
% 2.69/2.06 (c3_1(a1465)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1334, 3933])).
% 2.69/2.06 tff(3936,plain,
% 2.69/2.06 (c2_1(a1465)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[1345, 3933])).
% 2.69/2.06 tff(3937,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3938,plain,
% 2.69/2.06 (((~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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3939,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3938])).
% 2.69/2.06 tff(3940,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3939, 3937])).
% 2.69/2.06 tff(3941,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3942,plain,
% 2.69/2.06 ((~![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))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3941, 3940])).
% 2.69/2.06 tff(3943,plain,
% 2.69/2.06 (~c1_1(a1427)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3942, 91, 3936, 3935, 3909, 3716, 3715, 3934, 3908, 1706, 3912])).
% 2.69/2.06 tff(3944,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3945,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3946,plain,
% 2.69/2.06 (((~![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))))),
% 2.69/2.06 inference(monotonicity,[status(thm)],[3945])).
% 2.69/2.06 tff(3947,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(transitivity,[status(thm)],[3946, 3944])).
% 2.69/2.06 tff(3948,plain,
% 2.69/2.06 ((~![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)))),
% 2.69/2.06 inference(quant_inst,[status(thm)],[])).
% 2.69/2.06 tff(3949,plain,
% 2.69/2.06 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1441) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | (~c0_1(a1427)) | c2_1(a1441) | (~c0_1(a1441))),
% 2.69/2.06 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 2.69/2.06 tff(3950,plain,
% 2.69/2.06 (hskp21),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3949, 91, 3910, 3716, 3715, 3908, 3714, 2557, 3912])).
% 2.69/2.06 tff(3951,plain,
% 2.69/2.06 (~c1_1(a1466)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2570, 3950])).
% 2.69/2.06 tff(3952,plain,
% 2.69/2.06 (c2_1(a1466)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2581, 3950])).
% 2.69/2.06 tff(3953,plain,
% 2.69/2.06 (c0_1(a1466)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2592, 3950])).
% 2.69/2.06 tff(3954,plain,
% 2.69/2.06 ($false),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[2599, 91, 3953, 3952, 3716, 3951, 3921, 3920, 3714, 23, 3943, 3932])).
% 2.69/2.06 tff(3955,plain,(c1_1(a1430) | c1_1(a1438) | hskp11 | c0_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.06 tff(3956,plain,
% 2.69/2.06 (c1_1(a1430)),
% 2.69/2.06 inference(unit_resolution,[status(thm)],[3955, 37, 1300, 24, 12])).
% 2.69/2.06 tff(3957,plain,
% 2.69/2.06 (((~![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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.06 tff(3958,plain,
% 2.69/2.06 ((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)))),
% 2.69/2.06 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3959,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[3958])).
% 2.69/2.07 tff(3960,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[3959, 3957])).
% 2.69/2.07 tff(3961,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(3962,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 2.69/2.07 tff(3963,plain,
% 2.69/2.07 (hskp17 | (~c1_1(a1430))),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3962, 91, 3578, 3577, 2185, 3575, 12, 336])).
% 2.69/2.07 tff(3964,plain,
% 2.69/2.07 (hskp17),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3963, 3956])).
% 2.69/2.07 tff(3965,plain,
% 2.69/2.07 (~c2_1(a1457)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[288, 3964])).
% 2.69/2.07 tff(3966,plain,
% 2.69/2.07 (~c1_1(a1457)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[269, 3964])).
% 2.69/2.07 tff(3967,plain,
% 2.69/2.07 (~c0_1(a1457)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[275, 3964])).
% 2.69/2.07 tff(3968,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3969,plain,
% 2.69/2.07 (((~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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3970,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[3969])).
% 2.69/2.07 tff(3971,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[3970, 3968])).
% 2.69/2.07 tff(3972,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(3973,plain,
% 2.69/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a1466) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1435) | (~ndr1_0) | c1_1(a1435) | (~c0_1(a1435)) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 2.69/2.07 tff(3974,plain,
% 2.69/2.07 ($false),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3973, 91, 3730, 3729, 114, 3728, 2642, 2641, 2640, 113, 23, 337])).
% 2.69/2.07 tff(3975,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,[]))).
% 2.69/2.07 tff(3976,plain,
% 2.69/2.07 (c1_1(a1435)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3975, 3967, 3286, 3966, 3965, 3285, 3284, 3695])).
% 2.69/2.07 tff(3977,plain,
% 2.69/2.07 (hskp7 | hskp4),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[130, 91, 114, 112, 113, 124])).
% 2.69/2.07 tff(3978,plain,
% 2.69/2.07 (hskp4),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3977, 13])).
% 2.69/2.07 tff(3979,plain,
% 2.69/2.07 (~c2_1(a1434)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[137, 3978])).
% 2.69/2.07 tff(3980,plain,
% 2.69/2.07 ($false),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[182, 3979, 3978, 112, 139, 113, 13])).
% 2.69/2.07 tff(3981,plain,(hskp7 | c2_1(a1435) | (~c1_1(a1435)) | c3_1(a1435) | (~c0_1(a1435))), inference(lemma,lemma(discharge,[]))).
% 2.69/2.07 tff(3982,plain,
% 2.69/2.07 (hskp7),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3981, 3976, 3284, 3285, 3286])).
% 2.69/2.07 tff(3983,plain,
% 2.69/2.07 (c3_1(a1438)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[110, 3982])).
% 2.69/2.07 tff(3984,plain,
% 2.69/2.07 (~c2_1(a1438)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3585, 3956, 37])).
% 2.69/2.07 tff(3985,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3986,plain,
% 2.69/2.07 ((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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3987,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[3986])).
% 2.69/2.07 tff(3988,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[3987, 3985])).
% 2.69/2.07 tff(3989,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(3990,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 2.69/2.07 tff(3991,plain,
% 2.69/2.07 (hskp10 | (~c1_1(a1435)) | (~c3_1(a1438))),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3990, 91, 3286, 37, 3284, 369, 3984])).
% 2.69/2.07 tff(3992,plain,
% 2.69/2.07 (hskp10),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3991, 3983, 3976])).
% 2.69/2.07 tff(3993,plain,
% 2.69/2.07 (~c3_1(a1445)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[439, 3992])).
% 2.69/2.07 tff(3994,plain,
% 2.69/2.07 (~c1_1(a1445)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[445, 3992])).
% 2.69/2.07 tff(3995,plain,
% 2.69/2.07 (c0_1(a1445)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[456, 3992])).
% 2.69/2.07 tff(3996,plain,
% 2.69/2.07 (~c2_1(a1445)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[463, 91, 3995, 3967, 3966, 3965, 3994, 3993, 23])).
% 2.69/2.07 tff(3997,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3998,plain,
% 2.69/2.07 ((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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(3999,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[3998])).
% 2.69/2.07 tff(4000,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[3999, 3997])).
% 2.69/2.07 tff(4001,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(4002,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 2.69/2.07 tff(4003,plain,
% 2.69/2.07 (hskp28 | (~c1_1(a1430)) | (~c1_1(a1435))),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4002, 91, 3286, 2185, 3284, 12, 3829])).
% 2.69/2.07 tff(4004,plain,
% 2.69/2.07 (hskp28),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4003, 3976, 3956])).
% 2.69/2.07 tff(4005,plain,
% 2.69/2.07 (c3_1(a1456)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3846, 4004])).
% 2.69/2.07 tff(4006,plain,
% 2.69/2.07 (c1_1(a1456)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3857, 4004])).
% 2.69/2.07 tff(4007,plain,
% 2.69/2.07 (c0_1(a1456)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3868, 4004])).
% 2.69/2.07 tff(4008,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4009,plain,
% 2.69/2.07 ((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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4010,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[4009])).
% 2.69/2.07 tff(4011,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[4010, 4008])).
% 2.69/2.07 tff(4012,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(4013,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[4012, 4011])).
% 2.69/2.07 tff(4014,plain,
% 2.69/2.07 (hskp6 | (~c3_1(a1438))),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4013, 91, 4007, 4006, 4005, 24, 3802, 3984])).
% 2.69/2.07 tff(4015,plain,
% 2.69/2.07 (hskp6),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4014, 3983])).
% 2.69/2.07 tff(4016,plain,
% 2.69/2.07 (~c2_1(a1437)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2209, 4015])).
% 2.69/2.07 tff(4017,plain,
% 2.69/2.07 (~c1_1(a1437)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2233, 4015])).
% 2.69/2.07 tff(4018,plain,
% 2.69/2.07 (c0_1(a1437)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2220, 4015])).
% 2.69/2.07 tff(4019,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4020,plain,
% 2.69/2.07 ((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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4021,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[4020])).
% 2.69/2.07 tff(4022,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[4021, 4019])).
% 2.69/2.07 tff(4023,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(4024,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 2.69/2.07 tff(4025,plain,
% 2.69/2.07 (hskp21),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4024, 91, 4018, 3716, 3715, 4017, 4016, 3714, 2557])).
% 2.69/2.07 tff(4026,plain,
% 2.69/2.07 (~c1_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2570, 4025])).
% 2.69/2.07 tff(4027,plain,
% 2.69/2.07 (c2_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2581, 4025])).
% 2.69/2.07 tff(4028,plain,
% 2.69/2.07 (((~![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))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4029,plain,
% 2.69/2.07 (((~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))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4030,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[4029])).
% 2.69/2.07 tff(4031,plain,
% 2.69/2.07 (((~![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))),
% 2.69/2.07 inference(transitivity,[status(thm)],[4030, 4028])).
% 2.69/2.07 tff(4032,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(4033,plain,
% 2.69/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c1_1(a1445) | c0_1(a1438) | (~ndr1_0) | c2_1(a1438) | (~c3_1(a1438)) | c2_1(a1445) | (~c0_1(a1445)) | (~c2_1(a1466)) | c3_1(a1466)),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[4032, 4031])).
% 2.69/2.07 tff(4034,plain,
% 2.69/2.07 (c3_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4033, 91, 4027, 3995, 3983, 4026, 3994, 37, 591, 3984, 3996])).
% 2.69/2.07 tff(4035,plain,
% 2.69/2.07 (c0_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2592, 4025])).
% 2.69/2.07 tff(4036,plain,
% 2.69/2.07 ($false),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3791, 91, 4035, 4027, 3983, 3286, 24, 3285, 2617, 3976, 3984, 4034])).
% 2.69/2.07 tff(4037,plain,(c0_1(a1438) | c1_1(a1438) | c0_1(a1430) | hskp11), inference(lemma,lemma(discharge,[]))).
% 2.69/2.07 tff(4038,plain,
% 2.69/2.07 (c0_1(a1438)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4037, 24, 12, 1300])).
% 2.69/2.07 tff(4039,plain,
% 2.69/2.07 (~hskp7),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[1099, 4038])).
% 2.69/2.07 tff(4040,plain,
% 2.69/2.07 (~c1_1(a1435)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3981, 4039, 3284, 3285, 3286])).
% 2.69/2.07 tff(4041,plain,
% 2.69/2.07 (hskp19 | c1_1(a1435)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3722, 91, 3286, 3716, 3715, 3284, 3714, 1191])).
% 2.69/2.07 tff(4042,plain,
% 2.69/2.07 (hskp19),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4041, 4040])).
% 2.69/2.07 tff(4043,plain,
% 2.69/2.07 (~c1_1(a1460)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[1268, 4042])).
% 2.69/2.07 tff(4044,plain,
% 2.69/2.07 (~c0_1(a1460)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[1255, 4042])).
% 2.69/2.07 tff(4045,plain,
% 2.69/2.07 (hskp21),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3700, 4040, 3286, 3284, 3695])).
% 2.69/2.07 tff(4046,plain,
% 2.69/2.07 (~c1_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2570, 4045])).
% 2.69/2.07 tff(4047,plain,
% 2.69/2.07 (c2_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2581, 4045])).
% 2.69/2.07 tff(4048,plain,
% 2.69/2.07 (c0_1(a1466)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[2592, 4045])).
% 2.69/2.07 tff(4049,plain,
% 2.69/2.07 (c2_1(a1460)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[3736, 91, 4048, 4047, 3286, 4046, 4044, 4043, 3285, 23, 4040])).
% 2.69/2.07 tff(4050,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4051,plain,
% 2.69/2.07 (((~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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4052,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[4051])).
% 2.69/2.07 tff(4053,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(transitivity,[status(thm)],[4052, 4050])).
% 2.69/2.07 tff(4054,plain,
% 2.69/2.07 ((~![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)))),
% 2.69/2.07 inference(quant_inst,[status(thm)],[])).
% 2.69/2.07 tff(4055,plain,
% 2.69/2.07 ((~![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))),
% 2.69/2.07 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 2.69/2.07 tff(4056,plain,
% 2.69/2.07 (~c1_1(a1430)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[4055, 91, 3578, 3577, 2185, 4044, 4043, 3575, 12, 1374, 4049])).
% 2.69/2.07 tff(4057,plain,
% 2.69/2.07 (~c3_1(a1460)),
% 2.69/2.07 inference(unit_resolution,[status(thm)],[1249, 4042])).
% 2.69/2.07 tff(4058,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4059,plain,
% 2.69/2.07 (((~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)))),
% 2.69/2.07 inference(rewrite,[status(thm)],[])).
% 2.69/2.07 tff(4060,plain,
% 2.69/2.07 (((~![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))))),
% 2.69/2.07 inference(monotonicity,[status(thm)],[4059])).
% 2.69/2.07 tff(4061,plain,
% 2.69/2.07 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4060, 4058])).
% 2.69/2.08 tff(4062,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4063,plain,
% 2.69/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1460) | c3_1(a1460) | c2_1(a1435) | c3_1(a1435) | c0_1(a1430) | (~ndr1_0) | c1_1(a1430) | (~c3_1(a1430)) | c1_1(a1435) | (~c2_1(a1460))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4062, 4061])).
% 2.69/2.08 tff(4064,plain,
% 2.69/2.08 ($false),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4063, 91, 2185, 4043, 4057, 3284, 3285, 12, 626, 4056, 4040, 4049])).
% 2.69/2.08 tff(4065,plain,(c1_1(a1438) | c0_1(a1430) | hskp11), inference(lemma,lemma(discharge,[]))).
% 2.69/2.08 tff(4066,plain,
% 2.69/2.08 (c1_1(a1438)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4065, 1300, 12])).
% 2.69/2.08 tff(4067,plain,
% 2.69/2.08 (~hskp7),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[1514, 4066])).
% 2.69/2.08 tff(4068,plain,
% 2.69/2.08 (~c1_1(a1435)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3981, 4067, 3284, 3285, 3286])).
% 2.69/2.08 tff(4069,plain,
% 2.69/2.08 (~hskp25),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3668, 4068, 3286, 3285, 4067])).
% 2.69/2.08 tff(4070,plain,
% 2.69/2.08 (hskp4),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3346, 4067])).
% 2.69/2.08 tff(4071,plain,
% 2.69/2.08 (c3_1(a1434)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[161, 4070])).
% 2.69/2.08 tff(4072,plain,
% 2.69/2.08 (c1_1(a1434)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[150, 4070])).
% 2.69/2.08 tff(4073,assumption,(~hskp25), introduced(assumption)).
% 2.69/2.08 tff(4074,plain,
% 2.69/2.08 (hskp0 | (~c0_1(a1434))),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3637, 91, 4073, 3610, 3609, 3631])).
% 2.69/2.08 tff(4075,plain,
% 2.69/2.08 (~c0_1(a1434)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4074, 2757])).
% 2.69/2.08 tff(4076,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4077,plain,
% 2.69/2.08 ((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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4078,plain,
% 2.69/2.08 (((~![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))))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4077])).
% 2.69/2.08 tff(4079,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4078, 4076])).
% 2.69/2.08 tff(4080,plain,
% 2.69/2.08 ((~![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)))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4081,plain,
% 2.69/2.08 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a1448) | (~ndr1_0) | c0_1(a1434) | (~c1_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1448)) | (~c0_1(a1448))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4080, 4079])).
% 2.69/2.08 tff(4082,plain,
% 2.69/2.08 (hskp17),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4081, 91, 3612, 3611, 3610, 3609, 254, 336, 4075])).
% 2.69/2.08 tff(4083,plain,
% 2.69/2.08 (~c2_1(a1457)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[288, 4082])).
% 2.69/2.08 tff(4084,plain,
% 2.69/2.08 (~c1_1(a1457)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[269, 4082])).
% 2.69/2.08 tff(4085,plain,
% 2.69/2.08 (~c0_1(a1457)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[275, 4082])).
% 2.69/2.08 tff(4086,plain,
% 2.69/2.08 ($false),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3467, 91, 2757, 114, 4085, 4084, 4083, 112, 113, 1201])).
% 2.69/2.08 tff(4087,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,[]))).
% 2.69/2.08 tff(4088,plain,
% 2.69/2.08 (hskp0),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4087, 4072, 3284, 3285, 3578, 3577, 3286, 4071, 3575, 4069])).
% 2.69/2.08 tff(4089,plain,
% 2.69/2.08 (hskp21),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3700, 4088, 3286, 3284, 4068])).
% 2.69/2.08 tff(4090,plain,
% 2.69/2.08 (c2_1(a1466)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[2581, 4089])).
% 2.69/2.08 tff(4091,plain,
% 2.69/2.08 (c0_1(a1466)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[2592, 4089])).
% 2.69/2.08 tff(4092,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4093,plain,
% 2.69/2.08 ((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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4094,plain,
% 2.69/2.08 (((~![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))))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4093])).
% 2.69/2.08 tff(4095,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4094, 4092])).
% 2.69/2.08 tff(4096,plain,
% 2.69/2.08 ((~![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)))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4097,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 2.69/2.08 tff(4098,plain,
% 2.69/2.08 (~c3_1(a1466)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4097, 91, 1300, 4091, 4090, 3286, 3284, 3285, 3062])).
% 2.69/2.08 tff(4099,plain,
% 2.69/2.08 (~c1_1(a1466)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[2570, 4089])).
% 2.69/2.08 tff(4100,plain,
% 2.69/2.08 (((~![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))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4101,plain,
% 2.69/2.08 (((~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))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4102,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4101])).
% 2.69/2.08 tff(4103,plain,
% 2.69/2.08 (((~![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))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4102, 4100])).
% 2.69/2.08 tff(4104,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4105,plain,
% 2.69/2.08 ((~![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)),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4104, 4103])).
% 2.69/2.08 tff(4106,plain,
% 2.69/2.08 (c1_1(a1430)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4105, 91, 4090, 2185, 4099, 3284, 3285, 12, 626, 4068, 4098])).
% 2.69/2.08 tff(4107,plain,
% 2.69/2.08 (((~![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))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4108,plain,
% 2.69/2.08 (((~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))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4109,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4108])).
% 2.69/2.08 tff(4110,plain,
% 2.69/2.08 (((~![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))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4109, 4107])).
% 2.69/2.08 tff(4111,plain,
% 2.69/2.08 ((~![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)))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4112,plain,
% 2.69/2.08 ((~![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)),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 2.69/2.08 tff(4113,plain,
% 2.69/2.08 (c2_1(a1430)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4112, 91, 4090, 3286, 2185, 4099, 3284, 12, 591, 4068, 4098])).
% 2.69/2.08 tff(4114,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4115,plain,
% 2.69/2.08 ((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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4116,plain,
% 2.69/2.08 (((~![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))))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4115])).
% 2.69/2.08 tff(4117,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4116, 4114])).
% 2.69/2.08 tff(4118,plain,
% 2.69/2.08 ((~![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)))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4119,plain,
% 2.69/2.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp7 | c1_1(a1466) | c0_1(a1430) | (~c2_1(a1430)) | (~ndr1_0) | (~c1_1(a1430)) | c3_1(a1466) | (~c0_1(a1466))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 2.69/2.08 tff(4120,plain,
% 2.69/2.08 ($false),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4119, 91, 4067, 4091, 4099, 12, 4113, 193, 4106, 4098])).
% 2.69/2.08 tff(4121,plain,(hskp11 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.08 tff(4122,plain,
% 2.69/2.08 (hskp11),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4121, 12])).
% 2.69/2.08 tff(4123,plain,
% 2.69/2.08 (~c3_1(a1447)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[757, 4122])).
% 2.69/2.08 tff(4124,plain,
% 2.69/2.08 (~c2_1(a1447)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[745, 4122])).
% 2.69/2.08 tff(4125,plain,
% 2.69/2.08 (~c0_1(a1447)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[751, 4122])).
% 2.69/2.08 tff(4126,plain,
% 2.69/2.08 (hskp0 | c1_1(a1447)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[3293, 91, 114, 759, 761, 112, 113, 1201])).
% 2.69/2.08 tff(4127,plain,
% 2.69/2.08 (c1_1(a1447)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4126, 2757])).
% 2.69/2.08 tff(4128,plain,
% 2.69/2.08 (^[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))))),
% 2.69/2.08 inference(bind,[status(th)],[])).
% 2.69/2.08 tff(4129,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(quant_intro,[status(thm)],[4128])).
% 2.69/2.08 tff(4130,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4131,plain,
% 2.69/2.08 (^[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)))))),
% 2.69/2.08 inference(bind,[status(th)],[])).
% 2.69/2.08 tff(4132,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(quant_intro,[status(thm)],[4131])).
% 2.69/2.08 tff(4133,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')).
% 2.69/2.08 tff(4134,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 2.69/2.08 tff(4135,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4134, 4130])).
% 2.69/2.08 tff(4136,plain,(
% 2.69/2.08 ![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)))),
% 2.69/2.08 inference(skolemize,[status(sab)],[4135])).
% 2.69/2.08 tff(4137,plain,
% 2.69/2.08 (![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)))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4136, 4129])).
% 2.69/2.08 tff(4138,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4139,plain,
% 2.69/2.08 ((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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4140,plain,
% 2.69/2.08 (((~![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))))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4139])).
% 2.69/2.08 tff(4141,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4140, 4138])).
% 2.69/2.08 tff(4142,plain,
% 2.69/2.08 ((~![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)))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4143,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 2.69/2.08 tff(4144,plain,
% 2.69/2.08 (hskp18 | (~c1_1(a1447))),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4143, 91, 114, 761, 760, 112, 113, 380])).
% 2.69/2.08 tff(4145,plain,
% 2.69/2.08 (hskp18),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4144, 4127])).
% 2.69/2.08 tff(4146,plain,
% 2.69/2.08 (~c2_1(a1458)),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[403, 4145])).
% 2.69/2.08 tff(4147,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4148,plain,
% 2.69/2.08 ((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)))),
% 2.69/2.08 inference(rewrite,[status(thm)],[])).
% 2.69/2.08 tff(4149,plain,
% 2.69/2.08 (((~![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))))),
% 2.69/2.08 inference(monotonicity,[status(thm)],[4148])).
% 2.69/2.08 tff(4150,plain,
% 2.69/2.08 (((~![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)))),
% 2.69/2.08 inference(transitivity,[status(thm)],[4149, 4147])).
% 2.69/2.08 tff(4151,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(quant_inst,[status(thm)],[])).
% 2.69/2.08 tff(4152,plain,
% 2.69/2.08 ((~![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))),
% 2.69/2.08 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 2.69/2.08 tff(4153,plain,
% 2.69/2.08 (hskp0 | (~c1_1(a1448))),
% 2.69/2.08 inference(unit_resolution,[status(thm)],[4152, 91, 3611, 254, 759, 761, 760, 2440])).
% 2.69/2.09 tff(4154,plain,
% 2.69/2.09 (~c1_1(a1448)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4153, 2757])).
% 2.69/2.09 tff(4155,plain,
% 2.69/2.09 (hskp22 | c1_1(a1448)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2535, 91, 3612, 3611, 254, 1385])).
% 2.69/2.09 tff(4156,plain,
% 2.69/2.09 (hskp22),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4155, 4154])).
% 2.69/2.09 tff(4157,plain,
% 2.69/2.09 (~c0_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[891, 4156])).
% 2.69/2.09 tff(4158,plain,
% 2.69/2.09 (c1_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[414, 4145])).
% 2.69/2.09 tff(4159,plain,
% 2.69/2.09 (c0_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[425, 4145])).
% 2.69/2.09 tff(4160,plain,
% 2.69/2.09 (c3_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[902, 4156])).
% 2.69/2.09 tff(4161,plain,
% 2.69/2.09 (c1_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[913, 4156])).
% 2.69/2.09 tff(4162,plain,
% 2.69/2.09 (hskp28),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3835, 91, 4161, 4160, 4159, 4158, 4157, 4146, 3829])).
% 2.69/2.09 tff(4163,plain,
% 2.69/2.09 (c3_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3846, 4162])).
% 2.69/2.09 tff(4164,plain,
% 2.69/2.09 (c1_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3857, 4162])).
% 2.69/2.09 tff(4165,plain,
% 2.69/2.09 (c0_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3868, 4162])).
% 2.69/2.09 tff(4166,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4167,plain,
% 2.69/2.09 ((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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4168,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4167])).
% 2.69/2.09 tff(4169,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4168, 4166])).
% 2.69/2.09 tff(4170,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4171,plain,
% 2.69/2.09 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp0 | c0_1(a1447) | c2_1(a1447) | (~ndr1_0) | (~c3_1(a1456)) | (~c1_1(a1456)) | (~c0_1(a1456)) | (~c1_1(a1447))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 2.69/2.09 tff(4172,plain,
% 2.69/2.09 ($false),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4171, 91, 2757, 4165, 4164, 4163, 759, 761, 4137, 4127])).
% 2.69/2.09 tff(4173,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,[]))).
% 2.69/2.09 tff(4174,plain,
% 2.69/2.09 (hskp0),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4173, 4125, 4124, 3578, 3577, 3575, 3286, 4123, 3284, 3285])).
% 2.69/2.09 tff(4175,plain,
% 2.69/2.09 (~c3_1(a1427)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1213, 4174])).
% 2.69/2.09 tff(4176,plain,
% 2.69/2.09 (c0_1(a1427)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1235, 4174])).
% 2.69/2.09 tff(4177,plain,
% 2.69/2.09 (c2_1(a1427)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1224, 4174])).
% 2.69/2.09 tff(4178,plain,
% 2.69/2.09 (c1_1(a1447)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3324, 4177, 3286, 3285, 4125, 4123, 4124, 4176, 4175, 3284])).
% 2.69/2.09 tff(4179,plain,
% 2.69/2.09 (hskp18 | (~c1_1(a1447))),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4143, 91, 3286, 4124, 4123, 3284, 3285, 380])).
% 2.69/2.09 tff(4180,plain,
% 2.69/2.09 (hskp18),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4179, 4178])).
% 2.69/2.09 tff(4181,plain,
% 2.69/2.09 (~c2_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[403, 4180])).
% 2.69/2.09 tff(4182,plain,
% 2.69/2.09 (c1_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[414, 4180])).
% 2.69/2.09 tff(4183,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4184,plain,
% 2.69/2.09 ((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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4185,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4184])).
% 2.69/2.09 tff(4186,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4185, 4183])).
% 2.69/2.09 tff(4187,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4188,plain,
% 2.69/2.09 ((~![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))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4187, 4186])).
% 2.69/2.09 tff(4189,plain,
% 2.69/2.09 (hskp7 | (~c3_1(a1458))),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4188, 91, 4182, 4181, 4124, 4123, 172, 4178])).
% 2.69/2.09 tff(4190,plain,
% 2.69/2.09 (~c3_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4189, 13])).
% 2.69/2.09 tff(4191,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4192,plain,
% 2.69/2.09 ((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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4193,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4192])).
% 2.69/2.09 tff(4194,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4193, 4191])).
% 2.69/2.09 tff(4195,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4196,plain,
% 2.69/2.09 ((~![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))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 2.69/2.09 tff(4197,plain,
% 2.69/2.09 (hskp7 | (~c1_1(a1447)) | (~c1_1(a1448))),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4196, 91, 3577, 3575, 4124, 4123, 172])).
% 2.69/2.09 tff(4198,plain,
% 2.69/2.09 (~c1_1(a1448)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4197, 13, 4178])).
% 2.69/2.09 tff(4199,plain,
% 2.69/2.09 (c0_1(a1458)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[425, 4180])).
% 2.69/2.09 tff(4200,plain,
% 2.69/2.09 (~c1_1(a1435)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3981, 13, 3284, 3285, 3286])).
% 2.69/2.09 tff(4201,plain,
% 2.69/2.09 (hskp21),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3700, 4200, 3286, 3284, 4174])).
% 2.69/2.09 tff(4202,plain,
% 2.69/2.09 (c2_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2581, 4201])).
% 2.69/2.09 tff(4203,plain,
% 2.69/2.09 (c0_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2592, 4201])).
% 2.69/2.09 tff(4204,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4205,plain,
% 2.69/2.09 (((~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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4206,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4205])).
% 2.69/2.09 tff(4207,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4206, 4204])).
% 2.69/2.09 tff(4208,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4209,plain,
% 2.69/2.09 ((~![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))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 2.69/2.09 tff(4210,plain,
% 2.69/2.09 (~c3_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4209, 91, 4203, 4202, 4199, 4182, 3577, 3575, 2617, 4198, 4190])).
% 2.69/2.09 tff(4211,plain,
% 2.69/2.09 (((~![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))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4212,plain,
% 2.69/2.09 ((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))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4213,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4212])).
% 2.69/2.09 tff(4214,plain,
% 2.69/2.09 (((~![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))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4213, 4211])).
% 2.69/2.09 tff(4215,plain,
% 2.69/2.09 ((~![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))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4216,plain,
% 2.69/2.09 ((~![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)),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 2.69/2.09 tff(4217,plain,
% 2.69/2.09 (hskp2 | c1_1(a1435)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4216, 91, 4125, 4124, 4123, 3284, 3285, 60])).
% 2.69/2.09 tff(4218,plain,
% 2.69/2.09 (hskp2),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4217, 4200])).
% 2.69/2.09 tff(4219,plain,
% 2.69/2.09 (~c2_1(a1430)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2296, 4218])).
% 2.69/2.09 tff(4220,plain,
% 2.69/2.09 (~c1_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2570, 4201])).
% 2.69/2.09 tff(4221,plain,
% 2.69/2.09 (((~![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))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4222,plain,
% 2.69/2.09 (((~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))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4223,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4222])).
% 2.69/2.09 tff(4224,plain,
% 2.69/2.09 (((~![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))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4223, 4221])).
% 2.69/2.09 tff(4225,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4226,plain,
% 2.69/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1466) | c2_1(a1448) | c0_1(a1430) | c2_1(a1430) | (~ndr1_0) | (~c3_1(a1430)) | (~c0_1(a1448)) | c1_1(a1448) | (~c2_1(a1466)) | c3_1(a1466)),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 2.69/2.09 tff(4227,plain,
% 2.69/2.09 ($false),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4226, 91, 4202, 3578, 2185, 4220, 3575, 12, 4219, 591, 4198, 4210])).
% 2.69/2.09 tff(4228,plain,(hskp7 | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.09 tff(4229,plain,
% 2.69/2.09 (hskp7),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4228, 12])).
% 2.69/2.09 tff(4230,plain,
% 2.69/2.09 (~c0_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1099, 4229])).
% 2.69/2.09 tff(4231,plain,
% 2.69/2.09 (~c1_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1514, 4229])).
% 2.69/2.09 tff(4232,plain,
% 2.69/2.09 (c3_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3712, 592, 24, 4174, 37, 12])).
% 2.69/2.09 tff(4233,plain,
% 2.69/2.09 (c1_1(a1435)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3753, 4232, 24, 37, 3284, 3285, 3286, 4174])).
% 2.69/2.09 tff(4234,plain,
% 2.69/2.09 (c2_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3888, 4232, 37, 24, 592, 4233, 4176, 4177, 4175, 12])).
% 2.69/2.09 tff(4235,plain,
% 2.69/2.09 (hskp23 | (~c2_1(a1438)) | (~c3_1(a1438))),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3895, 91, 4176, 4177, 24, 4175, 1801])).
% 2.69/2.09 tff(4236,plain,
% 2.69/2.09 (hskp23),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4235, 4232, 4234])).
% 2.69/2.09 tff(4237,plain,
% 2.69/2.09 (c2_1(a1477)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1622, 4236])).
% 2.69/2.09 tff(4238,plain,
% 2.69/2.09 (~c0_1(a1477)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1679, 4236])).
% 2.69/2.09 tff(4239,plain,
% 2.69/2.09 (hskp8),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3906, 4232, 4233, 4234])).
% 2.69/2.09 tff(4240,plain,
% 2.69/2.09 (~c1_1(a1441)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1651, 4239])).
% 2.69/2.09 tff(4241,plain,
% 2.69/2.09 (c3_1(a1441)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1662, 4239])).
% 2.69/2.09 tff(4242,plain,
% 2.69/2.09 (c0_1(a1441)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1673, 4239])).
% 2.69/2.09 tff(4243,plain,
% 2.69/2.09 (~c1_1(a1477)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1628, 4236])).
% 2.69/2.09 tff(4244,plain,
% 2.69/2.09 (~c2_1(a1441)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1695, 4243, 4242, 4241, 4240, 4238, 4237])).
% 2.69/2.09 tff(4245,plain,
% 2.69/2.09 (hskp19),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3918, 91, 4242, 4176, 4177, 4240, 4175, 1191, 4244])).
% 2.69/2.09 tff(4246,plain,
% 2.69/2.09 (~c1_1(a1460)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1268, 4245])).
% 2.69/2.09 tff(4247,plain,
% 2.69/2.09 (~c0_1(a1460)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[1255, 4245])).
% 2.69/2.09 tff(4248,plain,
% 2.69/2.09 (hskp22),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3927, 91, 3578, 3577, 4241, 3575, 4240, 1385, 4244])).
% 2.69/2.09 tff(4249,plain,
% 2.69/2.09 (~c0_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[891, 4248])).
% 2.69/2.09 tff(4250,plain,
% 2.69/2.09 (c3_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[902, 4248])).
% 2.69/2.09 tff(4251,plain,
% 2.69/2.09 (c1_1(a1468)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[913, 4248])).
% 2.69/2.09 tff(4252,plain,
% 2.69/2.09 (~c2_1(a1460)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2546, 91, 4251, 4250, 3578, 3577, 4249, 4247, 4246, 3575, 1374])).
% 2.69/2.09 tff(4253,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4254,plain,
% 2.69/2.09 (((~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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4255,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4254])).
% 2.69/2.09 tff(4256,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4255, 4253])).
% 2.69/2.09 tff(4257,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4258,plain,
% 2.69/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1441) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1427)) | (~c1_1(a1427)) | (~c0_1(a1427)) | (~c2_1(a1438)) | (~c3_1(a1438)) | c2_1(a1441) | (~c3_1(a1441))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4257, 4256])).
% 2.69/2.09 tff(4259,plain,
% 2.69/2.09 (~c1_1(a1427)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4258, 91, 4241, 4232, 4176, 4177, 4240, 24, 1706, 4234, 4244])).
% 2.69/2.09 tff(4260,plain,
% 2.69/2.09 (hskp21),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3949, 91, 4242, 4176, 4177, 4240, 4175, 2557, 4244])).
% 2.69/2.09 tff(4261,plain,
% 2.69/2.09 (~c1_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2570, 4260])).
% 2.69/2.09 tff(4262,plain,
% 2.69/2.09 (c2_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2581, 4260])).
% 2.69/2.09 tff(4263,plain,
% 2.69/2.09 (c0_1(a1466)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2592, 4260])).
% 2.69/2.09 tff(4264,plain,
% 2.69/2.09 ($false),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2599, 91, 4263, 4262, 4176, 4261, 4247, 4246, 4175, 23, 4259, 4252])).
% 2.69/2.09 tff(4265,plain,(c1_1(a1430) | c1_1(a1438) | c0_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.09 tff(4266,plain,
% 2.69/2.09 (c1_1(a1430)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4265, 37, 24, 12])).
% 2.69/2.09 tff(4267,plain,
% 2.69/2.09 (~c2_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3585, 4266, 37])).
% 2.69/2.09 tff(4268,plain,
% 2.69/2.09 (hskp17),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3963, 4266])).
% 2.69/2.09 tff(4269,plain,
% 2.69/2.09 (~c0_1(a1457)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[275, 4268])).
% 2.69/2.09 tff(4270,plain,
% 2.69/2.09 (~c2_1(a1457)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[288, 4268])).
% 2.69/2.09 tff(4271,plain,
% 2.69/2.09 (~c1_1(a1457)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[269, 4268])).
% 2.69/2.09 tff(4272,plain,
% 2.69/2.09 (c1_1(a1435)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3975, 4271, 3286, 4174, 4270, 3285, 3284, 4269])).
% 2.69/2.09 tff(4273,plain,
% 2.69/2.09 (hskp7),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3981, 4272, 3284, 3285, 3286])).
% 2.69/2.09 tff(4274,plain,
% 2.69/2.09 (c3_1(a1438)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[110, 4273])).
% 2.69/2.09 tff(4275,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4276,plain,
% 2.69/2.09 ((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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4277,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.09 inference(monotonicity,[status(thm)],[4276])).
% 2.69/2.09 tff(4278,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(transitivity,[status(thm)],[4277, 4275])).
% 2.69/2.09 tff(4279,plain,
% 2.69/2.09 ((~![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)))),
% 2.69/2.09 inference(quant_inst,[status(thm)],[])).
% 2.69/2.09 tff(4280,plain,
% 2.69/2.09 ((~![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))),
% 2.69/2.09 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 2.69/2.09 tff(4281,plain,
% 2.69/2.09 (hskp28 | (~c1_1(a1430))),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4280, 91, 4199, 4182, 2185, 4181, 12, 3829])).
% 2.69/2.09 tff(4282,plain,
% 2.69/2.09 (hskp28),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4281, 4266])).
% 2.69/2.09 tff(4283,plain,
% 2.69/2.09 (c3_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3846, 4282])).
% 2.69/2.09 tff(4284,plain,
% 2.69/2.09 (c1_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3857, 4282])).
% 2.69/2.09 tff(4285,plain,
% 2.69/2.09 (c0_1(a1456)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3868, 4282])).
% 2.69/2.09 tff(4286,plain,
% 2.69/2.09 (hskp6),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[4013, 91, 4285, 4284, 4283, 4274, 24, 3802, 4267])).
% 2.69/2.09 tff(4287,plain,
% 2.69/2.09 (~c2_1(a1437)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2209, 4286])).
% 2.69/2.09 tff(4288,plain,
% 2.69/2.09 (~c1_1(a1437)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2233, 4286])).
% 2.69/2.09 tff(4289,plain,
% 2.69/2.09 (hskp10),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[3765, 91, 4199, 4182, 4274, 4181, 37, 369, 4267])).
% 2.69/2.09 tff(4290,plain,
% 2.69/2.09 (~c3_1(a1445)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[439, 4289])).
% 2.69/2.09 tff(4291,plain,
% 2.69/2.09 (~c1_1(a1445)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[445, 4289])).
% 2.69/2.09 tff(4292,plain,
% 2.69/2.09 (c0_1(a1437)),
% 2.69/2.09 inference(unit_resolution,[status(thm)],[2220, 4286])).
% 2.69/2.09 tff(4293,plain,
% 2.69/2.09 (((~![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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4294,plain,
% 2.69/2.09 (((~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)))),
% 2.69/2.09 inference(rewrite,[status(thm)],[])).
% 2.69/2.09 tff(4295,plain,
% 2.69/2.09 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4294])).
% 2.69/2.10 tff(4296,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4295, 4293])).
% 2.69/2.10 tff(4297,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4298,plain,
% 2.69/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1445) | c3_1(a1445) | c0_1(a1438) | c1_1(a1437) | c2_1(a1437) | (~ndr1_0) | (~c0_1(a1437)) | c2_1(a1438) | (~c3_1(a1438)) | (~c2_1(a1445))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4297, 4296])).
% 2.69/2.10 tff(4299,plain,
% 2.69/2.10 (~c2_1(a1445)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4298, 91, 4274, 4292, 4291, 4290, 37, 4288, 4287, 591, 4267])).
% 2.69/2.10 tff(4300,plain,
% 2.69/2.10 (hskp21),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4024, 91, 4292, 4176, 4177, 4288, 4287, 4175, 2557])).
% 2.69/2.10 tff(4301,plain,
% 2.69/2.10 (~c1_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2570, 4300])).
% 2.69/2.10 tff(4302,plain,
% 2.69/2.10 (c0_1(a1445)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[456, 4289])).
% 2.69/2.10 tff(4303,plain,
% 2.69/2.10 (c2_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2581, 4300])).
% 2.69/2.10 tff(4304,plain,
% 2.69/2.10 (c3_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4033, 91, 4303, 4302, 4274, 4301, 4291, 37, 591, 4267, 4299])).
% 2.69/2.10 tff(4305,plain,
% 2.69/2.10 (c0_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2592, 4300])).
% 2.69/2.10 tff(4306,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[3791, 91, 4305, 4303, 4274, 3286, 24, 3285, 2617, 4272, 4267, 4304])).
% 2.69/2.10 tff(4307,plain,(c0_1(a1438) | c1_1(a1438) | c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4308,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4307, 4231, 4230, 12])).
% 2.69/2.10 tff(4309,plain,(c0_1(a1430)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4310,plain,
% 2.69/2.10 (((~hskp2) | (~c0_1(a1430))) <=> ((~hskp2) | (~c0_1(a1430)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4311,plain,
% 2.69/2.10 (((~c0_1(a1430)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1430)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4312,axiom,((~c0_1(a1430)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 2.69/2.10 tff(4313,plain,
% 2.69/2.10 ((~hskp2) | (~c0_1(a1430))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 2.69/2.10 tff(4314,plain,
% 2.69/2.10 ((~hskp2) | (~c0_1(a1430))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4313, 4310])).
% 2.69/2.10 tff(4315,plain,
% 2.69/2.10 (~hskp2),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4314, 4309])).
% 2.69/2.10 tff(4316,plain,
% 2.69/2.10 ((~hskp11) | hskp5),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[795, 4315])).
% 2.69/2.10 tff(4317,plain,
% 2.69/2.10 (~hskp11),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4316, 11])).
% 2.69/2.10 tff(4318,plain,
% 2.69/2.10 (hskp5 | (~c3_1(a1487)) | c2_1(a1487)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1020, 4315])).
% 2.69/2.10 tff(4319,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4318, 972, 983, 11])).
% 2.69/2.10 tff(4320,plain,((~hskp24) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4321,plain,
% 2.69/2.10 (~hskp24),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4320, 11])).
% 2.69/2.10 tff(4322,plain,
% 2.69/2.10 (hskp30),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[89, 4321])).
% 2.69/2.10 tff(4323,plain,
% 2.69/2.10 (c1_1(a1507)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1604, 4322])).
% 2.69/2.10 tff(4324,plain,
% 2.69/2.10 (c2_1(a1507)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1528, 4322])).
% 2.69/2.10 tff(4325,plain,
% 2.69/2.10 (c0_1(a1507)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1539, 4322])).
% 2.69/2.10 tff(4326,plain,
% 2.69/2.10 (^[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))))),
% 2.69/2.10 inference(bind,[status(th)],[])).
% 2.69/2.10 tff(4327,plain,
% 2.69/2.10 (![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)))),
% 2.69/2.10 inference(quant_intro,[status(thm)],[4326])).
% 2.69/2.10 tff(4328,plain,
% 2.69/2.10 (![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4329,plain,
% 2.69/2.10 (^[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)))))),
% 2.69/2.10 inference(bind,[status(th)],[])).
% 2.69/2.10 tff(4330,plain,
% 2.69/2.10 (![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)))),
% 2.69/2.10 inference(quant_intro,[status(thm)],[4329])).
% 2.69/2.10 tff(4331,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp21) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 2.69/2.10 tff(4332,plain,
% 2.69/2.10 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4331, 4330])).
% 2.69/2.10 tff(4333,plain,
% 2.69/2.10 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4332, 4328])).
% 2.69/2.10 tff(4334,plain,(
% 2.69/2.10 ![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.69/2.10 inference(skolemize,[status(sab)],[4333])).
% 2.69/2.10 tff(4335,plain,
% 2.69/2.10 (![U: $i] : (hskp21 | hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4334, 4327])).
% 2.69/2.10 tff(4336,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4337,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4338,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4337])).
% 2.69/2.10 tff(4339,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4338, 4336])).
% 2.69/2.10 tff(4340,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4341,plain,
% 2.69/2.10 ((~![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))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 2.69/2.10 tff(4342,plain,
% 2.69/2.10 (hskp21 | hskp9),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4341, 91, 1550, 1981, 1549, 4335])).
% 2.69/2.10 tff(4343,plain,
% 2.69/2.10 (hskp9),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4342, 3698])).
% 2.69/2.10 tff(4344,plain,
% 2.69/2.10 (~c3_1(a1444)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1131, 4343])).
% 2.69/2.10 tff(4345,plain,
% 2.69/2.10 (~c2_1(a1444)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1137, 4343])).
% 2.69/2.10 tff(4346,plain,
% 2.69/2.10 (~c1_1(a1444)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1143, 4343])).
% 2.69/2.10 tff(4347,plain,
% 2.69/2.10 (c0_1(a1444)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1180, 91, 4315, 4346, 4345, 4344, 60])).
% 2.69/2.10 tff(4348,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4349,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4350,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4349])).
% 2.69/2.10 tff(4351,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4350, 4348])).
% 2.69/2.10 tff(4352,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4353,plain,
% 2.69/2.10 ((~![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))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 2.69/2.10 tff(4354,plain,
% 2.69/2.10 (~c3_1(a1507)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4353, 91, 1300, 1550, 1549, 4345, 4344, 3062, 4347])).
% 2.69/2.10 tff(4355,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4356,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4357,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4356])).
% 2.69/2.10 tff(4358,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4357, 4355])).
% 2.69/2.10 tff(4359,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4360,plain,
% 2.69/2.10 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1444) | c2_1(a1444) | (~ndr1_0) | (~c0_1(a1507)) | c3_1(a1507) | (~c2_1(a1507)) | (~c0_1(a1444))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 2.69/2.10 tff(4361,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4360, 91, 3698, 1550, 1549, 4346, 4345, 2557, 4354, 4347])).
% 2.69/2.10 tff(4362,plain,(hskp21 | (~c0_1(a1507)) | (~c2_1(a1507)) | hskp11 | (~c1_1(a1507))), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4363,plain,
% 2.69/2.10 (hskp21),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4362, 4325, 4324, 4317, 4323])).
% 2.69/2.10 tff(4364,assumption,(hskp21), introduced(assumption)).
% 2.69/2.10 tff(4365,plain,
% 2.69/2.10 (~c1_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2570, 4364])).
% 2.69/2.10 tff(4366,plain,
% 2.69/2.10 (c2_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2581, 4364])).
% 2.69/2.10 tff(4367,plain,
% 2.69/2.10 (c0_1(a1466)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[2592, 4364])).
% 2.69/2.10 tff(4368,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4369,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4370,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4369])).
% 2.69/2.10 tff(4371,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4370, 4368])).
% 2.69/2.10 tff(4372,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4373,plain,
% 2.69/2.10 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c1_1(a1466) | (~ndr1_0) | (~c2_1(a1466)) | (~c0_1(a1466))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 2.69/2.10 tff(4374,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4373, 91, 1300, 2757, 4367, 4366, 4365, 1811])).
% 2.69/2.10 tff(4375,plain,((~hskp21) | hskp11 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4376,plain,
% 2.69/2.10 (hskp0),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4375, 4363, 4317])).
% 2.69/2.10 tff(4377,plain,
% 2.69/2.10 (hskp12),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[3330, 4376, 4317])).
% 2.69/2.10 tff(4378,plain,
% 2.69/2.10 (~c2_1(a1448)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[220, 4377])).
% 2.69/2.10 tff(4379,plain,
% 2.69/2.10 (hskp17),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[263, 4378, 11, 4377])).
% 2.69/2.10 tff(4380,plain,
% 2.69/2.10 (~c1_1(a1457)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[269, 4379])).
% 2.69/2.10 tff(4381,plain,
% 2.69/2.10 (~c0_1(a1457)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[275, 4379])).
% 2.69/2.10 tff(4382,plain,
% 2.69/2.10 (c3_1(a1448)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[242, 4377])).
% 2.69/2.10 tff(4383,plain,
% 2.69/2.10 (c0_1(a1448)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[231, 4377])).
% 2.69/2.10 tff(4384,plain,
% 2.69/2.10 (~c3_1(a1457)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[282, 91, 11, 4383, 4382, 4381, 4380, 4378, 10])).
% 2.69/2.10 tff(4385,plain,
% 2.69/2.10 (~c2_1(a1457)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[288, 4379])).
% 2.69/2.10 tff(4386,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[1018, 91, 4315, 4381, 4380, 4385, 60, 4384])).
% 2.69/2.10 tff(4387,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4388,plain,
% 2.69/2.10 (~c3_1(a1435)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[319, 4387])).
% 2.69/2.10 tff(4389,plain,
% 2.69/2.10 (~hskp5),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[390, 700])).
% 2.69/2.10 tff(4390,plain,
% 2.69/2.10 (c0_1(a1435) | c2_1(a1435) | c3_1(a1435) | hskp5),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[735, 4315])).
% 2.69/2.10 tff(4391,plain,
% 2.69/2.10 (c2_1(a1435)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4390, 700, 4389, 113])).
% 2.69/2.10 tff(4392,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4393,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4394,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4393])).
% 2.69/2.10 tff(4395,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4394, 4392])).
% 2.69/2.10 tff(4396,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4397,plain,
% 2.69/2.10 ((~![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))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4396, 4395])).
% 2.69/2.10 tff(4398,plain,
% 2.69/2.10 (~c3_1(a1438)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4397, 91, 4389, 37, 24, 4391, 113, 848, 337])).
% 2.69/2.10 tff(4399,plain,
% 2.69/2.10 (c2_1(a1438) | c3_1(a1438) | c0_1(a1438) | c1_1(a1438)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[99, 4315])).
% 2.69/2.10 tff(4400,plain,
% 2.69/2.10 (c2_1(a1438)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4399, 4398, 24, 37])).
% 2.69/2.10 tff(4401,plain,
% 2.69/2.10 (((~![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))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4402,plain,
% 2.69/2.10 ((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))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4403,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4402])).
% 2.69/2.10 tff(4404,plain,
% 2.69/2.10 (((~![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))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4403, 4401])).
% 2.69/2.10 tff(4405,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4406,plain,
% 2.69/2.10 ((~![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)),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 2.69/2.10 tff(4407,plain,
% 2.69/2.10 (hskp4 | c1_1(a1435)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4406, 91, 2757, 700, 4391, 2774])).
% 2.69/2.10 tff(4408,plain,
% 2.69/2.10 (hskp4),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4407, 337])).
% 2.69/2.10 tff(4409,plain,
% 2.69/2.10 (~c2_1(a1434)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[137, 4408])).
% 2.69/2.10 tff(4410,plain,
% 2.69/2.10 (c3_1(a1434)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[161, 4408])).
% 2.69/2.10 tff(4411,plain,
% 2.69/2.10 (~hskp11),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4316, 4389])).
% 2.69/2.10 tff(4412,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4413,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4414,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4413])).
% 2.69/2.10 tff(4415,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4414, 4412])).
% 2.69/2.10 tff(4416,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4417,plain,
% 2.69/2.10 ((~![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))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 2.69/2.10 tff(4418,plain,
% 2.69/2.10 (c0_1(a1434)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4417, 91, 4411, 4389, 4410, 4409, 34])).
% 2.69/2.10 tff(4419,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4420,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4421,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4420])).
% 2.69/2.10 tff(4422,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4421, 4419])).
% 2.69/2.10 tff(4423,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.10 tff(4424,plain,
% 2.69/2.10 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434))),
% 2.69/2.10 inference(modus_ponens,[status(thm)],[4423, 4422])).
% 2.69/2.10 tff(4425,plain,
% 2.69/2.10 (hskp17 | (~c0_1(a1434))),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4424, 91, 4389, 4410, 4409, 253])).
% 2.69/2.10 tff(4426,plain,
% 2.69/2.10 (hskp17),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4425, 4418])).
% 2.69/2.10 tff(4427,plain,
% 2.69/2.10 ((~hskp17) | c3_1(a1438) | c1_1(a1438) | (~c2_1(a1438)) | hskp5),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[862, 4315])).
% 2.69/2.10 tff(4428,plain,
% 2.69/2.10 ($false),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4427, 4426, 4400, 24, 4398, 4389])).
% 2.69/2.10 tff(4429,plain,(c1_1(a1435) | c1_1(a1438) | c0_1(a1438) | c3_1(a1435) | hskp0 | c0_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.10 tff(4430,plain,
% 2.69/2.10 (c1_1(a1435)),
% 2.69/2.10 inference(unit_resolution,[status(thm)],[4429, 37, 24, 113, 2757, 700])).
% 2.69/2.10 tff(4431,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4432,plain,
% 2.69/2.10 ((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)))),
% 2.69/2.10 inference(rewrite,[status(thm)],[])).
% 2.69/2.10 tff(4433,plain,
% 2.69/2.10 (((~![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))))),
% 2.69/2.10 inference(monotonicity,[status(thm)],[4432])).
% 2.69/2.10 tff(4434,plain,
% 2.69/2.10 (((~![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)))),
% 2.69/2.10 inference(transitivity,[status(thm)],[4433, 4431])).
% 2.69/2.10 tff(4435,plain,
% 2.69/2.10 ((~![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)))),
% 2.69/2.10 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4436,plain,
% 2.69/2.11 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a1435) | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c1_1(a1435))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 2.69/2.11 tff(4437,plain,
% 2.69/2.11 (hskp14 | (~c1_1(a1435))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4436, 91, 700, 4391, 113, 524])).
% 2.69/2.11 tff(4438,plain,
% 2.69/2.11 (hskp14),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4437, 4430])).
% 2.69/2.11 tff(4439,plain,
% 2.69/2.11 (~c3_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[2903, 4438, 4389, 24, 37])).
% 2.69/2.11 tff(4440,plain,
% 2.69/2.11 (c2_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4399, 4439, 24, 37])).
% 2.69/2.11 tff(4441,plain,
% 2.69/2.11 (hskp4 | c0_1(a1438) | (~c2_1(a1438))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[3340, 91, 2757, 24, 2774])).
% 2.69/2.11 tff(4442,plain,
% 2.69/2.11 (hskp4),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4441, 4440, 37])).
% 2.69/2.11 tff(4443,plain,
% 2.69/2.11 (~c2_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[137, 4442])).
% 2.69/2.11 tff(4444,plain,
% 2.69/2.11 (c3_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[161, 4442])).
% 2.69/2.11 tff(4445,plain,
% 2.69/2.11 (~hskp17),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4427, 4440, 24, 4439, 4389])).
% 2.69/2.11 tff(4446,plain,
% 2.69/2.11 (~c0_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4424, 91, 4445, 4389, 4444, 4443, 253])).
% 2.69/2.11 tff(4447,plain,
% 2.69/2.11 ($false),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4417, 91, 4411, 4389, 4444, 4443, 34, 4446])).
% 2.69/2.11 tff(4448,plain,(c0_1(a1438) | hskp0 | c1_1(a1438) | c0_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.11 tff(4449,plain,
% 2.69/2.11 (c0_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4448, 24, 2757, 700, 113])).
% 2.69/2.11 tff(4450,plain,
% 2.69/2.11 (hskp5 | c3_1(a1438) | (~c0_1(a1438)) | c1_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1757, 4315])).
% 2.69/2.11 tff(4451,plain,
% 2.69/2.11 (c3_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4450, 4449, 4389, 24])).
% 2.69/2.11 tff(4452,plain,
% 2.69/2.11 ((~c0_1(a1438)) | (~c2_1(a1438))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1817, 91, 4411, 2757, 24, 1811])).
% 2.69/2.11 tff(4453,plain,
% 2.69/2.11 (~c2_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4452, 4449])).
% 2.69/2.11 tff(4454,plain,
% 2.69/2.11 (c2_1(a1438) | hskp5 | (~c3_1(a1438)) | (~c0_1(a1438))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1778, 4315])).
% 2.69/2.11 tff(4455,plain,
% 2.69/2.11 ($false),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4454, 4453, 4451, 4389, 4449])).
% 2.69/2.11 tff(4456,plain,(c1_1(a1438) | hskp0 | c0_1(a1435) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.11 tff(4457,plain,
% 2.69/2.11 (c1_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4456, 700, 2757, 113])).
% 2.69/2.11 tff(4458,plain,
% 2.69/2.11 (~hskp24),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4320, 4389])).
% 2.69/2.11 tff(4459,plain,
% 2.69/2.11 (c3_1(a1438) | hskp5 | (~c1_1(a1438)) | hskp24),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[2107, 4315])).
% 2.69/2.11 tff(4460,plain,
% 2.69/2.11 (c3_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4459, 4458, 4389, 4457])).
% 2.69/2.11 tff(4461,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4462,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4463,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4462])).
% 2.69/2.11 tff(4464,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4463, 4461])).
% 2.69/2.11 tff(4465,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4466,plain,
% 2.69/2.11 ((~![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))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4465, 4464])).
% 2.69/2.11 tff(4467,plain,
% 2.69/2.11 (c1_1(a1435)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4466, 91, 2757, 4460, 700, 37, 4457, 4391, 2274])).
% 2.69/2.11 tff(4468,plain,
% 2.69/2.11 (hskp30),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[89, 4458])).
% 2.69/2.11 tff(4469,plain,
% 2.69/2.11 (c2_1(a1507)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1528, 4468])).
% 2.69/2.11 tff(4470,plain,
% 2.69/2.11 (c1_1(a1507)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1604, 4468])).
% 2.69/2.11 tff(4471,plain,
% 2.69/2.11 (c0_1(a1507)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1539, 4468])).
% 2.69/2.11 tff(4472,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4473,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4474,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4473])).
% 2.69/2.11 tff(4475,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4474, 4472])).
% 2.69/2.11 tff(4476,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4477,plain,
% 2.69/2.11 ((~![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))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4476, 4475])).
% 2.69/2.11 tff(4478,plain,
% 2.69/2.11 (hskp23 | (~c1_1(a1435))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4477, 91, 4471, 4470, 4469, 4391, 113, 1594])).
% 2.69/2.11 tff(4479,plain,
% 2.69/2.11 (hskp23),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4478, 4467])).
% 2.69/2.11 tff(4480,plain,
% 2.69/2.11 (~c1_1(a1477)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1628, 4479])).
% 2.69/2.11 tff(4481,plain,
% 2.69/2.11 (~c0_1(a1477)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1679, 4479])).
% 2.69/2.11 tff(4482,plain,
% 2.69/2.11 (c2_1(a1477)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[1622, 4479])).
% 2.69/2.11 tff(4483,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4484,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4485,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4484])).
% 2.69/2.11 tff(4486,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4485, 4483])).
% 2.69/2.11 tff(4487,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4488,plain,
% 2.69/2.11 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a1477) | c1_1(a1477) | c0_1(a1438) | (~c1_1(a1438)) | (~ndr1_0) | (~c3_1(a1438)) | (~c2_1(a1477))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 2.69/2.11 tff(4489,plain,
% 2.69/2.11 ($false),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4488, 91, 2757, 4482, 4460, 4481, 4480, 37, 4457, 2274])).
% 2.69/2.11 tff(4490,plain,(c0_1(a1438) | hskp0 | c3_1(a1435) | c0_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.11 tff(4491,plain,
% 2.69/2.11 (c0_1(a1438)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4490, 700, 113, 2757])).
% 2.69/2.11 tff(4492,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4493,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4494,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4493])).
% 2.69/2.11 tff(4495,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4494, 4492])).
% 2.69/2.11 tff(4496,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4497,plain,
% 2.69/2.11 ((~![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))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 2.69/2.11 tff(4498,plain,
% 2.69/2.11 (hskp25 | (~c0_1(a1438)) | (~c3_1(a1438))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4497, 91, 2757, 4457, 3631])).
% 2.69/2.11 tff(4499,plain,
% 2.69/2.11 (hskp25),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4498, 4491, 4460])).
% 2.69/2.11 tff(4500,plain,
% 2.69/2.11 (~c0_1(a1504)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[493, 4499])).
% 2.69/2.11 tff(4501,plain,
% 2.69/2.11 (c2_1(a1504)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[534, 4499])).
% 2.69/2.11 tff(4502,plain,
% 2.69/2.11 (c1_1(a1504)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[506, 4499])).
% 2.69/2.11 tff(4503,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4504,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4505,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4504])).
% 2.69/2.11 tff(4506,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4505, 4503])).
% 2.69/2.11 tff(4507,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4508,plain,
% 2.69/2.11 ((~![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))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 2.69/2.11 tff(4509,plain,
% 2.69/2.11 (hskp14),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4508, 91, 4502, 4501, 700, 4500, 4391, 113, 524])).
% 2.69/2.11 tff(4510,plain,
% 2.69/2.11 (~c1_1(a1451)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[553, 4509])).
% 2.69/2.11 tff(4511,plain,
% 2.69/2.11 (c2_1(a1451)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[564, 4509])).
% 2.69/2.11 tff(4512,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4513,plain,
% 2.69/2.11 ((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)))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4514,plain,
% 2.69/2.11 (((~![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))))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4513])).
% 2.69/2.11 tff(4515,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4514, 4512])).
% 2.69/2.11 tff(4516,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4517,plain,
% 2.69/2.11 ((~![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))),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 2.69/2.11 tff(4518,plain,
% 2.69/2.11 (~c0_1(a1451)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4517, 91, 4411, 2757, 4511, 4510, 1811])).
% 2.69/2.11 tff(4519,plain,
% 2.69/2.11 (((~![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))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4520,plain,
% 2.69/2.11 ((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))),
% 2.69/2.11 inference(rewrite,[status(thm)],[])).
% 2.69/2.11 tff(4521,plain,
% 2.69/2.11 (((~![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)))),
% 2.69/2.11 inference(monotonicity,[status(thm)],[4520])).
% 2.69/2.11 tff(4522,plain,
% 2.69/2.11 (((~![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))),
% 2.69/2.11 inference(transitivity,[status(thm)],[4521, 4519])).
% 2.69/2.11 tff(4523,plain,
% 2.69/2.11 ((~![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)))),
% 2.69/2.11 inference(quant_inst,[status(thm)],[])).
% 2.69/2.11 tff(4524,plain,
% 2.69/2.11 ((~![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)),
% 2.69/2.11 inference(modus_ponens,[status(thm)],[4523, 4522])).
% 2.69/2.11 tff(4525,plain,
% 2.69/2.11 (hskp4),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4524, 91, 2757, 4511, 4510, 2774, 4518])).
% 2.69/2.11 tff(4526,plain,
% 2.69/2.11 (~c2_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[137, 4525])).
% 2.69/2.11 tff(4527,plain,
% 2.69/2.11 (c3_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[161, 4525])).
% 2.69/2.11 tff(4528,plain,
% 2.69/2.11 (c0_1(a1434)),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4417, 91, 4411, 4389, 4527, 4526, 34])).
% 2.69/2.11 tff(4529,plain,
% 2.69/2.11 (hskp17 | (~c0_1(a1434))),
% 2.69/2.11 inference(unit_resolution,[status(thm)],[4424, 91, 4389, 4527, 4526, 253])).
% 2.75/2.11 tff(4530,plain,
% 2.75/2.11 (hskp17),
% 2.75/2.11 inference(unit_resolution,[status(thm)],[4529, 4528])).
% 2.75/2.11 tff(4531,plain,
% 2.75/2.11 (~c1_1(a1457)),
% 2.75/2.11 inference(unit_resolution,[status(thm)],[269, 4530])).
% 2.75/2.11 tff(4532,plain,
% 2.75/2.11 (~c0_1(a1457)),
% 2.75/2.11 inference(unit_resolution,[status(thm)],[275, 4530])).
% 2.75/2.11 tff(4533,plain,
% 2.75/2.11 (((~![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)))),
% 2.75/2.11 inference(rewrite,[status(thm)],[])).
% 2.75/2.11 tff(4534,plain,
% 2.75/2.11 ((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)))),
% 2.75/2.11 inference(rewrite,[status(thm)],[])).
% 2.75/2.11 tff(4535,plain,
% 2.75/2.11 (((~![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))))),
% 2.75/2.11 inference(monotonicity,[status(thm)],[4534])).
% 2.75/2.11 tff(4536,plain,
% 2.75/2.11 (((~![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)))),
% 2.75/2.11 inference(transitivity,[status(thm)],[4535, 4533])).
% 2.75/2.11 tff(4537,plain,
% 2.75/2.11 ((~![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)))),
% 2.75/2.11 inference(quant_inst,[status(thm)],[])).
% 2.75/2.11 tff(4538,plain,
% 2.75/2.11 ((~![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))),
% 2.75/2.11 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 2.75/2.11 tff(4539,plain,
% 2.75/2.11 (~c3_1(a1457)),
% 2.75/2.11 inference(unit_resolution,[status(thm)],[4538, 91, 4389, 4527, 4532, 4531, 4526, 10, 4528])).
% 2.75/2.11 tff(4540,plain,
% 2.75/2.11 (^[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))))),
% 2.75/2.11 inference(bind,[status(th)],[])).
% 2.75/2.11 tff(4541,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(quant_intro,[status(thm)],[4540])).
% 2.75/2.11 tff(4542,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(rewrite,[status(thm)],[])).
% 2.75/2.11 tff(4543,plain,
% 2.75/2.11 (^[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)))))),
% 2.75/2.11 inference(bind,[status(th)],[])).
% 2.75/2.11 tff(4544,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(quant_intro,[status(thm)],[4543])).
% 2.75/2.11 tff(4545,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')).
% 2.75/2.11 tff(4546,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(modus_ponens,[status(thm)],[4545, 4544])).
% 2.75/2.11 tff(4547,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(modus_ponens,[status(thm)],[4546, 4542])).
% 2.75/2.11 tff(4548,plain,(
% 2.75/2.11 ![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)))),
% 2.75/2.11 inference(skolemize,[status(sab)],[4547])).
% 2.75/2.11 tff(4549,plain,
% 2.75/2.11 (![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)))),
% 2.75/2.11 inference(modus_ponens,[status(thm)],[4548, 4541])).
% 2.75/2.11 tff(4550,plain,
% 2.75/2.11 (~c3_1(a1451)),
% 2.75/2.11 inference(unit_resolution,[status(thm)],[547, 4509])).
% 2.75/2.11 tff(4551,plain,
% 2.75/2.11 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4552,plain,
% 2.75/2.12 ((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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4553,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4552])).
% 2.75/2.12 tff(4554,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4553, 4551])).
% 2.75/2.12 tff(4555,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4556,plain,
% 2.75/2.12 ((~![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))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 2.75/2.12 tff(4557,plain,
% 2.75/2.12 (hskp13),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4556, 91, 4511, 4460, 4510, 4550, 4491, 4457, 4549])).
% 2.75/2.12 tff(4558,plain,
% 2.75/2.12 (((~hskp13) | (~c3_1(a1449))) <=> ((~hskp13) | (~c3_1(a1449)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4559,plain,
% 2.75/2.12 (((~c3_1(a1449)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1449)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4560,axiom,((~c3_1(a1449)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 2.75/2.12 tff(4561,plain,
% 2.75/2.12 ((~hskp13) | (~c3_1(a1449))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 2.75/2.12 tff(4562,plain,
% 2.75/2.12 ((~hskp13) | (~c3_1(a1449))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4561, 4558])).
% 2.75/2.12 tff(4563,plain,
% 2.75/2.12 (~c3_1(a1449)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4562, 4557])).
% 2.75/2.12 tff(4564,plain,
% 2.75/2.12 (((~hskp13) | c2_1(a1449)) <=> ((~hskp13) | c2_1(a1449))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4565,axiom,((~hskp13) | c2_1(a1449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 2.75/2.12 tff(4566,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4565, 4564])).
% 2.75/2.12 tff(4567,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4566, 4564])).
% 2.75/2.12 tff(4568,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4567, 4564])).
% 2.75/2.12 tff(4569,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4568, 4564])).
% 2.75/2.12 tff(4570,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4569, 4564])).
% 2.75/2.12 tff(4571,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4570, 4564])).
% 2.75/2.12 tff(4572,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4571, 4564])).
% 2.75/2.12 tff(4573,plain,
% 2.75/2.12 ((~hskp13) | c2_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4572, 4564])).
% 2.75/2.12 tff(4574,plain,
% 2.75/2.12 (c2_1(a1449)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4573, 4557])).
% 2.75/2.12 tff(4575,plain,
% 2.75/2.12 (((~hskp13) | c1_1(a1449)) <=> ((~hskp13) | c1_1(a1449))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4576,axiom,((~hskp13) | c1_1(a1449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 2.75/2.12 tff(4577,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4576, 4575])).
% 2.75/2.12 tff(4578,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4577, 4575])).
% 2.75/2.12 tff(4579,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4578, 4575])).
% 2.75/2.12 tff(4580,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4579, 4575])).
% 2.75/2.12 tff(4581,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4580, 4575])).
% 2.75/2.12 tff(4582,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4581, 4575])).
% 2.75/2.12 tff(4583,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4582, 4575])).
% 2.75/2.12 tff(4584,plain,
% 2.75/2.12 ((~hskp13) | c1_1(a1449)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4583, 4575])).
% 2.75/2.12 tff(4585,plain,
% 2.75/2.12 (c1_1(a1449)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4584, 4557])).
% 2.75/2.12 tff(4586,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4587,plain,
% 2.75/2.12 ((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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4588,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4587])).
% 2.75/2.12 tff(4589,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4588, 4586])).
% 2.75/2.12 tff(4590,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4591,plain,
% 2.75/2.12 ((~![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))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 2.75/2.12 tff(4592,plain,
% 2.75/2.12 (hskp23),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4591, 91, 4471, 4470, 4469, 4585, 4574, 4563, 1594])).
% 2.75/2.12 tff(4593,plain,
% 2.75/2.12 (~c1_1(a1477)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1628, 4592])).
% 2.75/2.12 tff(4594,plain,
% 2.75/2.12 (~c0_1(a1477)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1679, 4592])).
% 2.75/2.12 tff(4595,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4596,plain,
% 2.75/2.12 ((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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4597,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4596])).
% 2.75/2.12 tff(4598,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4597, 4595])).
% 2.75/2.12 tff(4599,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4600,plain,
% 2.75/2.12 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1477) | c1_1(a1477) | c2_1(a1434) | (~ndr1_0) | (~c0_1(a1434)) | (~c3_1(a1434)) | (~c3_1(a1477))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 2.75/2.12 tff(4601,plain,
% 2.75/2.12 (~c3_1(a1477)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4600, 91, 4389, 4527, 4594, 4593, 4526, 10, 4528])).
% 2.75/2.12 tff(4602,plain,
% 2.75/2.12 (~c2_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[288, 4530])).
% 2.75/2.12 tff(4603,plain,
% 2.75/2.12 (hskp1),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[643, 91, 4315, 4532, 4531, 4602, 636])).
% 2.75/2.12 tff(4604,plain,
% 2.75/2.12 (~c0_1(a1429)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[649, 4603])).
% 2.75/2.12 tff(4605,plain,
% 2.75/2.12 (c3_1(a1429)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[660, 4603])).
% 2.75/2.12 tff(4606,plain,
% 2.75/2.12 (c2_1(a1477)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1622, 4592])).
% 2.75/2.12 tff(4607,plain,
% 2.75/2.12 (c1_1(a1429)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[2043, 91, 4606, 4605, 4593, 4531, 4602, 4604, 626, 4601, 4539])).
% 2.75/2.12 tff(4608,plain,
% 2.75/2.12 (c2_1(a1429)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[688, 4603])).
% 2.75/2.12 tff(4609,plain,
% 2.75/2.12 (~hskp7),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1514, 4457])).
% 2.75/2.12 tff(4610,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[695, 91, 4609, 4608, 4605, 4531, 4602, 678, 4539, 4607])).
% 2.75/2.12 tff(4611,plain,(c0_1(a1435) | hskp0 | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4612,plain,
% 2.75/2.12 (c0_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4611, 113, 2757])).
% 2.75/2.12 tff(4613,assumption,(c2_1(a1435)), introduced(assumption)).
% 2.75/2.12 tff(4614,plain,
% 2.75/2.12 (~hskp5),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[325, 4613])).
% 2.75/2.12 tff(4615,plain,
% 2.75/2.12 (~hskp11),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4316, 4614])).
% 2.75/2.12 tff(4616,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4617,plain,
% 2.75/2.12 ((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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4618,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4617])).
% 2.75/2.12 tff(4619,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4618, 4616])).
% 2.75/2.12 tff(4620,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4621,plain,
% 2.75/2.12 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp12 | hskp11 | (~c2_1(a1435)) | c3_1(a1435) | (~ndr1_0) | (~c0_1(a1435))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 2.75/2.12 tff(4622,plain,
% 2.75/2.12 (hskp12 | hskp11 | (~c2_1(a1435)) | (~c0_1(a1435))),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4621, 91, 113, 1288])).
% 2.75/2.12 tff(4623,plain,
% 2.75/2.12 (hskp12),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4622, 4615, 114, 4613])).
% 2.75/2.12 tff(4624,plain,
% 2.75/2.12 (~c2_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[220, 4623])).
% 2.75/2.12 tff(4625,plain,
% 2.75/2.12 (hskp17),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[263, 4623, 4614, 4624])).
% 2.75/2.12 tff(4626,plain,
% 2.75/2.12 (~c1_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[269, 4625])).
% 2.75/2.12 tff(4627,plain,
% 2.75/2.12 (~c0_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[275, 4625])).
% 2.75/2.12 tff(4628,plain,
% 2.75/2.12 (c3_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[242, 4623])).
% 2.75/2.12 tff(4629,plain,
% 2.75/2.12 (c0_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[231, 4623])).
% 2.75/2.12 tff(4630,plain,
% 2.75/2.12 (~c3_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[282, 91, 4614, 4629, 4628, 4627, 4626, 4624, 10])).
% 2.75/2.12 tff(4631,plain,
% 2.75/2.12 (~c2_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[288, 4625])).
% 2.75/2.12 tff(4632,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1018, 91, 4315, 4627, 4626, 4631, 60, 4630])).
% 2.75/2.12 tff(4633,plain,((~c2_1(a1435)) | (~c0_1(a1435)) | c3_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4634,plain,
% 2.75/2.12 (~c2_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4633, 4612, 113])).
% 2.75/2.12 tff(4635,plain,
% 2.75/2.12 (c2_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3333, 37, 2757, 4612, 24, 112, 113])).
% 2.75/2.12 tff(4636,plain,
% 2.75/2.12 (hskp4),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4441, 37, 4635])).
% 2.75/2.12 tff(4637,plain,
% 2.75/2.12 (~c2_1(a1434)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[137, 4636])).
% 2.75/2.12 tff(4638,plain,
% 2.75/2.12 (~c1_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3981, 111, 112, 113, 4612])).
% 2.75/2.12 tff(4639,plain,
% 2.75/2.12 (~hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3668, 4638, 4612, 113, 111])).
% 2.75/2.12 tff(4640,plain,
% 2.75/2.12 (c3_1(a1434)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[161, 4636])).
% 2.75/2.12 tff(4641,plain,
% 2.75/2.12 (c1_1(a1434)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[150, 4636])).
% 2.75/2.12 tff(4642,plain,
% 2.75/2.12 (hskp25 | (~c0_1(a1434))),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3637, 91, 2757, 4641, 4640, 3631])).
% 2.75/2.12 tff(4643,plain,
% 2.75/2.12 (~c0_1(a1434)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4642, 4639])).
% 2.75/2.12 tff(4644,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4645,plain,
% 2.75/2.12 ((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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4646,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4645])).
% 2.75/2.12 tff(4647,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4646, 4644])).
% 2.75/2.12 tff(4648,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4649,plain,
% 2.75/2.12 ((~![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))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 2.75/2.12 tff(4650,plain,
% 2.75/2.12 (hskp9 | c3_1(a1438) | c0_1(a1434)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4649, 91, 4640, 37, 4637, 1118, 4635])).
% 2.75/2.12 tff(4651,plain,
% 2.75/2.12 (hskp9),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4650, 4643, 49])).
% 2.75/2.12 tff(4652,plain,
% 2.75/2.12 (~c3_1(a1444)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1131, 4651])).
% 2.75/2.12 tff(4653,plain,
% 2.75/2.12 (~c2_1(a1444)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1137, 4651])).
% 2.75/2.12 tff(4654,plain,
% 2.75/2.12 (((~![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))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4655,plain,
% 2.75/2.12 ((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))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4656,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4655])).
% 2.75/2.12 tff(4657,plain,
% 2.75/2.12 (((~![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))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4656, 4654])).
% 2.75/2.12 tff(4658,plain,
% 2.75/2.12 ((~![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))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4659,plain,
% 2.75/2.12 ((~![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)),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4658, 4657])).
% 2.75/2.12 tff(4660,plain,
% 2.75/2.12 (c0_1(a1444)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4659, 91, 2757, 4641, 4640, 4653, 4652, 4637, 2440])).
% 2.75/2.12 tff(4661,plain,
% 2.75/2.12 (~c1_1(a1444)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1143, 4651])).
% 2.75/2.12 tff(4662,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4663,plain,
% 2.75/2.12 (((~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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4664,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4663])).
% 2.75/2.12 tff(4665,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4664, 4662])).
% 2.75/2.12 tff(4666,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4667,plain,
% 2.75/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a1438) | c1_1(a1444) | c2_1(a1444) | c1_1(a1438) | c2_1(a1434) | (~ndr1_0) | c0_1(a1434) | (~c3_1(a1434)) | (~c2_1(a1438)) | (~c0_1(a1444))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 2.75/2.12 tff(4668,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4667, 91, 49, 4640, 4661, 4653, 24, 4637, 591, 4635, 4643, 4660])).
% 2.75/2.12 tff(4669,plain,(c3_1(a1438) | c1_1(a1438) | hskp0 | c0_1(a1438) | c3_1(a1435) | c2_1(a1435)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4670,plain,
% 2.75/2.12 (c3_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4669, 37, 2757, 24, 113, 112])).
% 2.75/2.12 tff(4671,plain,
% 2.75/2.12 (hskp12 | (~c3_1(a1438))),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3381, 91, 4641, 4640, 37, 4637, 1363, 4635])).
% 2.75/2.12 tff(4672,plain,
% 2.75/2.12 (hskp12),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4671, 4670])).
% 2.75/2.12 tff(4673,plain,
% 2.75/2.12 (~c2_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[220, 4672])).
% 2.75/2.12 tff(4674,plain,
% 2.75/2.12 (c0_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[231, 4672])).
% 2.75/2.12 tff(4675,plain,
% 2.75/2.12 (c3_1(a1448)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[242, 4672])).
% 2.75/2.12 tff(4676,plain,
% 2.75/2.12 (hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4087, 4675, 2757, 113, 112, 4640, 4612, 4641, 4673, 4674])).
% 2.75/2.12 tff(4677,plain,
% 2.75/2.12 (~c0_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[493, 4676])).
% 2.75/2.12 tff(4678,plain,
% 2.75/2.12 (c1_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[506, 4676])).
% 2.75/2.12 tff(4679,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4680,plain,
% 2.75/2.12 (((~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)))),
% 2.75/2.12 inference(rewrite,[status(thm)],[])).
% 2.75/2.12 tff(4681,plain,
% 2.75/2.12 (((~![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))))),
% 2.75/2.12 inference(monotonicity,[status(thm)],[4680])).
% 2.75/2.12 tff(4682,plain,
% 2.75/2.12 (((~![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)))),
% 2.75/2.12 inference(transitivity,[status(thm)],[4681, 4679])).
% 2.75/2.12 tff(4683,plain,
% 2.75/2.12 ((~![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)))),
% 2.75/2.12 inference(quant_inst,[status(thm)],[])).
% 2.75/2.12 tff(4684,plain,
% 2.75/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1504) | c2_1(a1448) | c0_1(a1438) | c1_1(a1438) | (~ndr1_0) | (~c2_1(a1438)) | (~c3_1(a1448)) | (~c0_1(a1448)) | (~c3_1(a1504)) | (~c1_1(a1504))),
% 2.75/2.12 inference(modus_ponens,[status(thm)],[4683, 4682])).
% 2.75/2.12 tff(4685,plain,
% 2.75/2.12 (~c3_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4684, 91, 4678, 4674, 4675, 4677, 4673, 37, 24, 1374, 4635])).
% 2.75/2.12 tff(4686,plain,
% 2.75/2.12 (c2_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[534, 4676])).
% 2.75/2.12 tff(4687,plain,
% 2.75/2.12 (hskp14),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[541, 91, 4678, 4686, 4677, 524, 4685])).
% 2.75/2.12 tff(4688,plain,
% 2.75/2.12 (~c3_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[547, 4687])).
% 2.75/2.12 tff(4689,plain,
% 2.75/2.12 (~c1_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[553, 4687])).
% 2.75/2.12 tff(4690,plain,
% 2.75/2.12 (c2_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[564, 4687])).
% 2.75/2.12 tff(4691,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[571, 91, 4678, 4686, 4690, 4612, 4677, 4689, 4688, 112, 113, 203])).
% 2.75/2.12 tff(4692,plain,(c0_1(a1438) | c2_1(a1435) | c3_1(a1435) | c1_1(a1438) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4693,plain,
% 2.75/2.12 (c0_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4692, 112, 113, 24, 2757])).
% 2.75/2.12 tff(4694,plain,
% 2.75/2.12 (~hskp7),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1099, 4693])).
% 2.75/2.12 tff(4695,plain,
% 2.75/2.12 (~c1_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3981, 4694, 112, 113, 4612])).
% 2.75/2.12 tff(4696,plain,
% 2.75/2.12 (~hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3668, 4695, 4612, 113, 4694])).
% 2.75/2.12 tff(4697,plain,
% 2.75/2.12 (hskp25 | hskp17),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[487, 4315])).
% 2.75/2.12 tff(4698,plain,
% 2.75/2.12 (hskp17),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4697, 4696])).
% 2.75/2.12 tff(4699,plain,
% 2.75/2.12 (~c2_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[288, 4698])).
% 2.75/2.12 tff(4700,plain,
% 2.75/2.12 (~c1_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[269, 4698])).
% 2.75/2.12 tff(4701,plain,
% 2.75/2.12 (~c0_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[275, 4698])).
% 2.75/2.12 tff(4702,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3467, 91, 2757, 4612, 4701, 4700, 4699, 112, 113, 1201])).
% 2.75/2.12 tff(4703,plain,(c2_1(a1435) | hskp0 | c3_1(a1435) | c1_1(a1438)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4704,plain,
% 2.75/2.12 (c1_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4703, 4634, 113, 2757])).
% 2.75/2.12 tff(4705,plain,
% 2.75/2.12 (~hskp7),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1514, 4704])).
% 2.75/2.12 tff(4706,plain,
% 2.75/2.12 (~c1_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3981, 4705, 4634, 113, 4612])).
% 2.75/2.12 tff(4707,plain,
% 2.75/2.12 (~hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3668, 4706, 4612, 113, 4705])).
% 2.75/2.12 tff(4708,plain,
% 2.75/2.12 (hskp17),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4697, 4707])).
% 2.75/2.12 tff(4709,plain,
% 2.75/2.12 (~c2_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[288, 4708])).
% 2.75/2.12 tff(4710,plain,
% 2.75/2.12 (~c1_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[269, 4708])).
% 2.75/2.12 tff(4711,plain,
% 2.75/2.12 (~c0_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[275, 4708])).
% 2.75/2.12 tff(4712,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3467, 91, 2757, 4612, 4711, 4710, 4709, 4634, 113, 1201])).
% 2.75/2.12 tff(4713,plain,(c3_1(a1435) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4714,plain,
% 2.75/2.12 (hskp0),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4713, 4388])).
% 2.75/2.12 tff(4715,plain,
% 2.75/2.12 (c0_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[390, 4387])).
% 2.75/2.12 tff(4716,plain,
% 2.75/2.12 (~c2_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[325, 4387])).
% 2.75/2.12 tff(4717,plain,
% 2.75/2.12 (~c1_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3981, 13, 4388, 4716, 4715])).
% 2.75/2.12 tff(4718,plain,
% 2.75/2.12 (~hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3668, 4717, 4715, 4388, 13])).
% 2.75/2.12 tff(4719,plain,
% 2.75/2.12 (hskp17),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4697, 4718])).
% 2.75/2.12 tff(4720,plain,
% 2.75/2.12 (~c0_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[275, 4719])).
% 2.75/2.12 tff(4721,plain,
% 2.75/2.12 (~c1_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[269, 4719])).
% 2.75/2.12 tff(4722,plain,
% 2.75/2.12 (~c2_1(a1457)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[288, 4719])).
% 2.75/2.12 tff(4723,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3975, 4722, 4721, 4715, 4714, 4717, 4388, 4716, 4720])).
% 2.75/2.12 tff(4724,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 2.75/2.12 tff(4725,plain,
% 2.75/2.12 (~c0_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1099, 4724])).
% 2.75/2.12 tff(4726,plain,
% 2.75/2.12 (~c1_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[1514, 4724])).
% 2.75/2.12 tff(4727,plain,
% 2.75/2.12 (c3_1(a1438)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[110, 4724])).
% 2.75/2.12 tff(4728,plain,
% 2.75/2.12 (c1_1(a1435)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3753, 4727, 4714, 4716, 4726, 4388, 4715, 4725])).
% 2.75/2.12 tff(4729,plain,
% 2.75/2.12 (hskp18 | (~c1_1(a1435))),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[397, 91, 4715, 4716, 4388, 380])).
% 2.75/2.12 tff(4730,plain,
% 2.75/2.12 (hskp18),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4729, 4728])).
% 2.75/2.12 tff(4731,plain,
% 2.75/2.12 (~c2_1(a1458)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[403, 4730])).
% 2.75/2.12 tff(4732,plain,
% 2.75/2.12 (c1_1(a1458)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[414, 4730])).
% 2.75/2.12 tff(4733,plain,
% 2.75/2.12 (c0_1(a1458)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[425, 4730])).
% 2.75/2.12 tff(4734,plain,
% 2.75/2.12 (hskp10),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[3765, 91, 4733, 4732, 4727, 4731, 4725, 369, 50])).
% 2.75/2.12 tff(4735,plain,
% 2.75/2.12 (~c3_1(a1445)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[439, 4734])).
% 2.75/2.12 tff(4736,plain,
% 2.75/2.12 (~c1_1(a1445)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[445, 4734])).
% 2.75/2.12 tff(4737,plain,
% 2.75/2.12 (hskp25),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[4697, 36])).
% 2.75/2.12 tff(4738,plain,
% 2.75/2.12 (~c0_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[493, 4737])).
% 2.75/2.12 tff(4739,plain,
% 2.75/2.12 (c1_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[506, 4737])).
% 2.75/2.12 tff(4740,plain,
% 2.75/2.12 (~c3_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[513, 91, 36, 4739, 3612, 3611, 4738, 254, 336])).
% 2.75/2.12 tff(4741,plain,
% 2.75/2.12 (c2_1(a1504)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[534, 4737])).
% 2.75/2.12 tff(4742,plain,
% 2.75/2.12 (hskp14),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[541, 91, 4739, 4741, 4738, 524, 4740])).
% 2.75/2.12 tff(4743,plain,
% 2.75/2.12 (~c3_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[547, 4742])).
% 2.75/2.12 tff(4744,plain,
% 2.75/2.12 (~c1_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[553, 4742])).
% 2.75/2.12 tff(4745,plain,
% 2.75/2.12 (c2_1(a1451)),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[564, 4742])).
% 2.75/2.12 tff(4746,plain,
% 2.75/2.12 ($false),
% 2.75/2.12 inference(unit_resolution,[status(thm)],[571, 91, 4739, 4741, 4745, 4715, 4738, 4744, 4743, 4716, 4388, 203])).
% 2.75/2.12 tff(4747,plain,(hskp17 | (~c0_1(a1448)) | (~c3_1(a1448)) | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.13 tff(4748,plain,
% 2.75/2.13 (hskp17),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4747, 3612, 3611, 254])).
% 2.75/2.13 tff(4749,plain,
% 2.75/2.13 (~c2_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[288, 4748])).
% 2.75/2.13 tff(4750,plain,
% 2.75/2.13 (~c1_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[269, 4748])).
% 2.75/2.13 tff(4751,plain,
% 2.75/2.13 (~c0_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[275, 4748])).
% 2.75/2.13 tff(4752,plain,
% 2.75/2.13 (c0_1(a1445)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[456, 4734])).
% 2.75/2.13 tff(4753,plain,
% 2.75/2.13 (~c2_1(a1445)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[463, 91, 4752, 4751, 4750, 4749, 4736, 4735, 23])).
% 2.75/2.13 tff(4754,plain,
% 2.75/2.13 (~c3_1(a1427)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1213, 4714])).
% 2.75/2.13 tff(4755,plain,
% 2.75/2.13 (c2_1(a1427)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1224, 4714])).
% 2.75/2.13 tff(4756,plain,
% 2.75/2.13 (c0_1(a1427)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1235, 4714])).
% 2.75/2.13 tff(4757,plain,
% 2.75/2.13 (hskp21),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3782, 91, 4752, 4756, 4755, 4736, 4754, 2557, 4753])).
% 2.75/2.13 tff(4758,plain,
% 2.75/2.13 (c2_1(a1466)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2581, 4757])).
% 2.75/2.13 tff(4759,plain,
% 2.75/2.13 (c0_1(a1466)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2592, 4757])).
% 2.75/2.13 tff(4760,plain,
% 2.75/2.13 (~c3_1(a1466)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3791, 91, 4759, 4758, 4727, 4715, 4726, 4388, 2617, 4728, 50])).
% 2.75/2.13 tff(4761,plain,
% 2.75/2.13 (hskp22),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3808, 91, 3612, 3611, 4727, 254, 4726, 1385, 50])).
% 2.75/2.13 tff(4762,plain,
% 2.75/2.13 (~c0_1(a1468)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[891, 4761])).
% 2.75/2.13 tff(4763,plain,
% 2.75/2.13 (c3_1(a1468)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[902, 4761])).
% 2.75/2.13 tff(4764,plain,
% 2.75/2.13 (c1_1(a1468)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[913, 4761])).
% 2.75/2.13 tff(4765,plain,
% 2.75/2.13 (hskp28),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3835, 91, 4764, 4763, 4733, 4732, 4762, 4731, 3829])).
% 2.75/2.13 tff(4766,plain,
% 2.75/2.13 (c3_1(a1456)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3846, 4765])).
% 2.75/2.13 tff(4767,plain,
% 2.75/2.13 (c1_1(a1456)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3857, 4765])).
% 2.75/2.13 tff(4768,plain,
% 2.75/2.13 (c0_1(a1456)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3868, 4765])).
% 2.75/2.13 tff(4769,plain,
% 2.75/2.13 (hskp6),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4013, 91, 4768, 4767, 4766, 4727, 4726, 3802, 50])).
% 2.75/2.13 tff(4770,plain,
% 2.75/2.13 (~c2_1(a1437)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2209, 4769])).
% 2.75/2.13 tff(4771,plain,
% 2.75/2.13 (~c1_1(a1437)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2233, 4769])).
% 2.75/2.13 tff(4772,plain,
% 2.75/2.13 (~c1_1(a1466)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2570, 4757])).
% 2.75/2.13 tff(4773,plain,
% 2.75/2.13 (c0_1(a1437)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[2220, 4769])).
% 2.75/2.13 tff(4774,plain,
% 2.75/2.13 ($false),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3886, 91, 4758, 4727, 4773, 4772, 4725, 4771, 4770, 591, 50, 4760])).
% 2.75/2.13 tff(4775,plain,(c2_1(a1438) | (~c0_1(a1448)) | (~c3_1(a1448)) | c2_1(a1448)), inference(lemma,lemma(discharge,[]))).
% 2.75/2.13 tff(4776,plain,
% 2.75/2.13 (c2_1(a1438)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4775, 232, 243, 221])).
% 2.75/2.13 tff(4777,plain,
% 2.75/2.13 (hskp17),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4747, 232, 243, 221])).
% 2.75/2.13 tff(4778,plain,
% 2.75/2.13 (~c2_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[288, 4777])).
% 2.75/2.13 tff(4779,plain,
% 2.75/2.13 (~c1_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[269, 4777])).
% 2.75/2.13 tff(4780,plain,
% 2.75/2.13 (~c0_1(a1457)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[275, 4777])).
% 2.75/2.13 tff(4781,plain,
% 2.75/2.13 (hskp1),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[643, 91, 4315, 4780, 4779, 4778, 636])).
% 2.75/2.13 tff(4782,plain,
% 2.75/2.13 (~c0_1(a1429)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[649, 4781])).
% 2.75/2.13 tff(4783,plain,
% 2.75/2.13 (c3_1(a1429)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[660, 4781])).
% 2.75/2.13 tff(4784,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4785,plain,
% 2.75/2.13 (((~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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4786,plain,
% 2.75/2.13 (((~![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))))),
% 2.75/2.13 inference(monotonicity,[status(thm)],[4785])).
% 2.75/2.13 tff(4787,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(transitivity,[status(thm)],[4786, 4784])).
% 2.75/2.13 tff(4788,plain,
% 2.75/2.13 ((~![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)))),
% 2.75/2.13 inference(quant_inst,[status(thm)],[])).
% 2.75/2.13 tff(4789,plain,
% 2.75/2.13 ((~![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))),
% 2.75/2.13 inference(modus_ponens,[status(thm)],[4788, 4787])).
% 2.75/2.13 tff(4790,plain,
% 2.75/2.13 ((~c1_1(a1429)) | (~c2_1(a1438))),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4789, 91, 232, 243, 4783, 221, 4725, 4726, 4782, 1374])).
% 2.75/2.13 tff(4791,plain,
% 2.75/2.13 (~c1_1(a1429)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4790, 4776])).
% 2.75/2.13 tff(4792,plain,
% 2.75/2.13 (hskp23 | (~c2_1(a1438))),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3895, 91, 4727, 4756, 4755, 4726, 4754, 1801])).
% 2.75/2.13 tff(4793,plain,
% 2.75/2.13 (hskp23),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4792, 4776])).
% 2.75/2.13 tff(4794,plain,
% 2.75/2.13 (c2_1(a1477)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1622, 4793])).
% 2.75/2.13 tff(4795,plain,
% 2.75/2.13 (~c0_1(a1477)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1679, 4793])).
% 2.75/2.13 tff(4796,plain,
% 2.75/2.13 (hskp8 | (~c2_1(a1438))),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3905, 91, 4727, 4715, 4726, 4388, 1639, 4728])).
% 2.75/2.13 tff(4797,plain,
% 2.75/2.13 (hskp8),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4796, 4776])).
% 2.75/2.13 tff(4798,plain,
% 2.75/2.13 (~c1_1(a1441)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1651, 4797])).
% 2.75/2.13 tff(4799,plain,
% 2.75/2.13 (c3_1(a1441)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1662, 4797])).
% 2.75/2.13 tff(4800,plain,
% 2.75/2.13 (~c1_1(a1477)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1628, 4793])).
% 2.75/2.13 tff(4801,plain,
% 2.75/2.13 (c0_1(a1441)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1673, 4797])).
% 2.75/2.13 tff(4802,plain,
% 2.75/2.13 (~c2_1(a1441)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[1695, 4801, 4800, 4799, 4798, 4795, 4794])).
% 2.75/2.13 tff(4803,plain,
% 2.75/2.13 (c2_1(a1429)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[688, 4781])).
% 2.75/2.13 tff(4804,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4805,plain,
% 2.75/2.13 (((~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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4806,plain,
% 2.75/2.13 (((~![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))))),
% 2.75/2.13 inference(monotonicity,[status(thm)],[4805])).
% 2.75/2.13 tff(4807,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(transitivity,[status(thm)],[4806, 4804])).
% 2.75/2.13 tff(4808,plain,
% 2.75/2.13 ((~![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)))),
% 2.75/2.13 inference(quant_inst,[status(thm)],[])).
% 2.75/2.13 tff(4809,plain,
% 2.75/2.13 ((~![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))),
% 2.75/2.13 inference(modus_ponens,[status(thm)],[4808, 4807])).
% 2.75/2.13 tff(4810,plain,
% 2.75/2.13 (~c1_1(a1427)),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4809, 91, 4799, 4803, 4783, 4756, 4755, 4798, 1706, 4802, 4791])).
% 2.75/2.13 tff(4811,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4812,plain,
% 2.75/2.13 (((~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)))),
% 2.75/2.13 inference(rewrite,[status(thm)],[])).
% 2.75/2.13 tff(4813,plain,
% 2.75/2.13 (((~![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))))),
% 2.75/2.13 inference(monotonicity,[status(thm)],[4812])).
% 2.75/2.13 tff(4814,plain,
% 2.75/2.13 (((~![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)))),
% 2.75/2.13 inference(transitivity,[status(thm)],[4813, 4811])).
% 2.75/2.13 tff(4815,plain,
% 2.75/2.13 ((~![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))),
% 2.75/2.13 inference(quant_inst,[status(thm)],[])).
% 2.75/2.13 tff(4816,plain,
% 2.75/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a1457) | c1_1(a1457) | c2_1(a1457) | c3_1(a1427) | (~ndr1_0) | (~c2_1(a1427)) | c1_1(a1427) | (~c0_1(a1427))),
% 2.75/2.13 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 2.75/2.13 tff(4817,plain,
% 2.75/2.13 ($false),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[4816, 91, 4756, 4755, 4780, 4779, 4778, 4754, 23, 4810])).
% 2.75/2.13 tff(4818,plain,(~hskp12), inference(lemma,lemma(discharge,[]))).
% 2.75/2.13 tff(4819,plain,
% 2.75/2.13 (~hskp11),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3326, 4818, 4388, 4716, 4715])).
% 2.75/2.13 tff(4820,plain,
% 2.75/2.13 ($false),
% 2.75/2.13 inference(unit_resolution,[status(thm)],[3330, 4819, 4818, 4714])).
% 2.75/2.13 % SZS output end Proof
%------------------------------------------------------------------------------