TSTP Solution File: SYN487-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN487-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:55:52 EDT 2022
% Result : Unsatisfiable 1.10s 1.00s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN487-1 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:26:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.10/1.00 % SZS status Unsatisfiable
% 1.10/1.00 % SZS output start Proof
% 1.10/1.00 tff(c1_1_type, type, (
% 1.10/1.00 c1_1: $i > $o)).
% 1.10/1.00 tff(a2308_type, type, (
% 1.10/1.00 a2308: $i)).
% 1.10/1.00 tff(hskp18_type, type, (
% 1.10/1.00 hskp18: $o)).
% 1.10/1.00 tff(a2282_type, type, (
% 1.10/1.00 a2282: $i)).
% 1.10/1.00 tff(hskp23_type, type, (
% 1.10/1.00 hskp23: $o)).
% 1.10/1.00 tff(hskp25_type, type, (
% 1.10/1.00 hskp25: $o)).
% 1.10/1.00 tff(c3_1_type, type, (
% 1.10/1.00 c3_1: $i > $o)).
% 1.10/1.00 tff(c0_1_type, type, (
% 1.10/1.00 c0_1: $i > $o)).
% 1.10/1.00 tff(c2_1_type, type, (
% 1.10/1.00 c2_1: $i > $o)).
% 1.10/1.00 tff(ndr1_0_type, type, (
% 1.10/1.00 ndr1_0: $o)).
% 1.10/1.00 tff(hskp12_type, type, (
% 1.10/1.00 hskp12: $o)).
% 1.10/1.00 tff(hskp19_type, type, (
% 1.10/1.00 hskp19: $o)).
% 1.10/1.00 tff(a2342_type, type, (
% 1.10/1.00 a2342: $i)).
% 1.10/1.00 tff(hskp1_type, type, (
% 1.10/1.00 hskp1: $o)).
% 1.10/1.00 tff(a2277_type, type, (
% 1.10/1.00 a2277: $i)).
% 1.10/1.00 tff(a2278_type, type, (
% 1.10/1.00 a2278: $i)).
% 1.10/1.00 tff(hskp28_type, type, (
% 1.10/1.00 hskp28: $o)).
% 1.10/1.00 tff(a2323_type, type, (
% 1.10/1.00 a2323: $i)).
% 1.10/1.00 tff(a2285_type, type, (
% 1.10/1.00 a2285: $i)).
% 1.10/1.00 tff(hskp4_type, type, (
% 1.10/1.00 hskp4: $o)).
% 1.10/1.00 tff(hskp20_type, type, (
% 1.10/1.00 hskp20: $o)).
% 1.10/1.00 tff(a2302_type, type, (
% 1.10/1.00 a2302: $i)).
% 1.10/1.00 tff(hskp14_type, type, (
% 1.10/1.00 hskp14: $o)).
% 1.10/1.00 tff(hskp2_type, type, (
% 1.10/1.00 hskp2: $o)).
% 1.10/1.00 tff(hskp6_type, type, (
% 1.10/1.00 hskp6: $o)).
% 1.10/1.00 tff(hskp0_type, type, (
% 1.10/1.00 hskp0: $o)).
% 1.10/1.00 tff(hskp17_type, type, (
% 1.10/1.00 hskp17: $o)).
% 1.10/1.00 tff(a2294_type, type, (
% 1.10/1.00 a2294: $i)).
% 1.10/1.00 tff(a2327_type, type, (
% 1.10/1.00 a2327: $i)).
% 1.10/1.00 tff(hskp7_type, type, (
% 1.10/1.00 hskp7: $o)).
% 1.10/1.00 tff(hskp31_type, type, (
% 1.10/1.00 hskp31: $o)).
% 1.10/1.00 tff(a2306_type, type, (
% 1.10/1.00 a2306: $i)).
% 1.10/1.00 tff(hskp11_type, type, (
% 1.10/1.00 hskp11: $o)).
% 1.10/1.00 tff(hskp30_type, type, (
% 1.10/1.00 hskp30: $o)).
% 1.10/1.00 tff(a2295_type, type, (
% 1.10/1.00 a2295: $i)).
% 1.10/1.00 tff(a2280_type, type, (
% 1.10/1.00 a2280: $i)).
% 1.10/1.00 tff(hskp3_type, type, (
% 1.10/1.00 hskp3: $o)).
% 1.10/1.00 tff(a2325_type, type, (
% 1.10/1.00 a2325: $i)).
% 1.10/1.00 tff(hskp22_type, type, (
% 1.10/1.00 hskp22: $o)).
% 1.10/1.00 tff(a2279_type, type, (
% 1.10/1.00 a2279: $i)).
% 1.10/1.00 tff(a2315_type, type, (
% 1.10/1.00 a2315: $i)).
% 1.10/1.00 tff(a2276_type, type, (
% 1.10/1.00 a2276: $i)).
% 1.10/1.00 tff(hskp9_type, type, (
% 1.10/1.00 hskp9: $o)).
% 1.10/1.00 tff(a2291_type, type, (
% 1.10/1.00 a2291: $i)).
% 1.10/1.00 tff(a2286_type, type, (
% 1.10/1.00 a2286: $i)).
% 1.10/1.00 tff(hskp26_type, type, (
% 1.10/1.00 hskp26: $o)).
% 1.10/1.00 tff(hskp16_type, type, (
% 1.10/1.00 hskp16: $o)).
% 1.10/1.00 tff(a2304_type, type, (
% 1.10/1.00 a2304: $i)).
% 1.10/1.00 tff(a2345_type, type, (
% 1.10/1.00 a2345: $i)).
% 1.10/1.00 tff(hskp10_type, type, (
% 1.10/1.00 hskp10: $o)).
% 1.10/1.00 tff(a2293_type, type, (
% 1.10/1.00 a2293: $i)).
% 1.10/1.00 tff(a2287_type, type, (
% 1.10/1.00 a2287: $i)).
% 1.10/1.00 tff(hskp8_type, type, (
% 1.10/1.00 hskp8: $o)).
% 1.10/1.00 tff(hskp13_type, type, (
% 1.10/1.00 hskp13: $o)).
% 1.10/1.00 tff(a2299_type, type, (
% 1.10/1.00 a2299: $i)).
% 1.10/1.00 tff(a2303_type, type, (
% 1.10/1.00 a2303: $i)).
% 1.10/1.00 tff(hskp15_type, type, (
% 1.10/1.00 hskp15: $o)).
% 1.10/1.00 tff(a2367_type, type, (
% 1.10/1.00 a2367: $i)).
% 1.10/1.00 tff(hskp27_type, type, (
% 1.10/1.00 hskp27: $o)).
% 1.10/1.00 tff(a2316_type, type, (
% 1.10/1.00 a2316: $i)).
% 1.10/1.00 tff(hskp21_type, type, (
% 1.10/1.00 hskp21: $o)).
% 1.10/1.00 tff(a2324_type, type, (
% 1.10/1.00 a2324: $i)).
% 1.10/1.00 tff(hskp24_type, type, (
% 1.10/1.00 hskp24: $o)).
% 1.10/1.00 tff(a2337_type, type, (
% 1.10/1.00 a2337: $i)).
% 1.10/1.00 tff(1,plain,
% 1.10/1.00 (^[U: $i] : refl((hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(2,plain,
% 1.10/1.00 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[1])).
% 1.10/1.00 tff(3,plain,
% 1.10/1.00 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(4,plain,
% 1.10/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(5,plain,
% 1.10/1.00 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[4])).
% 1.10/1.00 tff(6,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.10/1.00 tff(7,plain,
% 1.10/1.00 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.10/1.00 tff(8,plain,
% 1.10/1.00 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.10/1.00 tff(9,plain,(
% 1.10/1.00 ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(skolemize,[status(sab)],[8])).
% 1.10/1.00 tff(10,plain,
% 1.10/1.00 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.10/1.00 tff(11,assumption,(hskp25), introduced(assumption)).
% 1.10/1.00 tff(12,plain,
% 1.10/1.00 (((~hskp25) | (~c2_1(a2342))) <=> ((~hskp25) | (~c2_1(a2342)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(13,plain,
% 1.10/1.00 (((~c2_1(a2342)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a2342)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(14,axiom,((~c2_1(a2342)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.10/1.00 tff(15,plain,
% 1.10/1.00 ((~hskp25) | (~c2_1(a2342))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.10/1.00 tff(16,plain,
% 1.10/1.00 ((~hskp25) | (~c2_1(a2342))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.10/1.00 tff(17,plain,
% 1.10/1.00 (~c2_1(a2342)),
% 1.10/1.00 inference(unit_resolution,[status(thm)],[16, 11])).
% 1.10/1.00 tff(18,plain,
% 1.10/1.00 (((~hskp25) | c3_1(a2342)) <=> ((~hskp25) | c3_1(a2342))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(19,axiom,((~hskp25) | c3_1(a2342)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.10/1.00 tff(20,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.10/1.00 tff(21,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[20, 18])).
% 1.10/1.00 tff(22,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[21, 18])).
% 1.10/1.00 tff(23,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.10/1.00 tff(24,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[23, 18])).
% 1.10/1.00 tff(25,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[24, 18])).
% 1.10/1.00 tff(26,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[25, 18])).
% 1.10/1.00 tff(27,plain,
% 1.10/1.00 ((~hskp25) | c3_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[26, 18])).
% 1.10/1.00 tff(28,plain,
% 1.10/1.00 (c3_1(a2342)),
% 1.10/1.00 inference(unit_resolution,[status(thm)],[27, 11])).
% 1.10/1.00 tff(29,plain,
% 1.10/1.00 (((~hskp25) | c0_1(a2342)) <=> ((~hskp25) | c0_1(a2342))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(30,axiom,((~hskp25) | c0_1(a2342)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.10/1.00 tff(31,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.10/1.00 tff(32,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[31, 29])).
% 1.10/1.00 tff(33,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[32, 29])).
% 1.10/1.00 tff(34,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.10/1.00 tff(35,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[34, 29])).
% 1.10/1.00 tff(36,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[35, 29])).
% 1.10/1.00 tff(37,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[36, 29])).
% 1.10/1.00 tff(38,plain,
% 1.10/1.00 ((~hskp25) | c0_1(a2342)),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[37, 29])).
% 1.10/1.00 tff(39,plain,
% 1.10/1.00 (c0_1(a2342)),
% 1.10/1.00 inference(unit_resolution,[status(thm)],[38, 11])).
% 1.10/1.00 tff(40,assumption,(~c2_1(a2277)), introduced(assumption)).
% 1.10/1.00 tff(41,assumption,(~hskp28), introduced(assumption)).
% 1.10/1.00 tff(42,assumption,(~hskp1), introduced(assumption)).
% 1.10/1.00 tff(43,assumption,(~c1_1(a2282)), introduced(assumption)).
% 1.10/1.00 tff(44,plain,
% 1.10/1.00 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(45,plain,
% 1.10/1.00 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[44])).
% 1.10/1.00 tff(46,plain,
% 1.10/1.00 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(47,plain,
% 1.10/1.00 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(48,plain,
% 1.10/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[47])).
% 1.10/1.00 tff(49,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.10/1.00 tff(50,plain,
% 1.10/1.00 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.10/1.00 tff(51,plain,
% 1.10/1.00 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.10/1.00 tff(52,plain,(
% 1.10/1.00 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(skolemize,[status(sab)],[51])).
% 1.10/1.00 tff(53,plain,
% 1.10/1.00 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.10/1.00 tff(54,plain,
% 1.10/1.00 (^[U: $i] : refl((hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(55,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[54])).
% 1.10/1.00 tff(56,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(57,plain,
% 1.10/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(58,plain,
% 1.10/1.00 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[57])).
% 1.10/1.00 tff(59,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.10/1.00 tff(60,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.10/1.00 tff(61,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.10/1.00 tff(62,plain,(
% 1.10/1.00 ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(skolemize,[status(sab)],[61])).
% 1.10/1.00 tff(63,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.10/1.00 tff(64,plain,
% 1.10/1.00 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(65,plain,
% 1.10/1.00 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[64])).
% 1.10/1.00 tff(66,plain,
% 1.10/1.00 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(67,plain,
% 1.10/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(68,plain,
% 1.10/1.00 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[67])).
% 1.10/1.00 tff(69,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.10/1.00 tff(70,plain,
% 1.10/1.00 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.10/1.00 tff(71,plain,
% 1.10/1.00 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.10/1.00 tff(72,plain,(
% 1.10/1.00 ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(skolemize,[status(sab)],[71])).
% 1.10/1.00 tff(73,plain,
% 1.10/1.00 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(modus_ponens,[status(thm)],[72, 65])).
% 1.10/1.00 tff(74,plain,
% 1.10/1.00 (^[U: $i] : refl((hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.10/1.00 inference(bind,[status(th)],[])).
% 1.10/1.00 tff(75,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(quant_intro,[status(thm)],[74])).
% 1.10/1.00 tff(76,plain,
% 1.10/1.00 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.00 inference(rewrite,[status(thm)],[])).
% 1.10/1.00 tff(77,plain,
% 1.10/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(78,plain,
% 1.10/1.01 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[77])).
% 1.10/1.01 tff(79,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.10/1.01 tff(80,plain,
% 1.10/1.01 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.10/1.01 tff(81,plain,
% 1.10/1.01 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.10/1.01 tff(82,plain,(
% 1.10/1.01 ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.01 inference(skolemize,[status(sab)],[81])).
% 1.10/1.01 tff(83,plain,
% 1.10/1.01 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[82, 75])).
% 1.10/1.01 tff(84,assumption,(~hskp14), introduced(assumption)).
% 1.10/1.01 tff(85,plain,
% 1.10/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(86,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[85])).
% 1.10/1.01 tff(87,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(88,plain,
% 1.10/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(89,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[88])).
% 1.10/1.01 tff(90,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 1.10/1.01 tff(91,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.10/1.01 tff(92,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.10/1.01 tff(93,plain,(
% 1.10/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(skolemize,[status(sab)],[92])).
% 1.10/1.01 tff(94,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[93, 86])).
% 1.10/1.01 tff(95,plain,
% 1.10/1.01 (^[U: $i] : refl((hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(96,plain,
% 1.10/1.01 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[95])).
% 1.10/1.01 tff(97,plain,
% 1.10/1.01 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(98,plain,
% 1.10/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(99,plain,
% 1.10/1.01 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[98])).
% 1.10/1.01 tff(100,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.10/1.01 tff(101,plain,
% 1.10/1.01 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.10/1.01 tff(102,plain,
% 1.10/1.01 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[101, 97])).
% 1.10/1.01 tff(103,plain,(
% 1.10/1.01 ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(skolemize,[status(sab)],[102])).
% 1.10/1.01 tff(104,plain,
% 1.10/1.01 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[103, 96])).
% 1.10/1.01 tff(105,plain,
% 1.10/1.01 ((hskp20 | hskp14 | hskp1) <=> (hskp20 | hskp14 | hskp1)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(106,plain,
% 1.10/1.01 (((hskp1 | hskp14) | hskp20) <=> (hskp20 | hskp14 | hskp1)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(107,axiom,((hskp1 | hskp14) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.10/1.01 tff(108,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.10/1.01 tff(109,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[108, 105])).
% 1.10/1.01 tff(110,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.10/1.01 tff(111,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[110, 105])).
% 1.10/1.01 tff(112,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[111, 105])).
% 1.10/1.01 tff(113,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.10/1.01 tff(114,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[113, 105])).
% 1.10/1.01 tff(115,plain,
% 1.10/1.01 (hskp20 | hskp14 | hskp1),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[114, 105])).
% 1.10/1.01 tff(116,plain,
% 1.10/1.01 (hskp20),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[115, 42, 84])).
% 1.10/1.01 tff(117,plain,
% 1.10/1.01 (((~hskp20) | (~c1_1(a2323))) <=> ((~hskp20) | (~c1_1(a2323)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(118,plain,
% 1.10/1.01 (((~c1_1(a2323)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a2323)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(119,axiom,((~c1_1(a2323)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.10/1.01 tff(120,plain,
% 1.10/1.01 ((~hskp20) | (~c1_1(a2323))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.10/1.01 tff(121,plain,
% 1.10/1.01 ((~hskp20) | (~c1_1(a2323))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[120, 117])).
% 1.10/1.01 tff(122,plain,
% 1.10/1.01 (~c1_1(a2323)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[121, 116])).
% 1.10/1.01 tff(123,plain,
% 1.10/1.01 (((~hskp20) | c3_1(a2323)) <=> ((~hskp20) | c3_1(a2323))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(124,axiom,((~hskp20) | c3_1(a2323)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.10/1.01 tff(125,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.10/1.01 tff(126,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[125, 123])).
% 1.10/1.01 tff(127,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[126, 123])).
% 1.10/1.01 tff(128,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.10/1.01 tff(129,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[128, 123])).
% 1.10/1.01 tff(130,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[129, 123])).
% 1.10/1.01 tff(131,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[130, 123])).
% 1.10/1.01 tff(132,plain,
% 1.10/1.01 ((~hskp20) | c3_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[131, 123])).
% 1.10/1.01 tff(133,plain,
% 1.10/1.01 (c3_1(a2323)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[132, 116])).
% 1.10/1.01 tff(134,plain,
% 1.10/1.01 (((~hskp20) | c2_1(a2323)) <=> ((~hskp20) | c2_1(a2323))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(135,axiom,((~hskp20) | c2_1(a2323)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.10/1.01 tff(136,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.10/1.01 tff(137,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[136, 134])).
% 1.10/1.01 tff(138,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[137, 134])).
% 1.10/1.01 tff(139,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.10/1.01 tff(140,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[139, 134])).
% 1.10/1.01 tff(141,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[140, 134])).
% 1.10/1.01 tff(142,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[141, 134])).
% 1.10/1.01 tff(143,plain,
% 1.10/1.01 ((~hskp20) | c2_1(a2323)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[142, 134])).
% 1.10/1.01 tff(144,plain,
% 1.10/1.01 (c2_1(a2323)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[143, 116])).
% 1.10/1.01 tff(145,assumption,(~ndr1_0), introduced(assumption)).
% 1.10/1.01 tff(146,plain,
% 1.10/1.01 ((ndr1_0 | (~hskp7)) <=> (ndr1_0 | (~hskp7))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(147,plain,
% 1.10/1.01 (((~hskp7) | ndr1_0) <=> (ndr1_0 | (~hskp7))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(148,axiom,((~hskp7) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause25')).
% 1.10/1.01 tff(149,plain,
% 1.10/1.01 (ndr1_0 | (~hskp7)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.10/1.01 tff(150,plain,
% 1.10/1.01 (ndr1_0 | (~hskp7)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[149, 146])).
% 1.10/1.01 tff(151,plain,
% 1.10/1.01 (~hskp7),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[150, 145])).
% 1.10/1.01 tff(152,plain,
% 1.10/1.01 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(153,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.10/1.01 tff(154,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.10/1.01 tff(155,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[154, 152])).
% 1.10/1.01 tff(156,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[155, 152])).
% 1.10/1.01 tff(157,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.10/1.01 tff(158,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.10/1.01 tff(159,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[158, 152])).
% 1.10/1.01 tff(160,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[159, 152])).
% 1.10/1.01 tff(161,plain,
% 1.10/1.01 ((~hskp31) | ndr1_0),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[160, 152])).
% 1.10/1.01 tff(162,plain,
% 1.10/1.01 (~hskp31),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[161, 145])).
% 1.10/1.01 tff(163,plain,
% 1.10/1.01 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(164,plain,
% 1.10/1.01 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(165,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 1.10/1.01 tff(166,plain,
% 1.10/1.01 (ndr1_0 | (~hskp14)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.10/1.01 tff(167,plain,
% 1.10/1.01 (ndr1_0 | (~hskp14)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[166, 163])).
% 1.10/1.01 tff(168,plain,
% 1.10/1.01 (~hskp14),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[167, 145])).
% 1.10/1.01 tff(169,plain,
% 1.10/1.01 ((hskp31 | hskp14 | hskp7) <=> (hskp31 | hskp14 | hskp7)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(170,plain,
% 1.10/1.01 (((hskp31 | hskp7) | hskp14) <=> (hskp31 | hskp14 | hskp7)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(171,axiom,((hskp31 | hskp7) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.10/1.01 tff(172,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.10/1.01 tff(173,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[172, 169])).
% 1.10/1.01 tff(174,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.10/1.01 tff(175,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[174, 169])).
% 1.10/1.01 tff(176,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[175, 169])).
% 1.10/1.01 tff(177,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[176, 169])).
% 1.10/1.01 tff(178,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[177, 169])).
% 1.10/1.01 tff(179,plain,
% 1.10/1.01 (hskp31 | hskp14 | hskp7),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[178, 169])).
% 1.10/1.01 tff(180,plain,
% 1.10/1.01 ($false),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[179, 168, 162, 151])).
% 1.10/1.01 tff(181,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.10/1.01 tff(182,plain,
% 1.10/1.01 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(183,plain,
% 1.10/1.01 ((hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(184,plain,
% 1.10/1.01 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.10/1.01 inference(monotonicity,[status(thm)],[183])).
% 1.10/1.01 tff(185,plain,
% 1.10/1.01 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.10/1.01 inference(transitivity,[status(thm)],[184, 182])).
% 1.10/1.01 tff(186,plain,
% 1.10/1.01 ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(187,plain,
% 1.10/1.01 ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.10/1.01 tff(188,plain,
% 1.10/1.01 (hskp4),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[187, 181, 42, 144, 133, 122, 63])).
% 1.10/1.01 tff(189,plain,
% 1.10/1.01 (((~hskp4) | (~c3_1(a2282))) <=> ((~hskp4) | (~c3_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(190,plain,
% 1.10/1.01 (((~c3_1(a2282)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(191,axiom,((~c3_1(a2282)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.10/1.01 tff(192,plain,
% 1.10/1.01 ((~hskp4) | (~c3_1(a2282))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.10/1.01 tff(193,plain,
% 1.10/1.01 ((~hskp4) | (~c3_1(a2282))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[192, 189])).
% 1.10/1.01 tff(194,plain,
% 1.10/1.01 (~c3_1(a2282)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[193, 188])).
% 1.10/1.01 tff(195,plain,
% 1.10/1.01 (((~hskp4) | (~c0_1(a2282))) <=> ((~hskp4) | (~c0_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(196,plain,
% 1.10/1.01 (((~c0_1(a2282)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(197,axiom,((~c0_1(a2282)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.10/1.01 tff(198,plain,
% 1.10/1.01 ((~hskp4) | (~c0_1(a2282))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.10/1.01 tff(199,plain,
% 1.10/1.01 ((~hskp4) | (~c0_1(a2282))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[198, 195])).
% 1.10/1.01 tff(200,plain,
% 1.10/1.01 (~c0_1(a2282)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[199, 188])).
% 1.10/1.01 tff(201,plain,
% 1.10/1.01 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(202,plain,
% 1.10/1.01 ((hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(203,plain,
% 1.10/1.01 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))))),
% 1.10/1.01 inference(monotonicity,[status(thm)],[202])).
% 1.10/1.01 tff(204,plain,
% 1.10/1.01 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.10/1.01 inference(transitivity,[status(thm)],[203, 201])).
% 1.10/1.01 tff(205,plain,
% 1.10/1.01 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(206,plain,
% 1.10/1.01 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.10/1.01 tff(207,plain,
% 1.10/1.01 (~c1_1(a2282)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[206, 181, 84, 42, 200, 194, 104])).
% 1.10/1.01 tff(208,plain,
% 1.10/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(209,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[208])).
% 1.10/1.01 tff(210,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(211,plain,
% 1.10/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c2_1(V)) | (~c3_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))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(212,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[211])).
% 1.10/1.01 tff(213,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.10/1.01 tff(214,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.10/1.01 tff(215,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[214, 210])).
% 1.10/1.01 tff(216,plain,(
% 1.10/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(skolemize,[status(sab)],[215])).
% 1.10/1.01 tff(217,plain,
% 1.10/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.10/1.01 tff(218,plain,
% 1.10/1.01 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(219,plain,
% 1.10/1.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[218])).
% 1.10/1.01 tff(220,plain,
% 1.10/1.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(221,plain,
% 1.10/1.01 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | 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)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_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))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | 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)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(222,plain,
% 1.10/1.01 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[221])).
% 1.10/1.01 tff(223,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.10/1.01 tff(224,plain,
% 1.10/1.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.10/1.01 tff(225,plain,
% 1.10/1.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.10/1.01 tff(226,plain,(
% 1.10/1.01 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(skolemize,[status(sab)],[225])).
% 1.10/1.01 tff(227,plain,
% 1.10/1.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[226, 219])).
% 1.10/1.01 tff(228,plain,
% 1.10/1.01 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.10/1.01 inference(bind,[status(th)],[])).
% 1.10/1.01 tff(229,plain,
% 1.10/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.01 inference(quant_intro,[status(thm)],[228])).
% 1.10/1.01 tff(230,plain,
% 1.10/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(231,plain,
% 1.10/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.10/1.02 inference(bind,[status(th)],[])).
% 1.10/1.02 tff(232,plain,
% 1.10/1.02 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(quant_intro,[status(thm)],[231])).
% 1.10/1.02 tff(233,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.10/1.02 tff(234,plain,
% 1.10/1.02 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.10/1.02 tff(235,plain,
% 1.10/1.02 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[234, 230])).
% 1.10/1.02 tff(236,plain,(
% 1.10/1.02 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(skolemize,[status(sab)],[235])).
% 1.10/1.02 tff(237,plain,
% 1.10/1.02 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[236, 229])).
% 1.10/1.02 tff(238,plain,
% 1.10/1.02 (((~hskp4) | c2_1(a2282)) <=> ((~hskp4) | c2_1(a2282))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(239,axiom,((~hskp4) | c2_1(a2282)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.10/1.02 tff(240,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.10/1.02 tff(241,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[240, 238])).
% 1.10/1.02 tff(242,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[241, 238])).
% 1.10/1.02 tff(243,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.10/1.02 tff(244,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[243, 238])).
% 1.10/1.02 tff(245,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[244, 238])).
% 1.10/1.02 tff(246,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.10/1.02 tff(247,plain,
% 1.10/1.02 ((~hskp4) | c2_1(a2282)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[246, 238])).
% 1.10/1.02 tff(248,plain,
% 1.10/1.02 (c2_1(a2282)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[247, 188])).
% 1.10/1.02 tff(249,plain,
% 1.10/1.02 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(250,plain,
% 1.10/1.02 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(251,plain,
% 1.10/1.02 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282))))),
% 1.10/1.02 inference(monotonicity,[status(thm)],[250])).
% 1.10/1.02 tff(252,plain,
% 1.10/1.02 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 1.10/1.02 inference(transitivity,[status(thm)],[251, 249])).
% 1.10/1.02 tff(253,plain,
% 1.10/1.02 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(254,plain,
% 1.10/1.02 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.10/1.02 tff(255,plain,
% 1.10/1.02 (hskp17),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[254, 181, 84, 248, 200, 194, 237])).
% 1.10/1.02 tff(256,plain,
% 1.10/1.02 (((~hskp17) | (~c2_1(a2306))) <=> ((~hskp17) | (~c2_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(257,plain,
% 1.10/1.02 (((~c2_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(258,axiom,((~c2_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.10/1.02 tff(259,plain,
% 1.10/1.02 ((~hskp17) | (~c2_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.10/1.02 tff(260,plain,
% 1.10/1.02 ((~hskp17) | (~c2_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[259, 256])).
% 1.10/1.02 tff(261,plain,
% 1.10/1.02 (~c2_1(a2306)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[260, 255])).
% 1.10/1.02 tff(262,plain,
% 1.10/1.02 (((~hskp17) | (~c1_1(a2306))) <=> ((~hskp17) | (~c1_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(263,plain,
% 1.10/1.02 (((~c1_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(264,axiom,((~c1_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.10/1.02 tff(265,plain,
% 1.10/1.02 ((~hskp17) | (~c1_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.10/1.02 tff(266,plain,
% 1.10/1.02 ((~hskp17) | (~c1_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[265, 262])).
% 1.10/1.02 tff(267,plain,
% 1.10/1.02 (~c1_1(a2306)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[266, 255])).
% 1.10/1.02 tff(268,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(269,plain,
% 1.10/1.02 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(270,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306)))),
% 1.10/1.02 inference(monotonicity,[status(thm)],[269])).
% 1.10/1.02 tff(271,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 1.10/1.02 inference(transitivity,[status(thm)],[270, 268])).
% 1.10/1.02 tff(272,plain,
% 1.10/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(273,plain,
% 1.10/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.10/1.02 tff(274,plain,
% 1.10/1.02 (c0_1(a2306)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[273, 181, 42, 248, 267, 261, 194, 227, 207])).
% 1.10/1.02 tff(275,plain,
% 1.10/1.02 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.10/1.02 inference(bind,[status(th)],[])).
% 1.10/1.02 tff(276,plain,
% 1.10/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(quant_intro,[status(thm)],[275])).
% 1.10/1.02 tff(277,plain,
% 1.10/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(278,plain,
% 1.10/1.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | 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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | 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) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | 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) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.10/1.02 inference(bind,[status(th)],[])).
% 1.10/1.02 tff(279,plain,
% 1.10/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(quant_intro,[status(thm)],[278])).
% 1.10/1.02 tff(280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.10/1.02 tff(281,plain,
% 1.10/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.10/1.02 tff(282,plain,
% 1.10/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[281, 277])).
% 1.10/1.02 tff(283,plain,(
% 1.10/1.02 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(skolemize,[status(sab)],[282])).
% 1.10/1.02 tff(284,plain,
% 1.10/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[283, 276])).
% 1.10/1.02 tff(285,plain,
% 1.10/1.02 (((~hskp17) | (~c3_1(a2306))) <=> ((~hskp17) | (~c3_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(286,plain,
% 1.10/1.02 (((~c3_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(287,axiom,((~c3_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.10/1.02 tff(288,plain,
% 1.10/1.02 ((~hskp17) | (~c3_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.10/1.02 tff(289,plain,
% 1.10/1.02 ((~hskp17) | (~c3_1(a2306))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[288, 285])).
% 1.10/1.02 tff(290,plain,
% 1.10/1.02 (~c3_1(a2306)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[289, 255])).
% 1.10/1.02 tff(291,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(292,plain,
% 1.10/1.02 ((hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(293,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 1.10/1.02 inference(monotonicity,[status(thm)],[292])).
% 1.10/1.02 tff(294,plain,
% 1.10/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.23/1.02 inference(transitivity,[status(thm)],[293, 291])).
% 1.23/1.02 tff(295,plain,
% 1.23/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.23/1.02 inference(quant_inst,[status(thm)],[])).
% 1.23/1.02 tff(296,plain,
% 1.23/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.23/1.02 tff(297,plain,
% 1.23/1.02 (hskp23),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[296, 181, 267, 261, 290, 284, 274])).
% 1.23/1.02 tff(298,plain,
% 1.23/1.02 (((~hskp23) | (~c2_1(a2327))) <=> ((~hskp23) | (~c2_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(299,plain,
% 1.23/1.02 (((~c2_1(a2327)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(300,axiom,((~c2_1(a2327)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.23/1.02 tff(301,plain,
% 1.23/1.02 ((~hskp23) | (~c2_1(a2327))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.23/1.02 tff(302,plain,
% 1.23/1.02 ((~hskp23) | (~c2_1(a2327))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[301, 298])).
% 1.23/1.02 tff(303,plain,
% 1.23/1.02 (~c2_1(a2327)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[302, 297])).
% 1.23/1.02 tff(304,plain,
% 1.23/1.02 (((~hskp23) | c3_1(a2327)) <=> ((~hskp23) | c3_1(a2327))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(305,axiom,((~hskp23) | c3_1(a2327)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.23/1.02 tff(306,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.23/1.02 tff(307,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[306, 304])).
% 1.23/1.02 tff(308,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.23/1.02 tff(309,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.23/1.02 tff(310,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[309, 304])).
% 1.23/1.02 tff(311,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[310, 304])).
% 1.23/1.02 tff(312,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[311, 304])).
% 1.23/1.02 tff(313,plain,
% 1.23/1.02 ((~hskp23) | c3_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[312, 304])).
% 1.23/1.02 tff(314,plain,
% 1.23/1.02 (c3_1(a2327)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[313, 297])).
% 1.23/1.02 tff(315,plain,
% 1.23/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(316,plain,
% 1.23/1.02 (((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(317,plain,
% 1.23/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 1.23/1.02 inference(monotonicity,[status(thm)],[316])).
% 1.23/1.02 tff(318,plain,
% 1.23/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.23/1.02 inference(transitivity,[status(thm)],[317, 315])).
% 1.23/1.02 tff(319,plain,
% 1.23/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.02 inference(quant_inst,[status(thm)],[])).
% 1.23/1.02 tff(320,plain,
% 1.23/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.23/1.02 tff(321,plain,
% 1.23/1.02 (~c1_1(a2327)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[320, 181, 314, 144, 133, 248, 303, 122, 200, 217, 207])).
% 1.23/1.02 tff(322,plain,
% 1.23/1.02 (((~hskp23) | (~c0_1(a2327))) <=> ((~hskp23) | (~c0_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(323,plain,
% 1.23/1.02 (((~c0_1(a2327)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a2327)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(324,axiom,((~c0_1(a2327)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.23/1.02 tff(325,plain,
% 1.23/1.02 ((~hskp23) | (~c0_1(a2327))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.23/1.02 tff(326,plain,
% 1.23/1.02 ((~hskp23) | (~c0_1(a2327))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[325, 322])).
% 1.23/1.02 tff(327,plain,
% 1.23/1.02 (~c0_1(a2327)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[326, 297])).
% 1.23/1.02 tff(328,plain,
% 1.23/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(329,plain,
% 1.23/1.02 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(330,plain,
% 1.23/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327)))),
% 1.23/1.02 inference(monotonicity,[status(thm)],[329])).
% 1.23/1.02 tff(331,plain,
% 1.23/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 1.23/1.02 inference(transitivity,[status(thm)],[330, 328])).
% 1.23/1.02 tff(332,plain,
% 1.23/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.23/1.02 inference(quant_inst,[status(thm)],[])).
% 1.23/1.02 tff(333,plain,
% 1.23/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.23/1.02 tff(334,plain,
% 1.23/1.02 ($false),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[333, 181, 42, 248, 327, 303, 194, 227, 207, 321])).
% 1.23/1.02 tff(335,plain,(hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.02 tff(336,plain,
% 1.23/1.02 (hskp1),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[335, 84])).
% 1.23/1.02 tff(337,plain,
% 1.23/1.02 (((~hskp1) | (~c2_1(a2277))) <=> ((~hskp1) | (~c2_1(a2277)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(338,plain,
% 1.23/1.02 (((~c2_1(a2277)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2277)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(339,axiom,((~c2_1(a2277)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.23/1.02 tff(340,plain,
% 1.23/1.02 ((~hskp1) | (~c2_1(a2277))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.23/1.02 tff(341,plain,
% 1.23/1.02 ((~hskp1) | (~c2_1(a2277))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[340, 337])).
% 1.23/1.02 tff(342,plain,
% 1.23/1.02 (~c2_1(a2277)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[341, 336])).
% 1.23/1.02 tff(343,assumption,(hskp17), introduced(assumption)).
% 1.23/1.02 tff(344,plain,
% 1.23/1.02 (~c3_1(a2306)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[289, 343])).
% 1.23/1.02 tff(345,plain,
% 1.23/1.02 (~c2_1(a2306)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[260, 343])).
% 1.23/1.02 tff(346,plain,
% 1.23/1.02 (~c1_1(a2306)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[266, 343])).
% 1.23/1.02 tff(347,plain,
% 1.23/1.02 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.23/1.02 inference(bind,[status(th)],[])).
% 1.23/1.02 tff(348,plain,
% 1.23/1.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(quant_intro,[status(thm)],[347])).
% 1.23/1.02 tff(349,plain,
% 1.23/1.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(350,plain,
% 1.23/1.02 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.23/1.02 inference(bind,[status(th)],[])).
% 1.23/1.02 tff(351,plain,
% 1.23/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(quant_intro,[status(thm)],[350])).
% 1.23/1.02 tff(352,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.23/1.02 tff(353,plain,
% 1.23/1.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.23/1.02 tff(354,plain,
% 1.23/1.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.23/1.02 tff(355,plain,(
% 1.23/1.02 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(skolemize,[status(sab)],[354])).
% 1.23/1.02 tff(356,plain,
% 1.23/1.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[355, 348])).
% 1.23/1.02 tff(357,plain,
% 1.23/1.02 (((~hskp1) | c1_1(a2277)) <=> ((~hskp1) | c1_1(a2277))),
% 1.23/1.02 inference(rewrite,[status(thm)],[])).
% 1.23/1.02 tff(358,axiom,((~hskp1) | c1_1(a2277)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.23/1.02 tff(359,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[358, 357])).
% 1.23/1.02 tff(360,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[359, 357])).
% 1.23/1.02 tff(361,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[360, 357])).
% 1.23/1.02 tff(362,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[361, 357])).
% 1.23/1.02 tff(363,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[362, 357])).
% 1.23/1.02 tff(364,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[363, 357])).
% 1.23/1.02 tff(365,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[364, 357])).
% 1.23/1.02 tff(366,plain,
% 1.23/1.02 ((~hskp1) | c1_1(a2277)),
% 1.23/1.02 inference(modus_ponens,[status(thm)],[365, 357])).
% 1.23/1.02 tff(367,plain,
% 1.23/1.02 (c1_1(a2277)),
% 1.23/1.02 inference(unit_resolution,[status(thm)],[366, 336])).
% 1.23/1.02 tff(368,plain,
% 1.23/1.02 (((~hskp1) | c0_1(a2277)) <=> ((~hskp1) | c0_1(a2277))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(369,axiom,((~hskp1) | c0_1(a2277)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.23/1.03 tff(370,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.23/1.03 tff(371,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[370, 368])).
% 1.23/1.03 tff(372,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[371, 368])).
% 1.23/1.03 tff(373,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[372, 368])).
% 1.23/1.03 tff(374,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[373, 368])).
% 1.23/1.03 tff(375,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[374, 368])).
% 1.23/1.03 tff(376,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[375, 368])).
% 1.23/1.03 tff(377,plain,
% 1.23/1.03 ((~hskp1) | c0_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[376, 368])).
% 1.23/1.03 tff(378,plain,
% 1.23/1.03 (c0_1(a2277)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[377, 336])).
% 1.23/1.03 tff(379,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(380,plain,
% 1.23/1.03 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(381,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[380])).
% 1.23/1.03 tff(382,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.23/1.03 inference(transitivity,[status(thm)],[381, 379])).
% 1.23/1.03 tff(383,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(384,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.23/1.03 tff(385,plain,
% 1.23/1.03 (c3_1(a2277)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[384, 181, 84, 378, 367, 342, 356])).
% 1.23/1.03 tff(386,plain,
% 1.23/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(387,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[386])).
% 1.23/1.03 tff(388,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(389,plain,
% 1.23/1.03 (^[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))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(390,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[389])).
% 1.23/1.03 tff(391,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 1.23/1.03 tff(392,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.23/1.03 tff(393,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[392, 388])).
% 1.23/1.03 tff(394,plain,(
% 1.23/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(skolemize,[status(sab)],[393])).
% 1.23/1.03 tff(395,plain,
% 1.23/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[394, 387])).
% 1.23/1.03 tff(396,assumption,(~c3_1(a2306)), introduced(assumption)).
% 1.23/1.03 tff(397,assumption,(~c2_1(a2306)), introduced(assumption)).
% 1.23/1.03 tff(398,assumption,(~c1_1(a2306)), introduced(assumption)).
% 1.23/1.03 tff(399,assumption,(hskp6), introduced(assumption)).
% 1.23/1.03 tff(400,plain,
% 1.23/1.03 (((~hskp6) | c1_1(a2285)) <=> ((~hskp6) | c1_1(a2285))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(401,axiom,((~hskp6) | c1_1(a2285)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.23/1.03 tff(402,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.23/1.03 tff(403,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[402, 400])).
% 1.23/1.03 tff(404,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.23/1.03 tff(405,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[404, 400])).
% 1.23/1.03 tff(406,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[405, 400])).
% 1.23/1.03 tff(407,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[406, 400])).
% 1.23/1.03 tff(408,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[407, 400])).
% 1.23/1.03 tff(409,plain,
% 1.23/1.03 ((~hskp6) | c1_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[408, 400])).
% 1.23/1.03 tff(410,plain,
% 1.23/1.03 (c1_1(a2285)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[409, 399])).
% 1.23/1.03 tff(411,plain,
% 1.23/1.03 (((~hskp6) | c0_1(a2285)) <=> ((~hskp6) | c0_1(a2285))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(412,axiom,((~hskp6) | c0_1(a2285)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.23/1.03 tff(413,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.23/1.03 tff(414,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[413, 411])).
% 1.23/1.03 tff(415,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[414, 411])).
% 1.23/1.03 tff(416,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[415, 411])).
% 1.23/1.03 tff(417,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[416, 411])).
% 1.23/1.03 tff(418,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[417, 411])).
% 1.23/1.03 tff(419,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[418, 411])).
% 1.23/1.03 tff(420,plain,
% 1.23/1.03 ((~hskp6) | c0_1(a2285)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[419, 411])).
% 1.23/1.03 tff(421,plain,
% 1.23/1.03 (c0_1(a2285)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[420, 399])).
% 1.23/1.03 tff(422,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(423,plain,
% 1.23/1.03 (((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(424,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[423])).
% 1.23/1.03 tff(425,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.03 inference(transitivity,[status(thm)],[424, 422])).
% 1.23/1.03 tff(426,plain,
% 1.23/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(427,plain,
% 1.23/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.23/1.03 tff(428,plain,
% 1.23/1.03 (~c2_1(a2285)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[427, 181, 421, 410, 378, 398, 397, 396, 342, 395, 385])).
% 1.23/1.03 tff(429,plain,
% 1.23/1.03 (((~hskp6) | (~c3_1(a2285))) <=> ((~hskp6) | (~c3_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(430,plain,
% 1.23/1.03 (((~c3_1(a2285)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(431,axiom,((~c3_1(a2285)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.23/1.03 tff(432,plain,
% 1.23/1.03 ((~hskp6) | (~c3_1(a2285))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.23/1.03 tff(433,plain,
% 1.23/1.03 ((~hskp6) | (~c3_1(a2285))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[432, 429])).
% 1.23/1.03 tff(434,plain,
% 1.23/1.03 (~c3_1(a2285)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[433, 399])).
% 1.23/1.03 tff(435,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(436,plain,
% 1.23/1.03 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285))) <=> (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(437,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285))))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[436])).
% 1.23/1.03 tff(438,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.03 inference(transitivity,[status(thm)],[437, 435])).
% 1.23/1.03 tff(439,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(440,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.23/1.03 tff(441,plain,
% 1.23/1.03 ($false),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[440, 181, 84, 421, 378, 367, 434, 342, 356, 428])).
% 1.23/1.03 tff(442,plain,((~hskp6) | hskp14 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.03 tff(443,plain,
% 1.23/1.03 (~hskp6),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[442, 346, 84, 345, 344])).
% 1.23/1.03 tff(444,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(445,plain,
% 1.23/1.03 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(446,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306))))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[445])).
% 1.23/1.03 tff(447,plain,
% 1.23/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 1.23/1.03 inference(transitivity,[status(thm)],[446, 444])).
% 1.23/1.03 tff(448,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.23/1.03 inference(quant_inst,[status(thm)],[])).
% 1.23/1.03 tff(449,plain,
% 1.23/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.23/1.03 tff(450,plain,
% 1.23/1.03 (~c0_1(a2306)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[449, 181, 84, 378, 367, 345, 344, 342, 356])).
% 1.23/1.03 tff(451,plain,
% 1.23/1.03 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(452,plain,
% 1.23/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[451])).
% 1.23/1.03 tff(453,plain,
% 1.23/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(454,plain,
% 1.23/1.03 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.23/1.03 inference(bind,[status(th)],[])).
% 1.23/1.03 tff(455,plain,
% 1.23/1.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(quant_intro,[status(thm)],[454])).
% 1.23/1.03 tff(456,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.23/1.03 tff(457,plain,
% 1.23/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[456, 455])).
% 1.23/1.03 tff(458,plain,
% 1.23/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[457, 453])).
% 1.23/1.03 tff(459,plain,(
% 1.23/1.03 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(skolemize,[status(sab)],[458])).
% 1.23/1.03 tff(460,plain,
% 1.23/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[459, 452])).
% 1.23/1.03 tff(461,assumption,(~hskp3), introduced(assumption)).
% 1.23/1.03 tff(462,plain,
% 1.23/1.03 ((hskp22 | hskp14 | hskp3) <=> (hskp22 | hskp14 | hskp3)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(463,plain,
% 1.23/1.03 (((hskp14 | hskp3) | hskp22) <=> (hskp22 | hskp14 | hskp3)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(464,plain,
% 1.23/1.03 ((hskp3 | hskp14) <=> (hskp14 | hskp3)),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(465,plain,
% 1.23/1.03 (((hskp3 | hskp14) | hskp22) <=> ((hskp14 | hskp3) | hskp22)),
% 1.23/1.03 inference(monotonicity,[status(thm)],[464])).
% 1.23/1.03 tff(466,plain,
% 1.23/1.03 (((hskp3 | hskp14) | hskp22) <=> (hskp22 | hskp14 | hskp3)),
% 1.23/1.03 inference(transitivity,[status(thm)],[465, 463])).
% 1.23/1.03 tff(467,axiom,((hskp3 | hskp14) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.23/1.03 tff(468,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.23/1.03 tff(469,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[468, 462])).
% 1.23/1.03 tff(470,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[469, 462])).
% 1.23/1.03 tff(471,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[470, 462])).
% 1.23/1.03 tff(472,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[471, 462])).
% 1.23/1.03 tff(473,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[472, 462])).
% 1.23/1.03 tff(474,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[473, 462])).
% 1.23/1.03 tff(475,plain,
% 1.23/1.03 (hskp22 | hskp14 | hskp3),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[474, 462])).
% 1.23/1.03 tff(476,plain,
% 1.23/1.03 (hskp22),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[475, 461, 84])).
% 1.23/1.03 tff(477,plain,
% 1.23/1.03 (((~hskp22) | (~c1_1(a2325))) <=> ((~hskp22) | (~c1_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(478,plain,
% 1.23/1.03 (((~c1_1(a2325)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(479,axiom,((~c1_1(a2325)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.23/1.03 tff(480,plain,
% 1.23/1.03 ((~hskp22) | (~c1_1(a2325))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.23/1.03 tff(481,plain,
% 1.23/1.03 ((~hskp22) | (~c1_1(a2325))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[480, 477])).
% 1.23/1.03 tff(482,plain,
% 1.23/1.03 (~c1_1(a2325)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[481, 476])).
% 1.23/1.03 tff(483,plain,
% 1.23/1.03 (((~hskp22) | (~c0_1(a2325))) <=> ((~hskp22) | (~c0_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(484,plain,
% 1.23/1.03 (((~c0_1(a2325)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(485,axiom,((~c0_1(a2325)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.23/1.03 tff(486,plain,
% 1.23/1.03 ((~hskp22) | (~c0_1(a2325))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.23/1.03 tff(487,plain,
% 1.23/1.03 ((~hskp22) | (~c0_1(a2325))),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.23/1.03 tff(488,plain,
% 1.23/1.03 (~c0_1(a2325)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[487, 476])).
% 1.23/1.03 tff(489,plain,
% 1.23/1.03 (((~hskp22) | c2_1(a2325)) <=> ((~hskp22) | c2_1(a2325))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(490,axiom,((~hskp22) | c2_1(a2325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.23/1.03 tff(491,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.23/1.03 tff(492,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[491, 489])).
% 1.23/1.03 tff(493,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[492, 489])).
% 1.23/1.03 tff(494,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[493, 489])).
% 1.23/1.03 tff(495,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[494, 489])).
% 1.23/1.03 tff(496,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[495, 489])).
% 1.23/1.03 tff(497,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[496, 489])).
% 1.23/1.03 tff(498,plain,
% 1.23/1.03 ((~hskp22) | c2_1(a2325)),
% 1.23/1.03 inference(modus_ponens,[status(thm)],[497, 489])).
% 1.23/1.03 tff(499,plain,
% 1.23/1.03 (c2_1(a2325)),
% 1.23/1.03 inference(unit_resolution,[status(thm)],[498, 476])).
% 1.23/1.03 tff(500,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(501,plain,
% 1.23/1.03 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325))) <=> (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 1.23/1.03 inference(rewrite,[status(thm)],[])).
% 1.23/1.03 tff(502,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325))))),
% 1.23/1.03 inference(monotonicity,[status(thm)],[501])).
% 1.23/1.03 tff(503,plain,
% 1.23/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[502, 500])).
% 1.23/1.04 tff(504,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(505,plain,
% 1.23/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.23/1.04 tff(506,plain,
% 1.23/1.04 (~c3_1(a2325)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[505, 181, 499, 367, 488, 482, 342, 217, 385])).
% 1.23/1.04 tff(507,plain,
% 1.23/1.04 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(508,plain,
% 1.23/1.04 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325))) <=> (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(509,plain,
% 1.23/1.04 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325)))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[508])).
% 1.23/1.04 tff(510,plain,
% 1.23/1.04 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 1.23/1.04 inference(transitivity,[status(thm)],[509, 507])).
% 1.23/1.04 tff(511,plain,
% 1.23/1.04 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(512,plain,
% 1.23/1.04 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.23/1.04 tff(513,plain,
% 1.23/1.04 (hskp17),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[512, 181, 84, 499, 488, 237, 506])).
% 1.23/1.04 tff(514,plain,
% 1.23/1.04 (~c3_1(a2306)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[289, 513])).
% 1.23/1.04 tff(515,plain,
% 1.23/1.04 (~c2_1(a2306)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[260, 513])).
% 1.23/1.04 tff(516,plain,
% 1.23/1.04 (~c0_1(a2306)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[449, 181, 84, 378, 367, 515, 514, 342, 356])).
% 1.23/1.04 tff(517,plain,
% 1.23/1.04 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(518,plain,
% 1.23/1.04 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[517])).
% 1.23/1.04 tff(519,plain,
% 1.23/1.04 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(520,plain,
% 1.23/1.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(521,plain,
% 1.23/1.04 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[520])).
% 1.23/1.04 tff(522,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.23/1.04 tff(523,plain,
% 1.23/1.04 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.23/1.04 tff(524,plain,
% 1.23/1.04 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[523, 519])).
% 1.23/1.04 tff(525,plain,(
% 1.23/1.04 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(skolemize,[status(sab)],[524])).
% 1.23/1.04 tff(526,plain,
% 1.23/1.04 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[525, 518])).
% 1.23/1.04 tff(527,plain,
% 1.23/1.04 (~c1_1(a2306)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[266, 513])).
% 1.23/1.04 tff(528,assumption,(hskp2), introduced(assumption)).
% 1.23/1.04 tff(529,plain,
% 1.23/1.04 (((~hskp2) | (~c3_1(a2279))) <=> ((~hskp2) | (~c3_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(530,plain,
% 1.23/1.04 (((~c3_1(a2279)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(531,axiom,((~c3_1(a2279)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.23/1.04 tff(532,plain,
% 1.23/1.04 ((~hskp2) | (~c3_1(a2279))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.23/1.04 tff(533,plain,
% 1.23/1.04 ((~hskp2) | (~c3_1(a2279))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[532, 529])).
% 1.23/1.04 tff(534,plain,
% 1.23/1.04 (~c3_1(a2279)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[533, 528])).
% 1.23/1.04 tff(535,plain,
% 1.23/1.04 (((~hskp2) | (~c2_1(a2279))) <=> ((~hskp2) | (~c2_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(536,plain,
% 1.23/1.04 (((~c2_1(a2279)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(537,axiom,((~c2_1(a2279)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.23/1.04 tff(538,plain,
% 1.23/1.04 ((~hskp2) | (~c2_1(a2279))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.23/1.04 tff(539,plain,
% 1.23/1.04 ((~hskp2) | (~c2_1(a2279))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[538, 535])).
% 1.23/1.04 tff(540,plain,
% 1.23/1.04 (~c2_1(a2279)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[539, 528])).
% 1.23/1.04 tff(541,plain,
% 1.23/1.04 (((~hskp2) | c0_1(a2279)) <=> ((~hskp2) | c0_1(a2279))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(542,axiom,((~hskp2) | c0_1(a2279)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.23/1.04 tff(543,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.23/1.04 tff(544,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[543, 541])).
% 1.23/1.04 tff(545,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[544, 541])).
% 1.23/1.04 tff(546,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[545, 541])).
% 1.23/1.04 tff(547,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[546, 541])).
% 1.23/1.04 tff(548,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[547, 541])).
% 1.23/1.04 tff(549,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[548, 541])).
% 1.23/1.04 tff(550,plain,
% 1.23/1.04 ((~hskp2) | c0_1(a2279)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[549, 541])).
% 1.23/1.04 tff(551,plain,
% 1.23/1.04 (c0_1(a2279)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[550, 528])).
% 1.23/1.04 tff(552,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(553,plain,
% 1.23/1.04 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279))) <=> (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(554,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279))))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[553])).
% 1.23/1.04 tff(555,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 1.23/1.04 inference(transitivity,[status(thm)],[554, 552])).
% 1.23/1.04 tff(556,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(557,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.23/1.04 tff(558,plain,
% 1.23/1.04 ($false),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[557, 181, 84, 551, 378, 367, 540, 534, 342, 356])).
% 1.23/1.04 tff(559,plain,((~hskp2) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.04 tff(560,plain,
% 1.23/1.04 (~hskp2),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[559, 84])).
% 1.23/1.04 tff(561,plain,
% 1.23/1.04 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(562,plain,
% 1.23/1.04 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(563,plain,
% 1.23/1.04 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[562])).
% 1.23/1.04 tff(564,plain,
% 1.23/1.04 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(transitivity,[status(thm)],[563, 561])).
% 1.23/1.04 tff(565,plain,
% 1.23/1.04 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(566,plain,
% 1.23/1.04 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.23/1.04 tff(567,plain,
% 1.23/1.04 ($false),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[566, 181, 461, 560, 527, 515, 526, 516])).
% 1.23/1.04 tff(568,plain,(hskp3 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.04 tff(569,plain,
% 1.23/1.04 (hskp3),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[568, 84])).
% 1.23/1.04 tff(570,plain,
% 1.23/1.04 (((~hskp3) | (~c2_1(a2280))) <=> ((~hskp3) | (~c2_1(a2280)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(571,plain,
% 1.23/1.04 (((~c2_1(a2280)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a2280)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(572,axiom,((~c2_1(a2280)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.23/1.04 tff(573,plain,
% 1.23/1.04 ((~hskp3) | (~c2_1(a2280))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.23/1.04 tff(574,plain,
% 1.23/1.04 ((~hskp3) | (~c2_1(a2280))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[573, 570])).
% 1.23/1.04 tff(575,plain,
% 1.23/1.04 (~c2_1(a2280)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[574, 569])).
% 1.23/1.04 tff(576,plain,
% 1.23/1.04 (((~hskp3) | c3_1(a2280)) <=> ((~hskp3) | c3_1(a2280))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(577,axiom,((~hskp3) | c3_1(a2280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.23/1.04 tff(578,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.23/1.04 tff(579,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[578, 576])).
% 1.23/1.04 tff(580,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[579, 576])).
% 1.23/1.04 tff(581,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[580, 576])).
% 1.23/1.04 tff(582,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[581, 576])).
% 1.23/1.04 tff(583,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[582, 576])).
% 1.23/1.04 tff(584,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[583, 576])).
% 1.23/1.04 tff(585,plain,
% 1.23/1.04 ((~hskp3) | c3_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[584, 576])).
% 1.23/1.04 tff(586,plain,
% 1.23/1.04 (c3_1(a2280)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[585, 569])).
% 1.23/1.04 tff(587,plain,
% 1.23/1.04 (((~hskp3) | c1_1(a2280)) <=> ((~hskp3) | c1_1(a2280))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(588,axiom,((~hskp3) | c1_1(a2280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.23/1.04 tff(589,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[588, 587])).
% 1.23/1.04 tff(590,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[589, 587])).
% 1.23/1.04 tff(591,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[590, 587])).
% 1.23/1.04 tff(592,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[591, 587])).
% 1.23/1.04 tff(593,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[592, 587])).
% 1.23/1.04 tff(594,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[593, 587])).
% 1.23/1.04 tff(595,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[594, 587])).
% 1.23/1.04 tff(596,plain,
% 1.23/1.04 ((~hskp3) | c1_1(a2280)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[595, 587])).
% 1.23/1.04 tff(597,plain,
% 1.23/1.04 (c1_1(a2280)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[596, 569])).
% 1.23/1.04 tff(598,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(599,plain,
% 1.23/1.04 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(600,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306)))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[599])).
% 1.23/1.04 tff(601,plain,
% 1.23/1.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 1.23/1.04 inference(transitivity,[status(thm)],[600, 598])).
% 1.23/1.04 tff(602,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(603,plain,
% 1.23/1.04 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[602, 601])).
% 1.23/1.04 tff(604,plain,
% 1.23/1.04 (hskp28),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[603, 181, 597, 586, 346, 345, 575, 460, 450])).
% 1.23/1.04 tff(605,plain,
% 1.23/1.04 (((~hskp28) | c3_1(a2278)) <=> ((~hskp28) | c3_1(a2278))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(606,axiom,((~hskp28) | c3_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.23/1.04 tff(607,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.23/1.04 tff(608,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[607, 605])).
% 1.23/1.04 tff(609,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[608, 605])).
% 1.23/1.04 tff(610,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.23/1.04 tff(611,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[610, 605])).
% 1.23/1.04 tff(612,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[611, 605])).
% 1.23/1.04 tff(613,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[612, 605])).
% 1.23/1.04 tff(614,plain,
% 1.23/1.04 ((~hskp28) | c3_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[613, 605])).
% 1.23/1.04 tff(615,plain,
% 1.23/1.04 (c3_1(a2278)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[614, 604])).
% 1.23/1.04 tff(616,plain,
% 1.23/1.04 (((~hskp28) | c1_1(a2278)) <=> ((~hskp28) | c1_1(a2278))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(617,axiom,((~hskp28) | c1_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.23/1.04 tff(618,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.23/1.04 tff(619,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[618, 616])).
% 1.23/1.04 tff(620,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[619, 616])).
% 1.23/1.04 tff(621,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[620, 616])).
% 1.23/1.04 tff(622,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[621, 616])).
% 1.23/1.04 tff(623,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[622, 616])).
% 1.23/1.04 tff(624,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[623, 616])).
% 1.23/1.04 tff(625,plain,
% 1.23/1.04 ((~hskp28) | c1_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[624, 616])).
% 1.23/1.04 tff(626,plain,
% 1.23/1.04 (c1_1(a2278)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[625, 604])).
% 1.23/1.04 tff(627,plain,
% 1.23/1.04 (((~hskp28) | c0_1(a2278)) <=> ((~hskp28) | c0_1(a2278))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(628,axiom,((~hskp28) | c0_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.23/1.04 tff(629,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.23/1.04 tff(630,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[629, 627])).
% 1.23/1.04 tff(631,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[630, 627])).
% 1.23/1.04 tff(632,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[631, 627])).
% 1.23/1.04 tff(633,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[632, 627])).
% 1.23/1.04 tff(634,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[633, 627])).
% 1.23/1.04 tff(635,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[634, 627])).
% 1.23/1.04 tff(636,plain,
% 1.23/1.04 ((~hskp28) | c0_1(a2278)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[635, 627])).
% 1.23/1.04 tff(637,plain,
% 1.23/1.04 (c0_1(a2278)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[636, 604])).
% 1.23/1.04 tff(638,assumption,(~hskp12), introduced(assumption)).
% 1.23/1.04 tff(639,assumption,(~c0_1(a2306)), introduced(assumption)).
% 1.23/1.04 tff(640,plain,
% 1.23/1.04 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(641,plain,
% 1.23/1.04 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[640])).
% 1.23/1.04 tff(642,plain,
% 1.23/1.04 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(643,plain,
% 1.23/1.04 (^[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)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.23/1.04 inference(bind,[status(th)],[])).
% 1.23/1.04 tff(644,plain,
% 1.23/1.04 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(quant_intro,[status(thm)],[643])).
% 1.23/1.04 tff(645,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.23/1.04 tff(646,plain,
% 1.23/1.04 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.23/1.04 tff(647,plain,
% 1.23/1.04 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[646, 642])).
% 1.23/1.04 tff(648,plain,(
% 1.23/1.04 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(skolemize,[status(sab)],[647])).
% 1.23/1.04 tff(649,plain,
% 1.23/1.04 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[648, 641])).
% 1.23/1.04 tff(650,plain,
% 1.23/1.04 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(651,plain,
% 1.23/1.04 ((hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(652,plain,
% 1.23/1.04 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 1.23/1.04 inference(monotonicity,[status(thm)],[651])).
% 1.23/1.04 tff(653,plain,
% 1.23/1.04 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.04 inference(transitivity,[status(thm)],[652, 650])).
% 1.23/1.04 tff(654,plain,
% 1.23/1.04 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 1.23/1.04 inference(quant_inst,[status(thm)],[])).
% 1.23/1.04 tff(655,plain,
% 1.23/1.04 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[654, 653])).
% 1.23/1.04 tff(656,plain,
% 1.23/1.04 (hskp12 | hskp11),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[655, 181, 397, 396, 649, 639])).
% 1.23/1.04 tff(657,plain,
% 1.23/1.04 (hskp11),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[656, 638])).
% 1.23/1.04 tff(658,plain,
% 1.23/1.04 (((~hskp11) | (~c1_1(a2294))) <=> ((~hskp11) | (~c1_1(a2294)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(659,plain,
% 1.23/1.04 (((~c1_1(a2294)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2294)))),
% 1.23/1.04 inference(rewrite,[status(thm)],[])).
% 1.23/1.04 tff(660,axiom,((~c1_1(a2294)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.23/1.04 tff(661,plain,
% 1.23/1.04 ((~hskp11) | (~c1_1(a2294))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.23/1.04 tff(662,plain,
% 1.23/1.04 ((~hskp11) | (~c1_1(a2294))),
% 1.23/1.04 inference(modus_ponens,[status(thm)],[661, 658])).
% 1.23/1.04 tff(663,plain,
% 1.23/1.04 (~c1_1(a2294)),
% 1.23/1.04 inference(unit_resolution,[status(thm)],[662, 657])).
% 1.23/1.04 tff(664,assumption,(c1_1(a2277)), introduced(assumption)).
% 1.23/1.05 tff(665,assumption,(c0_1(a2277)), introduced(assumption)).
% 1.23/1.05 tff(666,plain,
% 1.23/1.05 (((~hskp11) | c0_1(a2294)) <=> ((~hskp11) | c0_1(a2294))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(667,axiom,((~hskp11) | c0_1(a2294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.23/1.05 tff(668,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.23/1.05 tff(669,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[668, 666])).
% 1.23/1.05 tff(670,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[669, 666])).
% 1.23/1.05 tff(671,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[670, 666])).
% 1.23/1.05 tff(672,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[671, 666])).
% 1.23/1.05 tff(673,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[672, 666])).
% 1.23/1.05 tff(674,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[673, 666])).
% 1.23/1.05 tff(675,plain,
% 1.23/1.05 ((~hskp11) | c0_1(a2294)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[674, 666])).
% 1.23/1.05 tff(676,plain,
% 1.23/1.05 (c0_1(a2294)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[675, 657])).
% 1.23/1.05 tff(677,assumption,(c3_1(a2278)), introduced(assumption)).
% 1.23/1.05 tff(678,assumption,(c1_1(a2278)), introduced(assumption)).
% 1.23/1.05 tff(679,assumption,(c0_1(a2278)), introduced(assumption)).
% 1.23/1.05 tff(680,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(681,plain,
% 1.23/1.05 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294))) <=> (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(682,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[681])).
% 1.23/1.05 tff(683,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[682, 680])).
% 1.23/1.05 tff(684,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(685,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.23/1.05 tff(686,plain,
% 1.23/1.05 (~c3_1(a2294)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[685, 181, 679, 678, 677, 676, 665, 664, 663, 40, 94])).
% 1.23/1.05 tff(687,plain,
% 1.23/1.05 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(688,plain,
% 1.23/1.05 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[687])).
% 1.23/1.05 tff(689,plain,
% 1.23/1.05 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(690,plain,
% 1.23/1.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(691,plain,
% 1.23/1.05 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[690])).
% 1.23/1.05 tff(692,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.23/1.05 tff(693,plain,
% 1.23/1.05 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.23/1.05 tff(694,plain,
% 1.23/1.05 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[693, 689])).
% 1.23/1.05 tff(695,plain,(
% 1.23/1.05 ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[694])).
% 1.23/1.05 tff(696,plain,
% 1.23/1.05 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[695, 688])).
% 1.23/1.05 tff(697,plain,
% 1.23/1.05 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(698,plain,
% 1.23/1.05 ((hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(699,plain,
% 1.23/1.05 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[698])).
% 1.23/1.05 tff(700,plain,
% 1.23/1.05 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[699, 697])).
% 1.23/1.05 tff(701,plain,
% 1.23/1.05 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(702,plain,
% 1.23/1.05 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.23/1.05 tff(703,plain,
% 1.23/1.05 ($false),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[702, 181, 638, 676, 663, 696, 686])).
% 1.23/1.05 tff(704,plain,(hskp12 | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c2_1(a2306) | c3_1(a2306) | c0_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.05 tff(705,plain,
% 1.23/1.05 (hskp12),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[704, 637, 626, 615, 378, 367, 342, 345, 344, 450])).
% 1.23/1.05 tff(706,plain,
% 1.23/1.05 (((~hskp12) | (~c3_1(a2295))) <=> ((~hskp12) | (~c3_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(707,plain,
% 1.23/1.05 (((~c3_1(a2295)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(708,axiom,((~c3_1(a2295)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.23/1.05 tff(709,plain,
% 1.23/1.05 ((~hskp12) | (~c3_1(a2295))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[708, 707])).
% 1.23/1.05 tff(710,plain,
% 1.23/1.05 ((~hskp12) | (~c3_1(a2295))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[709, 706])).
% 1.23/1.05 tff(711,plain,
% 1.23/1.05 (~c3_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[710, 705])).
% 1.23/1.05 tff(712,plain,
% 1.23/1.05 (((~hskp12) | c0_1(a2295)) <=> ((~hskp12) | c0_1(a2295))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(713,axiom,((~hskp12) | c0_1(a2295)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.23/1.05 tff(714,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.23/1.05 tff(715,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[714, 712])).
% 1.23/1.05 tff(716,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[715, 712])).
% 1.23/1.05 tff(717,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[716, 712])).
% 1.23/1.05 tff(718,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[717, 712])).
% 1.23/1.05 tff(719,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[718, 712])).
% 1.23/1.05 tff(720,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[719, 712])).
% 1.23/1.05 tff(721,plain,
% 1.23/1.05 ((~hskp12) | c0_1(a2295)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[720, 712])).
% 1.23/1.05 tff(722,plain,
% 1.23/1.05 (c0_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[721, 705])).
% 1.23/1.05 tff(723,assumption,(~c2_1(a2295)), introduced(assumption)).
% 1.23/1.05 tff(724,assumption,(~c3_1(a2295)), introduced(assumption)).
% 1.23/1.05 tff(725,assumption,(c0_1(a2295)), introduced(assumption)).
% 1.23/1.05 tff(726,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(727,plain,
% 1.23/1.05 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(728,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[727])).
% 1.23/1.05 tff(729,plain,
% 1.23/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[728, 726])).
% 1.23/1.05 tff(730,plain,
% 1.23/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(731,plain,
% 1.23/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[730, 729])).
% 1.23/1.05 tff(732,plain,
% 1.23/1.05 ($false),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[731, 181, 84, 725, 378, 367, 724, 342, 356, 723])).
% 1.23/1.05 tff(733,plain,(c2_1(a2295) | hskp14 | (~c0_1(a2295)) | c3_1(a2295)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.05 tff(734,plain,
% 1.23/1.05 (c2_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[733, 722, 84, 711])).
% 1.23/1.05 tff(735,plain,
% 1.23/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(736,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[735])).
% 1.23/1.05 tff(737,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(738,plain,
% 1.23/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.23/1.05 inference(bind,[status(th)],[])).
% 1.23/1.05 tff(739,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(quant_intro,[status(thm)],[738])).
% 1.23/1.05 tff(740,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 1.23/1.05 tff(741,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[740, 739])).
% 1.23/1.05 tff(742,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[741, 737])).
% 1.23/1.05 tff(743,plain,(
% 1.23/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(skolemize,[status(sab)],[742])).
% 1.23/1.05 tff(744,plain,
% 1.23/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[743, 736])).
% 1.23/1.05 tff(745,assumption,(hskp12), introduced(assumption)).
% 1.23/1.05 tff(746,plain,
% 1.23/1.05 (~c3_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[710, 745])).
% 1.23/1.05 tff(747,plain,
% 1.23/1.05 (c0_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[721, 745])).
% 1.23/1.05 tff(748,assumption,(~hskp4), introduced(assumption)).
% 1.23/1.05 tff(749,plain,
% 1.23/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(750,plain,
% 1.23/1.05 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295))) <=> (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(751,plain,
% 1.23/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[750])).
% 1.23/1.05 tff(752,plain,
% 1.23/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[751, 749])).
% 1.23/1.05 tff(753,plain,
% 1.23/1.05 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(754,plain,
% 1.23/1.05 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.23/1.05 tff(755,plain,
% 1.23/1.05 (~c2_1(a2295)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[754, 181, 748, 560, 747, 746, 83])).
% 1.23/1.05 tff(756,plain,
% 1.23/1.05 ($false),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[731, 181, 84, 747, 378, 367, 746, 342, 356, 755])).
% 1.23/1.05 tff(757,plain,((~hskp12) | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.23/1.05 tff(758,plain,
% 1.23/1.05 (hskp4),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[757, 705, 84])).
% 1.23/1.05 tff(759,plain,
% 1.23/1.05 (~c3_1(a2282)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[193, 758])).
% 1.23/1.05 tff(760,plain,
% 1.23/1.05 (~c0_1(a2282)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[199, 758])).
% 1.23/1.05 tff(761,plain,
% 1.23/1.05 (c2_1(a2282)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[247, 758])).
% 1.23/1.05 tff(762,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(763,plain,
% 1.23/1.05 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(764,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[763])).
% 1.23/1.05 tff(765,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[764, 762])).
% 1.23/1.05 tff(766,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(767,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[766, 765])).
% 1.23/1.05 tff(768,plain,
% 1.23/1.05 ((~c1_1(a2282)) | (~c2_1(a2295))),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[767, 181, 722, 761, 711, 760, 759, 744])).
% 1.23/1.05 tff(769,plain,
% 1.23/1.05 (~c1_1(a2282)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[768, 734])).
% 1.23/1.05 tff(770,assumption,(~c2_1(a2280)), introduced(assumption)).
% 1.23/1.05 tff(771,assumption,(~c0_1(a2282)), introduced(assumption)).
% 1.23/1.05 tff(772,assumption,(hskp20), introduced(assumption)).
% 1.23/1.05 tff(773,plain,
% 1.23/1.05 (~c1_1(a2323)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[121, 772])).
% 1.23/1.05 tff(774,assumption,(c3_1(a2280)), introduced(assumption)).
% 1.23/1.05 tff(775,assumption,(c1_1(a2280)), introduced(assumption)).
% 1.23/1.05 tff(776,assumption,(c2_1(a2282)), introduced(assumption)).
% 1.23/1.05 tff(777,plain,
% 1.23/1.05 (c3_1(a2323)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[132, 772])).
% 1.23/1.05 tff(778,plain,
% 1.23/1.05 (c2_1(a2323)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[143, 772])).
% 1.23/1.05 tff(779,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(780,plain,
% 1.23/1.05 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(781,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.23/1.05 inference(monotonicity,[status(thm)],[780])).
% 1.23/1.05 tff(782,plain,
% 1.23/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.05 inference(transitivity,[status(thm)],[781, 779])).
% 1.23/1.05 tff(783,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.05 inference(quant_inst,[status(thm)],[])).
% 1.23/1.05 tff(784,plain,
% 1.23/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[783, 782])).
% 1.23/1.05 tff(785,plain,
% 1.23/1.05 ($false),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[784, 181, 778, 777, 776, 775, 774, 773, 771, 770, 217, 43])).
% 1.23/1.05 tff(786,plain,((~hskp20) | (~c2_1(a2282)) | (~c1_1(a2280)) | (~c3_1(a2280)) | c0_1(a2282) | c2_1(a2280) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.05 tff(787,plain,
% 1.23/1.05 (~hskp20),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[786, 761, 597, 586, 760, 575, 769])).
% 1.23/1.05 tff(788,assumption,(hskp30), introduced(assumption)).
% 1.23/1.05 tff(789,plain,
% 1.23/1.05 (((~hskp30) | c3_1(a2315)) <=> ((~hskp30) | c3_1(a2315))),
% 1.23/1.05 inference(rewrite,[status(thm)],[])).
% 1.23/1.05 tff(790,axiom,((~hskp30) | c3_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.23/1.05 tff(791,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.23/1.05 tff(792,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[791, 789])).
% 1.23/1.05 tff(793,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[792, 789])).
% 1.23/1.05 tff(794,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[793, 789])).
% 1.23/1.05 tff(795,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[794, 789])).
% 1.23/1.05 tff(796,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[795, 789])).
% 1.23/1.05 tff(797,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[796, 789])).
% 1.23/1.05 tff(798,plain,
% 1.23/1.05 ((~hskp30) | c3_1(a2315)),
% 1.23/1.05 inference(modus_ponens,[status(thm)],[797, 789])).
% 1.23/1.05 tff(799,plain,
% 1.23/1.05 (c3_1(a2315)),
% 1.23/1.05 inference(unit_resolution,[status(thm)],[798, 788])).
% 1.23/1.05 tff(800,plain,
% 1.23/1.05 (((~hskp30) | c2_1(a2315)) <=> ((~hskp30) | c2_1(a2315))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(801,axiom,((~hskp30) | c2_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.23/1.06 tff(802,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.23/1.06 tff(803,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[802, 800])).
% 1.23/1.06 tff(804,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[803, 800])).
% 1.23/1.06 tff(805,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[804, 800])).
% 1.23/1.06 tff(806,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[805, 800])).
% 1.23/1.06 tff(807,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[806, 800])).
% 1.23/1.06 tff(808,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[807, 800])).
% 1.23/1.06 tff(809,plain,
% 1.23/1.06 ((~hskp30) | c2_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[808, 800])).
% 1.23/1.06 tff(810,plain,
% 1.23/1.06 (c2_1(a2315)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[809, 788])).
% 1.23/1.06 tff(811,assumption,(~hskp20), introduced(assumption)).
% 1.23/1.06 tff(812,plain,
% 1.23/1.06 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(813,plain,
% 1.23/1.06 ((hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315))) <=> (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(814,plain,
% 1.23/1.06 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315)))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[813])).
% 1.23/1.06 tff(815,plain,
% 1.23/1.06 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 1.23/1.06 inference(transitivity,[status(thm)],[814, 812])).
% 1.23/1.06 tff(816,plain,
% 1.23/1.06 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(817,plain,
% 1.23/1.06 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.23/1.06 tff(818,plain,
% 1.23/1.06 (c0_1(a2315)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[817, 181, 811, 810, 799, 73])).
% 1.23/1.06 tff(819,assumption,(c3_1(a2277)), introduced(assumption)).
% 1.23/1.06 tff(820,plain,
% 1.23/1.06 (((~hskp30) | c1_1(a2315)) <=> ((~hskp30) | c1_1(a2315))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(821,axiom,((~hskp30) | c1_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.23/1.06 tff(822,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.23/1.06 tff(823,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[822, 820])).
% 1.23/1.06 tff(824,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[823, 820])).
% 1.23/1.06 tff(825,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[824, 820])).
% 1.23/1.06 tff(826,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[825, 820])).
% 1.23/1.06 tff(827,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[826, 820])).
% 1.23/1.06 tff(828,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[827, 820])).
% 1.23/1.06 tff(829,plain,
% 1.23/1.06 ((~hskp30) | c1_1(a2315)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[828, 820])).
% 1.23/1.06 tff(830,plain,
% 1.23/1.06 (c1_1(a2315)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[829, 788])).
% 1.23/1.06 tff(831,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(832,plain,
% 1.23/1.06 (((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(833,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[832])).
% 1.23/1.06 tff(834,plain,
% 1.23/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[833, 831])).
% 1.23/1.06 tff(835,plain,
% 1.23/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(836,plain,
% 1.23/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[835, 834])).
% 1.23/1.06 tff(837,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[836, 181, 830, 810, 665, 398, 397, 396, 40, 395, 819, 818])).
% 1.23/1.06 tff(838,plain,((~hskp30) | (~c0_1(a2277)) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~c3_1(a2277)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(839,plain,
% 1.23/1.06 (~hskp30),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[838, 346, 378, 345, 344, 342, 385, 787])).
% 1.23/1.06 tff(840,plain,
% 1.23/1.06 ((hskp30 | hskp11 | hskp6) <=> (hskp30 | hskp11 | hskp6)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(841,plain,
% 1.23/1.06 (((hskp11 | hskp6) | hskp30) <=> (hskp30 | hskp11 | hskp6)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(842,plain,
% 1.23/1.06 ((hskp6 | hskp11) <=> (hskp11 | hskp6)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(843,plain,
% 1.23/1.06 (((hskp6 | hskp11) | hskp30) <=> ((hskp11 | hskp6) | hskp30)),
% 1.23/1.06 inference(monotonicity,[status(thm)],[842])).
% 1.23/1.06 tff(844,plain,
% 1.23/1.06 (((hskp6 | hskp11) | hskp30) <=> (hskp30 | hskp11 | hskp6)),
% 1.23/1.06 inference(transitivity,[status(thm)],[843, 841])).
% 1.23/1.06 tff(845,axiom,((hskp6 | hskp11) | hskp30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.23/1.06 tff(846,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.23/1.06 tff(847,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[846, 840])).
% 1.23/1.06 tff(848,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[847, 840])).
% 1.23/1.06 tff(849,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[848, 840])).
% 1.23/1.06 tff(850,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[849, 840])).
% 1.23/1.06 tff(851,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[850, 840])).
% 1.23/1.06 tff(852,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[851, 840])).
% 1.23/1.06 tff(853,plain,
% 1.23/1.06 (hskp30 | hskp11 | hskp6),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[852, 840])).
% 1.23/1.06 tff(854,plain,
% 1.23/1.06 (hskp11),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[853, 839, 443])).
% 1.23/1.06 tff(855,plain,
% 1.23/1.06 (~c1_1(a2294)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[662, 854])).
% 1.23/1.06 tff(856,plain,
% 1.23/1.06 (c0_1(a2294)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[675, 854])).
% 1.23/1.06 tff(857,plain,
% 1.23/1.06 (~c3_1(a2294)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[685, 181, 637, 626, 615, 856, 378, 367, 855, 342, 94])).
% 1.23/1.06 tff(858,plain,
% 1.23/1.06 (((~hskp11) | (~c2_1(a2294))) <=> ((~hskp11) | (~c2_1(a2294)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(859,plain,
% 1.23/1.06 (((~c2_1(a2294)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a2294)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(860,axiom,((~c2_1(a2294)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.23/1.06 tff(861,plain,
% 1.23/1.06 ((~hskp11) | (~c2_1(a2294))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[860, 859])).
% 1.23/1.06 tff(862,plain,
% 1.23/1.06 ((~hskp11) | (~c2_1(a2294))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[861, 858])).
% 1.23/1.06 tff(863,plain,
% 1.23/1.06 (~c2_1(a2294)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[862, 854])).
% 1.23/1.06 tff(864,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(865,plain,
% 1.23/1.06 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(866,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[865])).
% 1.23/1.06 tff(867,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[866, 864])).
% 1.23/1.06 tff(868,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(869,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.23/1.06 tff(870,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[869, 181, 84, 856, 378, 367, 863, 342, 356, 857])).
% 1.23/1.06 tff(871,plain,((~hskp17) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(872,plain,
% 1.23/1.06 (~hskp17),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[871, 84])).
% 1.23/1.06 tff(873,plain,
% 1.23/1.06 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(874,plain,
% 1.23/1.06 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[873])).
% 1.23/1.06 tff(875,plain,
% 1.23/1.06 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(876,plain,
% 1.23/1.06 (^[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)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.23/1.06 inference(bind,[status(th)],[])).
% 1.23/1.06 tff(877,plain,
% 1.23/1.06 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(quant_intro,[status(thm)],[876])).
% 1.23/1.06 tff(878,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.23/1.06 tff(879,plain,
% 1.23/1.06 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.23/1.06 tff(880,plain,
% 1.23/1.06 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[879, 875])).
% 1.23/1.06 tff(881,plain,(
% 1.23/1.06 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(skolemize,[status(sab)],[880])).
% 1.23/1.06 tff(882,plain,
% 1.23/1.06 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[881, 874])).
% 1.23/1.06 tff(883,assumption,(hskp0), introduced(assumption)).
% 1.23/1.06 tff(884,plain,
% 1.23/1.06 (((~hskp0) | (~c0_1(a2276))) <=> ((~hskp0) | (~c0_1(a2276)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(885,plain,
% 1.23/1.06 (((~c0_1(a2276)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2276)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(886,axiom,((~c0_1(a2276)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.23/1.06 tff(887,plain,
% 1.23/1.06 ((~hskp0) | (~c0_1(a2276))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[886, 885])).
% 1.23/1.06 tff(888,plain,
% 1.23/1.06 ((~hskp0) | (~c0_1(a2276))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[887, 884])).
% 1.23/1.06 tff(889,plain,
% 1.23/1.06 (~c0_1(a2276)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[888, 883])).
% 1.23/1.06 tff(890,plain,
% 1.23/1.06 (((~hskp0) | c3_1(a2276)) <=> ((~hskp0) | c3_1(a2276))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(891,axiom,((~hskp0) | c3_1(a2276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.23/1.06 tff(892,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.23/1.06 tff(893,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[892, 890])).
% 1.23/1.06 tff(894,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[893, 890])).
% 1.23/1.06 tff(895,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[894, 890])).
% 1.23/1.06 tff(896,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[895, 890])).
% 1.23/1.06 tff(897,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[896, 890])).
% 1.23/1.06 tff(898,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[897, 890])).
% 1.23/1.06 tff(899,plain,
% 1.23/1.06 ((~hskp0) | c3_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[898, 890])).
% 1.23/1.06 tff(900,plain,
% 1.23/1.06 (c3_1(a2276)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[899, 883])).
% 1.23/1.06 tff(901,plain,
% 1.23/1.06 (((~hskp0) | c1_1(a2276)) <=> ((~hskp0) | c1_1(a2276))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(902,axiom,((~hskp0) | c1_1(a2276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.23/1.06 tff(903,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[902, 901])).
% 1.23/1.06 tff(904,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[903, 901])).
% 1.23/1.06 tff(905,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[904, 901])).
% 1.23/1.06 tff(906,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[905, 901])).
% 1.23/1.06 tff(907,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[906, 901])).
% 1.23/1.06 tff(908,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[907, 901])).
% 1.23/1.06 tff(909,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[908, 901])).
% 1.23/1.06 tff(910,plain,
% 1.23/1.06 ((~hskp0) | c1_1(a2276)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[909, 901])).
% 1.23/1.06 tff(911,plain,
% 1.23/1.06 (c1_1(a2276)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[910, 883])).
% 1.23/1.06 tff(912,assumption,(~hskp17), introduced(assumption)).
% 1.23/1.06 tff(913,plain,
% 1.23/1.06 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(914,plain,
% 1.23/1.06 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276))) <=> (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(915,plain,
% 1.23/1.06 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[914])).
% 1.23/1.06 tff(916,plain,
% 1.23/1.06 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[915, 913])).
% 1.23/1.06 tff(917,plain,
% 1.23/1.06 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(918,plain,
% 1.23/1.06 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.23/1.06 tff(919,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[918, 181, 912, 84, 911, 900, 889, 882])).
% 1.23/1.06 tff(920,plain,((~hskp0) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(921,plain,
% 1.23/1.06 (~hskp0),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[920, 872, 84])).
% 1.23/1.06 tff(922,assumption,(hskp4), introduced(assumption)).
% 1.23/1.06 tff(923,plain,
% 1.23/1.06 (~c3_1(a2282)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[193, 922])).
% 1.23/1.06 tff(924,plain,
% 1.23/1.06 (~c0_1(a2282)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[199, 922])).
% 1.23/1.06 tff(925,plain,
% 1.23/1.06 (c2_1(a2282)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[247, 922])).
% 1.23/1.06 tff(926,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[254, 181, 912, 84, 925, 924, 923, 237])).
% 1.23/1.06 tff(927,plain,((~hskp4) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(928,plain,
% 1.23/1.06 (~hskp4),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[927, 872, 84])).
% 1.23/1.06 tff(929,plain,
% 1.23/1.06 (~hskp12),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[757, 928, 84])).
% 1.23/1.06 tff(930,plain,
% 1.23/1.06 ((hskp12 | hskp6 | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(931,plain,
% 1.23/1.06 (((hskp12 | hskp6) | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(932,plain,
% 1.23/1.06 ((hskp6 | hskp12) <=> (hskp12 | hskp6)),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(933,plain,
% 1.23/1.06 (((hskp6 | hskp12) | hskp0) <=> ((hskp12 | hskp6) | hskp0)),
% 1.23/1.06 inference(monotonicity,[status(thm)],[932])).
% 1.23/1.06 tff(934,plain,
% 1.23/1.06 (((hskp6 | hskp12) | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 1.23/1.06 inference(transitivity,[status(thm)],[933, 931])).
% 1.23/1.06 tff(935,axiom,((hskp6 | hskp12) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.23/1.06 tff(936,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.23/1.06 tff(937,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[936, 930])).
% 1.23/1.06 tff(938,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[937, 930])).
% 1.23/1.06 tff(939,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[938, 930])).
% 1.23/1.06 tff(940,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[939, 930])).
% 1.23/1.06 tff(941,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[940, 930])).
% 1.23/1.06 tff(942,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[941, 930])).
% 1.23/1.06 tff(943,plain,
% 1.23/1.06 (hskp12 | hskp6 | hskp0),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[942, 930])).
% 1.23/1.06 tff(944,plain,
% 1.23/1.06 (hskp6),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[943, 929, 921])).
% 1.23/1.06 tff(945,plain,
% 1.23/1.06 (~c3_1(a2285)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[433, 944])).
% 1.23/1.06 tff(946,plain,
% 1.23/1.06 (c0_1(a2285)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[420, 944])).
% 1.23/1.06 tff(947,plain,
% 1.23/1.06 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(948,plain,
% 1.23/1.06 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285))) <=> (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(949,plain,
% 1.23/1.06 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[948])).
% 1.23/1.06 tff(950,plain,
% 1.23/1.06 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[949, 947])).
% 1.23/1.06 tff(951,plain,
% 1.23/1.06 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(952,plain,
% 1.23/1.06 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[951, 950])).
% 1.23/1.06 tff(953,plain,
% 1.23/1.06 (~c2_1(a2285)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[952, 181, 928, 560, 946, 945, 83])).
% 1.23/1.06 tff(954,plain,
% 1.23/1.06 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(955,plain,
% 1.23/1.06 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(956,plain,
% 1.23/1.06 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.23/1.06 tff(957,plain,
% 1.23/1.06 (hskp17 | c0_1(a2280)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[956, 181, 84, 597, 586, 882])).
% 1.23/1.06 tff(958,plain,
% 1.23/1.06 (c0_1(a2280)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[957, 872])).
% 1.23/1.06 tff(959,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(960,plain,
% 1.23/1.06 ((hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285))) <=> (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(961,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285))))),
% 1.23/1.06 inference(monotonicity,[status(thm)],[960])).
% 1.23/1.06 tff(962,plain,
% 1.23/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.06 inference(transitivity,[status(thm)],[961, 959])).
% 1.23/1.06 tff(963,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))),
% 1.23/1.06 inference(quant_inst,[status(thm)],[])).
% 1.23/1.06 tff(964,plain,
% 1.23/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.23/1.06 tff(965,plain,
% 1.23/1.06 ($false),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[964, 181, 84, 946, 597, 945, 575, 356, 958, 953])).
% 1.23/1.06 tff(966,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 1.23/1.06 tff(967,plain,
% 1.23/1.06 (((~hskp14) | (~c0_1(a2302))) <=> ((~hskp14) | (~c0_1(a2302)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(968,plain,
% 1.23/1.06 (((~c0_1(a2302)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a2302)))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(969,axiom,((~c0_1(a2302)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.23/1.06 tff(970,plain,
% 1.23/1.06 ((~hskp14) | (~c0_1(a2302))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.23/1.06 tff(971,plain,
% 1.23/1.06 ((~hskp14) | (~c0_1(a2302))),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[970, 967])).
% 1.23/1.06 tff(972,plain,
% 1.23/1.06 (~c0_1(a2302)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[971, 966])).
% 1.23/1.06 tff(973,plain,
% 1.23/1.06 (((~hskp14) | c3_1(a2302)) <=> ((~hskp14) | c3_1(a2302))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(974,axiom,((~hskp14) | c3_1(a2302)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.23/1.06 tff(975,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.23/1.06 tff(976,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[975, 973])).
% 1.23/1.06 tff(977,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[976, 973])).
% 1.23/1.06 tff(978,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[977, 973])).
% 1.23/1.06 tff(979,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[978, 973])).
% 1.23/1.06 tff(980,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[979, 973])).
% 1.23/1.06 tff(981,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[980, 973])).
% 1.23/1.06 tff(982,plain,
% 1.23/1.06 ((~hskp14) | c3_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[981, 973])).
% 1.23/1.06 tff(983,plain,
% 1.23/1.06 (c3_1(a2302)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[982, 966])).
% 1.23/1.06 tff(984,plain,
% 1.23/1.06 (((~hskp14) | c2_1(a2302)) <=> ((~hskp14) | c2_1(a2302))),
% 1.23/1.06 inference(rewrite,[status(thm)],[])).
% 1.23/1.06 tff(985,axiom,((~hskp14) | c2_1(a2302)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.23/1.06 tff(986,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[985, 984])).
% 1.23/1.06 tff(987,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[986, 984])).
% 1.23/1.06 tff(988,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[987, 984])).
% 1.23/1.06 tff(989,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[988, 984])).
% 1.23/1.06 tff(990,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[989, 984])).
% 1.23/1.06 tff(991,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[990, 984])).
% 1.23/1.06 tff(992,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[991, 984])).
% 1.23/1.06 tff(993,plain,
% 1.23/1.06 ((~hskp14) | c2_1(a2302)),
% 1.23/1.06 inference(modus_ponens,[status(thm)],[992, 984])).
% 1.23/1.06 tff(994,plain,
% 1.23/1.06 (c2_1(a2302)),
% 1.23/1.06 inference(unit_resolution,[status(thm)],[993, 966])).
% 1.23/1.06 tff(995,plain,
% 1.23/1.06 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(996,plain,
% 1.23/1.07 ((hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302))) <=> (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(997,plain,
% 1.23/1.07 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[996])).
% 1.23/1.07 tff(998,plain,
% 1.23/1.07 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[997, 995])).
% 1.23/1.07 tff(999,plain,
% 1.23/1.07 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1000,plain,
% 1.23/1.07 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[999, 998])).
% 1.23/1.07 tff(1001,plain,
% 1.23/1.07 (hskp20),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1000, 181, 994, 983, 972, 73])).
% 1.23/1.07 tff(1002,plain,
% 1.23/1.07 (~c1_1(a2323)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[121, 1001])).
% 1.23/1.07 tff(1003,plain,
% 1.23/1.07 (c3_1(a2323)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[132, 1001])).
% 1.23/1.07 tff(1004,plain,
% 1.23/1.07 (c2_1(a2323)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[143, 1001])).
% 1.23/1.07 tff(1005,plain,
% 1.23/1.07 (hskp4 | hskp1),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[187, 181, 1004, 1003, 1002, 63])).
% 1.23/1.07 tff(1006,plain,
% 1.23/1.07 (hskp4),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1005, 42])).
% 1.23/1.07 tff(1007,plain,
% 1.23/1.07 (~c3_1(a2282)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[193, 1006])).
% 1.23/1.07 tff(1008,plain,
% 1.23/1.07 (c2_1(a2282)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[247, 1006])).
% 1.23/1.07 tff(1009,plain,
% 1.23/1.07 (~c0_1(a2282)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[199, 1006])).
% 1.23/1.07 tff(1010,assumption,(hskp9), introduced(assumption)).
% 1.23/1.07 tff(1011,plain,
% 1.23/1.07 (((~hskp9) | (~c2_1(a2291))) <=> ((~hskp9) | (~c2_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1012,plain,
% 1.23/1.07 (((~c2_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1013,axiom,((~c2_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.23/1.07 tff(1014,plain,
% 1.23/1.07 ((~hskp9) | (~c2_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.23/1.07 tff(1015,plain,
% 1.23/1.07 ((~hskp9) | (~c2_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 1.23/1.07 tff(1016,plain,
% 1.23/1.07 (~c2_1(a2291)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1015, 1010])).
% 1.23/1.07 tff(1017,plain,
% 1.23/1.07 (((~hskp9) | (~c1_1(a2291))) <=> ((~hskp9) | (~c1_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1018,plain,
% 1.23/1.07 (((~c1_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1019,axiom,((~c1_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.23/1.07 tff(1020,plain,
% 1.23/1.07 ((~hskp9) | (~c1_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.23/1.07 tff(1021,plain,
% 1.23/1.07 ((~hskp9) | (~c1_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1020, 1017])).
% 1.23/1.07 tff(1022,plain,
% 1.23/1.07 (~c1_1(a2291)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1021, 1010])).
% 1.23/1.07 tff(1023,plain,
% 1.23/1.07 (((~hskp9) | (~c0_1(a2291))) <=> ((~hskp9) | (~c0_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1024,plain,
% 1.23/1.07 (((~c0_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2291)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1025,axiom,((~c0_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.23/1.07 tff(1026,plain,
% 1.23/1.07 ((~hskp9) | (~c0_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 1.23/1.07 tff(1027,plain,
% 1.23/1.07 ((~hskp9) | (~c0_1(a2291))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1026, 1023])).
% 1.23/1.07 tff(1028,plain,
% 1.23/1.07 (~c0_1(a2291)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1027, 1010])).
% 1.23/1.07 tff(1029,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1030,plain,
% 1.23/1.07 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1031,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1030])).
% 1.23/1.07 tff(1032,plain,
% 1.23/1.07 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1031, 1029])).
% 1.23/1.07 tff(1033,plain,
% 1.23/1.07 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1034,plain,
% 1.23/1.07 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 1.23/1.07 tff(1035,plain,
% 1.23/1.07 ($false),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1034, 181, 42, 1008, 1028, 1022, 1016, 1007, 227, 43])).
% 1.23/1.07 tff(1036,plain,((~hskp9) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.07 tff(1037,plain,
% 1.23/1.07 (~hskp9),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1036, 43, 42])).
% 1.23/1.07 tff(1038,plain,
% 1.23/1.07 (^[U: $i] : refl((hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1039,plain,
% 1.23/1.07 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1038])).
% 1.23/1.07 tff(1040,plain,
% 1.23/1.07 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1041,plain,
% 1.23/1.07 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1042,plain,
% 1.23/1.07 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1041])).
% 1.23/1.07 tff(1043,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.23/1.07 tff(1044,plain,
% 1.23/1.07 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.23/1.07 tff(1045,plain,
% 1.23/1.07 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1044, 1040])).
% 1.23/1.07 tff(1046,plain,(
% 1.23/1.07 ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(skolemize,[status(sab)],[1045])).
% 1.23/1.07 tff(1047,plain,
% 1.23/1.07 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1046, 1039])).
% 1.23/1.07 tff(1048,assumption,(hskp7), introduced(assumption)).
% 1.23/1.07 tff(1049,plain,
% 1.23/1.07 (((~hskp7) | (~c2_1(a2286))) <=> ((~hskp7) | (~c2_1(a2286)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1050,plain,
% 1.23/1.07 (((~c2_1(a2286)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a2286)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1051,axiom,((~c2_1(a2286)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.23/1.07 tff(1052,plain,
% 1.23/1.07 ((~hskp7) | (~c2_1(a2286))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.23/1.07 tff(1053,plain,
% 1.23/1.07 ((~hskp7) | (~c2_1(a2286))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1052, 1049])).
% 1.23/1.07 tff(1054,plain,
% 1.23/1.07 (~c2_1(a2286)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1053, 1048])).
% 1.23/1.07 tff(1055,plain,
% 1.23/1.07 (((~hskp7) | (~c0_1(a2286))) <=> ((~hskp7) | (~c0_1(a2286)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1056,plain,
% 1.23/1.07 (((~c0_1(a2286)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a2286)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1057,axiom,((~c0_1(a2286)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.23/1.07 tff(1058,plain,
% 1.23/1.07 ((~hskp7) | (~c0_1(a2286))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.23/1.07 tff(1059,plain,
% 1.23/1.07 ((~hskp7) | (~c0_1(a2286))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1058, 1055])).
% 1.23/1.07 tff(1060,plain,
% 1.23/1.07 (~c0_1(a2286)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1059, 1048])).
% 1.23/1.07 tff(1061,assumption,(~hskp9), introduced(assumption)).
% 1.23/1.07 tff(1062,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1063,plain,
% 1.23/1.07 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286)) <=> (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1064,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1063])).
% 1.23/1.07 tff(1065,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1064, 1062])).
% 1.23/1.07 tff(1066,plain,
% 1.23/1.07 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1067,plain,
% 1.23/1.07 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 1.23/1.07 tff(1068,plain,
% 1.23/1.07 (c3_1(a2286)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1067, 181, 41, 1061, 1060, 1054, 1047])).
% 1.23/1.07 tff(1069,plain,
% 1.23/1.07 (((~hskp7) | c1_1(a2286)) <=> ((~hskp7) | c1_1(a2286))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1070,axiom,((~hskp7) | c1_1(a2286)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.23/1.07 tff(1071,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.23/1.07 tff(1072,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1071, 1069])).
% 1.23/1.07 tff(1073,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1072, 1069])).
% 1.23/1.07 tff(1074,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1073, 1069])).
% 1.23/1.07 tff(1075,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1074, 1069])).
% 1.23/1.07 tff(1076,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1075, 1069])).
% 1.23/1.07 tff(1077,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1076, 1069])).
% 1.23/1.07 tff(1078,plain,
% 1.23/1.07 ((~hskp7) | c1_1(a2286)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1077, 1069])).
% 1.23/1.07 tff(1079,plain,
% 1.23/1.07 (c1_1(a2286)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1078, 1048])).
% 1.23/1.07 tff(1080,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1081,plain,
% 1.23/1.07 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1082,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1081])).
% 1.23/1.07 tff(1083,plain,
% 1.23/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1082, 1080])).
% 1.23/1.07 tff(1084,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1085,plain,
% 1.23/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.23/1.07 tff(1086,plain,
% 1.23/1.07 ($false),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1085, 181, 1004, 1003, 1079, 776, 1002, 1054, 771, 217, 43, 1068])).
% 1.23/1.07 tff(1087,plain,((~hskp7) | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282) | hskp28 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.23/1.07 tff(1088,plain,
% 1.23/1.07 (~hskp7),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1087, 1037, 1009, 43, 41, 1008])).
% 1.23/1.07 tff(1089,assumption,(hskp16), introduced(assumption)).
% 1.23/1.07 tff(1090,plain,
% 1.23/1.07 (((~hskp16) | (~c3_1(a2304))) <=> ((~hskp16) | (~c3_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1091,plain,
% 1.23/1.07 (((~c3_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1092,axiom,((~c3_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.23/1.07 tff(1093,plain,
% 1.23/1.07 ((~hskp16) | (~c3_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 1.23/1.07 tff(1094,plain,
% 1.23/1.07 ((~hskp16) | (~c3_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 1.23/1.07 tff(1095,plain,
% 1.23/1.07 (~c3_1(a2304)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1094, 1089])).
% 1.23/1.07 tff(1096,plain,
% 1.23/1.07 (((~hskp16) | (~c2_1(a2304))) <=> ((~hskp16) | (~c2_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1097,plain,
% 1.23/1.07 (((~c2_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1098,axiom,((~c2_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.23/1.07 tff(1099,plain,
% 1.23/1.07 ((~hskp16) | (~c2_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 1.23/1.07 tff(1100,plain,
% 1.23/1.07 ((~hskp16) | (~c2_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 1.23/1.07 tff(1101,plain,
% 1.23/1.07 (~c2_1(a2304)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1100, 1089])).
% 1.23/1.07 tff(1102,plain,
% 1.23/1.07 (((~hskp16) | (~c0_1(a2304))) <=> ((~hskp16) | (~c0_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1103,plain,
% 1.23/1.07 (((~c0_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a2304)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1104,axiom,((~c0_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.23/1.07 tff(1105,plain,
% 1.23/1.07 ((~hskp16) | (~c0_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.23/1.07 tff(1106,plain,
% 1.23/1.07 ((~hskp16) | (~c0_1(a2304))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1105, 1102])).
% 1.23/1.07 tff(1107,plain,
% 1.23/1.07 (~c0_1(a2304)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1106, 1089])).
% 1.23/1.07 tff(1108,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1109,plain,
% 1.23/1.07 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304)) <=> (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1110,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1109])).
% 1.23/1.07 tff(1111,plain,
% 1.23/1.07 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1110, 1108])).
% 1.23/1.07 tff(1112,plain,
% 1.23/1.07 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1113,plain,
% 1.23/1.07 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 1.23/1.07 tff(1114,plain,
% 1.23/1.07 ($false),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1113, 181, 41, 1061, 1107, 1101, 1095, 1047])).
% 1.23/1.07 tff(1115,plain,((~hskp16) | hskp28 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.23/1.07 tff(1116,plain,
% 1.23/1.07 (~hskp16),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1115, 1037, 41])).
% 1.23/1.07 tff(1117,plain,
% 1.23/1.07 ((hskp28 | hskp26 | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1118,plain,
% 1.23/1.07 (((hskp28 | hskp26) | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1119,plain,
% 1.23/1.07 ((hskp28 | hskp26) <=> (hskp28 | hskp26)),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1120,plain,
% 1.23/1.07 (((hskp28 | hskp26) | hskp16) <=> ((hskp28 | hskp26) | hskp16)),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1119])).
% 1.23/1.07 tff(1121,plain,
% 1.23/1.07 (((hskp28 | hskp26) | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 1.23/1.07 inference(transitivity,[status(thm)],[1120, 1118])).
% 1.23/1.07 tff(1122,axiom,((hskp28 | hskp26) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.23/1.07 tff(1123,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.23/1.07 tff(1124,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1123, 1117])).
% 1.23/1.07 tff(1125,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1124, 1117])).
% 1.23/1.07 tff(1126,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1125, 1117])).
% 1.23/1.07 tff(1127,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1126, 1117])).
% 1.23/1.07 tff(1128,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1127, 1117])).
% 1.23/1.07 tff(1129,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1128, 1117])).
% 1.23/1.07 tff(1130,plain,
% 1.23/1.07 (hskp28 | hskp26 | hskp16),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1129, 1117])).
% 1.23/1.07 tff(1131,plain,
% 1.23/1.07 (hskp26),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1130, 1116, 41])).
% 1.23/1.07 tff(1132,plain,
% 1.23/1.07 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1133,plain,
% 1.23/1.07 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1132])).
% 1.23/1.07 tff(1134,plain,
% 1.23/1.07 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1135,plain,
% 1.23/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.23/1.07 inference(bind,[status(th)],[])).
% 1.23/1.07 tff(1136,plain,
% 1.23/1.07 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(quant_intro,[status(thm)],[1135])).
% 1.23/1.07 tff(1137,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.23/1.07 tff(1138,plain,
% 1.23/1.07 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.23/1.07 tff(1139,plain,
% 1.23/1.07 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1138, 1134])).
% 1.23/1.07 tff(1140,plain,(
% 1.23/1.07 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(skolemize,[status(sab)],[1139])).
% 1.23/1.07 tff(1141,plain,
% 1.23/1.07 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1140, 1133])).
% 1.23/1.07 tff(1142,assumption,(hskp26), introduced(assumption)).
% 1.23/1.07 tff(1143,plain,
% 1.23/1.07 (((~hskp26) | (~c1_1(a2345))) <=> ((~hskp26) | (~c1_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1144,plain,
% 1.23/1.07 (((~c1_1(a2345)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1145,axiom,((~c1_1(a2345)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.23/1.07 tff(1146,plain,
% 1.23/1.07 ((~hskp26) | (~c1_1(a2345))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.23/1.07 tff(1147,plain,
% 1.23/1.07 ((~hskp26) | (~c1_1(a2345))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1146, 1143])).
% 1.23/1.07 tff(1148,plain,
% 1.23/1.07 (~c1_1(a2345)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1147, 1142])).
% 1.23/1.07 tff(1149,plain,
% 1.23/1.07 (((~hskp26) | (~c0_1(a2345))) <=> ((~hskp26) | (~c0_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1150,plain,
% 1.23/1.07 (((~c0_1(a2345)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1151,axiom,((~c0_1(a2345)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.23/1.07 tff(1152,plain,
% 1.23/1.07 ((~hskp26) | (~c0_1(a2345))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.23/1.07 tff(1153,plain,
% 1.23/1.07 ((~hskp26) | (~c0_1(a2345))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 1.23/1.07 tff(1154,plain,
% 1.23/1.07 (~c0_1(a2345)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1153, 1142])).
% 1.23/1.07 tff(1155,plain,
% 1.23/1.07 (((~hskp26) | c3_1(a2345)) <=> ((~hskp26) | c3_1(a2345))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1156,axiom,((~hskp26) | c3_1(a2345)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.23/1.07 tff(1157,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.23/1.07 tff(1158,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1157, 1155])).
% 1.23/1.07 tff(1159,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 1.23/1.07 tff(1160,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1159, 1155])).
% 1.23/1.07 tff(1161,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1160, 1155])).
% 1.23/1.07 tff(1162,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1161, 1155])).
% 1.23/1.07 tff(1163,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1162, 1155])).
% 1.23/1.07 tff(1164,plain,
% 1.23/1.07 ((~hskp26) | c3_1(a2345)),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1163, 1155])).
% 1.23/1.07 tff(1165,plain,
% 1.23/1.07 (c3_1(a2345)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1164, 1142])).
% 1.23/1.07 tff(1166,assumption,(~hskp6), introduced(assumption)).
% 1.23/1.07 tff(1167,assumption,(~hskp7), introduced(assumption)).
% 1.23/1.07 tff(1168,plain,
% 1.23/1.07 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1169,plain,
% 1.23/1.07 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345))) <=> (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 1.23/1.07 inference(rewrite,[status(thm)],[])).
% 1.23/1.07 tff(1170,plain,
% 1.23/1.07 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345))))),
% 1.23/1.07 inference(monotonicity,[status(thm)],[1169])).
% 1.23/1.07 tff(1171,plain,
% 1.23/1.07 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 1.23/1.07 inference(transitivity,[status(thm)],[1170, 1168])).
% 1.23/1.07 tff(1172,plain,
% 1.23/1.07 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))),
% 1.23/1.07 inference(quant_inst,[status(thm)],[])).
% 1.23/1.07 tff(1173,plain,
% 1.23/1.07 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345))),
% 1.23/1.07 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 1.23/1.07 tff(1174,plain,
% 1.23/1.07 ($false),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1173, 181, 1167, 1166, 1165, 1154, 1148, 1141])).
% 1.23/1.07 tff(1175,plain,((~hskp26) | hskp7 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.23/1.07 tff(1176,plain,
% 1.23/1.07 (hskp6),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[1175, 1131, 1088])).
% 1.23/1.07 tff(1177,plain,
% 1.23/1.07 (~c3_1(a2285)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[433, 1176])).
% 1.23/1.07 tff(1178,plain,
% 1.23/1.07 (c1_1(a2285)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[409, 1176])).
% 1.23/1.07 tff(1179,plain,
% 1.23/1.07 (c0_1(a2285)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[420, 1176])).
% 1.23/1.07 tff(1180,assumption,(hskp23), introduced(assumption)).
% 1.23/1.07 tff(1181,plain,
% 1.23/1.07 (~c2_1(a2327)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[302, 1180])).
% 1.23/1.07 tff(1182,plain,
% 1.23/1.07 (c3_1(a2327)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[313, 1180])).
% 1.23/1.07 tff(1183,plain,
% 1.23/1.07 (~c1_1(a2327)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[320, 181, 1182, 1004, 1003, 1008, 1181, 1002, 1009, 217, 43])).
% 1.23/1.07 tff(1184,plain,
% 1.23/1.07 (~c0_1(a2327)),
% 1.23/1.07 inference(unit_resolution,[status(thm)],[326, 1180])).
% 1.23/1.08 tff(1185,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[333, 181, 42, 1008, 1184, 1181, 1007, 227, 43, 1183])).
% 1.23/1.08 tff(1186,plain,((~hskp23) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1187,plain,
% 1.23/1.08 (~hskp23),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1186, 43, 42])).
% 1.23/1.08 tff(1188,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1189,plain,
% 1.23/1.08 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1190,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1189])).
% 1.23/1.08 tff(1191,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1190, 1188])).
% 1.23/1.08 tff(1192,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1193,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.23/1.08 tff(1194,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1193, 181, 1187, 1179, 1178, 1008, 1177, 1007, 53, 43])).
% 1.23/1.08 tff(1195,plain,(c1_1(a2282) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1196,plain,
% 1.23/1.08 (c1_1(a2282)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1195, 42, 41])).
% 1.23/1.08 tff(1197,assumption,(c1_1(a2282)), introduced(assumption)).
% 1.23/1.08 tff(1198,assumption,(~c3_1(a2282)), introduced(assumption)).
% 1.23/1.08 tff(1199,assumption,(hskp10), introduced(assumption)).
% 1.23/1.08 tff(1200,plain,
% 1.23/1.08 (((~hskp10) | (~c3_1(a2293))) <=> ((~hskp10) | (~c3_1(a2293)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1201,plain,
% 1.23/1.08 (((~c3_1(a2293)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2293)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1202,axiom,((~c3_1(a2293)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.23/1.08 tff(1203,plain,
% 1.23/1.08 ((~hskp10) | (~c3_1(a2293))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.23/1.08 tff(1204,plain,
% 1.23/1.08 ((~hskp10) | (~c3_1(a2293))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1203, 1200])).
% 1.23/1.08 tff(1205,plain,
% 1.23/1.08 (~c3_1(a2293)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1204, 1199])).
% 1.23/1.08 tff(1206,plain,
% 1.23/1.08 (((~hskp10) | c2_1(a2293)) <=> ((~hskp10) | c2_1(a2293))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1207,axiom,((~hskp10) | c2_1(a2293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.23/1.08 tff(1208,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.23/1.08 tff(1209,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1208, 1206])).
% 1.23/1.08 tff(1210,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1209, 1206])).
% 1.23/1.08 tff(1211,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1210, 1206])).
% 1.23/1.08 tff(1212,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1211, 1206])).
% 1.23/1.08 tff(1213,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1212, 1206])).
% 1.23/1.08 tff(1214,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1213, 1206])).
% 1.23/1.08 tff(1215,plain,
% 1.23/1.08 ((~hskp10) | c2_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1214, 1206])).
% 1.23/1.08 tff(1216,plain,
% 1.23/1.08 (c2_1(a2293)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1215, 1199])).
% 1.23/1.08 tff(1217,plain,
% 1.23/1.08 (((~hskp10) | c0_1(a2293)) <=> ((~hskp10) | c0_1(a2293))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1218,axiom,((~hskp10) | c0_1(a2293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.23/1.08 tff(1219,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.23/1.08 tff(1220,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1219, 1217])).
% 1.23/1.08 tff(1221,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1220, 1217])).
% 1.23/1.08 tff(1222,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1221, 1217])).
% 1.23/1.08 tff(1223,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1222, 1217])).
% 1.23/1.08 tff(1224,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1223, 1217])).
% 1.23/1.08 tff(1225,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1224, 1217])).
% 1.23/1.08 tff(1226,plain,
% 1.23/1.08 ((~hskp10) | c0_1(a2293)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1225, 1217])).
% 1.23/1.08 tff(1227,plain,
% 1.23/1.08 (c0_1(a2293)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1226, 1199])).
% 1.23/1.08 tff(1228,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1229,plain,
% 1.23/1.08 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1230,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1229])).
% 1.23/1.08 tff(1231,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.23/1.08 tff(1232,plain,
% 1.23/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1233,plain,
% 1.23/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.23/1.08 tff(1234,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1233, 181, 1227, 1216, 776, 1205, 771, 1198, 744, 1197])).
% 1.23/1.08 tff(1235,plain,((~hskp10) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1236,plain,
% 1.23/1.08 (~hskp10),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1235, 1196, 1009, 1007, 1008])).
% 1.23/1.08 tff(1237,plain,
% 1.23/1.08 (c1_1(a2306) | c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[273, 181, 42, 1008, 397, 1007, 227, 43])).
% 1.23/1.08 tff(1238,plain,
% 1.23/1.08 (c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1237, 398])).
% 1.23/1.08 tff(1239,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[296, 181, 1187, 398, 397, 396, 284, 1238])).
% 1.23/1.08 tff(1240,plain,(c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1241,plain,
% 1.23/1.08 (c1_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1240, 43, 396, 42, 397])).
% 1.23/1.08 tff(1242,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1243,plain,
% 1.23/1.08 ((hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1244,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1243])).
% 1.23/1.08 tff(1245,plain,
% 1.23/1.08 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1244, 1242])).
% 1.23/1.08 tff(1246,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1247,plain,
% 1.23/1.08 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 1.23/1.08 tff(1248,plain,
% 1.23/1.08 (hskp23 | (~c1_1(a2306)) | (~c0_1(a2306))),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1247, 181, 1008, 396, 1007, 53, 43])).
% 1.23/1.08 tff(1249,plain,
% 1.23/1.08 (~c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1248, 1241, 1187])).
% 1.23/1.08 tff(1250,plain,
% 1.23/1.08 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1251,plain,
% 1.23/1.08 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1252,plain,
% 1.23/1.08 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1251])).
% 1.23/1.08 tff(1253,plain,
% 1.23/1.08 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1252, 1250])).
% 1.23/1.08 tff(1254,plain,
% 1.23/1.08 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1255,plain,
% 1.23/1.08 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.23/1.08 tff(1256,plain,
% 1.23/1.08 (hskp9 | c2_1(a2306) | c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1255, 181, 41, 396, 1047])).
% 1.23/1.08 tff(1257,plain,
% 1.23/1.08 (hskp9),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1256, 1249, 397])).
% 1.23/1.08 tff(1258,plain,
% 1.23/1.08 (~c2_1(a2291)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1015, 1257])).
% 1.23/1.08 tff(1259,plain,
% 1.23/1.08 (~c1_1(a2291)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1021, 1257])).
% 1.23/1.08 tff(1260,plain,
% 1.23/1.08 (~c0_1(a2291)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1027, 1257])).
% 1.23/1.08 tff(1261,plain,
% 1.23/1.08 ($false),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1034, 181, 42, 1008, 1260, 1259, 1258, 1007, 227, 43])).
% 1.23/1.08 tff(1262,plain,(c1_1(a2282) | hskp1 | c2_1(a2306) | hskp28 | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.08 tff(1263,plain,
% 1.23/1.08 (c1_1(a2282)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1262, 397, 42, 41, 396])).
% 1.23/1.08 tff(1264,plain,
% 1.23/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.23/1.08 inference(bind,[status(th)],[])).
% 1.23/1.08 tff(1265,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(quant_intro,[status(thm)],[1264])).
% 1.23/1.08 tff(1266,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1267,plain,
% 1.23/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.23/1.08 inference(bind,[status(th)],[])).
% 1.23/1.08 tff(1268,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(quant_intro,[status(thm)],[1267])).
% 1.23/1.08 tff(1269,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.23/1.08 tff(1270,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.23/1.08 tff(1271,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1270, 1266])).
% 1.23/1.08 tff(1272,plain,(
% 1.23/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(skolemize,[status(sab)],[1271])).
% 1.23/1.08 tff(1273,plain,
% 1.23/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1272, 1265])).
% 1.23/1.08 tff(1274,plain,
% 1.23/1.08 (~hskp10),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1235, 1197, 771, 1198, 776])).
% 1.23/1.08 tff(1275,assumption,(~hskp10), introduced(assumption)).
% 1.23/1.08 tff(1276,assumption,(~hskp23), introduced(assumption)).
% 1.23/1.08 tff(1277,plain,
% 1.23/1.08 (hskp23 | (~c0_1(a2306))),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[296, 181, 398, 397, 396, 284])).
% 1.23/1.08 tff(1278,plain,
% 1.23/1.08 (~c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1277, 1276])).
% 1.23/1.08 tff(1279,plain,
% 1.23/1.08 (^[U: $i] : refl((hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.23/1.08 inference(bind,[status(th)],[])).
% 1.23/1.08 tff(1280,plain,
% 1.23/1.08 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(quant_intro,[status(thm)],[1279])).
% 1.23/1.08 tff(1281,plain,
% 1.23/1.08 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1282,plain,
% 1.23/1.08 (^[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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.23/1.08 inference(bind,[status(th)],[])).
% 1.23/1.08 tff(1283,plain,
% 1.23/1.08 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(quant_intro,[status(thm)],[1282])).
% 1.23/1.08 tff(1284,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.23/1.08 tff(1285,plain,
% 1.23/1.08 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.23/1.08 tff(1286,plain,
% 1.23/1.08 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1285, 1281])).
% 1.23/1.08 tff(1287,plain,(
% 1.23/1.08 ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(skolemize,[status(sab)],[1286])).
% 1.23/1.08 tff(1288,plain,
% 1.23/1.08 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1287, 1280])).
% 1.23/1.08 tff(1289,plain,
% 1.23/1.08 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1290,plain,
% 1.23/1.08 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1291,plain,
% 1.23/1.08 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1290])).
% 1.23/1.08 tff(1292,plain,
% 1.23/1.08 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.23/1.08 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.23/1.08 tff(1293,plain,
% 1.23/1.08 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 1.23/1.08 inference(quant_inst,[status(thm)],[])).
% 1.23/1.08 tff(1294,plain,
% 1.23/1.08 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 1.23/1.08 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.23/1.08 tff(1295,plain,
% 1.23/1.08 (hskp10 | hskp6 | c2_1(a2306) | c0_1(a2306)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1294, 181, 396, 1288])).
% 1.23/1.08 tff(1296,plain,
% 1.23/1.08 (hskp6),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[1295, 1278, 397, 1275])).
% 1.23/1.08 tff(1297,plain,
% 1.23/1.08 (~c3_1(a2285)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[433, 1296])).
% 1.23/1.08 tff(1298,plain,
% 1.23/1.08 (c1_1(a2285)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[409, 1296])).
% 1.23/1.08 tff(1299,plain,
% 1.23/1.08 (c0_1(a2285)),
% 1.23/1.08 inference(unit_resolution,[status(thm)],[420, 1296])).
% 1.23/1.08 tff(1300,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1301,plain,
% 1.23/1.08 (((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.08 inference(rewrite,[status(thm)],[])).
% 1.23/1.08 tff(1302,plain,
% 1.23/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 1.23/1.08 inference(monotonicity,[status(thm)],[1301])).
% 1.23/1.08 tff(1303,plain,
% 1.23/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.23/1.09 inference(transitivity,[status(thm)],[1302, 1300])).
% 1.23/1.09 tff(1304,plain,
% 1.23/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.23/1.09 inference(quant_inst,[status(thm)],[])).
% 1.23/1.09 tff(1305,plain,
% 1.23/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.23/1.09 tff(1306,plain,
% 1.23/1.09 (~c2_1(a2285)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1305, 181, 1299, 1298, 776, 1297, 771, 744, 1197])).
% 1.23/1.09 tff(1307,assumption,(hskp13), introduced(assumption)).
% 1.23/1.09 tff(1308,plain,
% 1.23/1.09 (((~hskp13) | (~c3_1(a2299))) <=> ((~hskp13) | (~c3_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1309,plain,
% 1.23/1.09 (((~c3_1(a2299)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1310,axiom,((~c3_1(a2299)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.23/1.09 tff(1311,plain,
% 1.23/1.09 ((~hskp13) | (~c3_1(a2299))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 1.23/1.09 tff(1312,plain,
% 1.23/1.09 ((~hskp13) | (~c3_1(a2299))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1311, 1308])).
% 1.23/1.09 tff(1313,plain,
% 1.23/1.09 (~c3_1(a2299)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1312, 1307])).
% 1.23/1.09 tff(1314,plain,
% 1.23/1.09 (((~hskp13) | c2_1(a2299)) <=> ((~hskp13) | c2_1(a2299))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1315,axiom,((~hskp13) | c2_1(a2299)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.23/1.09 tff(1316,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.23/1.09 tff(1317,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1316, 1314])).
% 1.23/1.09 tff(1318,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1317, 1314])).
% 1.23/1.09 tff(1319,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1318, 1314])).
% 1.23/1.09 tff(1320,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1319, 1314])).
% 1.23/1.09 tff(1321,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1320, 1314])).
% 1.23/1.09 tff(1322,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1321, 1314])).
% 1.23/1.09 tff(1323,plain,
% 1.23/1.09 ((~hskp13) | c2_1(a2299)),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1322, 1314])).
% 1.23/1.09 tff(1324,plain,
% 1.23/1.09 (c2_1(a2299)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1323, 1307])).
% 1.23/1.09 tff(1325,plain,
% 1.23/1.09 (((~hskp13) | (~c1_1(a2299))) <=> ((~hskp13) | (~c1_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1326,plain,
% 1.23/1.09 (((~c1_1(a2299)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1327,axiom,((~c1_1(a2299)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.23/1.09 tff(1328,plain,
% 1.23/1.09 ((~hskp13) | (~c1_1(a2299))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.23/1.09 tff(1329,plain,
% 1.23/1.09 ((~hskp13) | (~c1_1(a2299))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1328, 1325])).
% 1.23/1.09 tff(1330,plain,
% 1.23/1.09 (~c1_1(a2299)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1329, 1307])).
% 1.23/1.09 tff(1331,assumption,(~c3_1(a2299)), introduced(assumption)).
% 1.23/1.09 tff(1332,assumption,(~c1_1(a2299)), introduced(assumption)).
% 1.23/1.09 tff(1333,assumption,(c2_1(a2299)), introduced(assumption)).
% 1.23/1.09 tff(1334,plain,
% 1.23/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1335,plain,
% 1.23/1.09 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299))) <=> (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1336,plain,
% 1.23/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299))))),
% 1.23/1.09 inference(monotonicity,[status(thm)],[1335])).
% 1.23/1.09 tff(1337,plain,
% 1.23/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 1.23/1.09 inference(transitivity,[status(thm)],[1336, 1334])).
% 1.23/1.09 tff(1338,plain,
% 1.23/1.09 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))),
% 1.23/1.09 inference(quant_inst,[status(thm)],[])).
% 1.23/1.09 tff(1339,plain,
% 1.23/1.09 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.23/1.09 tff(1340,plain,
% 1.23/1.09 ($false),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1339, 181, 1276, 1333, 421, 410, 1332, 1331, 434, 53])).
% 1.23/1.09 tff(1341,plain,((~hskp6) | hskp23 | (~c2_1(a2299)) | c1_1(a2299) | c3_1(a2299)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.09 tff(1342,plain,
% 1.23/1.09 ($false),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1341, 1330, 1324, 399, 1276, 1313])).
% 1.23/1.09 tff(1343,plain,((~hskp13) | (~hskp6) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.23/1.09 tff(1344,plain,
% 1.23/1.09 (~hskp13),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1343, 1296, 1276])).
% 1.23/1.09 tff(1345,plain,
% 1.23/1.09 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.23/1.09 inference(bind,[status(th)],[])).
% 1.23/1.09 tff(1346,plain,
% 1.23/1.09 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(quant_intro,[status(thm)],[1345])).
% 1.23/1.09 tff(1347,plain,
% 1.23/1.09 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1348,plain,
% 1.23/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.23/1.09 inference(bind,[status(th)],[])).
% 1.23/1.09 tff(1349,plain,
% 1.23/1.09 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(quant_intro,[status(thm)],[1348])).
% 1.23/1.09 tff(1350,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.23/1.09 tff(1351,plain,
% 1.23/1.09 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.23/1.09 tff(1352,plain,
% 1.23/1.09 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1351, 1347])).
% 1.23/1.09 tff(1353,plain,(
% 1.23/1.09 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(skolemize,[status(sab)],[1352])).
% 1.23/1.09 tff(1354,plain,
% 1.23/1.09 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1353, 1346])).
% 1.23/1.09 tff(1355,plain,
% 1.23/1.09 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1356,plain,
% 1.23/1.09 ((hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302))) <=> (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1357,plain,
% 1.23/1.09 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.23/1.09 inference(monotonicity,[status(thm)],[1356])).
% 1.23/1.09 tff(1358,plain,
% 1.23/1.09 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.23/1.09 inference(transitivity,[status(thm)],[1357, 1355])).
% 1.23/1.09 tff(1359,plain,
% 1.23/1.09 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))),
% 1.23/1.09 inference(quant_inst,[status(thm)],[])).
% 1.23/1.09 tff(1360,plain,
% 1.23/1.09 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.23/1.09 tff(1361,plain,
% 1.23/1.09 (hskp13 | hskp12),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1360, 181, 994, 983, 972, 1354])).
% 1.23/1.09 tff(1362,plain,
% 1.23/1.09 (hskp12),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1361, 1344])).
% 1.23/1.09 tff(1363,plain,
% 1.23/1.09 (~c3_1(a2295)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[710, 1362])).
% 1.23/1.09 tff(1364,plain,
% 1.23/1.09 (((~hskp12) | (~c1_1(a2295))) <=> ((~hskp12) | (~c1_1(a2295)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1365,plain,
% 1.23/1.09 (((~c1_1(a2295)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a2295)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1366,axiom,((~c1_1(a2295)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.23/1.09 tff(1367,plain,
% 1.23/1.09 ((~hskp12) | (~c1_1(a2295))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.23/1.09 tff(1368,plain,
% 1.23/1.09 ((~hskp12) | (~c1_1(a2295))),
% 1.23/1.09 inference(modus_ponens,[status(thm)],[1367, 1364])).
% 1.23/1.09 tff(1369,plain,
% 1.23/1.09 (~c1_1(a2295)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[1368, 1362])).
% 1.23/1.09 tff(1370,plain,
% 1.23/1.09 (c0_1(a2295)),
% 1.23/1.09 inference(unit_resolution,[status(thm)],[721, 1362])).
% 1.23/1.09 tff(1371,plain,
% 1.23/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1372,plain,
% 1.23/1.09 ((hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 1.23/1.09 inference(rewrite,[status(thm)],[])).
% 1.23/1.09 tff(1373,plain,
% 1.23/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295))))),
% 1.30/1.09 inference(monotonicity,[status(thm)],[1372])).
% 1.30/1.09 tff(1374,plain,
% 1.30/1.09 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 1.30/1.09 inference(transitivity,[status(thm)],[1373, 1371])).
% 1.30/1.09 tff(1375,plain,
% 1.30/1.09 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 1.30/1.09 inference(quant_inst,[status(thm)],[])).
% 1.30/1.09 tff(1376,plain,
% 1.30/1.09 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.30/1.09 tff(1377,plain,
% 1.30/1.09 ($false),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1376, 181, 1276, 1370, 1299, 1369, 1363, 1297, 284, 1306])).
% 1.30/1.09 tff(1378,plain,(hskp23 | (~c2_1(a2282)) | c0_1(a2282) | (~c1_1(a2282)) | c2_1(a2306) | hskp10 | c3_1(a2306) | c1_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.09 tff(1379,plain,
% 1.30/1.09 (hskp23),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1378, 398, 771, 1197, 397, 1274, 396, 776])).
% 1.30/1.09 tff(1380,plain,
% 1.30/1.09 (~c2_1(a2327)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[302, 1379])).
% 1.30/1.09 tff(1381,plain,
% 1.30/1.09 (~c0_1(a2327)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[326, 1379])).
% 1.30/1.09 tff(1382,plain,
% 1.30/1.09 (c3_1(a2327)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[313, 1379])).
% 1.30/1.09 tff(1383,plain,
% 1.30/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1384,plain,
% 1.30/1.09 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306)) <=> (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1385,plain,
% 1.30/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327))))),
% 1.30/1.09 inference(monotonicity,[status(thm)],[1384])).
% 1.30/1.09 tff(1386,plain,
% 1.30/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 1.30/1.09 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.30/1.09 tff(1387,plain,
% 1.30/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))),
% 1.30/1.09 inference(quant_inst,[status(thm)],[])).
% 1.30/1.09 tff(1388,plain,
% 1.30/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.30/1.09 tff(1389,plain,
% 1.30/1.09 (c0_1(a2306)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1388, 181, 1382, 776, 1381, 1380, 397, 396, 771, 1273, 1197])).
% 1.30/1.09 tff(1390,plain,
% 1.30/1.09 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.30/1.09 inference(bind,[status(th)],[])).
% 1.30/1.09 tff(1391,plain,
% 1.30/1.09 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(quant_intro,[status(thm)],[1390])).
% 1.30/1.09 tff(1392,plain,
% 1.30/1.09 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1393,plain,
% 1.30/1.09 (^[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)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_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)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_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)) | (~c2_1(V)) | (~c3_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)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_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) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.30/1.09 inference(bind,[status(th)],[])).
% 1.30/1.09 tff(1394,plain,
% 1.30/1.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(quant_intro,[status(thm)],[1393])).
% 1.30/1.09 tff(1395,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)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.30/1.09 tff(1396,plain,
% 1.30/1.09 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.30/1.09 tff(1397,plain,
% 1.30/1.09 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1396, 1392])).
% 1.30/1.09 tff(1398,plain,(
% 1.30/1.09 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(skolemize,[status(sab)],[1397])).
% 1.30/1.09 tff(1399,plain,
% 1.30/1.09 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1398, 1391])).
% 1.30/1.09 tff(1400,plain,
% 1.30/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1401,plain,
% 1.30/1.09 ((hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1402,plain,
% 1.30/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306))))),
% 1.30/1.09 inference(monotonicity,[status(thm)],[1401])).
% 1.30/1.09 tff(1403,plain,
% 1.30/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 1.30/1.09 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.30/1.09 tff(1404,plain,
% 1.30/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.09 inference(quant_inst,[status(thm)],[])).
% 1.30/1.09 tff(1405,plain,
% 1.30/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306))),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.30/1.09 tff(1406,plain,
% 1.30/1.09 (hskp8 | (~c0_1(a2306))),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1405, 181, 994, 983, 398, 396, 972, 1399])).
% 1.30/1.09 tff(1407,plain,
% 1.30/1.09 (hskp8),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1406, 1389])).
% 1.30/1.09 tff(1408,plain,
% 1.30/1.09 (((~hskp8) | c0_1(a2287)) <=> ((~hskp8) | c0_1(a2287))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1409,axiom,((~hskp8) | c0_1(a2287)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.30/1.09 tff(1410,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.30/1.09 tff(1411,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1410, 1408])).
% 1.30/1.09 tff(1412,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1411, 1408])).
% 1.30/1.09 tff(1413,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1412, 1408])).
% 1.30/1.09 tff(1414,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1413, 1408])).
% 1.30/1.09 tff(1415,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1414, 1408])).
% 1.30/1.09 tff(1416,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1415, 1408])).
% 1.30/1.09 tff(1417,plain,
% 1.30/1.09 ((~hskp8) | c0_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1416, 1408])).
% 1.30/1.09 tff(1418,plain,
% 1.30/1.09 (c0_1(a2287)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1417, 1407])).
% 1.30/1.09 tff(1419,plain,
% 1.30/1.09 (((~hskp8) | c2_1(a2287)) <=> ((~hskp8) | c2_1(a2287))),
% 1.30/1.09 inference(rewrite,[status(thm)],[])).
% 1.30/1.09 tff(1420,axiom,((~hskp8) | c2_1(a2287)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.30/1.09 tff(1421,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.30/1.09 tff(1422,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1421, 1419])).
% 1.30/1.09 tff(1423,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1422, 1419])).
% 1.30/1.09 tff(1424,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1423, 1419])).
% 1.30/1.09 tff(1425,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1424, 1419])).
% 1.30/1.09 tff(1426,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1425, 1419])).
% 1.30/1.09 tff(1427,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1426, 1419])).
% 1.30/1.09 tff(1428,plain,
% 1.30/1.09 ((~hskp8) | c2_1(a2287)),
% 1.30/1.09 inference(modus_ponens,[status(thm)],[1427, 1419])).
% 1.30/1.09 tff(1429,plain,
% 1.30/1.09 (c2_1(a2287)),
% 1.30/1.09 inference(unit_resolution,[status(thm)],[1428, 1407])).
% 1.30/1.10 tff(1430,assumption,(~c3_1(a2287)), introduced(assumption)).
% 1.30/1.10 tff(1431,assumption,(c2_1(a2287)), introduced(assumption)).
% 1.30/1.10 tff(1432,assumption,(c0_1(a2287)), introduced(assumption)).
% 1.30/1.10 tff(1433,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1434,plain,
% 1.30/1.10 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1435,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1434])).
% 1.30/1.10 tff(1436,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1435, 1433])).
% 1.30/1.10 tff(1437,plain,
% 1.30/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1438,plain,
% 1.30/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.30/1.10 tff(1439,plain,
% 1.30/1.10 ($false),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1438, 181, 1432, 1431, 776, 771, 1198, 744, 1197, 1430])).
% 1.30/1.10 tff(1440,plain,(c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.10 tff(1441,plain,
% 1.30/1.10 (c3_1(a2287)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1440, 1429, 1197, 776, 771, 1198, 1418])).
% 1.30/1.10 tff(1442,plain,
% 1.30/1.10 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.30/1.10 inference(bind,[status(th)],[])).
% 1.30/1.10 tff(1443,plain,
% 1.30/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(quant_intro,[status(thm)],[1442])).
% 1.30/1.10 tff(1444,plain,
% 1.30/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1445,plain,
% 1.30/1.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_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) | (~c0_1(U)) | (~c3_1(U)) | (~c2_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(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~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(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~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(V)) | hskp3) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~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(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.30/1.10 inference(bind,[status(th)],[])).
% 1.30/1.10 tff(1446,plain,
% 1.30/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(quant_intro,[status(thm)],[1445])).
% 1.30/1.10 tff(1447,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.30/1.10 tff(1448,plain,
% 1.30/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.30/1.10 tff(1449,plain,
% 1.30/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1448, 1444])).
% 1.30/1.10 tff(1450,plain,(
% 1.30/1.10 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(skolemize,[status(sab)],[1449])).
% 1.30/1.10 tff(1451,plain,
% 1.30/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1450, 1443])).
% 1.30/1.10 tff(1452,assumption,(~c2_1(a2327)), introduced(assumption)).
% 1.30/1.10 tff(1453,assumption,(c3_1(a2327)), introduced(assumption)).
% 1.30/1.10 tff(1454,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1455,plain,
% 1.30/1.10 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304)) <=> (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1456,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1455])).
% 1.30/1.10 tff(1457,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1456, 1454])).
% 1.30/1.10 tff(1458,plain,
% 1.30/1.10 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1459,plain,
% 1.30/1.10 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.30/1.10 tff(1460,plain,
% 1.30/1.10 ($false),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1459, 181, 1275, 1166, 1107, 1101, 1095, 1288])).
% 1.30/1.10 tff(1461,plain,((~hskp16) | hskp10 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.30/1.10 tff(1462,plain,
% 1.30/1.10 (~hskp16),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1461, 1166, 1275])).
% 1.30/1.10 tff(1463,plain,
% 1.30/1.10 (hskp26),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1130, 1462, 41])).
% 1.30/1.10 tff(1464,assumption,(c1_1(a2327)), introduced(assumption)).
% 1.30/1.10 tff(1465,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1466,plain,
% 1.30/1.10 (((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345))) <=> (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1467,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345))))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1466])).
% 1.30/1.10 tff(1468,plain,
% 1.30/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1467, 1465])).
% 1.30/1.10 tff(1469,plain,
% 1.30/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1470,plain,
% 1.30/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345))),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.30/1.10 tff(1471,plain,
% 1.30/1.10 (~c2_1(a2345)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1470, 181, 1165, 1453, 1154, 1148, 1452, 217, 1464])).
% 1.30/1.10 tff(1472,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1473,plain,
% 1.30/1.10 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345)) <=> (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1474,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345)))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1473])).
% 1.30/1.10 tff(1475,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.30/1.10 tff(1476,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1477,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345)),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.30/1.10 tff(1478,plain,
% 1.30/1.10 ($false),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1477, 181, 41, 1453, 1154, 1148, 1452, 460, 1464, 1471])).
% 1.30/1.10 tff(1479,plain,((~hskp26) | hskp28 | (~c3_1(a2327)) | c2_1(a2327) | (~c1_1(a2327))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.10 tff(1480,plain,
% 1.30/1.10 (~c1_1(a2327)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1479, 1463, 1453, 1452, 41])).
% 1.30/1.10 tff(1481,assumption,(~c0_1(a2327)), introduced(assumption)).
% 1.30/1.10 tff(1482,plain,
% 1.30/1.10 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1483,plain,
% 1.30/1.10 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327))) <=> (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1484,plain,
% 1.30/1.10 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1483])).
% 1.30/1.10 tff(1485,plain,
% 1.30/1.10 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.30/1.10 tff(1486,plain,
% 1.30/1.10 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1487,plain,
% 1.30/1.10 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.30/1.10 tff(1488,plain,
% 1.30/1.10 (hskp7 | hskp6 | c1_1(a2327)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1487, 181, 1453, 1481, 1141])).
% 1.30/1.10 tff(1489,plain,
% 1.30/1.10 (hskp7),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1488, 1480, 1166])).
% 1.30/1.10 tff(1490,plain,
% 1.30/1.10 (~c2_1(a2286)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1053, 1489])).
% 1.30/1.10 tff(1491,plain,
% 1.30/1.10 (c1_1(a2286)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1078, 1489])).
% 1.30/1.10 tff(1492,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1493,plain,
% 1.30/1.10 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1494,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327)))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1493])).
% 1.30/1.10 tff(1495,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1494, 1492])).
% 1.30/1.10 tff(1496,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1497,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327)),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.30/1.10 tff(1498,plain,
% 1.30/1.10 (~c3_1(a2286)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1497, 181, 41, 1491, 1481, 1452, 1490, 460, 1480])).
% 1.30/1.10 tff(1499,plain,
% 1.30/1.10 (~c0_1(a2286)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1059, 1489])).
% 1.30/1.10 tff(1500,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1501,plain,
% 1.30/1.10 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286)) <=> (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1502,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1501])).
% 1.30/1.10 tff(1503,plain,
% 1.30/1.10 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1502, 1500])).
% 1.30/1.10 tff(1504,plain,
% 1.30/1.10 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1505,plain,
% 1.30/1.10 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)),
% 1.30/1.10 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.30/1.10 tff(1506,plain,
% 1.30/1.10 ($false),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1505, 181, 1275, 1166, 1499, 1490, 1288, 1498])).
% 1.30/1.10 tff(1507,plain,(hskp6 | hskp10 | hskp28 | c0_1(a2327) | c2_1(a2327) | (~c3_1(a2327))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.10 tff(1508,plain,
% 1.30/1.10 (hskp6),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[1507, 1381, 41, 1274, 1380, 1382])).
% 1.30/1.10 tff(1509,plain,
% 1.30/1.10 (~c3_1(a2285)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[433, 1508])).
% 1.30/1.10 tff(1510,plain,
% 1.30/1.10 (c1_1(a2285)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[409, 1508])).
% 1.30/1.10 tff(1511,plain,
% 1.30/1.10 (c0_1(a2285)),
% 1.30/1.10 inference(unit_resolution,[status(thm)],[420, 1508])).
% 1.30/1.10 tff(1512,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1513,plain,
% 1.30/1.10 ((hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285))) <=> (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.30/1.10 inference(rewrite,[status(thm)],[])).
% 1.30/1.10 tff(1514,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287))))),
% 1.30/1.10 inference(monotonicity,[status(thm)],[1513])).
% 1.30/1.10 tff(1515,plain,
% 1.30/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.30/1.10 inference(transitivity,[status(thm)],[1514, 1512])).
% 1.30/1.10 tff(1516,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.10 inference(quant_inst,[status(thm)],[])).
% 1.30/1.10 tff(1517,plain,
% 1.30/1.10 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 1.30/1.11 tff(1518,plain,
% 1.30/1.11 (hskp3),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1517, 181, 1418, 1429, 1511, 1510, 1509, 1451, 1441])).
% 1.30/1.11 tff(1519,plain,
% 1.30/1.11 (~c2_1(a2280)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[574, 1518])).
% 1.30/1.11 tff(1520,plain,
% 1.30/1.11 (c3_1(a2280)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[585, 1518])).
% 1.30/1.11 tff(1521,plain,
% 1.30/1.11 (c1_1(a2280)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[596, 1518])).
% 1.30/1.11 tff(1522,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1523,plain,
% 1.30/1.11 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1524,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1523])).
% 1.30/1.11 tff(1525,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1524, 1522])).
% 1.30/1.11 tff(1526,plain,
% 1.30/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1527,plain,
% 1.30/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.30/1.11 tff(1528,plain,
% 1.30/1.11 (c1_1(a2302)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1527, 181, 1004, 1003, 994, 1521, 1520, 1002, 972, 1519, 217])).
% 1.30/1.11 tff(1529,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1530,plain,
% 1.30/1.11 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1531,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327)))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1530])).
% 1.30/1.11 tff(1532,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.30/1.11 tff(1533,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1534,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327)),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.30/1.11 tff(1535,plain,
% 1.30/1.11 (c1_1(a2327)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1534, 181, 41, 1521, 1520, 1381, 1380, 1519, 460])).
% 1.30/1.11 tff(1536,plain,
% 1.30/1.11 (~hskp26),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1479, 1535, 1382, 1380, 41])).
% 1.30/1.11 tff(1537,plain,
% 1.30/1.11 (hskp16),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1130, 1536, 41])).
% 1.30/1.11 tff(1538,plain,
% 1.30/1.11 (~c3_1(a2304)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1094, 1537])).
% 1.30/1.11 tff(1539,plain,
% 1.30/1.11 (~c2_1(a2304)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1100, 1537])).
% 1.30/1.11 tff(1540,plain,
% 1.30/1.11 (~c0_1(a2304)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1106, 1537])).
% 1.30/1.11 tff(1541,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1542,plain,
% 1.30/1.11 (((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1543,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1542])).
% 1.30/1.11 tff(1544,plain,
% 1.30/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1543, 1541])).
% 1.30/1.11 tff(1545,plain,
% 1.30/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1546,plain,
% 1.30/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.30/1.11 tff(1547,plain,
% 1.30/1.11 ($false),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1546, 181, 1382, 994, 1381, 1380, 1540, 1539, 1538, 972, 1273, 1528])).
% 1.30/1.11 tff(1548,plain,(c1_1(a2306) | hskp28 | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | c3_1(a2306) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.11 tff(1549,plain,
% 1.30/1.11 (c1_1(a2306)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1548, 1263, 41, 1008, 1009, 1007, 396, 397])).
% 1.30/1.11 tff(1550,plain,
% 1.30/1.11 (~hskp17),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[266, 1549])).
% 1.30/1.11 tff(1551,plain,
% 1.30/1.11 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.30/1.11 inference(bind,[status(th)],[])).
% 1.30/1.11 tff(1552,plain,
% 1.30/1.11 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(quant_intro,[status(thm)],[1551])).
% 1.30/1.11 tff(1553,plain,
% 1.30/1.11 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1554,plain,
% 1.30/1.11 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_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)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_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)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.30/1.11 inference(bind,[status(th)],[])).
% 1.30/1.11 tff(1555,plain,
% 1.30/1.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(quant_intro,[status(thm)],[1554])).
% 1.30/1.11 tff(1556,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.30/1.11 tff(1557,plain,
% 1.30/1.11 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.30/1.11 tff(1558,plain,
% 1.30/1.11 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1557, 1553])).
% 1.30/1.11 tff(1559,plain,(
% 1.30/1.11 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(skolemize,[status(sab)],[1558])).
% 1.30/1.11 tff(1560,plain,
% 1.30/1.11 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1559, 1552])).
% 1.30/1.11 tff(1561,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1562,plain,
% 1.30/1.11 ((hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1563,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1562])).
% 1.30/1.11 tff(1564,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.30/1.11 tff(1565,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1566,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.30/1.11 tff(1567,plain,
% 1.30/1.11 (hskp17 | (~c1_1(a2306)) | (~c1_1(a2282))),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1566, 181, 1008, 397, 396, 1009, 1560])).
% 1.30/1.11 tff(1568,plain,
% 1.30/1.11 ($false),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1567, 1550, 1549, 1263])).
% 1.30/1.11 tff(1569,plain,(c2_1(a2306) | c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.30/1.11 tff(1570,plain,
% 1.30/1.11 (c2_1(a2306)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1569, 396, 41, 42])).
% 1.30/1.11 tff(1571,assumption,(c2_1(a2306)), introduced(assumption)).
% 1.30/1.11 tff(1572,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1573,plain,
% 1.30/1.11 ((hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1574,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0)))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1573])).
% 1.30/1.11 tff(1575,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1574, 1572])).
% 1.30/1.11 tff(1576,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1577,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0)),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.30/1.11 tff(1578,plain,
% 1.30/1.11 ($false),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1577, 181, 42, 398, 1571, 396, 1028, 1022, 1016, 227])).
% 1.30/1.11 tff(1579,plain,((~hskp9) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.11 tff(1580,plain,
% 1.30/1.11 (~hskp9),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1579, 398, 42, 1570, 396])).
% 1.30/1.11 tff(1581,plain,
% 1.30/1.11 (~hskp7),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1087, 1580, 1009, 43, 41, 1008])).
% 1.30/1.11 tff(1582,plain,
% 1.30/1.11 (hskp10),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1461, 1089, 1166])).
% 1.30/1.11 tff(1583,plain,
% 1.30/1.11 (~c3_1(a2293)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1204, 1582])).
% 1.30/1.11 tff(1584,plain,
% 1.30/1.11 (c0_1(a2293)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1226, 1582])).
% 1.30/1.11 tff(1585,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1586,plain,
% 1.30/1.11 ((hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306))) <=> (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1587,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293))))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1586])).
% 1.30/1.11 tff(1588,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1587, 1585])).
% 1.30/1.11 tff(1589,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1590,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 1.30/1.11 tff(1591,plain,
% 1.30/1.11 (~c1_1(a2293)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1590, 181, 1276, 1584, 398, 1570, 396, 1583, 53])).
% 1.30/1.11 tff(1592,plain,
% 1.30/1.11 (hskp9),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1113, 181, 41, 1107, 1101, 1095, 1047])).
% 1.30/1.11 tff(1593,plain,
% 1.30/1.11 (~c2_1(a2291)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1015, 1592])).
% 1.30/1.11 tff(1594,plain,
% 1.30/1.11 (~c1_1(a2291)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1021, 1592])).
% 1.30/1.11 tff(1595,plain,
% 1.30/1.11 (~c0_1(a2291)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1027, 1592])).
% 1.30/1.11 tff(1596,plain,
% 1.30/1.11 (c2_1(a2293)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1215, 1582])).
% 1.30/1.11 tff(1597,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1598,plain,
% 1.30/1.11 ((hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 1.30/1.11 inference(rewrite,[status(thm)],[])).
% 1.30/1.11 tff(1599,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293))))),
% 1.30/1.11 inference(monotonicity,[status(thm)],[1598])).
% 1.30/1.11 tff(1600,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 1.30/1.11 inference(transitivity,[status(thm)],[1599, 1597])).
% 1.30/1.11 tff(1601,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 1.30/1.11 inference(quant_inst,[status(thm)],[])).
% 1.30/1.11 tff(1602,plain,
% 1.30/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293))),
% 1.30/1.11 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 1.30/1.11 tff(1603,plain,
% 1.30/1.11 ($false),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1602, 181, 42, 1596, 1583, 1595, 1594, 1593, 227, 1591])).
% 1.30/1.11 tff(1604,plain,((~hskp16) | hskp1 | hskp23 | c1_1(a2306) | c3_1(a2306) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.30/1.11 tff(1605,plain,
% 1.30/1.11 (~hskp16),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1604, 1166, 1276, 398, 396, 41, 42])).
% 1.30/1.11 tff(1606,plain,
% 1.30/1.11 (hskp26),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1130, 1605, 41])).
% 1.30/1.11 tff(1607,plain,
% 1.30/1.11 (~c1_1(a2345)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1147, 1606])).
% 1.30/1.11 tff(1608,plain,
% 1.30/1.11 (~c0_1(a2345)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1153, 1606])).
% 1.30/1.11 tff(1609,plain,
% 1.30/1.11 (c3_1(a2345)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1164, 1606])).
% 1.30/1.11 tff(1610,plain,
% 1.30/1.11 ($false),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1173, 181, 1167, 1166, 1609, 1608, 1607, 1141])).
% 1.30/1.11 tff(1611,plain,(hskp6 | hskp7 | hskp28 | hskp23 | c1_1(a2306) | c3_1(a2306) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.30/1.11 tff(1612,plain,
% 1.30/1.11 (hskp6),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[1611, 1581, 41, 1187, 398, 396, 42])).
% 1.30/1.11 tff(1613,plain,
% 1.30/1.11 (~c3_1(a2285)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[433, 1612])).
% 1.30/1.11 tff(1614,plain,
% 1.30/1.11 (c1_1(a2285)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[409, 1612])).
% 1.30/1.11 tff(1615,plain,
% 1.30/1.11 (c0_1(a2285)),
% 1.30/1.11 inference(unit_resolution,[status(thm)],[420, 1612])).
% 1.30/1.11 tff(1616,plain,
% 1.30/1.11 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1617,plain,
% 1.30/1.12 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306))) <=> (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1618,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285))))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1617])).
% 1.30/1.12 tff(1619,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1618, 1616])).
% 1.30/1.12 tff(1620,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1621,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 1.30/1.12 tff(1622,plain,
% 1.30/1.12 ($false),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1621, 181, 1187, 1615, 1614, 398, 1570, 396, 1613, 53])).
% 1.30/1.12 tff(1623,plain,(c1_1(a2306) | c3_1(a2306) | hskp28 | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.12 tff(1624,plain,
% 1.30/1.12 (c1_1(a2306)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1623, 43, 41, 42, 396])).
% 1.30/1.12 tff(1625,plain,
% 1.30/1.12 ((~c1_1(a2306)) | (~c0_1(a2306))),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1247, 181, 1187, 1008, 396, 1007, 53, 43])).
% 1.30/1.12 tff(1626,plain,
% 1.30/1.12 (~c0_1(a2306)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1625, 1624])).
% 1.30/1.12 tff(1627,assumption,(c1_1(a2306)), introduced(assumption)).
% 1.30/1.12 tff(1628,plain,
% 1.30/1.12 (~hskp17),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[260, 1571])).
% 1.30/1.12 tff(1629,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1630,plain,
% 1.30/1.12 ((hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306))) <=> (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1631,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306)))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1630])).
% 1.30/1.12 tff(1632,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1631, 1629])).
% 1.30/1.12 tff(1633,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1634,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.30/1.12 tff(1635,plain,
% 1.30/1.12 (~c1_1(a2304)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1634, 181, 1628, 1627, 1571, 1101, 1095, 1560, 639])).
% 1.30/1.12 tff(1636,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1637,plain,
% 1.30/1.12 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304)) <=> (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1638,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304)))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1637])).
% 1.30/1.12 tff(1639,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1638, 1636])).
% 1.30/1.12 tff(1640,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1641,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 1.30/1.12 tff(1642,plain,
% 1.30/1.12 ($false),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1641, 181, 42, 1008, 1107, 1101, 1007, 227, 43, 1635])).
% 1.30/1.12 tff(1643,plain,((~hskp16) | hskp1 | c1_1(a2282) | (~c1_1(a2306)) | (~c2_1(a2306)) | c0_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.12 tff(1644,plain,
% 1.30/1.12 (~hskp16),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1643, 43, 42, 1624, 1570, 1626])).
% 1.30/1.12 tff(1645,assumption,(~hskp16), introduced(assumption)).
% 1.30/1.12 tff(1646,plain,
% 1.30/1.12 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.30/1.12 inference(bind,[status(th)],[])).
% 1.30/1.12 tff(1647,plain,
% 1.30/1.12 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(quant_intro,[status(thm)],[1646])).
% 1.30/1.12 tff(1648,plain,
% 1.30/1.12 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1649,plain,
% 1.30/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.30/1.12 inference(bind,[status(th)],[])).
% 1.30/1.12 tff(1650,plain,
% 1.30/1.12 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(quant_intro,[status(thm)],[1649])).
% 1.30/1.12 tff(1651,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.30/1.12 tff(1652,plain,
% 1.30/1.12 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 1.30/1.12 tff(1653,plain,
% 1.30/1.12 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1652, 1648])).
% 1.30/1.12 tff(1654,plain,(
% 1.30/1.12 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(skolemize,[status(sab)],[1653])).
% 1.30/1.12 tff(1655,plain,
% 1.30/1.12 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1654, 1647])).
% 1.30/1.12 tff(1656,plain,
% 1.30/1.12 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1657,plain,
% 1.30/1.12 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306))) <=> (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1658,plain,
% 1.30/1.12 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1657])).
% 1.30/1.12 tff(1659,plain,
% 1.30/1.12 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1658, 1656])).
% 1.30/1.12 tff(1660,plain,
% 1.30/1.12 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1661,plain,
% 1.30/1.12 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.30/1.12 tff(1662,plain,
% 1.30/1.12 (hskp16 | hskp15 | (~c1_1(a2306)) | c0_1(a2306)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1661, 181, 396, 1655])).
% 1.30/1.12 tff(1663,plain,
% 1.30/1.12 (hskp15),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1662, 1645, 1627, 639])).
% 1.30/1.12 tff(1664,plain,
% 1.30/1.12 (((~hskp15) | (~c3_1(a2303))) <=> ((~hskp15) | (~c3_1(a2303)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1665,plain,
% 1.30/1.12 (((~c3_1(a2303)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a2303)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1666,axiom,((~c3_1(a2303)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.30/1.12 tff(1667,plain,
% 1.30/1.12 ((~hskp15) | (~c3_1(a2303))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 1.30/1.12 tff(1668,plain,
% 1.30/1.12 ((~hskp15) | (~c3_1(a2303))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1667, 1664])).
% 1.30/1.12 tff(1669,plain,
% 1.30/1.12 (~c3_1(a2303)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1668, 1663])).
% 1.30/1.12 tff(1670,plain,
% 1.30/1.12 (((~hskp15) | c2_1(a2303)) <=> ((~hskp15) | c2_1(a2303))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1671,axiom,((~hskp15) | c2_1(a2303)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.30/1.12 tff(1672,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.30/1.12 tff(1673,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1672, 1670])).
% 1.30/1.12 tff(1674,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1673, 1670])).
% 1.30/1.12 tff(1675,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1674, 1670])).
% 1.30/1.12 tff(1676,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1675, 1670])).
% 1.30/1.12 tff(1677,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1676, 1670])).
% 1.30/1.12 tff(1678,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1677, 1670])).
% 1.30/1.12 tff(1679,plain,
% 1.30/1.12 ((~hskp15) | c2_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1678, 1670])).
% 1.30/1.12 tff(1680,plain,
% 1.30/1.12 (c2_1(a2303)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1679, 1663])).
% 1.30/1.12 tff(1681,plain,
% 1.30/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1682,plain,
% 1.30/1.12 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1683,plain,
% 1.30/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306)))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1682])).
% 1.30/1.12 tff(1684,plain,
% 1.30/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1683, 1681])).
% 1.30/1.12 tff(1685,plain,
% 1.30/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1686,plain,
% 1.30/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.30/1.12 tff(1687,plain,
% 1.30/1.12 (~c0_1(a2303)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1686, 181, 1680, 1627, 1571, 396, 1669, 744, 639])).
% 1.30/1.12 tff(1688,plain,
% 1.30/1.12 (hskp26),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1130, 1645, 41])).
% 1.30/1.12 tff(1689,plain,
% 1.30/1.12 (~c1_1(a2345)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1147, 1688])).
% 1.30/1.12 tff(1690,plain,
% 1.30/1.12 (~c0_1(a2345)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1153, 1688])).
% 1.30/1.12 tff(1691,plain,
% 1.30/1.12 (c3_1(a2345)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1164, 1688])).
% 1.30/1.12 tff(1692,plain,
% 1.30/1.12 (hskp7),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1173, 181, 1166, 1691, 1690, 1689, 1141])).
% 1.30/1.12 tff(1693,plain,
% 1.30/1.12 (~c2_1(a2286)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1053, 1692])).
% 1.30/1.12 tff(1694,plain,
% 1.30/1.12 (c1_1(a2286)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1078, 1692])).
% 1.30/1.12 tff(1695,plain,
% 1.30/1.12 (((~hskp15) | c1_1(a2303)) <=> ((~hskp15) | c1_1(a2303))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1696,axiom,((~hskp15) | c1_1(a2303)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.30/1.12 tff(1697,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 1.30/1.12 tff(1698,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1697, 1695])).
% 1.30/1.12 tff(1699,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1698, 1695])).
% 1.30/1.12 tff(1700,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1699, 1695])).
% 1.30/1.12 tff(1701,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1700, 1695])).
% 1.30/1.12 tff(1702,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1701, 1695])).
% 1.30/1.12 tff(1703,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1702, 1695])).
% 1.30/1.12 tff(1704,plain,
% 1.30/1.12 ((~hskp15) | c1_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1703, 1695])).
% 1.30/1.12 tff(1705,plain,
% 1.30/1.12 (c1_1(a2303)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1704, 1663])).
% 1.30/1.12 tff(1706,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1707,plain,
% 1.30/1.12 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303))) <=> (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1708,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303)))),
% 1.30/1.12 inference(monotonicity,[status(thm)],[1707])).
% 1.30/1.12 tff(1709,plain,
% 1.30/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 1.30/1.12 inference(transitivity,[status(thm)],[1708, 1706])).
% 1.30/1.12 tff(1710,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))),
% 1.30/1.12 inference(quant_inst,[status(thm)],[])).
% 1.30/1.12 tff(1711,plain,
% 1.30/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303)),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.30/1.12 tff(1712,plain,
% 1.30/1.12 (c3_1(a2286)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1711, 181, 1628, 1705, 1680, 1694, 1693, 1560, 1687])).
% 1.30/1.12 tff(1713,plain,
% 1.30/1.12 ($false),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1085, 181, 1004, 1003, 1694, 776, 1002, 1693, 771, 217, 43, 1712])).
% 1.30/1.12 tff(1714,plain,(hskp16 | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2306) | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.30/1.12 tff(1715,plain,
% 1.30/1.12 (hskp6),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1714, 1644, 1009, 43, 1624, 1570, 396, 1626, 1008, 41])).
% 1.30/1.12 tff(1716,plain,
% 1.30/1.12 (~c3_1(a2285)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[433, 1715])).
% 1.30/1.12 tff(1717,plain,
% 1.30/1.12 (c1_1(a2285)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[409, 1715])).
% 1.30/1.12 tff(1718,plain,
% 1.30/1.12 (c0_1(a2285)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[420, 1715])).
% 1.30/1.12 tff(1719,plain,
% 1.30/1.12 ($false),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1193, 181, 1187, 1718, 1717, 1008, 1716, 1007, 53, 43])).
% 1.30/1.12 tff(1720,plain,(c1_1(a2282) | c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.30/1.12 tff(1721,plain,
% 1.30/1.12 (c1_1(a2282)),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1720, 396, 41, 42])).
% 1.30/1.12 tff(1722,plain,
% 1.30/1.12 (~hskp10),
% 1.30/1.12 inference(unit_resolution,[status(thm)],[1235, 1721, 1009, 1007, 1008])).
% 1.30/1.12 tff(1723,plain,
% 1.30/1.12 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 1.30/1.12 inference(bind,[status(th)],[])).
% 1.30/1.12 tff(1724,plain,
% 1.30/1.12 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(quant_intro,[status(thm)],[1723])).
% 1.30/1.12 tff(1725,plain,
% 1.30/1.12 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1726,plain,
% 1.30/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.30/1.12 inference(bind,[status(th)],[])).
% 1.30/1.12 tff(1727,plain,
% 1.30/1.12 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(quant_intro,[status(thm)],[1726])).
% 1.30/1.12 tff(1728,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.30/1.12 tff(1729,plain,
% 1.30/1.12 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 1.30/1.12 tff(1730,plain,
% 1.30/1.12 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1729, 1725])).
% 1.30/1.12 tff(1731,plain,(
% 1.30/1.12 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(skolemize,[status(sab)],[1730])).
% 1.30/1.12 tff(1732,plain,
% 1.30/1.12 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.12 inference(modus_ponens,[status(thm)],[1731, 1724])).
% 1.30/1.12 tff(1733,plain,
% 1.30/1.12 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.30/1.12 inference(bind,[status(th)],[])).
% 1.30/1.12 tff(1734,plain,
% 1.30/1.12 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.12 inference(quant_intro,[status(thm)],[1733])).
% 1.30/1.12 tff(1735,plain,
% 1.30/1.12 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.12 inference(rewrite,[status(thm)],[])).
% 1.30/1.12 tff(1736,plain,
% 1.30/1.12 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c2_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) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c2_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) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.30/1.13 inference(bind,[status(th)],[])).
% 1.30/1.13 tff(1737,plain,
% 1.30/1.13 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.13 inference(quant_intro,[status(thm)],[1736])).
% 1.30/1.13 tff(1738,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.30/1.13 tff(1739,plain,
% 1.30/1.13 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.30/1.13 tff(1740,plain,
% 1.30/1.13 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1739, 1735])).
% 1.30/1.13 tff(1741,plain,(
% 1.30/1.13 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.13 inference(skolemize,[status(sab)],[1740])).
% 1.30/1.13 tff(1742,plain,
% 1.30/1.13 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1741, 1734])).
% 1.30/1.13 tff(1743,plain,
% 1.30/1.13 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1744,plain,
% 1.30/1.13 ((hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1745,plain,
% 1.30/1.13 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1744])).
% 1.30/1.13 tff(1746,plain,
% 1.30/1.13 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1745, 1743])).
% 1.30/1.13 tff(1747,plain,
% 1.30/1.13 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1748,plain,
% 1.30/1.13 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.30/1.13 tff(1749,plain,
% 1.30/1.13 (hskp30),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1748, 181, 994, 983, 398, 1570, 396, 972, 1742])).
% 1.30/1.13 tff(1750,plain,
% 1.30/1.13 (c3_1(a2315)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[798, 1749])).
% 1.30/1.13 tff(1751,plain,
% 1.30/1.13 (c2_1(a2315)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[809, 1749])).
% 1.30/1.13 tff(1752,plain,
% 1.30/1.13 (c1_1(a2315)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[829, 1749])).
% 1.30/1.13 tff(1753,plain,
% 1.30/1.13 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1754,plain,
% 1.30/1.13 ((hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315))) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1755,plain,
% 1.30/1.13 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1754])).
% 1.30/1.13 tff(1756,plain,
% 1.30/1.13 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1755, 1753])).
% 1.30/1.13 tff(1757,plain,
% 1.30/1.13 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1758,plain,
% 1.30/1.13 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 1.30/1.13 tff(1759,plain,
% 1.30/1.13 (hskp27),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1758, 181, 1580, 1752, 1751, 1750, 1732])).
% 1.30/1.13 tff(1760,plain,
% 1.30/1.13 (((~hskp27) | (~c0_1(a2367))) <=> ((~hskp27) | (~c0_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1761,plain,
% 1.30/1.13 (((~c0_1(a2367)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1762,axiom,((~c0_1(a2367)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.30/1.13 tff(1763,plain,
% 1.30/1.13 ((~hskp27) | (~c0_1(a2367))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.30/1.13 tff(1764,plain,
% 1.30/1.13 ((~hskp27) | (~c0_1(a2367))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1763, 1760])).
% 1.30/1.13 tff(1765,plain,
% 1.30/1.13 (~c0_1(a2367)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1764, 1759])).
% 1.30/1.13 tff(1766,plain,
% 1.30/1.13 (((~hskp27) | c2_1(a2367)) <=> ((~hskp27) | c2_1(a2367))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1767,axiom,((~hskp27) | c2_1(a2367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.30/1.13 tff(1768,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.30/1.13 tff(1769,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1768, 1766])).
% 1.30/1.13 tff(1770,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1769, 1766])).
% 1.30/1.13 tff(1771,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1770, 1766])).
% 1.30/1.13 tff(1772,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1771, 1766])).
% 1.30/1.13 tff(1773,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1772, 1766])).
% 1.30/1.13 tff(1774,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1773, 1766])).
% 1.30/1.13 tff(1775,plain,
% 1.30/1.13 ((~hskp27) | c2_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1774, 1766])).
% 1.30/1.13 tff(1776,plain,
% 1.30/1.13 (c2_1(a2367)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1775, 1759])).
% 1.30/1.13 tff(1777,plain,
% 1.30/1.13 (((~hskp27) | c1_1(a2367)) <=> ((~hskp27) | c1_1(a2367))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1778,axiom,((~hskp27) | c1_1(a2367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.30/1.13 tff(1779,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.30/1.13 tff(1780,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1779, 1777])).
% 1.30/1.13 tff(1781,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1780, 1777])).
% 1.30/1.13 tff(1782,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1781, 1777])).
% 1.30/1.13 tff(1783,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1782, 1777])).
% 1.30/1.13 tff(1784,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1783, 1777])).
% 1.30/1.13 tff(1785,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1784, 1777])).
% 1.30/1.13 tff(1786,plain,
% 1.30/1.13 ((~hskp27) | c1_1(a2367)),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1785, 1777])).
% 1.30/1.13 tff(1787,plain,
% 1.30/1.13 (c1_1(a2367)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1786, 1759])).
% 1.30/1.13 tff(1788,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1789,plain,
% 1.30/1.13 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1790,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1789])).
% 1.30/1.13 tff(1791,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.30/1.13 tff(1792,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1793,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.30/1.13 tff(1794,plain,
% 1.30/1.13 ((~c2_1(a2306)) | (~c1_1(a2282)) | (~c0_1(a2306))),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1793, 181, 1008, 396, 1009, 1007, 744])).
% 1.30/1.13 tff(1795,plain,
% 1.30/1.13 (~c0_1(a2306)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1794, 1721, 1570])).
% 1.30/1.13 tff(1796,plain,
% 1.30/1.13 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1797,plain,
% 1.30/1.13 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1798,plain,
% 1.30/1.13 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1797])).
% 1.30/1.13 tff(1799,plain,
% 1.30/1.13 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.30/1.13 tff(1800,plain,
% 1.30/1.13 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1801,plain,
% 1.30/1.13 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.30/1.13 tff(1802,plain,
% 1.30/1.13 (hskp16 | hskp15 | (~c1_1(a2282))),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1801, 181, 771, 1198, 1655])).
% 1.30/1.13 tff(1803,plain,
% 1.30/1.13 (hskp15),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1802, 1462, 1197])).
% 1.30/1.13 tff(1804,plain,
% 1.30/1.13 (~c3_1(a2303)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1668, 1803])).
% 1.30/1.13 tff(1805,assumption,(~c0_1(a2367)), introduced(assumption)).
% 1.30/1.13 tff(1806,plain,
% 1.30/1.13 (c2_1(a2303)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1679, 1803])).
% 1.30/1.13 tff(1807,plain,
% 1.30/1.13 (c1_1(a2303)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1704, 1803])).
% 1.30/1.13 tff(1808,assumption,(c2_1(a2367)), introduced(assumption)).
% 1.30/1.13 tff(1809,assumption,(c1_1(a2367)), introduced(assumption)).
% 1.30/1.13 tff(1810,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1811,plain,
% 1.30/1.13 (((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367))) <=> (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1812,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1811])).
% 1.30/1.13 tff(1813,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.30/1.13 tff(1814,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1815,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.30/1.13 tff(1816,plain,
% 1.30/1.13 (~c0_1(a2303)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1815, 181, 1809, 1808, 1807, 1806, 1805, 1804, 744])).
% 1.30/1.13 tff(1817,plain,
% 1.30/1.13 (~c1_1(a2345)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1147, 1463])).
% 1.30/1.13 tff(1818,plain,
% 1.30/1.13 (~c0_1(a2345)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1153, 1463])).
% 1.30/1.13 tff(1819,plain,
% 1.30/1.13 (c3_1(a2345)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1164, 1463])).
% 1.30/1.13 tff(1820,plain,
% 1.30/1.13 (hskp7),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1173, 181, 1166, 1819, 1818, 1817, 1141])).
% 1.30/1.13 tff(1821,plain,
% 1.30/1.13 (~c2_1(a2286)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1053, 1820])).
% 1.30/1.13 tff(1822,plain,
% 1.30/1.13 (c1_1(a2286)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1078, 1820])).
% 1.30/1.13 tff(1823,plain,
% 1.30/1.13 (c3_1(a2286)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1711, 181, 1628, 1807, 1806, 1822, 1821, 1560, 1816])).
% 1.30/1.13 tff(1824,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1825,plain,
% 1.30/1.13 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306))) <=> (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1826,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1825])).
% 1.30/1.13 tff(1827,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.30/1.13 tff(1828,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1829,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.30/1.13 tff(1830,plain,
% 1.30/1.13 ($false),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1829, 181, 1004, 1003, 1822, 1002, 398, 1571, 1821, 217, 639, 1823])).
% 1.30/1.13 tff(1831,plain,(hskp6 | c1_1(a2306) | (~c2_1(a2306)) | c0_1(a2306) | (~c1_1(a2367)) | (~c2_1(a2367)) | c0_1(a2367) | (~c1_1(a2282)) | c0_1(a2282) | c3_1(a2282) | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.30/1.13 tff(1832,plain,
% 1.30/1.13 (hskp6),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[1831, 398, 1570, 1795, 1787, 1776, 1765, 1721, 1009, 1007, 41, 1722])).
% 1.30/1.13 tff(1833,plain,
% 1.30/1.13 (~c3_1(a2285)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[433, 1832])).
% 1.30/1.13 tff(1834,plain,
% 1.30/1.13 (c1_1(a2285)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[409, 1832])).
% 1.30/1.13 tff(1835,plain,
% 1.30/1.13 (c0_1(a2285)),
% 1.30/1.13 inference(unit_resolution,[status(thm)],[420, 1832])).
% 1.30/1.13 tff(1836,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1837,plain,
% 1.30/1.13 (((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367))) <=> (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(rewrite,[status(thm)],[])).
% 1.30/1.13 tff(1838,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 1.30/1.13 inference(monotonicity,[status(thm)],[1837])).
% 1.30/1.13 tff(1839,plain,
% 1.30/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.30/1.13 tff(1840,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.13 inference(quant_inst,[status(thm)],[])).
% 1.30/1.13 tff(1841,plain,
% 1.30/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 1.30/1.13 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.30/1.14 tff(1842,plain,
% 1.30/1.14 (~c2_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1841, 181, 1787, 1776, 1835, 1834, 1765, 1833, 744])).
% 1.30/1.14 tff(1843,plain,
% 1.30/1.14 (~hskp17),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[260, 1570])).
% 1.30/1.14 tff(1844,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1845,plain,
% 1.30/1.14 ((hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367))) <=> (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1846,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1845])).
% 1.30/1.14 tff(1847,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.30/1.14 tff(1848,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1849,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.30/1.14 tff(1850,plain,
% 1.30/1.14 ($false),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1849, 181, 1843, 1787, 1776, 1834, 1765, 1833, 1560, 1842])).
% 1.30/1.14 tff(1851,plain,(c1_1(a2306) | hskp28 | c3_1(a2306) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.30/1.14 tff(1852,plain,
% 1.30/1.14 (c1_1(a2306)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1851, 396, 41, 42])).
% 1.30/1.14 tff(1853,plain,
% 1.30/1.14 (~hskp16),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1461, 1166, 1274])).
% 1.30/1.14 tff(1854,plain,
% 1.30/1.14 (hskp15),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1802, 1853, 1197])).
% 1.30/1.14 tff(1855,plain,
% 1.30/1.14 (~c3_1(a2303)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1668, 1854])).
% 1.30/1.14 tff(1856,plain,
% 1.30/1.14 (c2_1(a2303)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1679, 1854])).
% 1.30/1.14 tff(1857,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1858,plain,
% 1.30/1.14 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1859,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1858])).
% 1.30/1.14 tff(1860,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1859, 1857])).
% 1.30/1.14 tff(1861,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1862,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 1.30/1.14 tff(1863,plain,
% 1.30/1.14 (~c0_1(a2303)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1862, 181, 1856, 776, 1627, 1571, 396, 1855, 771, 744, 1197])).
% 1.30/1.14 tff(1864,plain,
% 1.30/1.14 (hskp26),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1130, 1853, 41])).
% 1.30/1.14 tff(1865,plain,
% 1.30/1.14 (~c1_1(a2345)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1147, 1864])).
% 1.30/1.14 tff(1866,plain,
% 1.30/1.14 (~c0_1(a2345)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1153, 1864])).
% 1.30/1.14 tff(1867,plain,
% 1.30/1.14 (c3_1(a2345)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1164, 1864])).
% 1.30/1.14 tff(1868,plain,
% 1.30/1.14 (hskp7),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1173, 181, 1166, 1867, 1866, 1865, 1141])).
% 1.30/1.14 tff(1869,plain,
% 1.30/1.14 (~c2_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1053, 1868])).
% 1.30/1.14 tff(1870,plain,
% 1.30/1.14 (c1_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1078, 1868])).
% 1.30/1.14 tff(1871,plain,
% 1.30/1.14 (c1_1(a2303)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1704, 1854])).
% 1.30/1.14 tff(1872,plain,
% 1.30/1.14 (c3_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1711, 181, 1628, 1871, 1856, 1870, 1869, 1560, 1863])).
% 1.30/1.14 tff(1873,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1874,plain,
% 1.30/1.14 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345))) <=> (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1875,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1874])).
% 1.30/1.14 tff(1876,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1875, 1873])).
% 1.30/1.14 tff(1877,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1878,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.30/1.14 tff(1879,plain,
% 1.30/1.14 (~c2_1(a2345)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1878, 181, 1867, 1870, 1866, 1865, 1869, 217, 1872])).
% 1.30/1.14 tff(1880,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1881,plain,
% 1.30/1.14 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345)) <=> (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1882,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345)))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1881])).
% 1.30/1.14 tff(1883,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1882, 1880])).
% 1.30/1.14 tff(1884,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1885,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345)),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.30/1.14 tff(1886,plain,
% 1.30/1.14 ($false),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1885, 181, 41, 1870, 1866, 1865, 1869, 460, 1879, 1872])).
% 1.30/1.14 tff(1887,plain,(hskp6 | hskp28 | (~c2_1(a2282)) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | (~c1_1(a2282)) | c3_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.14 tff(1888,plain,
% 1.30/1.14 (hskp6),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1887, 1852, 1008, 41, 1570, 396, 1009, 1721, 1007])).
% 1.30/1.14 tff(1889,plain,
% 1.30/1.14 (~c3_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[433, 1888])).
% 1.30/1.14 tff(1890,plain,
% 1.30/1.14 (c0_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[420, 1888])).
% 1.30/1.14 tff(1891,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1892,plain,
% 1.30/1.14 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1893,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1892])).
% 1.30/1.14 tff(1894,plain,
% 1.30/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.30/1.14 tff(1895,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1896,plain,
% 1.30/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.30/1.14 tff(1897,plain,
% 1.30/1.14 (~c2_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1896, 181, 1890, 1008, 1852, 1570, 396, 1889, 1009, 744, 1721])).
% 1.30/1.14 tff(1898,plain,
% 1.30/1.14 (c1_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[409, 1888])).
% 1.30/1.14 tff(1899,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1900,plain,
% 1.30/1.14 ((hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1901,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285)))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1900])).
% 1.30/1.14 tff(1902,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.30/1.14 tff(1903,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1904,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285)),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.30/1.14 tff(1905,plain,
% 1.30/1.14 ($false),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1904, 181, 1843, 1898, 1008, 1889, 1009, 1560, 1721, 1897])).
% 1.30/1.14 tff(1906,plain,(c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.30/1.14 tff(1907,plain,
% 1.30/1.14 (c3_1(a2306)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1906, 42, 41])).
% 1.30/1.14 tff(1908,plain,
% 1.30/1.14 (~hskp17),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[289, 1907])).
% 1.30/1.14 tff(1909,plain,
% 1.30/1.14 (hskp7),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1175, 1463, 1166])).
% 1.30/1.14 tff(1910,plain,
% 1.30/1.14 (~c2_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1053, 1909])).
% 1.30/1.14 tff(1911,plain,
% 1.30/1.14 (c1_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1078, 1909])).
% 1.30/1.14 tff(1912,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1913,plain,
% 1.30/1.14 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1914,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1913])).
% 1.30/1.14 tff(1915,plain,
% 1.30/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 1.30/1.14 inference(transitivity,[status(thm)],[1914, 1912])).
% 1.30/1.14 tff(1916,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.30/1.14 inference(quant_inst,[status(thm)],[])).
% 1.30/1.14 tff(1917,plain,
% 1.30/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 1.30/1.14 tff(1918,plain,
% 1.30/1.14 (c3_1(a2286)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1917, 181, 912, 1911, 776, 1910, 771, 1560, 1197])).
% 1.30/1.14 tff(1919,plain,
% 1.30/1.14 ((~c3_1(a2286)) | (~c2_1(a2345))),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1878, 181, 1819, 1911, 1818, 1817, 1910, 217])).
% 1.30/1.14 tff(1920,plain,
% 1.30/1.14 (~c2_1(a2345)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1919, 1918])).
% 1.30/1.14 tff(1921,plain,
% 1.30/1.14 ($false),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1885, 181, 41, 1911, 1818, 1817, 1910, 460, 1920, 1918])).
% 1.30/1.14 tff(1922,plain,(hskp6 | hskp28 | hskp17 | (~c2_1(a2282)) | c0_1(a2282) | (~c1_1(a2282)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.30/1.14 tff(1923,plain,
% 1.30/1.14 (hskp6),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1922, 1908, 41, 1008, 1009, 1196, 1236])).
% 1.30/1.14 tff(1924,plain,
% 1.30/1.14 (~c3_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[433, 1923])).
% 1.30/1.14 tff(1925,plain,
% 1.30/1.14 (c1_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[409, 1923])).
% 1.30/1.14 tff(1926,plain,
% 1.30/1.14 (c0_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[420, 1923])).
% 1.30/1.14 tff(1927,plain,
% 1.30/1.14 (~c2_1(a2285)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1305, 181, 1926, 1925, 1008, 1924, 1009, 744, 1196])).
% 1.30/1.14 tff(1928,plain,
% 1.30/1.14 ($false),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1904, 181, 1908, 1925, 1008, 1924, 1009, 1560, 1196, 1927])).
% 1.30/1.14 tff(1929,plain,(hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.30/1.14 tff(1930,plain,
% 1.30/1.14 (hskp1),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[1929, 41])).
% 1.30/1.14 tff(1931,plain,
% 1.30/1.14 (c1_1(a2277)),
% 1.30/1.14 inference(unit_resolution,[status(thm)],[366, 1930])).
% 1.30/1.14 tff(1932,plain,
% 1.30/1.14 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.30/1.14 inference(bind,[status(th)],[])).
% 1.30/1.14 tff(1933,plain,
% 1.30/1.14 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(quant_intro,[status(thm)],[1932])).
% 1.30/1.14 tff(1934,plain,
% 1.30/1.14 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1935,plain,
% 1.30/1.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.30/1.14 inference(bind,[status(th)],[])).
% 1.30/1.14 tff(1936,plain,
% 1.30/1.14 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(quant_intro,[status(thm)],[1935])).
% 1.30/1.14 tff(1937,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.30/1.14 tff(1938,plain,
% 1.30/1.14 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.30/1.14 tff(1939,plain,
% 1.30/1.14 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1938, 1934])).
% 1.30/1.14 tff(1940,plain,(
% 1.30/1.14 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(skolemize,[status(sab)],[1939])).
% 1.30/1.14 tff(1941,plain,
% 1.30/1.14 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.30/1.14 inference(modus_ponens,[status(thm)],[1940, 1933])).
% 1.30/1.14 tff(1942,plain,
% 1.30/1.14 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1943,plain,
% 1.30/1.14 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.14 inference(rewrite,[status(thm)],[])).
% 1.30/1.14 tff(1944,plain,
% 1.30/1.14 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.30/1.14 inference(monotonicity,[status(thm)],[1943])).
% 1.30/1.15 tff(1945,plain,
% 1.30/1.15 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.30/1.15 tff(1946,plain,
% 1.30/1.15 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(1947,plain,
% 1.30/1.15 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.30/1.15 tff(1948,plain,
% 1.30/1.15 (hskp4 | hskp3),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1947, 181, 1004, 1003, 1002, 1941])).
% 1.30/1.15 tff(1949,plain,
% 1.30/1.15 (hskp3),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1948, 748])).
% 1.30/1.15 tff(1950,plain,
% 1.30/1.15 (~c2_1(a2280)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[574, 1949])).
% 1.30/1.15 tff(1951,plain,
% 1.30/1.15 (c3_1(a2280)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[585, 1949])).
% 1.30/1.15 tff(1952,plain,
% 1.30/1.15 (c1_1(a2280)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[596, 1949])).
% 1.30/1.15 tff(1953,plain,
% 1.30/1.15 (c1_1(a2302)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1527, 181, 1004, 1003, 994, 1952, 1951, 1002, 972, 1950, 217])).
% 1.30/1.15 tff(1954,plain,
% 1.30/1.15 (c1_1(a2327)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1534, 181, 41, 775, 774, 1184, 1181, 770, 460])).
% 1.30/1.15 tff(1955,plain,
% 1.30/1.15 (~hskp26),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1479, 1954, 1182, 1181, 41])).
% 1.30/1.15 tff(1956,plain,
% 1.30/1.15 (hskp16),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1130, 1955, 41])).
% 1.30/1.15 tff(1957,plain,
% 1.30/1.15 (hskp9),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1115, 1956, 41])).
% 1.30/1.15 tff(1958,plain,
% 1.30/1.15 (~c2_1(a2291)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1015, 1957])).
% 1.30/1.15 tff(1959,plain,
% 1.30/1.15 (~c1_1(a2291)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1021, 1957])).
% 1.30/1.15 tff(1960,plain,
% 1.30/1.15 (~c0_1(a2291)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1027, 1957])).
% 1.30/1.15 tff(1961,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1962,plain,
% 1.30/1.15 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1963,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[1962])).
% 1.30/1.15 tff(1964,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[1963, 1961])).
% 1.30/1.15 tff(1965,plain,
% 1.30/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(1966,plain,
% 1.30/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 1.30/1.15 tff(1967,plain,
% 1.30/1.15 ($false),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1966, 181, 41, 1182, 1181, 1960, 1959, 1958, 460, 1954])).
% 1.30/1.15 tff(1968,plain,((~hskp23) | hskp28 | (~c1_1(a2280)) | (~c3_1(a2280)) | c2_1(a2280)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.15 tff(1969,plain,
% 1.30/1.15 (~hskp23),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1968, 775, 41, 774, 770])).
% 1.30/1.15 tff(1970,plain,
% 1.30/1.15 (~c0_1(a2306)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[296, 181, 1969, 398, 397, 396, 284])).
% 1.30/1.15 tff(1971,plain,
% 1.30/1.15 ($false),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[603, 181, 41, 775, 774, 398, 397, 770, 460, 1970])).
% 1.30/1.15 tff(1972,plain,(c2_1(a2306) | hskp28 | (~c1_1(a2280)) | (~c3_1(a2280)) | c1_1(a2306) | c2_1(a2280) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.15 tff(1973,plain,
% 1.30/1.15 ($false),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1972, 345, 346, 775, 774, 41, 770, 344])).
% 1.30/1.15 tff(1974,plain,((~hskp17) | (~c1_1(a2280)) | (~c3_1(a2280)) | hskp28 | c2_1(a2280)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.15 tff(1975,plain,
% 1.30/1.15 (~hskp17),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1974, 1952, 1951, 41, 1950])).
% 1.30/1.15 tff(1976,assumption,(c1_1(a2302)), introduced(assumption)).
% 1.30/1.15 tff(1977,assumption,(hskp19), introduced(assumption)).
% 1.30/1.15 tff(1978,plain,
% 1.30/1.15 (((~hskp19) | (~c3_1(a2316))) <=> ((~hskp19) | (~c3_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1979,plain,
% 1.30/1.15 (((~c3_1(a2316)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1980,axiom,((~c3_1(a2316)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.30/1.15 tff(1981,plain,
% 1.30/1.15 ((~hskp19) | (~c3_1(a2316))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 1.30/1.15 tff(1982,plain,
% 1.30/1.15 ((~hskp19) | (~c3_1(a2316))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1981, 1978])).
% 1.30/1.15 tff(1983,plain,
% 1.30/1.15 (~c3_1(a2316)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1982, 1977])).
% 1.30/1.15 tff(1984,plain,
% 1.30/1.15 (((~hskp19) | (~c2_1(a2316))) <=> ((~hskp19) | (~c2_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1985,plain,
% 1.30/1.15 (((~c2_1(a2316)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1986,axiom,((~c2_1(a2316)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.30/1.15 tff(1987,plain,
% 1.30/1.15 ((~hskp19) | (~c2_1(a2316))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.30/1.15 tff(1988,plain,
% 1.30/1.15 ((~hskp19) | (~c2_1(a2316))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1987, 1984])).
% 1.30/1.15 tff(1989,plain,
% 1.30/1.15 (~c2_1(a2316)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1988, 1977])).
% 1.30/1.15 tff(1990,plain,
% 1.30/1.15 (((~hskp19) | c1_1(a2316)) <=> ((~hskp19) | c1_1(a2316))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(1991,axiom,((~hskp19) | c1_1(a2316)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.30/1.15 tff(1992,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.30/1.15 tff(1993,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1992, 1990])).
% 1.30/1.15 tff(1994,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1993, 1990])).
% 1.30/1.15 tff(1995,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1994, 1990])).
% 1.30/1.15 tff(1996,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1995, 1990])).
% 1.30/1.15 tff(1997,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1996, 1990])).
% 1.30/1.15 tff(1998,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1997, 1990])).
% 1.30/1.15 tff(1999,plain,
% 1.30/1.15 ((~hskp19) | c1_1(a2316)),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[1998, 1990])).
% 1.30/1.15 tff(2000,plain,
% 1.30/1.15 (c1_1(a2316)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1999, 1977])).
% 1.30/1.15 tff(2001,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2002,plain,
% 1.30/1.15 ((hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2003,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[2002])).
% 1.30/1.15 tff(2004,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[2003, 2001])).
% 1.30/1.15 tff(2005,plain,
% 1.30/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(2006,plain,
% 1.30/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.30/1.15 tff(2007,plain,
% 1.30/1.15 ($false),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2006, 181, 912, 2000, 994, 1989, 1983, 972, 1560, 1976])).
% 1.30/1.15 tff(2008,plain,((~hskp19) | hskp17 | (~c1_1(a2302))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.15 tff(2009,plain,
% 1.30/1.15 (~hskp19),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2008, 1975, 1953])).
% 1.30/1.15 tff(2010,plain,
% 1.30/1.15 (^[U: $i] : refl((hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.30/1.15 inference(bind,[status(th)],[])).
% 1.30/1.15 tff(2011,plain,
% 1.30/1.15 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(quant_intro,[status(thm)],[2010])).
% 1.30/1.15 tff(2012,plain,
% 1.30/1.15 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2013,plain,
% 1.30/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(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)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.30/1.15 inference(bind,[status(th)],[])).
% 1.30/1.15 tff(2014,plain,
% 1.30/1.15 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(quant_intro,[status(thm)],[2013])).
% 1.30/1.15 tff(2015,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.30/1.15 tff(2016,plain,
% 1.30/1.15 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 1.30/1.15 tff(2017,plain,
% 1.30/1.15 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2016, 2012])).
% 1.30/1.15 tff(2018,plain,(
% 1.30/1.15 ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(skolemize,[status(sab)],[2017])).
% 1.30/1.15 tff(2019,plain,
% 1.30/1.15 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2018, 2011])).
% 1.30/1.15 tff(2020,plain,
% 1.30/1.15 (~hskp23),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[1968, 1952, 41, 1951, 1950])).
% 1.30/1.15 tff(2021,plain,
% 1.30/1.15 (^[U: $i] : refl((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 1.30/1.15 inference(bind,[status(th)],[])).
% 1.30/1.15 tff(2022,plain,
% 1.30/1.15 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(quant_intro,[status(thm)],[2021])).
% 1.30/1.15 tff(2023,plain,
% 1.30/1.15 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2024,plain,
% 1.30/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> ((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23))), rewrite(((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.30/1.15 inference(bind,[status(th)],[])).
% 1.30/1.15 tff(2025,plain,
% 1.30/1.15 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(quant_intro,[status(thm)],[2024])).
% 1.30/1.15 tff(2026,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.30/1.15 tff(2027,plain,
% 1.30/1.15 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.30/1.15 tff(2028,plain,
% 1.30/1.15 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2027, 2023])).
% 1.30/1.15 tff(2029,plain,(
% 1.30/1.15 ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(skolemize,[status(sab)],[2028])).
% 1.30/1.15 tff(2030,plain,
% 1.30/1.15 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2029, 2022])).
% 1.30/1.15 tff(2031,plain,
% 1.30/1.15 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2032,plain,
% 1.30/1.15 ((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2033,plain,
% 1.30/1.15 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[2032])).
% 1.30/1.15 tff(2034,plain,
% 1.30/1.15 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[2033, 2031])).
% 1.30/1.15 tff(2035,plain,
% 1.30/1.15 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(2036,plain,
% 1.30/1.15 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.30/1.15 tff(2037,plain,
% 1.30/1.15 (hskp25 | hskp23 | (~c1_1(a2302))),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2036, 181, 994, 983, 2030])).
% 1.30/1.15 tff(2038,plain,
% 1.30/1.15 (hskp25),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2037, 2020, 1953])).
% 1.30/1.15 tff(2039,plain,
% 1.30/1.15 (c3_1(a2342)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[27, 2038])).
% 1.30/1.15 tff(2040,plain,
% 1.30/1.15 (c0_1(a2342)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[38, 2038])).
% 1.30/1.15 tff(2041,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2042,plain,
% 1.30/1.15 ((hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342))) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2043,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[2042])).
% 1.30/1.15 tff(2044,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[2043, 2041])).
% 1.30/1.15 tff(2045,plain,
% 1.30/1.15 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(2046,plain,
% 1.30/1.15 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 1.30/1.15 tff(2047,plain,
% 1.30/1.15 (hskp19 | c1_1(a2342)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2046, 181, 748, 2040, 2039, 2019])).
% 1.30/1.15 tff(2048,plain,
% 1.30/1.15 (c1_1(a2342)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2047, 2009])).
% 1.30/1.15 tff(2049,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2050,plain,
% 1.30/1.15 ((hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323))) <=> (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2051,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[2050])).
% 1.30/1.15 tff(2052,plain,
% 1.30/1.15 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[2051, 2049])).
% 1.30/1.15 tff(2053,plain,
% 1.30/1.15 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(2054,plain,
% 1.30/1.15 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.30/1.15 tff(2055,plain,
% 1.30/1.15 (hskp19 | hskp4 | (~c0_1(a2323))),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2054, 181, 1003, 1002, 2019])).
% 1.30/1.15 tff(2056,plain,
% 1.30/1.15 (~c0_1(a2323)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2055, 2009, 748])).
% 1.30/1.15 tff(2057,plain,
% 1.30/1.15 (~c2_1(a2342)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[16, 2038])).
% 1.30/1.15 tff(2058,plain,
% 1.30/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2059,plain,
% 1.30/1.15 (((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2060,plain,
% 1.30/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342))))),
% 1.30/1.15 inference(monotonicity,[status(thm)],[2059])).
% 1.30/1.15 tff(2061,plain,
% 1.30/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 1.30/1.15 inference(transitivity,[status(thm)],[2060, 2058])).
% 1.30/1.15 tff(2062,plain,
% 1.30/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 1.30/1.15 inference(quant_inst,[status(thm)],[])).
% 1.30/1.15 tff(2063,plain,
% 1.30/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342))),
% 1.30/1.15 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.30/1.15 tff(2064,plain,
% 1.30/1.15 ($false),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2063, 181, 2039, 1004, 1003, 2057, 1002, 217, 2056, 2048])).
% 1.30/1.15 tff(2065,plain,(hskp4 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.30/1.15 tff(2066,plain,
% 1.30/1.15 (hskp4),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[2065, 41])).
% 1.30/1.15 tff(2067,plain,
% 1.30/1.15 (~c3_1(a2282)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[193, 2066])).
% 1.30/1.15 tff(2068,plain,
% 1.30/1.15 (c2_1(a2282)),
% 1.30/1.15 inference(unit_resolution,[status(thm)],[247, 2066])).
% 1.30/1.15 tff(2069,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2070,plain,
% 1.30/1.15 ((hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.15 inference(rewrite,[status(thm)],[])).
% 1.30/1.15 tff(2071,plain,
% 1.30/1.15 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2070])).
% 1.30/1.16 tff(2072,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2071, 2069])).
% 1.30/1.16 tff(2073,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2074,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.30/1.16 tff(2075,plain,
% 1.30/1.16 (hskp30),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2074, 181, 994, 983, 2068, 972, 2067, 1742, 43])).
% 1.30/1.16 tff(2076,plain,
% 1.30/1.16 (c1_1(a2315)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[829, 2075])).
% 1.30/1.16 tff(2077,plain,
% 1.30/1.16 (~c0_1(a2282)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[199, 2066])).
% 1.30/1.16 tff(2078,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2079,plain,
% 1.30/1.16 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2080,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2079])).
% 1.30/1.16 tff(2081,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2080, 2078])).
% 1.30/1.16 tff(2082,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2083,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 1.30/1.16 tff(2084,plain,
% 1.30/1.16 ((~c3_1(a2277)) | c1_1(a2282)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2083, 181, 1004, 1003, 2068, 1931, 1002, 2077, 40, 217])).
% 1.30/1.16 tff(2085,plain,
% 1.30/1.16 (~c3_1(a2277)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2084, 43])).
% 1.30/1.16 tff(2086,plain,
% 1.30/1.16 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.30/1.16 inference(bind,[status(th)],[])).
% 1.30/1.16 tff(2087,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(quant_intro,[status(thm)],[2086])).
% 1.30/1.16 tff(2088,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2089,plain,
% 1.30/1.16 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_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) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.30/1.16 inference(bind,[status(th)],[])).
% 1.30/1.16 tff(2090,plain,
% 1.30/1.16 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(quant_intro,[status(thm)],[2089])).
% 1.30/1.16 tff(2091,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.30/1.16 tff(2092,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 1.30/1.16 tff(2093,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2092, 2088])).
% 1.30/1.16 tff(2094,plain,(
% 1.30/1.16 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(skolemize,[status(sab)],[2093])).
% 1.30/1.16 tff(2095,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2094, 2087])).
% 1.30/1.16 tff(2096,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2097,plain,
% 1.30/1.16 ((hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2098,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2097])).
% 1.30/1.16 tff(2099,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2098, 2096])).
% 1.30/1.16 tff(2100,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2101,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.30/1.16 tff(2102,plain,
% 1.30/1.16 (hskp19 | (~c1_1(a2277)) | c3_1(a2277)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2101, 181, 994, 983, 972, 40, 2095])).
% 1.30/1.16 tff(2103,plain,
% 1.30/1.16 (hskp19),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2102, 2085, 1931])).
% 1.30/1.16 tff(2104,assumption,(~c0_1(a2277)), introduced(assumption)).
% 1.30/1.16 tff(2105,plain,
% 1.30/1.16 (~hskp1),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[377, 2104])).
% 1.30/1.16 tff(2106,assumption,(hskp28), introduced(assumption)).
% 1.30/1.16 tff(2107,plain,
% 1.30/1.16 (c0_1(a2278)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[636, 2106])).
% 1.30/1.16 tff(2108,plain,
% 1.30/1.16 (c3_1(a2278)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[614, 2106])).
% 1.30/1.16 tff(2109,plain,
% 1.30/1.16 (c1_1(a2278)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[625, 2106])).
% 1.30/1.16 tff(2110,assumption,(~c2_1(a2278)), introduced(assumption)).
% 1.30/1.16 tff(2111,assumption,(c0_1(a2323)), introduced(assumption)).
% 1.30/1.16 tff(2112,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2113,plain,
% 1.30/1.16 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2114,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2113])).
% 1.30/1.16 tff(2115,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.30/1.16 tff(2116,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2117,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.30/1.16 tff(2118,plain,
% 1.30/1.16 ($false),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2117, 181, 679, 678, 677, 1003, 1002, 94, 2111, 2110])).
% 1.30/1.16 tff(2119,plain,(c2_1(a2278) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2323))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.16 tff(2120,plain,
% 1.30/1.16 (~c0_1(a2323)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2119, 2110, 678, 677, 679])).
% 1.30/1.16 tff(2121,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2122,plain,
% 1.30/1.16 (((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2123,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2122])).
% 1.30/1.16 tff(2124,plain,
% 1.30/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2123, 2121])).
% 1.30/1.16 tff(2125,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2126,plain,
% 1.30/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 1.30/1.16 tff(2127,plain,
% 1.30/1.16 ($false),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2126, 181, 678, 677, 1004, 1003, 1002, 217, 2120, 2110])).
% 1.30/1.16 tff(2128,plain,(c2_1(a2278) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.16 tff(2129,plain,
% 1.30/1.16 (c2_1(a2278)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2128, 2109, 2108, 2107])).
% 1.30/1.16 tff(2130,plain,
% 1.30/1.16 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.30/1.16 inference(bind,[status(th)],[])).
% 1.30/1.16 tff(2131,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(quant_intro,[status(thm)],[2130])).
% 1.30/1.16 tff(2132,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2133,plain,
% 1.30/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.30/1.16 inference(bind,[status(th)],[])).
% 1.30/1.16 tff(2134,plain,
% 1.30/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(quant_intro,[status(thm)],[2133])).
% 1.30/1.16 tff(2135,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.30/1.16 tff(2136,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.30/1.16 tff(2137,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2136, 2132])).
% 1.30/1.16 tff(2138,plain,(
% 1.30/1.16 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(skolemize,[status(sab)],[2137])).
% 1.30/1.16 tff(2139,plain,
% 1.30/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2138, 2131])).
% 1.30/1.16 tff(2140,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2141,plain,
% 1.30/1.16 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2142,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2141])).
% 1.30/1.16 tff(2143,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 1.30/1.16 inference(transitivity,[status(thm)],[2142, 2140])).
% 1.30/1.16 tff(2144,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.30/1.16 inference(quant_inst,[status(thm)],[])).
% 1.30/1.16 tff(2145,plain,
% 1.30/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306))),
% 1.30/1.16 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 1.30/1.16 tff(2146,plain,
% 1.30/1.16 ((~c2_1(a2278)) | (~c0_1(a2306))),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2145, 181, 42, 2107, 2109, 398, 396, 2139])).
% 1.30/1.16 tff(2147,plain,
% 1.30/1.16 (~c0_1(a2306)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[2146, 2129])).
% 1.30/1.16 tff(2148,assumption,(c2_1(a2278)), introduced(assumption)).
% 1.30/1.16 tff(2149,plain,
% 1.30/1.16 (~c1_1(a2295)),
% 1.30/1.16 inference(unit_resolution,[status(thm)],[1368, 745])).
% 1.30/1.16 tff(2150,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2151,plain,
% 1.30/1.16 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 1.30/1.16 inference(rewrite,[status(thm)],[])).
% 1.30/1.16 tff(2152,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295))))),
% 1.30/1.16 inference(monotonicity,[status(thm)],[2151])).
% 1.30/1.16 tff(2153,plain,
% 1.30/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2152, 2150])).
% 1.30/1.17 tff(2154,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2155,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 1.30/1.17 tff(2156,plain,
% 1.30/1.17 ($false),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2155, 181, 42, 679, 678, 747, 2149, 746, 2139, 2148])).
% 1.30/1.17 tff(2157,plain,((~hskp12) | hskp1 | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.17 tff(2158,plain,
% 1.30/1.17 (~hskp12),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2157, 2129, 2107, 2109, 42])).
% 1.30/1.17 tff(2159,plain,
% 1.30/1.17 (hskp13),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1361, 2158])).
% 1.30/1.17 tff(2160,plain,
% 1.30/1.17 (~c3_1(a2299)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1312, 2159])).
% 1.30/1.17 tff(2161,plain,
% 1.30/1.17 (~c1_1(a2299)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1329, 2159])).
% 1.30/1.17 tff(2162,plain,
% 1.30/1.17 (c2_1(a2299)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1323, 2159])).
% 1.30/1.17 tff(2163,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2164,plain,
% 1.30/1.17 ((hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2165,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306)))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2164])).
% 1.30/1.17 tff(2166,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2165, 2163])).
% 1.30/1.17 tff(2167,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2168,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306)),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 1.30/1.17 tff(2169,plain,
% 1.30/1.17 ($false),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2168, 181, 42, 2162, 398, 397, 2161, 2160, 227, 2147])).
% 1.30/1.17 tff(2170,plain,((~hskp28) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.17 tff(2171,plain,
% 1.30/1.17 (~hskp28),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2170, 398, 2105, 397, 396])).
% 1.30/1.17 tff(2172,plain,
% 1.30/1.17 (hskp4),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1005, 2105])).
% 1.30/1.17 tff(2173,plain,
% 1.30/1.17 (~c3_1(a2282)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[193, 2172])).
% 1.30/1.17 tff(2174,assumption,(~c1_1(a2277)), introduced(assumption)).
% 1.30/1.17 tff(2175,plain,
% 1.30/1.17 (c2_1(a2282)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[247, 2172])).
% 1.30/1.17 tff(2176,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2177,plain,
% 1.30/1.17 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2178,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2177])).
% 1.30/1.17 tff(2179,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2178, 2176])).
% 1.30/1.17 tff(2180,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2181,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.30/1.17 tff(2182,plain,
% 1.30/1.17 ($false),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2181, 181, 2105, 2175, 2104, 2174, 2173, 40, 227, 43])).
% 1.30/1.17 tff(2183,plain,(c1_1(a2282) | c0_1(a2277) | c1_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.17 tff(2184,plain,
% 1.30/1.17 (c1_1(a2282)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2183, 2174, 2104, 40])).
% 1.30/1.17 tff(2185,plain,
% 1.30/1.17 (~c0_1(a2282)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[199, 2172])).
% 1.30/1.17 tff(2186,plain,
% 1.30/1.17 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.30/1.17 inference(bind,[status(th)],[])).
% 1.30/1.17 tff(2187,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(quant_intro,[status(thm)],[2186])).
% 1.30/1.17 tff(2188,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2189,plain,
% 1.30/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.30/1.17 inference(bind,[status(th)],[])).
% 1.30/1.17 tff(2190,plain,
% 1.30/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(quant_intro,[status(thm)],[2189])).
% 1.30/1.17 tff(2191,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.30/1.17 tff(2192,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 1.30/1.17 tff(2193,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2192, 2188])).
% 1.30/1.17 tff(2194,plain,(
% 1.30/1.17 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(skolemize,[status(sab)],[2193])).
% 1.30/1.17 tff(2195,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2194, 2187])).
% 1.30/1.17 tff(2196,plain,
% 1.30/1.17 (~hskp10),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1235, 2184, 2185, 2173, 2175])).
% 1.30/1.17 tff(2197,plain,
% 1.30/1.17 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2198,plain,
% 1.30/1.17 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277)) <=> (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2199,plain,
% 1.30/1.17 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2198])).
% 1.30/1.17 tff(2200,plain,
% 1.30/1.17 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2199, 2197])).
% 1.30/1.17 tff(2201,plain,
% 1.30/1.17 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2202,plain,
% 1.30/1.17 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 1.30/1.17 tff(2203,plain,
% 1.30/1.17 (hskp10 | hskp6 | c0_1(a2277) | c3_1(a2277)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2202, 181, 40, 1288])).
% 1.30/1.17 tff(2204,plain,
% 1.30/1.17 (c3_1(a2277)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2203, 1166, 2104, 2196])).
% 1.30/1.17 tff(2205,plain,
% 1.30/1.17 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2206,plain,
% 1.30/1.17 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277))) <=> (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2207,plain,
% 1.30/1.17 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277))))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2206])).
% 1.30/1.17 tff(2208,plain,
% 1.30/1.17 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2207, 2205])).
% 1.30/1.17 tff(2209,plain,
% 1.30/1.17 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2210,plain,
% 1.30/1.17 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 1.30/1.17 tff(2211,plain,
% 1.30/1.17 (hskp7 | hskp6 | c1_1(a2277) | (~c3_1(a2277))),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2210, 181, 2104, 1141])).
% 1.30/1.17 tff(2212,plain,
% 1.30/1.17 (hskp7),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2211, 2204, 2174, 1166])).
% 1.30/1.17 tff(2213,plain,
% 1.30/1.17 (~c2_1(a2286)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1053, 2212])).
% 1.30/1.17 tff(2214,plain,
% 1.30/1.17 (~c0_1(a2286)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1059, 2212])).
% 1.30/1.17 tff(2215,plain,
% 1.30/1.17 (c3_1(a2286)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1505, 181, 2196, 1166, 2214, 2213, 1288])).
% 1.30/1.17 tff(2216,plain,
% 1.30/1.17 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.30/1.17 inference(bind,[status(th)],[])).
% 1.30/1.17 tff(2217,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(quant_intro,[status(thm)],[2216])).
% 1.30/1.17 tff(2218,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2219,plain,
% 1.30/1.17 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.30/1.17 inference(bind,[status(th)],[])).
% 1.30/1.17 tff(2220,plain,
% 1.30/1.17 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(quant_intro,[status(thm)],[2219])).
% 1.30/1.17 tff(2221,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.30/1.17 tff(2222,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.30/1.17 tff(2223,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2222, 2218])).
% 1.30/1.17 tff(2224,plain,(
% 1.30/1.17 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(skolemize,[status(sab)],[2223])).
% 1.30/1.17 tff(2225,plain,
% 1.30/1.17 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2224, 2217])).
% 1.30/1.17 tff(2226,plain,
% 1.30/1.17 (c1_1(a2286)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1078, 2212])).
% 1.30/1.17 tff(2227,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2228,plain,
% 1.30/1.17 ((hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323))) <=> (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2229,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323)))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2228])).
% 1.30/1.17 tff(2230,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2229, 2227])).
% 1.30/1.17 tff(2231,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2232,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323)),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.30/1.17 tff(2233,plain,
% 1.30/1.17 (c0_1(a2323)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2232, 181, 2105, 1004, 2226, 1002, 2213, 2225, 2215])).
% 1.30/1.17 tff(2234,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2235,plain,
% 1.30/1.17 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 1.30/1.17 inference(rewrite,[status(thm)],[])).
% 1.30/1.17 tff(2236,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286))))),
% 1.30/1.17 inference(monotonicity,[status(thm)],[2235])).
% 1.30/1.17 tff(2237,plain,
% 1.30/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 1.30/1.17 inference(transitivity,[status(thm)],[2236, 2234])).
% 1.30/1.17 tff(2238,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 1.30/1.17 inference(quant_inst,[status(thm)],[])).
% 1.30/1.17 tff(2239,plain,
% 1.30/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286))),
% 1.30/1.17 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 1.30/1.17 tff(2240,plain,
% 1.30/1.17 (hskp28),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2239, 181, 2226, 2104, 2174, 2213, 40, 460, 2215])).
% 1.30/1.17 tff(2241,plain,
% 1.30/1.17 (c3_1(a2278)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[614, 2240])).
% 1.30/1.17 tff(2242,plain,
% 1.30/1.17 (c1_1(a2278)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[625, 2240])).
% 1.30/1.17 tff(2243,plain,
% 1.30/1.17 (c0_1(a2278)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[636, 2240])).
% 1.30/1.17 tff(2244,plain,
% 1.30/1.17 (c2_1(a2278)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2119, 2243, 2242, 2241, 2233])).
% 1.30/1.17 tff(2245,plain,
% 1.30/1.17 (~hskp12),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[2157, 2243, 2105, 2242, 2244])).
% 1.30/1.17 tff(2246,plain,
% 1.30/1.17 (hskp13),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1361, 2245])).
% 1.30/1.17 tff(2247,plain,
% 1.30/1.17 (~c3_1(a2299)),
% 1.30/1.17 inference(unit_resolution,[status(thm)],[1312, 2246])).
% 1.30/1.17 tff(2248,plain,
% 1.30/1.18 (~c1_1(a2299)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1329, 2246])).
% 1.30/1.18 tff(2249,plain,
% 1.30/1.18 (c2_1(a2299)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1323, 2246])).
% 1.30/1.18 tff(2250,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2251,plain,
% 1.30/1.18 ((hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299))) <=> (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2252,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299))))),
% 1.30/1.18 inference(monotonicity,[status(thm)],[2251])).
% 1.30/1.18 tff(2253,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 1.30/1.18 inference(transitivity,[status(thm)],[2252, 2250])).
% 1.30/1.18 tff(2254,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))),
% 1.30/1.18 inference(quant_inst,[status(thm)],[])).
% 1.30/1.18 tff(2255,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299))),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 1.30/1.18 tff(2256,plain,
% 1.30/1.18 (~c0_1(a2299)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2255, 181, 2245, 2249, 2248, 2247, 2195])).
% 1.30/1.18 tff(2257,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2258,plain,
% 1.30/1.18 ((hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299))) <=> (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2259,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299)))),
% 1.30/1.18 inference(monotonicity,[status(thm)],[2258])).
% 1.30/1.18 tff(2260,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.30/1.18 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.30/1.18 tff(2261,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))),
% 1.30/1.18 inference(quant_inst,[status(thm)],[])).
% 1.30/1.18 tff(2262,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299)),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.30/1.18 tff(2263,plain,
% 1.30/1.18 ($false),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2262, 181, 2105, 2249, 2226, 2248, 2213, 2225, 2215, 2256])).
% 1.30/1.18 tff(2264,plain,(hskp6 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.18 tff(2265,plain,
% 1.30/1.18 (hskp6),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2264, 2174, 2104, 40])).
% 1.30/1.18 tff(2266,plain,
% 1.30/1.18 (~c3_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[433, 2265])).
% 1.30/1.18 tff(2267,plain,
% 1.30/1.18 (c1_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[409, 2265])).
% 1.30/1.18 tff(2268,plain,
% 1.30/1.18 (c0_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[420, 2265])).
% 1.30/1.18 tff(2269,plain,
% 1.30/1.18 (~c2_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1305, 181, 2268, 2267, 2175, 2266, 2185, 744, 2184])).
% 1.30/1.18 tff(2270,plain,
% 1.30/1.18 (hskp17),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1904, 181, 2267, 2175, 2266, 2185, 1560, 2184, 2269])).
% 1.30/1.18 tff(2271,plain,
% 1.30/1.18 (~c3_1(a2306)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[289, 2270])).
% 1.30/1.18 tff(2272,plain,
% 1.30/1.18 (~c1_1(a2306)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[266, 2270])).
% 1.30/1.18 tff(2273,plain,
% 1.30/1.18 (~c2_1(a2306)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[260, 2270])).
% 1.30/1.18 tff(2274,plain,
% 1.30/1.18 (hskp6 | c2_1(a2306) | c0_1(a2306)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1294, 181, 2196, 396, 1288])).
% 1.30/1.18 tff(2275,plain,
% 1.30/1.18 (c0_1(a2306)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2274, 1166, 397])).
% 1.30/1.18 tff(2276,plain,
% 1.30/1.18 (~c2_1(a2278)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2145, 181, 2105, 2243, 2242, 398, 396, 2139, 2275])).
% 1.30/1.18 tff(2277,plain,
% 1.30/1.18 ($false),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2117, 181, 2243, 2242, 2241, 1003, 1002, 94, 2233, 2276])).
% 1.30/1.18 tff(2278,plain,(hskp6 | c1_1(a2306) | c3_1(a2306) | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.30/1.18 tff(2279,plain,
% 1.30/1.18 (hskp6),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2278, 398, 396, 2104, 2174, 40, 397])).
% 1.30/1.18 tff(2280,plain,
% 1.30/1.18 (~c3_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[433, 2279])).
% 1.30/1.18 tff(2281,plain,
% 1.30/1.18 (c1_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[409, 2279])).
% 1.30/1.18 tff(2282,plain,
% 1.30/1.18 (c0_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[420, 2279])).
% 1.30/1.18 tff(2283,plain,
% 1.30/1.18 (~c2_1(a2285)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[1305, 181, 2282, 2281, 2175, 2280, 2185, 744, 2184])).
% 1.30/1.18 tff(2284,plain,
% 1.30/1.18 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.30/1.18 inference(bind,[status(th)],[])).
% 1.30/1.18 tff(2285,plain,
% 1.30/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(quant_intro,[status(thm)],[2284])).
% 1.30/1.18 tff(2286,plain,
% 1.30/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2287,plain,
% 1.30/1.18 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_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) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_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)) | (~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) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.30/1.18 inference(bind,[status(th)],[])).
% 1.30/1.18 tff(2288,plain,
% 1.30/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(quant_intro,[status(thm)],[2287])).
% 1.30/1.18 tff(2289,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.30/1.18 tff(2290,plain,
% 1.30/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.30/1.18 tff(2291,plain,
% 1.30/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2290, 2286])).
% 1.30/1.18 tff(2292,plain,(
% 1.30/1.18 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(skolemize,[status(sab)],[2291])).
% 1.30/1.18 tff(2293,plain,
% 1.30/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2292, 2285])).
% 1.30/1.18 tff(2294,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2295,plain,
% 1.30/1.18 ((hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2296,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285))))),
% 1.30/1.18 inference(monotonicity,[status(thm)],[2295])).
% 1.30/1.18 tff(2297,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 1.30/1.18 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.30/1.18 tff(2298,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 1.30/1.18 inference(quant_inst,[status(thm)],[])).
% 1.30/1.18 tff(2299,plain,
% 1.30/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285))),
% 1.30/1.18 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.30/1.18 tff(2300,plain,
% 1.30/1.18 (hskp11),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[2299, 181, 2282, 2280, 2185, 2173, 2293, 2184, 2283])).
% 1.30/1.18 tff(2301,plain,
% 1.30/1.18 (~c1_1(a2294)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[662, 2300])).
% 1.30/1.18 tff(2302,plain,
% 1.30/1.18 (c0_1(a2294)),
% 1.30/1.18 inference(unit_resolution,[status(thm)],[675, 2300])).
% 1.30/1.18 tff(2303,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2304,plain,
% 1.30/1.18 ((hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.30/1.18 inference(rewrite,[status(thm)],[])).
% 1.30/1.18 tff(2305,plain,
% 1.30/1.18 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[2304])).
% 1.39/1.18 tff(2306,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.39/1.18 tff(2307,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(2308,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.39/1.18 tff(2309,plain,
% 1.39/1.18 (hskp19),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2308, 181, 994, 983, 2281, 972, 2280, 2095, 2283])).
% 1.39/1.18 tff(2310,plain,
% 1.39/1.18 (~c3_1(a2316)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1982, 2309])).
% 1.39/1.18 tff(2311,plain,
% 1.39/1.18 (~c2_1(a2316)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1988, 2309])).
% 1.39/1.18 tff(2312,plain,
% 1.39/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2313,plain,
% 1.39/1.18 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2314,plain,
% 1.39/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0)))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[2313])).
% 1.39/1.18 tff(2315,plain,
% 1.39/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 1.39/1.18 inference(transitivity,[status(thm)],[2314, 2312])).
% 1.39/1.18 tff(2316,plain,
% 1.39/1.18 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(2317,plain,
% 1.39/1.18 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.39/1.18 tff(2318,plain,
% 1.39/1.18 (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2317, 181, 40, 526])).
% 1.39/1.18 tff(2319,plain,
% 1.39/1.18 (hskp2),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2318, 461, 2104, 2174])).
% 1.39/1.18 tff(2320,plain,
% 1.39/1.18 (~c3_1(a2279)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[533, 2319])).
% 1.39/1.18 tff(2321,plain,
% 1.39/1.18 (~c2_1(a2279)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[539, 2319])).
% 1.39/1.18 tff(2322,plain,
% 1.39/1.18 (c0_1(a2279)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[550, 2319])).
% 1.39/1.18 tff(2323,assumption,(~c3_1(a2279)), introduced(assumption)).
% 1.39/1.18 tff(2324,assumption,(~c2_1(a2279)), introduced(assumption)).
% 1.39/1.18 tff(2325,plain,
% 1.39/1.18 (~hskp13),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1343, 1276, 399])).
% 1.39/1.18 tff(2326,plain,
% 1.39/1.18 (hskp12),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1361, 2325])).
% 1.39/1.18 tff(2327,plain,
% 1.39/1.18 (~c3_1(a2295)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[710, 2326])).
% 1.39/1.18 tff(2328,plain,
% 1.39/1.18 (~c1_1(a2295)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1368, 2326])).
% 1.39/1.18 tff(2329,assumption,(c0_1(a2279)), introduced(assumption)).
% 1.39/1.18 tff(2330,plain,
% 1.39/1.18 (c0_1(a2295)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[721, 2326])).
% 1.39/1.18 tff(2331,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2332,plain,
% 1.39/1.18 ((hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2333,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[2332])).
% 1.39/1.18 tff(2334,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[2333, 2331])).
% 1.39/1.18 tff(2335,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(2336,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.39/1.18 tff(2337,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2336, 181, 1276, 2330, 2329, 2328, 2327, 2324, 2323, 284])).
% 1.39/1.18 tff(2338,plain,(hskp23 | (~c0_1(a2279)) | c2_1(a2279) | c3_1(a2279) | (~hskp6)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(2339,plain,
% 1.39/1.18 (hskp23),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2338, 2322, 2321, 2320, 2279])).
% 1.39/1.18 tff(2340,plain,
% 1.39/1.18 (~c2_1(a2327)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[302, 2339])).
% 1.39/1.18 tff(2341,plain,
% 1.39/1.18 (~c0_1(a2327)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[326, 2339])).
% 1.39/1.18 tff(2342,plain,
% 1.39/1.18 (c3_1(a2327)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[313, 2339])).
% 1.39/1.18 tff(2343,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2344,plain,
% 1.39/1.18 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316)) <=> (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2345,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[2344])).
% 1.39/1.18 tff(2346,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[2345, 2343])).
% 1.39/1.18 tff(2347,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(2348,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 1.39/1.18 tff(2349,plain,
% 1.39/1.18 (c0_1(a2316)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[2348, 181, 2342, 2175, 2341, 2340, 2311, 2310, 2185, 1273, 2184])).
% 1.39/1.18 tff(2350,plain,
% 1.39/1.18 (c0_1(a2306)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1388, 181, 2342, 2175, 2341, 2340, 397, 396, 2185, 1273, 2184])).
% 1.39/1.18 tff(2351,plain,
% 1.39/1.18 (hskp8),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1406, 2350])).
% 1.39/1.18 tff(2352,plain,
% 1.39/1.18 (c2_1(a2287)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1428, 2351])).
% 1.39/1.18 tff(2353,plain,
% 1.39/1.18 (c0_1(a2287)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1417, 2351])).
% 1.39/1.18 tff(2354,plain,
% 1.39/1.18 (c1_1(a2316)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1999, 2309])).
% 1.39/1.18 tff(2355,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2356,plain,
% 1.39/1.18 ((hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316))) <=> (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(2357,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316))))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[2356])).
% 1.39/1.19 tff(2358,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[2357, 2355])).
% 1.39/1.19 tff(2359,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2360,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 1.40/1.19 tff(2361,plain,
% 1.40/1.19 (~c3_1(a2287)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2360, 181, 461, 2354, 2353, 2352, 2310, 1451, 2349])).
% 1.40/1.19 tff(2362,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2363,plain,
% 1.40/1.19 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2364,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2363])).
% 1.40/1.19 tff(2365,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2364, 2362])).
% 1.40/1.19 tff(2366,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2367,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.40/1.19 tff(2368,plain,
% 1.40/1.19 (~c1_1(a2327)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2367, 181, 41, 2342, 2104, 2174, 2340, 40, 460])).
% 1.40/1.19 tff(2369,plain,
% 1.40/1.19 (((~hskp8) | (~c1_1(a2287))) <=> ((~hskp8) | (~c1_1(a2287)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2370,plain,
% 1.40/1.19 (((~c1_1(a2287)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a2287)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2371,axiom,((~c1_1(a2287)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.40/1.19 tff(2372,plain,
% 1.40/1.19 ((~hskp8) | (~c1_1(a2287))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 1.40/1.19 tff(2373,plain,
% 1.40/1.19 ((~hskp8) | (~c1_1(a2287))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2372, 2369])).
% 1.40/1.19 tff(2374,plain,
% 1.40/1.19 (~c1_1(a2287)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2373, 2351])).
% 1.40/1.19 tff(2375,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2376,plain,
% 1.40/1.19 ((hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2377,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327)))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2376])).
% 1.40/1.19 tff(2378,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2377, 2375])).
% 1.40/1.19 tff(2379,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2380,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327)),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2379, 2378])).
% 1.40/1.19 tff(2381,plain,
% 1.40/1.19 ($false),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2380, 181, 2105, 2352, 2341, 2340, 2374, 227, 2368, 2361])).
% 1.40/1.19 tff(2382,plain,(hskp3 | c1_1(a2306) | c3_1(a2306) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.19 tff(2383,plain,
% 1.40/1.19 (hskp3),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2382, 41, 396, 398, 2104, 2174, 40, 397])).
% 1.40/1.19 tff(2384,plain,
% 1.40/1.19 (~c2_1(a2280)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[574, 2383])).
% 1.40/1.19 tff(2385,plain,
% 1.40/1.19 (c3_1(a2280)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[585, 2383])).
% 1.40/1.19 tff(2386,plain,
% 1.40/1.19 (c1_1(a2280)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[596, 2383])).
% 1.40/1.19 tff(2387,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2388,plain,
% 1.40/1.19 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2389,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280))))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2388])).
% 1.40/1.19 tff(2390,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.40/1.19 tff(2391,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2392,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.40/1.19 tff(2393,plain,
% 1.40/1.19 ($false),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2392, 181, 41, 2386, 2385, 2104, 2174, 2384, 40, 460])).
% 1.40/1.19 tff(2394,plain,(hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c3_1(a2306) | c1_1(a2306) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.19 tff(2395,plain,
% 1.40/1.19 (hskp28),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2394, 398, 2174, 40, 396, 2104, 397])).
% 1.40/1.19 tff(2396,plain,
% 1.40/1.19 (c3_1(a2278)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[614, 2395])).
% 1.40/1.19 tff(2397,plain,
% 1.40/1.19 (c1_1(a2278)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[625, 2395])).
% 1.40/1.19 tff(2398,plain,
% 1.40/1.19 (c0_1(a2278)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[636, 2395])).
% 1.40/1.19 tff(2399,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2400,plain,
% 1.40/1.19 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294))) <=> (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2401,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294))))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2400])).
% 1.40/1.19 tff(2402,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.40/1.19 tff(2403,plain,
% 1.40/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2404,plain,
% 1.40/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.40/1.19 tff(2405,plain,
% 1.40/1.19 (~c3_1(a2294)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2404, 181, 2398, 2397, 2396, 2302, 2282, 2281, 2301, 94, 2283])).
% 1.40/1.19 tff(2406,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2407,plain,
% 1.40/1.19 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2408,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294))))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2407])).
% 1.40/1.19 tff(2409,plain,
% 1.40/1.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2408, 2406])).
% 1.40/1.19 tff(2410,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2411,plain,
% 1.40/1.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.40/1.19 tff(2412,plain,
% 1.40/1.19 (~c2_1(a2278)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2411, 181, 2105, 2398, 2397, 2302, 2301, 2139, 2405])).
% 1.40/1.19 tff(2413,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2414,plain,
% 1.40/1.19 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2415,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2414])).
% 1.40/1.19 tff(2416,plain,
% 1.40/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2415, 2413])).
% 1.40/1.19 tff(2417,plain,
% 1.40/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2418,plain,
% 1.40/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.40/1.19 tff(2419,plain,
% 1.40/1.19 (~c0_1(a2323)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2418, 181, 2398, 2397, 2396, 1003, 2282, 2281, 1002, 94, 2283])).
% 1.40/1.19 tff(2420,plain,
% 1.40/1.19 ($false),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2126, 181, 2397, 2396, 1004, 1003, 1002, 217, 2419, 2412])).
% 1.40/1.19 tff(2421,plain,(c1_1(a2306) | c1_1(a2277) | c2_1(a2277) | c3_1(a2306) | c0_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.19 tff(2422,plain,
% 1.40/1.19 ($false),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2421, 2273, 2272, 40, 2271, 2104, 2174])).
% 1.40/1.19 tff(2423,plain,(c1_1(a2277) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.19 tff(2424,plain,
% 1.40/1.19 (c1_1(a2277)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2423, 2104, 40])).
% 1.40/1.19 tff(2425,plain,
% 1.40/1.19 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2083, 181, 1004, 1003, 2175, 1002, 2185, 40, 217])).
% 1.40/1.19 tff(2426,plain,
% 1.40/1.19 (~c3_1(a2277)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2425, 43, 2424])).
% 1.40/1.19 tff(2427,plain,
% 1.40/1.19 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2428,plain,
% 1.40/1.19 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277)) <=> (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2429,plain,
% 1.40/1.19 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)))),
% 1.40/1.19 inference(monotonicity,[status(thm)],[2428])).
% 1.40/1.19 tff(2430,plain,
% 1.40/1.19 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 1.40/1.19 inference(transitivity,[status(thm)],[2429, 2427])).
% 1.40/1.19 tff(2431,plain,
% 1.40/1.19 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))),
% 1.40/1.19 inference(quant_inst,[status(thm)],[])).
% 1.40/1.19 tff(2432,plain,
% 1.40/1.19 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.40/1.19 tff(2433,plain,
% 1.40/1.19 (hskp28 | hskp9 | c0_1(a2277) | c3_1(a2277)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2432, 181, 40, 1047])).
% 1.40/1.19 tff(2434,plain,
% 1.40/1.19 (hskp9),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2433, 2426, 2104, 41])).
% 1.40/1.19 tff(2435,plain,
% 1.40/1.19 (~c2_1(a2291)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[1015, 2434])).
% 1.40/1.19 tff(2436,plain,
% 1.40/1.19 (~c1_1(a2291)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[1021, 2434])).
% 1.40/1.19 tff(2437,plain,
% 1.40/1.19 (~c0_1(a2291)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[1027, 2434])).
% 1.40/1.19 tff(2438,plain,
% 1.40/1.19 ($false),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[1034, 181, 2105, 2175, 2437, 2436, 2435, 2173, 227, 43])).
% 1.40/1.19 tff(2439,plain,(c1_1(a2282) | c0_1(a2277) | hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.19 tff(2440,plain,
% 1.40/1.19 (c1_1(a2282)),
% 1.40/1.19 inference(unit_resolution,[status(thm)],[2439, 2171, 2104, 40])).
% 1.40/1.19 tff(2441,plain,
% 1.40/1.19 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.40/1.19 inference(bind,[status(th)],[])).
% 1.40/1.19 tff(2442,plain,
% 1.40/1.19 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(quant_intro,[status(thm)],[2441])).
% 1.40/1.19 tff(2443,plain,
% 1.40/1.19 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(rewrite,[status(thm)],[])).
% 1.40/1.19 tff(2444,plain,
% 1.40/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.40/1.19 inference(bind,[status(th)],[])).
% 1.40/1.19 tff(2445,plain,
% 1.40/1.19 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(quant_intro,[status(thm)],[2444])).
% 1.40/1.19 tff(2446,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.40/1.19 tff(2447,plain,
% 1.40/1.19 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.40/1.19 tff(2448,plain,
% 1.40/1.19 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2447, 2443])).
% 1.40/1.19 tff(2449,plain,(
% 1.40/1.19 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(skolemize,[status(sab)],[2448])).
% 1.40/1.19 tff(2450,plain,
% 1.40/1.19 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.40/1.19 inference(modus_ponens,[status(thm)],[2449, 2442])).
% 1.40/1.19 tff(2451,plain,
% 1.40/1.19 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2452,plain,
% 1.40/1.20 ((hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277))) <=> (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2453,plain,
% 1.40/1.20 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2452])).
% 1.40/1.20 tff(2454,plain,
% 1.40/1.20 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2453, 2451])).
% 1.40/1.20 tff(2455,plain,
% 1.40/1.20 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2456,plain,
% 1.40/1.20 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.40/1.20 tff(2457,plain,
% 1.40/1.20 (hskp28 | hskp8 | c0_1(a2277) | (~c1_1(a2277))),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2456, 181, 40, 2450])).
% 1.40/1.20 tff(2458,plain,
% 1.40/1.20 (hskp8),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2457, 2171, 2104, 2424])).
% 1.40/1.20 tff(2459,plain,
% 1.40/1.20 (c2_1(a2287)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1428, 2458])).
% 1.40/1.20 tff(2460,plain,
% 1.40/1.20 (c0_1(a2287)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1417, 2458])).
% 1.40/1.20 tff(2461,plain,
% 1.40/1.20 (c3_1(a2287)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1440, 2460, 2459, 2175, 2185, 2173, 2440])).
% 1.40/1.20 tff(2462,plain,
% 1.40/1.20 (c1_1(a2282)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2439, 41, 2104, 40])).
% 1.40/1.20 tff(2463,plain,
% 1.40/1.20 (~hskp10),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1235, 2462, 2185, 2173, 2175])).
% 1.40/1.20 tff(2464,plain,
% 1.40/1.20 (c3_1(a2277)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2203, 2463, 2104, 1166])).
% 1.40/1.20 tff(2465,plain,
% 1.40/1.20 (c0_1(a2306)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1295, 2463, 397, 1166])).
% 1.40/1.20 tff(2466,plain,
% 1.40/1.20 (hskp23),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1277, 2465])).
% 1.40/1.20 tff(2467,plain,
% 1.40/1.20 (~c2_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[302, 2466])).
% 1.40/1.20 tff(2468,plain,
% 1.40/1.20 (~c0_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[326, 2466])).
% 1.40/1.20 tff(2469,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2470,plain,
% 1.40/1.20 ((hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2471,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327)))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2470])).
% 1.40/1.20 tff(2472,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2471, 2469])).
% 1.40/1.20 tff(2473,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2474,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327)),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.40/1.20 tff(2475,plain,
% 1.40/1.20 (c1_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2474, 181, 41, 2424, 2468, 2467, 40, 460, 2464])).
% 1.40/1.20 tff(2476,plain,
% 1.40/1.20 (~hskp16),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1461, 2463, 1166])).
% 1.40/1.20 tff(2477,plain,
% 1.40/1.20 (hskp26),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1130, 2476, 41])).
% 1.40/1.20 tff(2478,plain,
% 1.40/1.20 (~c1_1(a2345)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1147, 2477])).
% 1.40/1.20 tff(2479,plain,
% 1.40/1.20 (~c0_1(a2345)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1153, 2477])).
% 1.40/1.20 tff(2480,plain,
% 1.40/1.20 (c3_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[313, 2466])).
% 1.40/1.20 tff(2481,plain,
% 1.40/1.20 (c3_1(a2345)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1164, 2477])).
% 1.40/1.20 tff(2482,plain,
% 1.40/1.20 (~c2_1(a2345)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1470, 181, 2481, 2480, 2479, 2478, 2467, 217, 2475])).
% 1.40/1.20 tff(2483,plain,
% 1.40/1.20 ($false),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1477, 181, 41, 2480, 2479, 2478, 2467, 460, 2475, 2482])).
% 1.40/1.20 tff(2484,plain,(hskp28 | hskp6 | c2_1(a2277) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.20 tff(2485,plain,
% 1.40/1.20 (hskp6),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2484, 2171, 40, 398, 397, 396, 2104])).
% 1.40/1.20 tff(2486,plain,
% 1.40/1.20 (~c3_1(a2285)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[433, 2485])).
% 1.40/1.20 tff(2487,plain,
% 1.40/1.20 (c1_1(a2285)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[409, 2485])).
% 1.40/1.20 tff(2488,plain,
% 1.40/1.20 (c0_1(a2285)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[420, 2485])).
% 1.40/1.20 tff(2489,plain,
% 1.40/1.20 (hskp3 | (~c3_1(a2287))),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1517, 181, 2460, 2459, 2488, 2487, 2486, 1451])).
% 1.40/1.20 tff(2490,plain,
% 1.40/1.20 (hskp3),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2489, 2461])).
% 1.40/1.20 tff(2491,plain,
% 1.40/1.20 (~c2_1(a2280)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[574, 2490])).
% 1.40/1.20 tff(2492,plain,
% 1.40/1.20 (c3_1(a2280)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[585, 2490])).
% 1.40/1.20 tff(2493,plain,
% 1.40/1.20 (c1_1(a2280)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[596, 2490])).
% 1.40/1.20 tff(2494,plain,
% 1.40/1.20 (c1_1(a2302)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1527, 181, 1004, 1003, 994, 2493, 2492, 1002, 972, 2491, 217])).
% 1.40/1.20 tff(2495,plain,
% 1.40/1.20 (c0_1(a2306)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[603, 181, 2171, 2493, 2492, 398, 397, 2491, 460])).
% 1.40/1.20 tff(2496,plain,
% 1.40/1.20 (hskp23),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1277, 2495])).
% 1.40/1.20 tff(2497,plain,
% 1.40/1.20 (~c2_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[302, 2496])).
% 1.40/1.20 tff(2498,plain,
% 1.40/1.20 (~c0_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[326, 2496])).
% 1.40/1.20 tff(2499,plain,
% 1.40/1.20 (c1_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1534, 181, 2171, 2493, 2492, 2498, 2497, 2491, 460])).
% 1.40/1.20 tff(2500,plain,
% 1.40/1.20 (c3_1(a2327)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[313, 2496])).
% 1.40/1.20 tff(2501,plain,
% 1.40/1.20 (~hskp26),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1479, 2171, 2500, 2497, 2499])).
% 1.40/1.20 tff(2502,plain,
% 1.40/1.20 (hskp16),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1130, 2501, 2171])).
% 1.40/1.20 tff(2503,plain,
% 1.40/1.20 (~c3_1(a2304)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1094, 2502])).
% 1.40/1.20 tff(2504,plain,
% 1.40/1.20 (~c2_1(a2304)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1100, 2502])).
% 1.40/1.20 tff(2505,plain,
% 1.40/1.20 (~c0_1(a2304)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1106, 2502])).
% 1.40/1.20 tff(2506,plain,
% 1.40/1.20 ($false),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1546, 181, 2500, 994, 2498, 2497, 2505, 2504, 2503, 972, 1273, 2494])).
% 1.40/1.20 tff(2507,plain,(c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.20 tff(2508,plain,
% 1.40/1.20 (c1_1(a2306)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2507, 397, 396, 40, 2104])).
% 1.40/1.20 tff(2509,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2510,plain,
% 1.40/1.20 ((hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2511,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2510])).
% 1.40/1.20 tff(2512,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2511, 2509])).
% 1.40/1.20 tff(2513,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2514,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 1.40/1.20 tff(2515,plain,
% 1.40/1.20 (hskp19 | (~c1_1(a2306))),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2514, 181, 994, 983, 397, 396, 972, 2095])).
% 1.40/1.20 tff(2516,plain,
% 1.40/1.20 (hskp19),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2515, 2508])).
% 1.40/1.20 tff(2517,plain,
% 1.40/1.20 (~hskp17),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[266, 2508])).
% 1.40/1.20 tff(2518,plain,
% 1.40/1.20 (~c1_1(a2302)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2008, 2517, 2516])).
% 1.40/1.20 tff(2519,plain,
% 1.40/1.20 (hskp17 | (~c1_1(a2306)) | (~c1_1(a2282))),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1566, 181, 2175, 397, 396, 2185, 1560])).
% 1.40/1.20 tff(2520,plain,
% 1.40/1.20 (~c1_1(a2282)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2519, 2517, 2508])).
% 1.40/1.20 tff(2521,plain,
% 1.40/1.20 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.40/1.20 inference(bind,[status(th)],[])).
% 1.40/1.20 tff(2522,plain,
% 1.40/1.20 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(quant_intro,[status(thm)],[2521])).
% 1.40/1.20 tff(2523,plain,
% 1.40/1.20 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2524,plain,
% 1.40/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_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)) | hskp0) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_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)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.40/1.20 inference(bind,[status(th)],[])).
% 1.40/1.20 tff(2525,plain,
% 1.40/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(quant_intro,[status(thm)],[2524])).
% 1.40/1.20 tff(2526,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)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.40/1.20 tff(2527,plain,
% 1.40/1.20 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 1.40/1.20 tff(2528,plain,
% 1.40/1.20 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2527, 2523])).
% 1.40/1.20 tff(2529,plain,(
% 1.40/1.20 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(skolemize,[status(sab)],[2528])).
% 1.40/1.20 tff(2530,plain,
% 1.40/1.20 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2529, 2522])).
% 1.40/1.20 tff(2531,plain,
% 1.40/1.20 (hskp28),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2439, 2520, 2104, 40])).
% 1.40/1.20 tff(2532,plain,
% 1.40/1.20 (c3_1(a2278)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[614, 2531])).
% 1.40/1.20 tff(2533,plain,
% 1.40/1.20 (c1_1(a2278)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[625, 2531])).
% 1.40/1.20 tff(2534,plain,
% 1.40/1.20 (c0_1(a2278)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[636, 2531])).
% 1.40/1.20 tff(2535,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2536,plain,
% 1.40/1.20 ((hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2537,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2536])).
% 1.40/1.20 tff(2538,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2537, 2535])).
% 1.40/1.20 tff(2539,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2540,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 1.40/1.20 tff(2541,plain,
% 1.40/1.20 (hskp0),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2540, 181, 2534, 2533, 2532, 2175, 2173, 2530, 2520])).
% 1.40/1.20 tff(2542,plain,
% 1.40/1.20 (~c0_1(a2276)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[888, 2541])).
% 1.40/1.20 tff(2543,plain,
% 1.40/1.20 (~c3_1(a2316)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1982, 2516])).
% 1.40/1.20 tff(2544,plain,
% 1.40/1.20 (~c2_1(a2316)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1988, 2516])).
% 1.40/1.20 tff(2545,plain,
% 1.40/1.20 (c1_1(a2276)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[910, 2541])).
% 1.40/1.20 tff(2546,plain,
% 1.40/1.20 (c1_1(a2316)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[1999, 2516])).
% 1.40/1.20 tff(2547,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2548,plain,
% 1.40/1.20 ((hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276))) <=> (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2549,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2548])).
% 1.40/1.20 tff(2550,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.40/1.20 tff(2551,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2552,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.40/1.20 tff(2553,plain,
% 1.40/1.20 (~c2_1(a2276)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2552, 181, 2517, 2546, 2545, 2544, 2543, 2542, 1560])).
% 1.40/1.20 tff(2554,plain,
% 1.40/1.20 (c3_1(a2276)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[899, 2541])).
% 1.40/1.20 tff(2555,plain,
% 1.40/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2556,plain,
% 1.40/1.20 (((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2557,plain,
% 1.40/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2556])).
% 1.40/1.20 tff(2558,plain,
% 1.40/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.40/1.20 tff(2559,plain,
% 1.40/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2560,plain,
% 1.40/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.40/1.20 tff(2561,plain,
% 1.40/1.20 ($false),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2560, 181, 1004, 1003, 994, 2545, 2554, 1002, 972, 217, 2553, 2518])).
% 1.40/1.20 tff(2562,plain,(c2_1(a2306) | c0_1(a2277) | c2_1(a2277) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.20 tff(2563,plain,
% 1.40/1.20 (c2_1(a2306)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2562, 396, 40, 2104])).
% 1.40/1.20 tff(2564,plain,
% 1.40/1.20 (~hskp17),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[260, 2563])).
% 1.40/1.20 tff(2565,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2566,plain,
% 1.40/1.20 ((hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.20 inference(rewrite,[status(thm)],[])).
% 1.40/1.20 tff(2567,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 1.40/1.20 inference(monotonicity,[status(thm)],[2566])).
% 1.40/1.20 tff(2568,plain,
% 1.40/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.20 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.40/1.20 tff(2569,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.20 inference(quant_inst,[status(thm)],[])).
% 1.40/1.20 tff(2570,plain,
% 1.40/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 1.40/1.20 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.40/1.20 tff(2571,plain,
% 1.40/1.20 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282))),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2570, 181, 2175, 2185, 40, 1560])).
% 1.40/1.20 tff(2572,plain,
% 1.40/1.20 (c3_1(a2277)),
% 1.40/1.20 inference(unit_resolution,[status(thm)],[2571, 2462, 2424, 2564])).
% 1.40/1.20 tff(2573,plain,
% 1.40/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2574,plain,
% 1.40/1.21 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2575,plain,
% 1.40/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2574])).
% 1.40/1.21 tff(2576,plain,
% 1.40/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2575, 2573])).
% 1.40/1.21 tff(2577,plain,
% 1.40/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2578,plain,
% 1.40/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 1.40/1.21 tff(2579,plain,
% 1.40/1.21 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2302)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2578, 181, 1004, 1003, 994, 1002, 972, 40, 217])).
% 1.40/1.21 tff(2580,plain,
% 1.40/1.21 (c1_1(a2302)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2579, 2572, 2424])).
% 1.40/1.21 tff(2581,plain,
% 1.40/1.21 ((~c2_1(a2306)) | (~c1_1(a2282)) | (~c0_1(a2306))),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1793, 181, 2175, 396, 2185, 2173, 744])).
% 1.40/1.21 tff(2582,plain,
% 1.40/1.21 (~c0_1(a2306)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2581, 2462, 2563])).
% 1.40/1.21 tff(2583,plain,
% 1.40/1.21 (~hskp19),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2008, 2580, 2564])).
% 1.40/1.21 tff(2584,plain,
% 1.40/1.21 (^[U: $i] : refl((hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.40/1.21 inference(bind,[status(th)],[])).
% 1.40/1.21 tff(2585,plain,
% 1.40/1.21 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(quant_intro,[status(thm)],[2584])).
% 1.40/1.21 tff(2586,plain,
% 1.40/1.21 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2587,plain,
% 1.40/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.40/1.21 inference(bind,[status(th)],[])).
% 1.40/1.21 tff(2588,plain,
% 1.40/1.21 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(quant_intro,[status(thm)],[2587])).
% 1.40/1.21 tff(2589,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.40/1.21 tff(2590,plain,
% 1.40/1.21 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 1.40/1.21 tff(2591,plain,
% 1.40/1.21 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2590, 2586])).
% 1.40/1.21 tff(2592,plain,(
% 1.40/1.21 ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(skolemize,[status(sab)],[2591])).
% 1.40/1.21 tff(2593,plain,
% 1.40/1.21 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2592, 2585])).
% 1.40/1.21 tff(2594,plain,
% 1.40/1.21 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2595,plain,
% 1.40/1.21 ((hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2596,plain,
% 1.40/1.21 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2595])).
% 1.40/1.21 tff(2597,plain,
% 1.40/1.21 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2596, 2594])).
% 1.40/1.21 tff(2598,plain,
% 1.40/1.21 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2599,plain,
% 1.40/1.21 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.40/1.21 tff(2600,plain,
% 1.40/1.21 (hskp19 | hskp7 | (~c1_1(a2282))),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2599, 181, 2175, 2173, 2593])).
% 1.40/1.21 tff(2601,plain,
% 1.40/1.21 (hskp7),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2600, 2583, 2462])).
% 1.40/1.21 tff(2602,plain,
% 1.40/1.21 (~c2_1(a2286)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1053, 2601])).
% 1.40/1.21 tff(2603,plain,
% 1.40/1.21 (hskp8),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2457, 41, 2104, 2424])).
% 1.40/1.21 tff(2604,plain,
% 1.40/1.21 (c0_1(a2287)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1417, 2603])).
% 1.40/1.21 tff(2605,plain,
% 1.40/1.21 (c2_1(a2287)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1428, 2603])).
% 1.40/1.21 tff(2606,plain,
% 1.40/1.21 (c3_1(a2287)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1440, 2462, 2605, 2175, 2185, 2173, 2604])).
% 1.40/1.21 tff(2607,plain,
% 1.40/1.21 (~c1_1(a2287)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2373, 2603])).
% 1.40/1.21 tff(2608,plain,
% 1.40/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2609,plain,
% 1.40/1.21 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306))) <=> (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2610,plain,
% 1.40/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306)))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2609])).
% 1.40/1.21 tff(2611,plain,
% 1.40/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2610, 2608])).
% 1.40/1.21 tff(2612,plain,
% 1.40/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2613,plain,
% 1.40/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 1.40/1.21 tff(2614,plain,
% 1.40/1.21 (c1_1(a2306)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2613, 181, 2605, 2424, 2563, 2607, 40, 217, 2572, 2582, 2606])).
% 1.40/1.21 tff(2615,plain,
% 1.40/1.21 (c1_1(a2286)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[1078, 2601])).
% 1.40/1.21 tff(2616,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2617,plain,
% 1.40/1.21 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306))) <=> (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2618,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306)))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2617])).
% 1.40/1.21 tff(2619,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2618, 2616])).
% 1.40/1.21 tff(2620,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2621,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 1.40/1.21 tff(2622,plain,
% 1.40/1.21 (c3_1(a2286)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2621, 181, 2564, 2615, 2614, 2563, 2602, 1560, 2582])).
% 1.40/1.21 tff(2623,plain,
% 1.40/1.21 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.40/1.21 inference(bind,[status(th)],[])).
% 1.40/1.21 tff(2624,plain,
% 1.40/1.21 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(quant_intro,[status(thm)],[2623])).
% 1.40/1.21 tff(2625,plain,
% 1.40/1.21 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2626,plain,
% 1.40/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.40/1.21 inference(bind,[status(th)],[])).
% 1.40/1.21 tff(2627,plain,
% 1.40/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(quant_intro,[status(thm)],[2626])).
% 1.40/1.21 tff(2628,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.40/1.21 tff(2629,plain,
% 1.40/1.21 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.40/1.21 tff(2630,plain,
% 1.40/1.21 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2629, 2625])).
% 1.40/1.21 tff(2631,plain,(
% 1.40/1.21 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(skolemize,[status(sab)],[2630])).
% 1.40/1.21 tff(2632,plain,
% 1.40/1.21 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2631, 2624])).
% 1.40/1.21 tff(2633,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2634,plain,
% 1.40/1.21 ((hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2635,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2634])).
% 1.40/1.21 tff(2636,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2635, 2633])).
% 1.40/1.21 tff(2637,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2638,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.40/1.21 tff(2639,plain,
% 1.40/1.21 (hskp18),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2638, 181, 994, 2604, 2605, 972, 2632, 2580, 2606])).
% 1.40/1.21 tff(2640,plain,
% 1.40/1.21 (((~hskp18) | (~c2_1(a2308))) <=> ((~hskp18) | (~c2_1(a2308)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2641,plain,
% 1.40/1.21 (((~c2_1(a2308)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2308)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2642,axiom,((~c2_1(a2308)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.40/1.21 tff(2643,plain,
% 1.40/1.21 ((~hskp18) | (~c2_1(a2308))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.40/1.21 tff(2644,plain,
% 1.40/1.21 ((~hskp18) | (~c2_1(a2308))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2643, 2640])).
% 1.40/1.21 tff(2645,plain,
% 1.40/1.21 (~c2_1(a2308)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2644, 2639])).
% 1.40/1.21 tff(2646,plain,
% 1.40/1.21 (((~hskp18) | (~c1_1(a2308))) <=> ((~hskp18) | (~c1_1(a2308)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2647,plain,
% 1.40/1.21 (((~c1_1(a2308)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a2308)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2648,axiom,((~c1_1(a2308)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.40/1.21 tff(2649,plain,
% 1.40/1.21 ((~hskp18) | (~c1_1(a2308))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.40/1.21 tff(2650,plain,
% 1.40/1.21 ((~hskp18) | (~c1_1(a2308))),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2649, 2646])).
% 1.40/1.21 tff(2651,plain,
% 1.40/1.21 (~c1_1(a2308)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2650, 2639])).
% 1.40/1.21 tff(2652,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2653,plain,
% 1.40/1.21 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308)) <=> (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2654,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308)))),
% 1.40/1.21 inference(monotonicity,[status(thm)],[2653])).
% 1.40/1.21 tff(2655,plain,
% 1.40/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 1.40/1.21 inference(transitivity,[status(thm)],[2654, 2652])).
% 1.40/1.21 tff(2656,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))),
% 1.40/1.21 inference(quant_inst,[status(thm)],[])).
% 1.40/1.21 tff(2657,plain,
% 1.40/1.21 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 1.40/1.21 tff(2658,plain,
% 1.40/1.21 (c0_1(a2308)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2657, 181, 41, 2615, 2651, 2645, 2602, 460, 2622])).
% 1.40/1.21 tff(2659,plain,
% 1.40/1.21 (((~hskp18) | c3_1(a2308)) <=> ((~hskp18) | c3_1(a2308))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2660,axiom,((~hskp18) | c3_1(a2308)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.40/1.21 tff(2661,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 1.40/1.21 tff(2662,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2661, 2659])).
% 1.40/1.21 tff(2663,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2662, 2659])).
% 1.40/1.21 tff(2664,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2663, 2659])).
% 1.40/1.21 tff(2665,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2664, 2659])).
% 1.40/1.21 tff(2666,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2665, 2659])).
% 1.40/1.21 tff(2667,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2666, 2659])).
% 1.40/1.21 tff(2668,plain,
% 1.40/1.21 ((~hskp18) | c3_1(a2308)),
% 1.40/1.21 inference(modus_ponens,[status(thm)],[2667, 2659])).
% 1.40/1.21 tff(2669,plain,
% 1.40/1.21 (c3_1(a2308)),
% 1.40/1.21 inference(unit_resolution,[status(thm)],[2668, 2639])).
% 1.40/1.21 tff(2670,plain,
% 1.40/1.21 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 1.40/1.21 inference(rewrite,[status(thm)],[])).
% 1.40/1.21 tff(2671,plain,
% 1.40/1.21 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308))) <=> (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 1.40/1.22 inference(rewrite,[status(thm)],[])).
% 1.40/1.22 tff(2672,plain,
% 1.40/1.22 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308))))),
% 1.40/1.22 inference(monotonicity,[status(thm)],[2671])).
% 1.40/1.22 tff(2673,plain,
% 1.40/1.22 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 1.40/1.22 inference(transitivity,[status(thm)],[2672, 2670])).
% 1.40/1.22 tff(2674,plain,
% 1.40/1.22 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))),
% 1.40/1.22 inference(quant_inst,[status(thm)],[])).
% 1.40/1.22 tff(2675,plain,
% 1.40/1.22 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308))),
% 1.40/1.22 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 1.40/1.22 tff(2676,plain,
% 1.40/1.22 (hskp12 | (~c0_1(a2308))),
% 1.40/1.22 inference(unit_resolution,[status(thm)],[2675, 181, 2583, 2669, 2645, 10])).
% 1.40/1.22 tff(2677,plain,
% 1.40/1.22 (hskp12),
% 1.40/1.22 inference(unit_resolution,[status(thm)],[2676, 2658])).
% 1.40/1.22 tff(2678,plain,
% 1.40/1.22 (~c3_1(a2295)),
% 1.40/1.22 inference(unit_resolution,[status(thm)],[710, 2677])).
% 1.40/1.22 tff(2679,plain,
% 1.40/1.22 (c0_1(a2295)),
% 1.40/1.22 inference(unit_resolution,[status(thm)],[721, 2677])).
% 1.40/1.22 tff(2680,plain,
% 1.40/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.40/1.22 inference(rewrite,[status(thm)],[])).
% 1.40/1.22 tff(2681,plain,
% 1.40/1.22 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.40/1.22 inference(rewrite,[status(thm)],[])).
% 1.40/1.22 tff(2682,plain,
% 1.40/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 1.40/1.22 inference(monotonicity,[status(thm)],[2681])).
% 1.40/1.22 tff(2683,plain,
% 1.40/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.43/1.22 tff(2684,plain,
% 1.43/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2685,plain,
% 1.43/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.43/1.22 tff(2686,plain,
% 1.43/1.22 (~c2_1(a2295)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2685, 181, 994, 2679, 2614, 2563, 396, 972, 2678, 744, 2580])).
% 1.43/1.22 tff(2687,plain,
% 1.43/1.22 (~c1_1(a2295)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1368, 2677])).
% 1.43/1.22 tff(2688,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2689,plain,
% 1.43/1.22 ((hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2690,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2689])).
% 1.43/1.22 tff(2691,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2690, 2688])).
% 1.43/1.22 tff(2692,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2693,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 1.43/1.22 tff(2694,plain,
% 1.43/1.22 (hskp23),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2693, 181, 2679, 2687, 2678, 284, 2686])).
% 1.43/1.22 tff(2695,plain,
% 1.43/1.22 (~c2_1(a2327)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[302, 2694])).
% 1.43/1.22 tff(2696,plain,
% 1.43/1.22 (c3_1(a2327)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[313, 2694])).
% 1.43/1.22 tff(2697,plain,
% 1.43/1.22 (~c0_1(a2327)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[326, 2694])).
% 1.43/1.22 tff(2698,plain,
% 1.43/1.22 (c1_1(a2327)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1497, 181, 41, 2615, 2697, 2695, 2602, 460, 2622])).
% 1.43/1.22 tff(2699,plain,
% 1.43/1.22 (~hskp26),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1479, 2698, 2696, 2695, 41])).
% 1.43/1.22 tff(2700,plain,
% 1.43/1.22 (hskp16),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1130, 2699, 41])).
% 1.43/1.22 tff(2701,plain,
% 1.43/1.22 (~c3_1(a2304)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1094, 2700])).
% 1.43/1.22 tff(2702,plain,
% 1.43/1.22 (~c2_1(a2304)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1100, 2700])).
% 1.43/1.22 tff(2703,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2704,plain,
% 1.43/1.22 ((hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2705,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2704])).
% 1.43/1.22 tff(2706,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2705, 2703])).
% 1.43/1.22 tff(2707,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2708,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 1.43/1.22 tff(2709,plain,
% 1.43/1.22 (~c1_1(a2304)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2708, 181, 2583, 994, 983, 2702, 2701, 972, 2095])).
% 1.43/1.22 tff(2710,plain,
% 1.43/1.22 (~c0_1(a2304)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1106, 2700])).
% 1.43/1.22 tff(2711,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2712,plain,
% 1.43/1.22 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304)) <=> (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2713,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2712])).
% 1.43/1.22 tff(2714,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2713, 2711])).
% 1.43/1.22 tff(2715,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2716,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.43/1.22 tff(2717,plain,
% 1.43/1.22 ($false),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2716, 181, 41, 2696, 2695, 2710, 2702, 460, 2698, 2709])).
% 1.43/1.22 tff(2718,plain,(hskp28 | c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.22 tff(2719,plain,
% 1.43/1.22 (hskp28),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2718, 396, 40, 2104])).
% 1.43/1.22 tff(2720,plain,
% 1.43/1.22 (c0_1(a2278)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[636, 2719])).
% 1.43/1.22 tff(2721,plain,
% 1.43/1.22 (c3_1(a2278)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[614, 2719])).
% 1.43/1.22 tff(2722,plain,
% 1.43/1.22 (c1_1(a2278)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[625, 2719])).
% 1.43/1.22 tff(2723,plain,
% 1.43/1.22 (c2_1(a2278)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2128, 2722, 2721, 2720])).
% 1.43/1.22 tff(2724,plain,
% 1.43/1.22 (~hskp12),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2157, 2723, 2720, 2722, 2105])).
% 1.43/1.22 tff(2725,plain,
% 1.43/1.22 (hskp13),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1361, 2724])).
% 1.43/1.22 tff(2726,plain,
% 1.43/1.22 (~c3_1(a2299)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1312, 2725])).
% 1.43/1.22 tff(2727,plain,
% 1.43/1.22 (~c1_1(a2299)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1329, 2725])).
% 1.43/1.22 tff(2728,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2729,plain,
% 1.43/1.22 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299))) <=> (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2730,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2729])).
% 1.43/1.22 tff(2731,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2730, 2728])).
% 1.43/1.22 tff(2732,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2733,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.43/1.22 tff(2734,plain,
% 1.43/1.22 (~c0_1(a2299)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2733, 181, 2105, 2720, 2722, 2727, 2726, 2139, 2723])).
% 1.43/1.22 tff(2735,plain,
% 1.43/1.22 (c2_1(a2299)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[1323, 2725])).
% 1.43/1.22 tff(2736,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2737,plain,
% 1.43/1.22 ((hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299))) <=> (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2738,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299)))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2737])).
% 1.43/1.22 tff(2739,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.43/1.22 tff(2740,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2741,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299)),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.43/1.22 tff(2742,plain,
% 1.43/1.22 (~c3_1(a2277)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2741, 181, 2105, 2735, 2424, 2727, 40, 2225, 2734])).
% 1.43/1.22 tff(2743,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2744,plain,
% 1.43/1.22 ((hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2745,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2744])).
% 1.43/1.22 tff(2746,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2745, 2743])).
% 1.43/1.22 tff(2747,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2748,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 1.43/1.22 tff(2749,plain,
% 1.43/1.22 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2302))),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2748, 181, 994, 972, 40, 1560])).
% 1.43/1.22 tff(2750,plain,
% 1.43/1.22 (~c1_1(a2302)),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2749, 2742, 2424, 2564])).
% 1.43/1.22 tff(2751,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2752,plain,
% 1.43/1.22 ((hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299))) <=> (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 1.43/1.22 inference(rewrite,[status(thm)],[])).
% 1.43/1.22 tff(2753,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299))))),
% 1.43/1.22 inference(monotonicity,[status(thm)],[2752])).
% 1.43/1.22 tff(2754,plain,
% 1.43/1.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 1.43/1.22 inference(transitivity,[status(thm)],[2753, 2751])).
% 1.43/1.22 tff(2755,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))),
% 1.43/1.22 inference(quant_inst,[status(thm)],[])).
% 1.43/1.22 tff(2756,plain,
% 1.43/1.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299))),
% 1.43/1.22 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.43/1.22 tff(2757,plain,
% 1.43/1.22 (hskp0),
% 1.43/1.22 inference(unit_resolution,[status(thm)],[2756, 181, 2720, 2722, 2721, 2735, 2727, 2726, 2530])).
% 1.43/1.23 tff(2758,plain,
% 1.43/1.23 (~c0_1(a2276)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[888, 2757])).
% 1.43/1.23 tff(2759,plain,
% 1.43/1.23 (hskp19),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2102, 2742, 2424])).
% 1.43/1.23 tff(2760,plain,
% 1.43/1.23 (~c3_1(a2316)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[1982, 2759])).
% 1.43/1.23 tff(2761,plain,
% 1.43/1.23 (~c2_1(a2316)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[1988, 2759])).
% 1.43/1.23 tff(2762,plain,
% 1.43/1.23 (c1_1(a2276)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[910, 2757])).
% 1.43/1.23 tff(2763,plain,
% 1.43/1.23 (c1_1(a2316)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[1999, 2759])).
% 1.43/1.23 tff(2764,plain,
% 1.43/1.23 (~c2_1(a2276)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2552, 181, 2564, 2763, 2762, 2761, 2760, 2758, 1560])).
% 1.43/1.23 tff(2765,plain,
% 1.43/1.23 (c3_1(a2276)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[899, 2757])).
% 1.43/1.23 tff(2766,plain,
% 1.43/1.23 ($false),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2560, 181, 1004, 1003, 994, 2762, 2765, 1002, 972, 217, 2764, 2750])).
% 1.43/1.23 tff(2767,plain,(c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.23 tff(2768,plain,
% 1.43/1.23 (c3_1(a2306)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2767, 2104, 40])).
% 1.43/1.23 tff(2769,plain,
% 1.43/1.23 (~hskp17),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[289, 2768])).
% 1.43/1.23 tff(2770,plain,
% 1.43/1.23 (c3_1(a2277)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2571, 2462, 2424, 2769])).
% 1.43/1.23 tff(2771,plain,
% 1.43/1.23 (c1_1(a2302)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2579, 2770, 2424])).
% 1.43/1.23 tff(2772,plain,
% 1.43/1.23 (~hskp19),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2008, 2771, 2769])).
% 1.43/1.23 tff(2773,plain,
% 1.43/1.23 (hskp7),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[2600, 2772, 2462])).
% 1.43/1.23 tff(2774,plain,
% 1.43/1.23 (~c2_1(a2286)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[1053, 2773])).
% 1.43/1.23 tff(2775,plain,
% 1.43/1.23 (c1_1(a2286)),
% 1.43/1.23 inference(unit_resolution,[status(thm)],[1078, 2773])).
% 1.43/1.23 tff(2776,plain,
% 1.43/1.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.43/1.23 inference(rewrite,[status(thm)],[])).
% 1.43/1.23 tff(2777,plain,
% 1.43/1.23 ((hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.43/1.23 inference(rewrite,[status(thm)],[])).
% 1.43/1.23 tff(2778,plain,
% 1.43/1.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2777])).
% 1.44/1.23 tff(2779,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2778, 2776])).
% 1.44/1.23 tff(2780,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2781,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 1.44/1.23 tff(2782,plain,
% 1.44/1.23 (c3_1(a2286)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2781, 181, 2772, 994, 983, 2775, 972, 2774, 2095])).
% 1.44/1.23 tff(2783,plain,
% 1.44/1.23 (hskp18),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2638, 181, 994, 2604, 2605, 972, 2632, 2771, 2606])).
% 1.44/1.23 tff(2784,plain,
% 1.44/1.23 (~c2_1(a2308)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2644, 2783])).
% 1.44/1.23 tff(2785,plain,
% 1.44/1.23 (~c1_1(a2308)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2650, 2783])).
% 1.44/1.23 tff(2786,plain,
% 1.44/1.23 (c0_1(a2308)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2657, 181, 41, 2775, 2785, 2784, 2774, 460, 2782])).
% 1.44/1.23 tff(2787,plain,
% 1.44/1.23 (c3_1(a2308)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2668, 2783])).
% 1.44/1.23 tff(2788,plain,
% 1.44/1.23 (hskp12 | (~c0_1(a2308))),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2675, 181, 2772, 2787, 2784, 10])).
% 1.44/1.23 tff(2789,plain,
% 1.44/1.23 (hskp12),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2788, 2786])).
% 1.44/1.23 tff(2790,plain,
% 1.44/1.23 (~c3_1(a2295)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[710, 2789])).
% 1.44/1.23 tff(2791,plain,
% 1.44/1.23 (c0_1(a2295)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[721, 2789])).
% 1.44/1.23 tff(2792,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2793,plain,
% 1.44/1.23 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302))) <=> (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2794,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2793])).
% 1.44/1.23 tff(2795,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2794, 2792])).
% 1.44/1.23 tff(2796,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2797,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 1.44/1.23 tff(2798,plain,
% 1.44/1.23 (~c2_1(a2295)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2797, 181, 994, 2791, 2175, 972, 2790, 2173, 744, 2462, 2771])).
% 1.44/1.23 tff(2799,plain,
% 1.44/1.23 (~c1_1(a2295)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1368, 2789])).
% 1.44/1.23 tff(2800,plain,
% 1.44/1.23 (hskp23),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2693, 181, 2791, 2799, 2790, 284, 2798])).
% 1.44/1.23 tff(2801,plain,
% 1.44/1.23 (~c2_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[302, 2800])).
% 1.44/1.23 tff(2802,plain,
% 1.44/1.23 (c3_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[313, 2800])).
% 1.44/1.23 tff(2803,plain,
% 1.44/1.23 (~c0_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[326, 2800])).
% 1.44/1.23 tff(2804,plain,
% 1.44/1.23 (c1_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1497, 181, 41, 2775, 2803, 2801, 2774, 460, 2782])).
% 1.44/1.23 tff(2805,plain,
% 1.44/1.23 (~hskp26),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1479, 2804, 2802, 2801, 41])).
% 1.44/1.23 tff(2806,plain,
% 1.44/1.23 (hskp16),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1130, 2805, 41])).
% 1.44/1.23 tff(2807,plain,
% 1.44/1.23 (~c3_1(a2304)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1094, 2806])).
% 1.44/1.23 tff(2808,plain,
% 1.44/1.23 (~c2_1(a2304)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1100, 2806])).
% 1.44/1.23 tff(2809,plain,
% 1.44/1.23 (~c1_1(a2304)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2708, 181, 2772, 994, 983, 2808, 2807, 972, 2095])).
% 1.44/1.23 tff(2810,plain,
% 1.44/1.23 (~c0_1(a2304)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1106, 2806])).
% 1.44/1.23 tff(2811,plain,
% 1.44/1.23 ($false),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2716, 181, 41, 2802, 2801, 2810, 2808, 460, 2804, 2809])).
% 1.44/1.23 tff(2812,plain,(hskp28 | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.23 tff(2813,plain,
% 1.44/1.23 (hskp28),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2812, 2104, 40])).
% 1.44/1.23 tff(2814,plain,
% 1.44/1.23 (c0_1(a2278)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[636, 2813])).
% 1.44/1.23 tff(2815,plain,
% 1.44/1.23 (c3_1(a2278)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[614, 2813])).
% 1.44/1.23 tff(2816,plain,
% 1.44/1.23 (c1_1(a2278)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[625, 2813])).
% 1.44/1.23 tff(2817,plain,
% 1.44/1.23 (c2_1(a2278)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2128, 2816, 2815, 2814])).
% 1.44/1.23 tff(2818,plain,
% 1.44/1.23 (~hskp12),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2157, 2817, 2814, 2816, 2105])).
% 1.44/1.23 tff(2819,plain,
% 1.44/1.23 (hskp13),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1361, 2818])).
% 1.44/1.23 tff(2820,plain,
% 1.44/1.23 (~c3_1(a2299)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1312, 2819])).
% 1.44/1.23 tff(2821,plain,
% 1.44/1.23 (~c1_1(a2299)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1329, 2819])).
% 1.44/1.23 tff(2822,plain,
% 1.44/1.23 (~c0_1(a2299)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2733, 181, 2105, 2814, 2816, 2821, 2820, 2139, 2817])).
% 1.44/1.23 tff(2823,plain,
% 1.44/1.23 (c2_1(a2299)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1323, 2819])).
% 1.44/1.23 tff(2824,plain,
% 1.44/1.23 (~c3_1(a2277)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2741, 181, 2105, 2823, 2424, 2821, 40, 2225, 2822])).
% 1.44/1.23 tff(2825,plain,
% 1.44/1.23 (~c1_1(a2302)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2749, 2824, 2424, 2769])).
% 1.44/1.23 tff(2826,plain,
% 1.44/1.23 (hskp0),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2756, 181, 2814, 2816, 2815, 2823, 2821, 2820, 2530])).
% 1.44/1.23 tff(2827,plain,
% 1.44/1.23 (~c0_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[888, 2826])).
% 1.44/1.23 tff(2828,plain,
% 1.44/1.23 (hskp19),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2102, 2824, 2424])).
% 1.44/1.23 tff(2829,plain,
% 1.44/1.23 (~c3_1(a2316)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1982, 2828])).
% 1.44/1.23 tff(2830,plain,
% 1.44/1.23 (~c2_1(a2316)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1988, 2828])).
% 1.44/1.23 tff(2831,plain,
% 1.44/1.23 (c1_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[910, 2826])).
% 1.44/1.23 tff(2832,plain,
% 1.44/1.23 (c1_1(a2316)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1999, 2828])).
% 1.44/1.23 tff(2833,plain,
% 1.44/1.23 (~c2_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2552, 181, 2769, 2832, 2831, 2830, 2829, 2827, 1560])).
% 1.44/1.23 tff(2834,plain,
% 1.44/1.23 (c3_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[899, 2826])).
% 1.44/1.23 tff(2835,plain,
% 1.44/1.23 ($false),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2560, 181, 1004, 1003, 994, 2831, 2834, 1002, 972, 217, 2833, 2825])).
% 1.44/1.23 tff(2836,plain,(c0_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.23 tff(2837,plain,
% 1.44/1.23 (c0_1(a2277)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2836, 40])).
% 1.44/1.23 tff(2838,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2839,plain,
% 1.44/1.23 ((hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2840,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282))))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2839])).
% 1.44/1.23 tff(2841,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2840, 2838])).
% 1.44/1.23 tff(2842,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2843,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 1.44/1.23 tff(2844,plain,
% 1.44/1.23 (hskp23),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2843, 181, 2068, 2837, 1931, 2067, 53, 2085, 43])).
% 1.44/1.23 tff(2845,plain,
% 1.44/1.23 (~c2_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[302, 2844])).
% 1.44/1.23 tff(2846,plain,
% 1.44/1.23 (c3_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[313, 2844])).
% 1.44/1.23 tff(2847,plain,
% 1.44/1.23 (~c1_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[320, 181, 2846, 1004, 1003, 2068, 2845, 1002, 2077, 217, 43])).
% 1.44/1.23 tff(2848,plain,
% 1.44/1.23 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.44/1.23 inference(bind,[status(th)],[])).
% 1.44/1.23 tff(2849,plain,
% 1.44/1.23 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(quant_intro,[status(thm)],[2848])).
% 1.44/1.23 tff(2850,plain,
% 1.44/1.23 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2851,plain,
% 1.44/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.44/1.23 inference(bind,[status(th)],[])).
% 1.44/1.23 tff(2852,plain,
% 1.44/1.23 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(quant_intro,[status(thm)],[2851])).
% 1.44/1.23 tff(2853,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.44/1.23 tff(2854,plain,
% 1.44/1.23 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.44/1.23 tff(2855,plain,
% 1.44/1.23 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2854, 2850])).
% 1.44/1.23 tff(2856,plain,(
% 1.44/1.23 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(skolemize,[status(sab)],[2855])).
% 1.44/1.23 tff(2857,plain,
% 1.44/1.23 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2856, 2849])).
% 1.44/1.23 tff(2858,plain,
% 1.44/1.23 (~c0_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[326, 2844])).
% 1.44/1.23 tff(2859,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2860,plain,
% 1.44/1.23 ((hskp0 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2861,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2860])).
% 1.44/1.23 tff(2862,plain,
% 1.44/1.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2861, 2859])).
% 1.44/1.23 tff(2863,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2864,plain,
% 1.44/1.23 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.44/1.23 tff(2865,plain,
% 1.44/1.23 (hskp0),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2864, 181, 2846, 2858, 2845, 2857, 2847])).
% 1.44/1.23 tff(2866,plain,
% 1.44/1.23 (~c0_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[888, 2865])).
% 1.44/1.23 tff(2867,plain,
% 1.44/1.23 (c3_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[899, 2865])).
% 1.44/1.23 tff(2868,plain,
% 1.44/1.23 (c1_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[910, 2865])).
% 1.44/1.23 tff(2869,plain,
% 1.44/1.23 (~c1_1(a2302)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2008, 912, 1977])).
% 1.44/1.23 tff(2870,assumption,(~c0_1(a2276)), introduced(assumption)).
% 1.44/1.23 tff(2871,assumption,(c1_1(a2276)), introduced(assumption)).
% 1.44/1.23 tff(2872,plain,
% 1.44/1.23 (hskp17 | (~c2_1(a2276))),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2552, 181, 2000, 2871, 1989, 1983, 2870, 1560])).
% 1.44/1.23 tff(2873,plain,
% 1.44/1.23 (~c2_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2872, 912])).
% 1.44/1.23 tff(2874,assumption,(c3_1(a2276)), introduced(assumption)).
% 1.44/1.23 tff(2875,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2876,plain,
% 1.44/1.23 (((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2877,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302))))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2876])).
% 1.44/1.23 tff(2878,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.44/1.23 tff(2879,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2880,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.44/1.23 tff(2881,plain,
% 1.44/1.23 ($false),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2880, 181, 994, 983, 2871, 2874, 972, 217, 2873, 2869])).
% 1.44/1.23 tff(2882,plain,(hskp17 | (~c1_1(a2276)) | (~c3_1(a2276)) | c0_1(a2276) | (~hskp19)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.23 tff(2883,plain,
% 1.44/1.23 (hskp17),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2882, 2868, 2867, 2866, 2103])).
% 1.44/1.23 tff(2884,plain,
% 1.44/1.23 (~c1_1(a2306)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[266, 2883])).
% 1.44/1.23 tff(2885,assumption,(hskp3), introduced(assumption)).
% 1.44/1.23 tff(2886,plain,
% 1.44/1.23 (~c2_1(a2280)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[574, 2885])).
% 1.44/1.23 tff(2887,plain,
% 1.44/1.23 (c1_1(a2280)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[596, 2885])).
% 1.44/1.23 tff(2888,plain,
% 1.44/1.23 (c3_1(a2280)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[585, 2885])).
% 1.44/1.23 tff(2889,plain,
% 1.44/1.23 ($false),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1968, 2888, 2887, 41, 1180, 2886])).
% 1.44/1.23 tff(2890,plain,((~hskp3) | hskp28 | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.23 tff(2891,plain,
% 1.44/1.23 (~hskp3),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2890, 2844, 41])).
% 1.44/1.23 tff(2892,plain,
% 1.44/1.23 (~c3_1(a2286)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[1085, 181, 1004, 1003, 1079, 776, 1002, 1054, 771, 217, 43])).
% 1.44/1.23 tff(2893,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2894,plain,
% 1.44/1.23 (((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.44/1.23 inference(rewrite,[status(thm)],[])).
% 1.44/1.23 tff(2895,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))))),
% 1.44/1.23 inference(monotonicity,[status(thm)],[2894])).
% 1.44/1.23 tff(2896,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 1.44/1.23 inference(transitivity,[status(thm)],[2895, 2893])).
% 1.44/1.23 tff(2897,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))),
% 1.44/1.23 inference(quant_inst,[status(thm)],[])).
% 1.44/1.23 tff(2898,plain,
% 1.44/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))),
% 1.44/1.23 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.44/1.23 tff(2899,plain,
% 1.44/1.23 (~c1_1(a2302)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2898, 181, 1453, 994, 1481, 1452, 972, 1060, 1054, 1273, 2892])).
% 1.44/1.23 tff(2900,plain,
% 1.44/1.23 (~c1_1(a2327)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[320, 181, 1453, 1004, 1003, 776, 1452, 1002, 771, 217, 43])).
% 1.44/1.23 tff(2901,plain,
% 1.44/1.23 (hskp0),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[2864, 181, 1453, 1481, 1452, 2857, 2900])).
% 1.44/1.23 tff(2902,plain,
% 1.44/1.23 (~c0_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[888, 2901])).
% 1.44/1.23 tff(2903,plain,
% 1.44/1.23 (c1_1(a2276)),
% 1.44/1.23 inference(unit_resolution,[status(thm)],[910, 2901])).
% 1.44/1.23 tff(2904,plain,
% 1.44/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2905,plain,
% 1.44/1.24 (((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2906,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327))))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[2905])).
% 1.44/1.24 tff(2907,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 1.44/1.24 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.44/1.24 tff(2908,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(2909,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.44/1.24 tff(2910,plain,
% 1.44/1.24 (~c2_1(a2276)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2909, 181, 1453, 2903, 1481, 1452, 1060, 1054, 2902, 1273, 2892])).
% 1.44/1.24 tff(2911,plain,
% 1.44/1.24 (c3_1(a2276)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[899, 2901])).
% 1.44/1.24 tff(2912,plain,
% 1.44/1.24 ($false),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2880, 181, 994, 983, 2903, 2911, 972, 217, 2910, 2899])).
% 1.44/1.24 tff(2913,plain,((~hskp7) | (~c3_1(a2327)) | c0_1(a2327) | c2_1(a2327) | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.24 tff(2914,plain,
% 1.44/1.24 (~hskp7),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2913, 2846, 2858, 2845, 2068, 2077, 43])).
% 1.44/1.24 tff(2915,plain,
% 1.44/1.24 (hskp7 | hskp6 | c1_1(a2327)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1487, 181, 2846, 2858, 1141])).
% 1.44/1.24 tff(2916,plain,
% 1.44/1.24 (hskp6),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2915, 2914, 2847])).
% 1.44/1.24 tff(2917,plain,
% 1.44/1.24 (~c3_1(a2285)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[433, 2916])).
% 1.44/1.24 tff(2918,plain,
% 1.44/1.24 (c1_1(a2285)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[409, 2916])).
% 1.44/1.24 tff(2919,plain,
% 1.44/1.24 (c0_1(a2285)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[420, 2916])).
% 1.44/1.24 tff(2920,plain,
% 1.44/1.24 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.44/1.24 inference(bind,[status(th)],[])).
% 1.44/1.24 tff(2921,plain,
% 1.44/1.24 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(quant_intro,[status(thm)],[2920])).
% 1.44/1.24 tff(2922,plain,
% 1.44/1.24 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2923,plain,
% 1.44/1.24 (^[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)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.44/1.24 inference(bind,[status(th)],[])).
% 1.44/1.24 tff(2924,plain,
% 1.44/1.24 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(quant_intro,[status(thm)],[2923])).
% 1.44/1.24 tff(2925,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.44/1.24 tff(2926,plain,
% 1.44/1.24 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.44/1.24 tff(2927,plain,
% 1.44/1.24 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2926, 2922])).
% 1.44/1.24 tff(2928,plain,(
% 1.44/1.24 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(skolemize,[status(sab)],[2927])).
% 1.44/1.24 tff(2929,plain,
% 1.44/1.24 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2928, 2921])).
% 1.44/1.24 tff(2930,plain,
% 1.44/1.24 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2931,plain,
% 1.44/1.24 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327))) <=> (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2932,plain,
% 1.44/1.24 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[2931])).
% 1.44/1.24 tff(2933,plain,
% 1.44/1.24 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 1.44/1.24 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.44/1.24 tff(2934,plain,
% 1.44/1.24 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(2935,plain,
% 1.44/1.24 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.44/1.24 tff(2936,plain,
% 1.44/1.24 (hskp8 | hskp7 | c1_1(a2327)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2935, 181, 2846, 2858, 2929])).
% 1.44/1.24 tff(2937,plain,
% 1.44/1.24 (hskp8),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2936, 2914, 2847])).
% 1.44/1.24 tff(2938,plain,
% 1.44/1.24 (c2_1(a2287)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1428, 2937])).
% 1.44/1.24 tff(2939,plain,
% 1.44/1.24 (c0_1(a2287)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1417, 2937])).
% 1.44/1.24 tff(2940,plain,
% 1.44/1.24 (hskp3 | (~c3_1(a2287))),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[1517, 181, 2939, 2938, 2919, 2918, 2917, 1451])).
% 1.44/1.24 tff(2941,plain,
% 1.44/1.24 (~c3_1(a2287)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2940, 2891])).
% 1.44/1.24 tff(2942,plain,
% 1.44/1.24 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.44/1.24 inference(bind,[status(th)],[])).
% 1.44/1.24 tff(2943,plain,
% 1.44/1.24 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(quant_intro,[status(thm)],[2942])).
% 1.44/1.24 tff(2944,plain,
% 1.44/1.24 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2945,plain,
% 1.44/1.24 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.44/1.24 inference(bind,[status(th)],[])).
% 1.44/1.24 tff(2946,plain,
% 1.44/1.24 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(quant_intro,[status(thm)],[2945])).
% 1.44/1.24 tff(2947,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.44/1.24 tff(2948,plain,
% 1.44/1.24 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2947, 2946])).
% 1.44/1.24 tff(2949,plain,
% 1.44/1.24 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2948, 2944])).
% 1.44/1.24 tff(2950,plain,(
% 1.44/1.24 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(skolemize,[status(sab)],[2949])).
% 1.44/1.24 tff(2951,plain,
% 1.44/1.24 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2950, 2943])).
% 1.44/1.24 tff(2952,plain,
% 1.44/1.24 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2953,plain,
% 1.44/1.24 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2954,plain,
% 1.44/1.24 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327)))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[2953])).
% 1.44/1.24 tff(2955,plain,
% 1.44/1.24 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 1.44/1.24 inference(transitivity,[status(thm)],[2954, 2952])).
% 1.44/1.24 tff(2956,plain,
% 1.44/1.24 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(2957,plain,
% 1.44/1.24 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.44/1.24 tff(2958,plain,
% 1.44/1.24 (hskp3 | hskp2),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2957, 181, 2858, 2845, 526, 2847])).
% 1.44/1.24 tff(2959,plain,
% 1.44/1.24 (hskp2),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2958, 2891])).
% 1.44/1.24 tff(2960,plain,
% 1.44/1.24 (~c3_1(a2279)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[533, 2959])).
% 1.44/1.24 tff(2961,plain,
% 1.44/1.24 (~c2_1(a2279)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[539, 2959])).
% 1.44/1.24 tff(2962,plain,
% 1.44/1.24 (c0_1(a2279)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[550, 2959])).
% 1.44/1.24 tff(2963,plain,
% 1.44/1.24 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2964,plain,
% 1.44/1.24 ((hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279))) <=> (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2965,plain,
% 1.44/1.24 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[2964])).
% 1.44/1.24 tff(2966,plain,
% 1.44/1.24 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 1.44/1.24 inference(transitivity,[status(thm)],[2965, 2963])).
% 1.44/1.24 tff(2967,plain,
% 1.44/1.24 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(2968,plain,
% 1.44/1.24 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 1.44/1.24 tff(2969,plain,
% 1.44/1.24 (hskp25),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2968, 181, 2939, 2938, 2962, 2961, 2960, 2951, 2941])).
% 1.44/1.24 tff(2970,plain,
% 1.44/1.24 (c0_1(a2342)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[38, 2969])).
% 1.44/1.24 tff(2971,plain,
% 1.44/1.24 (~c2_1(a2342)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[16, 2969])).
% 1.44/1.24 tff(2972,plain,
% 1.44/1.24 (~c2_1(a2306)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[260, 2883])).
% 1.44/1.24 tff(2973,plain,
% 1.44/1.24 (c2_1(a2315)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[809, 2075])).
% 1.44/1.24 tff(2974,plain,
% 1.44/1.24 (~c3_1(a2306)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[289, 2883])).
% 1.44/1.24 tff(2975,plain,
% 1.44/1.24 (c3_1(a2342)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[27, 2969])).
% 1.44/1.24 tff(2976,assumption,(c0_1(a2315)), introduced(assumption)).
% 1.44/1.24 tff(2977,assumption,(~c2_1(a2342)), introduced(assumption)).
% 1.44/1.24 tff(2978,assumption,(c3_1(a2342)), introduced(assumption)).
% 1.44/1.24 tff(2979,assumption,(c0_1(a2342)), introduced(assumption)).
% 1.44/1.24 tff(2980,assumption,(c2_1(a2315)), introduced(assumption)).
% 1.44/1.24 tff(2981,assumption,(c1_1(a2315)), introduced(assumption)).
% 1.44/1.24 tff(2982,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2983,plain,
% 1.44/1.24 (((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2984,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[2983])).
% 1.44/1.24 tff(2985,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.24 inference(transitivity,[status(thm)],[2984, 2982])).
% 1.44/1.24 tff(2986,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 1.44/1.24 inference(quant_inst,[status(thm)],[])).
% 1.44/1.24 tff(2987,plain,
% 1.44/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2986, 2985])).
% 1.44/1.24 tff(2988,plain,
% 1.44/1.24 ($false),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2987, 181, 2981, 2980, 2979, 2978, 2977, 398, 397, 396, 395, 2976])).
% 1.44/1.24 tff(2989,plain,((~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | (~c0_1(a2342)) | (~c3_1(a2342)) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.24 tff(2990,plain,
% 1.44/1.24 (~c0_1(a2315)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2989, 2975, 2974, 2973, 2972, 2971, 2970, 2884, 2076])).
% 1.44/1.24 tff(2991,assumption,(hskp21), introduced(assumption)).
% 1.44/1.24 tff(2992,plain,
% 1.44/1.24 (((~hskp21) | (~c3_1(a2324))) <=> ((~hskp21) | (~c3_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2993,plain,
% 1.44/1.24 (((~c3_1(a2324)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2994,axiom,((~c3_1(a2324)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.44/1.24 tff(2995,plain,
% 1.44/1.24 ((~hskp21) | (~c3_1(a2324))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 1.44/1.24 tff(2996,plain,
% 1.44/1.24 ((~hskp21) | (~c3_1(a2324))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[2995, 2992])).
% 1.44/1.24 tff(2997,plain,
% 1.44/1.24 (~c3_1(a2324)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[2996, 2991])).
% 1.44/1.24 tff(2998,plain,
% 1.44/1.24 (((~hskp21) | (~c0_1(a2324))) <=> ((~hskp21) | (~c0_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(2999,plain,
% 1.44/1.24 (((~c0_1(a2324)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3000,axiom,((~c0_1(a2324)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.44/1.24 tff(3001,plain,
% 1.44/1.24 ((~hskp21) | (~c0_1(a2324))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.44/1.24 tff(3002,plain,
% 1.44/1.24 ((~hskp21) | (~c0_1(a2324))),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3001, 2998])).
% 1.44/1.24 tff(3003,plain,
% 1.44/1.24 (~c0_1(a2324)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3002, 2991])).
% 1.44/1.24 tff(3004,plain,
% 1.44/1.24 (((~hskp21) | c1_1(a2324)) <=> ((~hskp21) | c1_1(a2324))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3005,axiom,((~hskp21) | c1_1(a2324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.44/1.24 tff(3006,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3005, 3004])).
% 1.44/1.24 tff(3007,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3006, 3004])).
% 1.44/1.24 tff(3008,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3007, 3004])).
% 1.44/1.24 tff(3009,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3008, 3004])).
% 1.44/1.24 tff(3010,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3009, 3004])).
% 1.44/1.24 tff(3011,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3010, 3004])).
% 1.44/1.24 tff(3012,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3011, 3004])).
% 1.44/1.24 tff(3013,plain,
% 1.44/1.24 ((~hskp21) | c1_1(a2324)),
% 1.44/1.24 inference(modus_ponens,[status(thm)],[3012, 3004])).
% 1.44/1.24 tff(3014,plain,
% 1.44/1.24 (c1_1(a2324)),
% 1.44/1.24 inference(unit_resolution,[status(thm)],[3013, 2991])).
% 1.44/1.24 tff(3015,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3016,plain,
% 1.44/1.24 (((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324))) <=> (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.24 inference(rewrite,[status(thm)],[])).
% 1.44/1.24 tff(3017,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324))))),
% 1.44/1.24 inference(monotonicity,[status(thm)],[3016])).
% 1.44/1.24 tff(3018,plain,
% 1.44/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3017, 3015])).
% 1.44/1.25 tff(3019,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3020,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.44/1.25 tff(3021,plain,
% 1.44/1.25 (~c2_1(a2324)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3020, 181, 3014, 1432, 1431, 3003, 2997, 744, 1430])).
% 1.44/1.25 tff(3022,assumption,(~c0_1(a2315)), introduced(assumption)).
% 1.44/1.25 tff(3023,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3024,plain,
% 1.44/1.25 (((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3025,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3024])).
% 1.44/1.25 tff(3026,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3025, 3023])).
% 1.44/1.25 tff(3027,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3028,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 1.44/1.25 tff(3029,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3028, 181, 2981, 2980, 1453, 1481, 1452, 3003, 2997, 1273, 3022, 3021])).
% 1.44/1.25 tff(3030,plain,((~hskp21) | (~c1_1(a2315)) | (~c2_1(a2315)) | (~c3_1(a2327)) | c0_1(a2327) | c2_1(a2327) | c0_1(a2315) | (~c0_1(a2287)) | (~c2_1(a2287)) | c3_1(a2287)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3031,plain,
% 1.44/1.25 (~hskp21),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3030, 2076, 2973, 2846, 2858, 2845, 2990, 2939, 2938, 2941])).
% 1.44/1.25 tff(3032,plain,
% 1.44/1.25 (^[U: $i] : refl((hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.44/1.25 inference(bind,[status(th)],[])).
% 1.44/1.25 tff(3033,plain,
% 1.44/1.25 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(quant_intro,[status(thm)],[3032])).
% 1.44/1.25 tff(3034,plain,
% 1.44/1.25 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3035,plain,
% 1.44/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.44/1.25 inference(bind,[status(th)],[])).
% 1.44/1.25 tff(3036,plain,
% 1.44/1.25 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(quant_intro,[status(thm)],[3035])).
% 1.44/1.25 tff(3037,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.44/1.25 tff(3038,plain,
% 1.44/1.25 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 1.44/1.25 tff(3039,plain,
% 1.44/1.25 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3038, 3034])).
% 1.44/1.25 tff(3040,plain,(
% 1.44/1.25 ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(skolemize,[status(sab)],[3039])).
% 1.44/1.25 tff(3041,plain,
% 1.44/1.25 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3040, 3033])).
% 1.44/1.25 tff(3042,plain,
% 1.44/1.25 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3043,plain,
% 1.44/1.25 ((hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277))) <=> (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3044,plain,
% 1.44/1.25 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3043])).
% 1.44/1.25 tff(3045,plain,
% 1.44/1.25 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3044, 3042])).
% 1.44/1.25 tff(3046,plain,
% 1.44/1.25 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3047,plain,
% 1.44/1.25 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 1.44/1.25 tff(3048,plain,
% 1.44/1.25 (hskp21 | hskp16 | (~c1_1(a2277)) | c3_1(a2277)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3047, 181, 2837, 3041])).
% 1.44/1.25 tff(3049,plain,
% 1.44/1.25 (hskp16),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3048, 3031, 1931, 2085])).
% 1.44/1.25 tff(3050,plain,
% 1.44/1.25 (~c3_1(a2304)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1094, 3049])).
% 1.44/1.25 tff(3051,plain,
% 1.44/1.25 (~c2_1(a2304)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1100, 3049])).
% 1.44/1.25 tff(3052,plain,
% 1.44/1.25 (~c0_1(a2304)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1106, 3049])).
% 1.44/1.25 tff(3053,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3054,plain,
% 1.44/1.25 (((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3055,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3054])).
% 1.44/1.25 tff(3056,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3055, 3053])).
% 1.44/1.25 tff(3057,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3058,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 1.44/1.25 tff(3059,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3058, 181, 2076, 2973, 2846, 2858, 2845, 3052, 3051, 3050, 1273, 2990])).
% 1.44/1.25 tff(3060,plain,(c1_1(a2282) | hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3061,plain,
% 1.44/1.25 (c1_1(a2282)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3060, 41, 40])).
% 1.44/1.25 tff(3062,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1548, 344, 345, 41, 2068, 2077, 2067, 1197, 346])).
% 1.44/1.25 tff(3063,plain,((~hskp17) | hskp28 | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3064,plain,
% 1.44/1.25 (~hskp17),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3063, 41, 3061])).
% 1.44/1.25 tff(3065,plain,
% 1.44/1.25 (hskp17 | c3_1(a2277) | (~c1_1(a2282))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2570, 181, 2068, 1931, 2077, 40, 1560])).
% 1.44/1.25 tff(3066,plain,
% 1.44/1.25 (c3_1(a2277)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3065, 3064, 3061])).
% 1.44/1.25 tff(3067,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3068,plain,
% 1.44/1.25 (((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3069,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3068])).
% 1.44/1.25 tff(3070,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3069, 3067])).
% 1.44/1.25 tff(3071,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3072,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 1.44/1.25 tff(3073,plain,
% 1.44/1.25 ((~c1_1(a2277)) | (~c3_1(a2277)) | (~c0_1(a2323))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3072, 181, 1003, 2837, 1002, 40, 94])).
% 1.44/1.25 tff(3074,plain,
% 1.44/1.25 (~c0_1(a2323)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3073, 3066, 1931])).
% 1.44/1.25 tff(3075,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3076,plain,
% 1.44/1.25 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3077,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3076])).
% 1.44/1.25 tff(3078,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3077, 3075])).
% 1.44/1.25 tff(3079,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3080,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 1.44/1.25 tff(3081,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3080, 181, 1004, 1003, 1931, 1002, 40, 217, 3066, 3074])).
% 1.44/1.25 tff(3082,plain,(hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3083,plain,
% 1.44/1.25 (hskp28),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3082, 40])).
% 1.44/1.25 tff(3084,plain,
% 1.44/1.25 (c1_1(a2278)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[625, 3083])).
% 1.44/1.25 tff(3085,plain,
% 1.44/1.25 (c3_1(a2278)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[614, 3083])).
% 1.44/1.25 tff(3086,plain,
% 1.44/1.25 (c0_1(a2278)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[636, 3083])).
% 1.44/1.25 tff(3087,plain,
% 1.44/1.25 (c2_1(a2278)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2128, 3086, 3085, 3084])).
% 1.44/1.25 tff(3088,plain,
% 1.44/1.25 (hskp1),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[1005, 748])).
% 1.44/1.25 tff(3089,plain,
% 1.44/1.25 (c1_1(a2277)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[366, 3088])).
% 1.44/1.25 tff(3090,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3091,plain,
% 1.44/1.25 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3092,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3091])).
% 1.44/1.25 tff(3093,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3092, 3090])).
% 1.44/1.25 tff(3094,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3095,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3094, 3093])).
% 1.44/1.25 tff(3096,plain,
% 1.44/1.25 ((~c1_1(a2277)) | (~c0_1(a2323))),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3095, 181, 3086, 3084, 3085, 1003, 2837, 1002, 40, 94])).
% 1.44/1.25 tff(3097,plain,
% 1.44/1.25 (~c0_1(a2323)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3096, 3089])).
% 1.44/1.25 tff(3098,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3099,plain,
% 1.44/1.25 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(rewrite,[status(thm)],[])).
% 1.44/1.25 tff(3100,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 1.44/1.25 inference(monotonicity,[status(thm)],[3099])).
% 1.44/1.25 tff(3101,plain,
% 1.44/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.44/1.25 inference(transitivity,[status(thm)],[3100, 3098])).
% 1.44/1.25 tff(3102,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 1.44/1.25 inference(quant_inst,[status(thm)],[])).
% 1.44/1.25 tff(3103,plain,
% 1.44/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 1.44/1.25 inference(modus_ponens,[status(thm)],[3102, 3101])).
% 1.44/1.25 tff(3104,plain,
% 1.44/1.25 ($false),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3103, 181, 1004, 1003, 1952, 1951, 1002, 1950, 217, 3097])).
% 1.44/1.25 tff(3105,plain,(hskp4 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.25 tff(3106,plain,
% 1.44/1.25 (hskp4),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[3105, 40])).
% 1.44/1.25 tff(3107,plain,
% 1.44/1.25 (~c3_1(a2282)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[193, 3106])).
% 1.44/1.25 tff(3108,plain,
% 1.44/1.25 (c2_1(a2282)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[247, 3106])).
% 1.44/1.25 tff(3109,plain,
% 1.44/1.25 (hskp0),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[2540, 181, 3086, 3084, 3085, 3108, 3107, 2530, 43])).
% 1.44/1.25 tff(3110,plain,
% 1.44/1.25 (c1_1(a2276)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[910, 3109])).
% 1.44/1.25 tff(3111,plain,
% 1.44/1.25 (~c0_1(a2276)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[888, 3109])).
% 1.44/1.25 tff(3112,plain,
% 1.44/1.25 (c3_1(a2276)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[899, 3109])).
% 1.44/1.25 tff(3113,assumption,(~hskp19), introduced(assumption)).
% 1.44/1.25 tff(3114,plain,
% 1.44/1.25 (~c0_1(a2282)),
% 1.44/1.25 inference(unit_resolution,[status(thm)],[199, 3106])).
% 1.44/1.26 tff(3115,plain,
% 1.44/1.26 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2083, 181, 1004, 1003, 3108, 1002, 3114, 40, 217])).
% 1.44/1.26 tff(3116,plain,
% 1.44/1.26 (~c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3115, 664, 43])).
% 1.44/1.26 tff(3117,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2102, 3116, 664, 3113])).
% 1.44/1.26 tff(3118,plain,((~c1_1(a2277)) | hskp19 | c2_1(a2277) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.26 tff(3119,plain,
% 1.44/1.26 (~c1_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3118, 3113, 40, 43])).
% 1.44/1.26 tff(3120,plain,
% 1.44/1.26 (~hskp1),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[366, 3119])).
% 1.44/1.26 tff(3121,plain,
% 1.44/1.26 (~hskp12),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2157, 3120, 3086, 3084, 3087])).
% 1.44/1.26 tff(3122,plain,
% 1.44/1.26 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3123,plain,
% 1.44/1.26 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277))) <=> (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3124,plain,
% 1.44/1.26 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277))))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3123])).
% 1.44/1.26 tff(3125,plain,
% 1.44/1.26 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3124, 3122])).
% 1.44/1.26 tff(3126,plain,
% 1.44/1.26 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3127,plain,
% 1.44/1.26 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 1.44/1.26 tff(3128,plain,
% 1.44/1.26 (hskp19 | hskp12 | (~c0_1(a2277)) | (~c3_1(a2277))),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3127, 181, 40, 10])).
% 1.44/1.26 tff(3129,plain,
% 1.44/1.26 (~c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3128, 3121, 2837, 3113])).
% 1.44/1.26 tff(3130,plain,
% 1.44/1.26 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3131,plain,
% 1.44/1.26 ((hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3132,plain,
% 1.44/1.26 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3131])).
% 1.44/1.26 tff(3133,plain,
% 1.44/1.26 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3132, 3130])).
% 1.44/1.26 tff(3134,plain,
% 1.44/1.26 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3135,plain,
% 1.44/1.26 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 1.44/1.26 tff(3136,plain,
% 1.44/1.26 (hskp12 | c1_1(a2277) | c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3135, 181, 2837, 696])).
% 1.44/1.26 tff(3137,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3136, 3129, 3121, 3119])).
% 1.44/1.26 tff(3138,plain,(hskp19 | c2_1(a2277) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.26 tff(3139,plain,
% 1.44/1.26 (hskp19),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3138, 43, 40])).
% 1.44/1.26 tff(3140,plain,
% 1.44/1.26 (hskp17),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2882, 3139, 3112, 3111, 3110])).
% 1.44/1.26 tff(3141,plain,
% 1.44/1.26 (~c3_1(a2306)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[289, 3140])).
% 1.44/1.26 tff(3142,plain,
% 1.44/1.26 (~c2_1(a2306)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[260, 3140])).
% 1.44/1.26 tff(3143,plain,
% 1.44/1.26 (~c1_1(a2306)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[266, 3140])).
% 1.44/1.26 tff(3144,plain,
% 1.44/1.26 (hskp1),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2170, 3142, 3083, 3143, 3141])).
% 1.44/1.26 tff(3145,plain,
% 1.44/1.26 (c1_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[366, 3144])).
% 1.44/1.26 tff(3146,assumption,(hskp24), introduced(assumption)).
% 1.44/1.26 tff(3147,plain,
% 1.44/1.26 (((~hskp24) | (~c1_1(a2337))) <=> ((~hskp24) | (~c1_1(a2337)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3148,plain,
% 1.44/1.26 (((~c1_1(a2337)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a2337)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3149,axiom,((~c1_1(a2337)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.44/1.26 tff(3150,plain,
% 1.44/1.26 ((~hskp24) | (~c1_1(a2337))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.44/1.26 tff(3151,plain,
% 1.44/1.26 ((~hskp24) | (~c1_1(a2337))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3150, 3147])).
% 1.44/1.26 tff(3152,plain,
% 1.44/1.26 (~c1_1(a2337)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3151, 3146])).
% 1.44/1.26 tff(3153,plain,
% 1.44/1.26 (((~hskp24) | c3_1(a2337)) <=> ((~hskp24) | c3_1(a2337))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3154,axiom,((~hskp24) | c3_1(a2337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.44/1.26 tff(3155,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.44/1.26 tff(3156,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3155, 3153])).
% 1.44/1.26 tff(3157,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3156, 3153])).
% 1.44/1.26 tff(3158,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3157, 3153])).
% 1.44/1.26 tff(3159,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3158, 3153])).
% 1.44/1.26 tff(3160,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3159, 3153])).
% 1.44/1.26 tff(3161,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3160, 3153])).
% 1.44/1.26 tff(3162,plain,
% 1.44/1.26 ((~hskp24) | c3_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3161, 3153])).
% 1.44/1.26 tff(3163,plain,
% 1.44/1.26 (c3_1(a2337)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3162, 3146])).
% 1.44/1.26 tff(3164,plain,
% 1.44/1.26 (((~hskp24) | c0_1(a2337)) <=> ((~hskp24) | c0_1(a2337))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3165,axiom,((~hskp24) | c0_1(a2337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.44/1.26 tff(3166,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.44/1.26 tff(3167,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3166, 3164])).
% 1.44/1.26 tff(3168,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3167, 3164])).
% 1.44/1.26 tff(3169,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3168, 3164])).
% 1.44/1.26 tff(3170,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3169, 3164])).
% 1.44/1.26 tff(3171,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3170, 3164])).
% 1.44/1.26 tff(3172,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3171, 3164])).
% 1.44/1.26 tff(3173,plain,
% 1.44/1.26 ((~hskp24) | c0_1(a2337)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3172, 3164])).
% 1.44/1.26 tff(3174,plain,
% 1.44/1.26 (c0_1(a2337)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3173, 3146])).
% 1.44/1.26 tff(3175,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3176,plain,
% 1.44/1.26 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337))) <=> (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3177,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337))))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3176])).
% 1.44/1.26 tff(3178,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3177, 3175])).
% 1.44/1.26 tff(3179,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3180,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 1.44/1.26 tff(3181,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3180, 181, 679, 678, 677, 3174, 3163, 665, 664, 3152, 40, 94])).
% 1.44/1.26 tff(3182,plain,((~hskp24) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.26 tff(3183,plain,
% 1.44/1.26 (~hskp24),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3182, 3145, 2837, 3084, 3086, 3085, 40])).
% 1.44/1.26 tff(3184,plain,
% 1.44/1.26 (~c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3115, 3145, 43])).
% 1.44/1.26 tff(3185,plain,
% 1.44/1.26 (^[U: $i] : refl((hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.44/1.26 inference(bind,[status(th)],[])).
% 1.44/1.26 tff(3186,plain,
% 1.44/1.26 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(quant_intro,[status(thm)],[3185])).
% 1.44/1.26 tff(3187,plain,
% 1.44/1.26 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3188,plain,
% 1.44/1.26 (^[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)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> ((hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25))), rewrite(((hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.44/1.26 inference(bind,[status(th)],[])).
% 1.44/1.26 tff(3189,plain,
% 1.44/1.26 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(quant_intro,[status(thm)],[3188])).
% 1.44/1.26 tff(3190,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.44/1.26 tff(3191,plain,
% 1.44/1.26 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 1.44/1.26 tff(3192,plain,
% 1.44/1.26 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3191, 3187])).
% 1.44/1.26 tff(3193,plain,(
% 1.44/1.26 ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(skolemize,[status(sab)],[3192])).
% 1.44/1.26 tff(3194,plain,
% 1.44/1.26 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3193, 3186])).
% 1.44/1.26 tff(3195,plain,
% 1.44/1.26 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3196,plain,
% 1.44/1.26 ((hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3197,plain,
% 1.44/1.26 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3196])).
% 1.44/1.26 tff(3198,plain,
% 1.44/1.26 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3197, 3195])).
% 1.44/1.26 tff(3199,plain,
% 1.44/1.26 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3200,plain,
% 1.44/1.26 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 1.44/1.26 tff(3201,plain,
% 1.44/1.26 (hskp25 | hskp24 | (~c0_1(a2277)) | c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3200, 181, 40, 3194])).
% 1.44/1.26 tff(3202,plain,
% 1.44/1.26 (hskp25),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3201, 3184, 2837, 3183])).
% 1.44/1.26 tff(3203,plain,
% 1.44/1.26 (~c2_1(a2342)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[16, 3202])).
% 1.44/1.26 tff(3204,plain,
% 1.44/1.26 (c3_1(a2342)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[27, 3202])).
% 1.44/1.26 tff(3205,plain,
% 1.44/1.26 (c0_1(a2342)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[38, 3202])).
% 1.44/1.26 tff(3206,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3207,plain,
% 1.44/1.26 (((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3208,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3207])).
% 1.44/1.26 tff(3209,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.44/1.26 tff(3210,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3211,plain,
% 1.44/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.44/1.26 tff(3212,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3211, 181, 3086, 3084, 3205, 3204, 3203, 3143, 3142, 3141, 395, 3087])).
% 1.44/1.26 tff(3213,plain,(c1_1(a2282) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.26 tff(3214,plain,
% 1.44/1.26 (c1_1(a2282)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3213, 40])).
% 1.44/1.26 tff(3215,plain,
% 1.44/1.26 (~hskp10),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1235, 3214, 3114, 3107, 3108])).
% 1.44/1.26 tff(3216,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3217,plain,
% 1.44/1.26 ((hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3218,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3217])).
% 1.44/1.26 tff(3219,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3218, 3216])).
% 1.44/1.26 tff(3220,plain,
% 1.44/1.26 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3221,plain,
% 1.44/1.26 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 1.44/1.26 tff(3222,plain,
% 1.44/1.26 (hskp18 | (~c1_1(a2282))),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3221, 181, 3086, 3085, 3108, 3114, 2632, 3087])).
% 1.44/1.26 tff(3223,plain,
% 1.44/1.26 (hskp18),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3222, 3214])).
% 1.44/1.26 tff(3224,plain,
% 1.44/1.26 (~c1_1(a2308)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2650, 3223])).
% 1.44/1.26 tff(3225,plain,
% 1.44/1.26 (~c2_1(a2308)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2644, 3223])).
% 1.44/1.26 tff(3226,plain,
% 1.44/1.26 (c3_1(a2308)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2668, 3223])).
% 1.44/1.26 tff(3227,plain,
% 1.44/1.26 (c2_1(a2278)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2128, 679, 677, 678])).
% 1.44/1.26 tff(3228,plain,
% 1.44/1.26 (~hskp12),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2157, 42, 679, 678, 3227])).
% 1.44/1.26 tff(3229,plain,
% 1.44/1.26 (hskp13),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1361, 3228])).
% 1.44/1.26 tff(3230,plain,
% 1.44/1.26 (~c3_1(a2299)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1312, 3229])).
% 1.44/1.26 tff(3231,plain,
% 1.44/1.26 (~c1_1(a2299)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1329, 3229])).
% 1.44/1.26 tff(3232,plain,
% 1.44/1.26 (c2_1(a2299)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1323, 3229])).
% 1.44/1.26 tff(3233,plain,
% 1.44/1.26 (hskp0),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2756, 181, 679, 678, 677, 3232, 3231, 3230, 2530])).
% 1.44/1.26 tff(3234,plain,
% 1.44/1.26 (c1_1(a2276)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[910, 3233])).
% 1.44/1.26 tff(3235,plain,
% 1.44/1.26 (~c0_1(a2276)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[888, 3233])).
% 1.44/1.26 tff(3236,plain,
% 1.44/1.26 (c3_1(a2276)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[899, 3233])).
% 1.44/1.26 tff(3237,assumption,(~c2_1(a2308)), introduced(assumption)).
% 1.44/1.26 tff(3238,assumption,(~c1_1(a2308)), introduced(assumption)).
% 1.44/1.26 tff(3239,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3240,plain,
% 1.44/1.26 ((hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308)) <=> (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3241,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308)))),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3240])).
% 1.44/1.26 tff(3242,plain,
% 1.44/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.44/1.26 inference(transitivity,[status(thm)],[3241, 3239])).
% 1.44/1.26 tff(3243,plain,
% 1.44/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))),
% 1.44/1.26 inference(quant_inst,[status(thm)],[])).
% 1.44/1.26 tff(3244,plain,
% 1.44/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308)),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 1.44/1.26 tff(3245,plain,
% 1.44/1.26 (c0_1(a2308)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3244, 181, 42, 3232, 3238, 3237, 3231, 3230, 227])).
% 1.44/1.26 tff(3246,assumption,(c3_1(a2308)), introduced(assumption)).
% 1.44/1.26 tff(3247,plain,
% 1.44/1.26 (hskp19 | hskp12 | (~c0_1(a2308))),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2675, 181, 3246, 3237, 10])).
% 1.44/1.26 tff(3248,plain,
% 1.44/1.26 (hskp19),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3247, 3245, 3228])).
% 1.44/1.26 tff(3249,plain,
% 1.44/1.26 ($false),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2882, 3248, 3236, 912, 3235, 3234])).
% 1.44/1.26 tff(3250,plain,(hskp1 | hskp17 | (~c3_1(a2308)) | c2_1(a2308) | c1_1(a2308) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.26 tff(3251,plain,
% 1.44/1.26 (hskp1),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3250, 912, 3226, 3225, 3224, 3086, 3084, 3085])).
% 1.44/1.26 tff(3252,plain,
% 1.44/1.26 (c1_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[366, 3251])).
% 1.44/1.26 tff(3253,plain,
% 1.44/1.26 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282))),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2570, 181, 3108, 3114, 40, 1560])).
% 1.44/1.26 tff(3254,plain,
% 1.44/1.26 (c3_1(a2277)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3253, 3252, 3214, 912])).
% 1.44/1.26 tff(3255,plain,
% 1.44/1.26 (c1_1(a2302)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2579, 3254, 3252])).
% 1.44/1.26 tff(3256,plain,
% 1.44/1.26 (~hskp19),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2008, 3255, 912])).
% 1.44/1.26 tff(3257,plain,
% 1.44/1.26 ((hskp19 | hskp10 | hskp8) <=> (hskp19 | hskp10 | hskp8)),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3258,plain,
% 1.44/1.26 (((hskp10 | hskp8) | hskp19) <=> (hskp19 | hskp10 | hskp8)),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3259,plain,
% 1.44/1.26 ((hskp8 | hskp10) <=> (hskp10 | hskp8)),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3260,plain,
% 1.44/1.26 (((hskp8 | hskp10) | hskp19) <=> ((hskp10 | hskp8) | hskp19)),
% 1.44/1.26 inference(monotonicity,[status(thm)],[3259])).
% 1.44/1.26 tff(3261,plain,
% 1.44/1.26 (((hskp8 | hskp10) | hskp19) <=> (hskp19 | hskp10 | hskp8)),
% 1.44/1.26 inference(transitivity,[status(thm)],[3260, 3258])).
% 1.44/1.26 tff(3262,axiom,((hskp8 | hskp10) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.44/1.26 tff(3263,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 1.44/1.26 tff(3264,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3263, 3257])).
% 1.44/1.26 tff(3265,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3264, 3257])).
% 1.44/1.26 tff(3266,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3265, 3257])).
% 1.44/1.26 tff(3267,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3266, 3257])).
% 1.44/1.26 tff(3268,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3267, 3257])).
% 1.44/1.26 tff(3269,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3268, 3257])).
% 1.44/1.26 tff(3270,plain,
% 1.44/1.26 (hskp19 | hskp10 | hskp8),
% 1.44/1.26 inference(modus_ponens,[status(thm)],[3269, 3257])).
% 1.44/1.26 tff(3271,plain,
% 1.44/1.26 (hskp8),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[3270, 3256, 3215])).
% 1.44/1.26 tff(3272,plain,
% 1.44/1.26 (c0_1(a2287)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1417, 3271])).
% 1.44/1.26 tff(3273,plain,
% 1.44/1.26 (c2_1(a2287)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1428, 3271])).
% 1.44/1.26 tff(3274,plain,
% 1.44/1.26 (c3_1(a2287)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[1440, 3273, 3214, 3108, 3114, 3107, 3272])).
% 1.44/1.26 tff(3275,plain,
% 1.44/1.26 (~c1_1(a2287)),
% 1.44/1.26 inference(unit_resolution,[status(thm)],[2373, 3271])).
% 1.44/1.26 tff(3276,plain,
% 1.44/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.44/1.26 inference(rewrite,[status(thm)],[])).
% 1.44/1.26 tff(3277,plain,
% 1.44/1.26 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287))) <=> (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3278,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3277])).
% 1.44/1.27 tff(3279,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3278, 3276])).
% 1.44/1.27 tff(3280,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3281,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3280, 3279])).
% 1.44/1.27 tff(3282,plain,
% 1.44/1.27 ($false),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3281, 181, 3086, 3084, 3085, 3272, 2837, 3252, 3275, 40, 94, 3274])).
% 1.44/1.27 tff(3283,plain,(hskp17 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.27 tff(3284,plain,
% 1.44/1.27 (hskp17),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3283, 40])).
% 1.44/1.27 tff(3285,plain,
% 1.44/1.27 (~c3_1(a2306)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[289, 3284])).
% 1.44/1.27 tff(3286,plain,
% 1.44/1.27 (~c1_1(a2306)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[266, 3284])).
% 1.44/1.27 tff(3287,plain,
% 1.44/1.27 (~c2_1(a2306)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[260, 3284])).
% 1.44/1.27 tff(3288,plain,
% 1.44/1.27 (hskp1),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2170, 3287, 3083, 3286, 3285])).
% 1.44/1.27 tff(3289,plain,
% 1.44/1.27 (c1_1(a2277)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[366, 3288])).
% 1.44/1.27 tff(3290,plain,
% 1.44/1.27 (~hskp24),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3182, 3289, 2837, 3084, 3086, 3085, 40])).
% 1.44/1.27 tff(3291,plain,
% 1.44/1.27 (^[U: $i] : refl((hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.44/1.27 inference(bind,[status(th)],[])).
% 1.44/1.27 tff(3292,plain,
% 1.44/1.27 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(quant_intro,[status(thm)],[3291])).
% 1.44/1.27 tff(3293,plain,
% 1.44/1.27 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3294,plain,
% 1.44/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.44/1.27 inference(bind,[status(th)],[])).
% 1.44/1.27 tff(3295,plain,
% 1.44/1.27 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(quant_intro,[status(thm)],[3294])).
% 1.44/1.27 tff(3296,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.44/1.27 tff(3297,plain,
% 1.44/1.27 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 1.44/1.27 tff(3298,plain,
% 1.44/1.27 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3297, 3293])).
% 1.44/1.27 tff(3299,plain,(
% 1.44/1.27 ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(skolemize,[status(sab)],[3298])).
% 1.44/1.27 tff(3300,plain,
% 1.44/1.27 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3299, 3292])).
% 1.44/1.27 tff(3301,plain,
% 1.44/1.27 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3302,plain,
% 1.44/1.27 ((hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3303,plain,
% 1.44/1.27 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3302])).
% 1.44/1.27 tff(3304,plain,
% 1.44/1.27 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3303, 3301])).
% 1.44/1.27 tff(3305,plain,
% 1.44/1.27 ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3306,plain,
% 1.44/1.27 ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 1.44/1.27 tff(3307,plain,
% 1.44/1.27 (hskp24 | hskp21),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3306, 181, 1004, 1003, 1002, 3300])).
% 1.44/1.27 tff(3308,plain,
% 1.44/1.27 (hskp21),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3307, 3290])).
% 1.44/1.27 tff(3309,plain,
% 1.44/1.27 (~c3_1(a2324)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2996, 3308])).
% 1.44/1.27 tff(3310,plain,
% 1.44/1.27 (~c0_1(a2324)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3002, 3308])).
% 1.44/1.27 tff(3311,plain,
% 1.44/1.27 (hskp23),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1378, 3285, 3114, 3214, 3286, 3215, 3287, 3108])).
% 1.44/1.27 tff(3312,plain,
% 1.44/1.27 (~c2_1(a2327)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[302, 3311])).
% 1.44/1.27 tff(3313,plain,
% 1.44/1.27 (~c0_1(a2327)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[326, 3311])).
% 1.44/1.27 tff(3314,plain,
% 1.44/1.27 (c3_1(a2327)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[313, 3311])).
% 1.44/1.27 tff(3315,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3316,plain,
% 1.44/1.27 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3317,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3316])).
% 1.44/1.27 tff(3318,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3317, 3315])).
% 1.44/1.27 tff(3319,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3320,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3319, 3318])).
% 1.44/1.27 tff(3321,plain,
% 1.44/1.27 (c2_1(a2324)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3320, 181, 3314, 3108, 3313, 3312, 3310, 3309, 3114, 1273, 3214])).
% 1.44/1.27 tff(3322,plain,
% 1.44/1.27 (c0_1(a2306)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1388, 181, 3314, 3108, 3313, 3312, 3287, 3285, 3114, 1273, 3214])).
% 1.44/1.27 tff(3323,plain,
% 1.44/1.27 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3324,plain,
% 1.44/1.27 ((hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3325,plain,
% 1.44/1.27 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3324])).
% 1.44/1.27 tff(3326,plain,
% 1.44/1.27 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3325, 3323])).
% 1.44/1.27 tff(3327,plain,
% 1.44/1.27 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3328,plain,
% 1.44/1.27 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 1.44/1.27 tff(3329,plain,
% 1.44/1.27 (hskp12 | (~c0_1(a2306))),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3328, 181, 3286, 3285, 696])).
% 1.44/1.27 tff(3330,plain,
% 1.44/1.27 (hskp12),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3329, 3322])).
% 1.44/1.27 tff(3331,plain,
% 1.44/1.27 (~c3_1(a2295)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[710, 3330])).
% 1.44/1.27 tff(3332,plain,
% 1.44/1.27 (c0_1(a2295)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[721, 3330])).
% 1.44/1.27 tff(3333,plain,
% 1.44/1.27 (c1_1(a2324)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3013, 3308])).
% 1.44/1.27 tff(3334,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3335,plain,
% 1.44/1.27 (((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324))) <=> (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3336,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3335])).
% 1.44/1.27 tff(3337,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3336, 3334])).
% 1.44/1.27 tff(3338,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3339,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 1.44/1.27 tff(3340,plain,
% 1.44/1.27 (~c2_1(a2295)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3339, 181, 3333, 3332, 3310, 3309, 3331, 744, 3321])).
% 1.44/1.27 tff(3341,plain,
% 1.44/1.27 (~c1_1(a2295)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1368, 3330])).
% 1.44/1.27 tff(3342,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3343,plain,
% 1.44/1.27 ((hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3344,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3343])).
% 1.44/1.27 tff(3345,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3344, 3342])).
% 1.44/1.27 tff(3346,plain,
% 1.44/1.27 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3347,plain,
% 1.44/1.27 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.44/1.27 tff(3348,plain,
% 1.44/1.27 (hskp25),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3347, 181, 3290, 3287, 3285, 3194, 3322])).
% 1.44/1.27 tff(3349,plain,
% 1.44/1.27 (~c2_1(a2342)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[16, 3348])).
% 1.44/1.27 tff(3350,plain,
% 1.44/1.27 (c3_1(a2342)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[27, 3348])).
% 1.44/1.27 tff(3351,plain,
% 1.44/1.27 (c0_1(a2342)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[38, 3348])).
% 1.44/1.27 tff(3352,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3353,plain,
% 1.44/1.27 (((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295)) <=> (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3354,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3353])).
% 1.44/1.27 tff(3355,plain,
% 1.44/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3354, 3352])).
% 1.44/1.27 tff(3356,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3357,plain,
% 1.44/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3356, 3355])).
% 1.44/1.27 tff(3358,plain,
% 1.44/1.27 ($false),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3357, 181, 3086, 3084, 3351, 3350, 3349, 3341, 3331, 395, 3340, 3087])).
% 1.44/1.27 tff(3359,plain,(c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.27 tff(3360,plain,
% 1.44/1.27 (~hskp1),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[341, 3359])).
% 1.44/1.27 tff(3361,plain,
% 1.44/1.27 (hskp28),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1929, 3360])).
% 1.44/1.27 tff(3362,plain,
% 1.44/1.27 (c1_1(a2278)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[625, 3361])).
% 1.44/1.27 tff(3363,plain,
% 1.44/1.27 (c0_1(a2278)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[636, 3361])).
% 1.44/1.27 tff(3364,plain,
% 1.44/1.27 (c3_1(a2278)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[614, 3361])).
% 1.44/1.27 tff(3365,plain,
% 1.44/1.27 (c2_1(a2278)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2128, 3363, 3364, 3362])).
% 1.44/1.27 tff(3366,plain,
% 1.44/1.27 (~hskp12),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2157, 3365, 3363, 3362, 3360])).
% 1.44/1.27 tff(3367,plain,
% 1.44/1.27 (c1_1(a2306) | c2_1(a2306) | c3_1(a2306)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2170, 3361, 3360])).
% 1.44/1.27 tff(3368,plain,
% 1.44/1.27 ($false),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3367, 345, 346, 344])).
% 1.44/1.27 tff(3369,plain,(~hskp17), inference(lemma,lemma(discharge,[]))).
% 1.44/1.27 tff(3370,plain,
% 1.44/1.27 (hskp13),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1361, 3366])).
% 1.44/1.27 tff(3371,plain,
% 1.44/1.27 (~c3_1(a2299)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1312, 3370])).
% 1.44/1.27 tff(3372,plain,
% 1.44/1.27 (~c1_1(a2299)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1329, 3370])).
% 1.44/1.27 tff(3373,plain,
% 1.44/1.27 (c2_1(a2299)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[1323, 3370])).
% 1.44/1.27 tff(3374,plain,
% 1.44/1.27 (hskp0),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2756, 181, 3363, 3362, 3364, 3373, 3372, 3371, 2530])).
% 1.44/1.27 tff(3375,plain,
% 1.44/1.27 (c1_1(a2276)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[910, 3374])).
% 1.44/1.27 tff(3376,plain,
% 1.44/1.27 (~c0_1(a2276)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[888, 3374])).
% 1.44/1.27 tff(3377,plain,
% 1.44/1.27 (c3_1(a2276)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[899, 3374])).
% 1.44/1.27 tff(3378,plain,
% 1.44/1.27 (hskp17 | (~hskp19)),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[2882, 3377, 3376, 3375])).
% 1.44/1.27 tff(3379,plain,
% 1.44/1.27 (~hskp19),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3378, 3369])).
% 1.44/1.27 tff(3380,plain,
% 1.44/1.27 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3381,plain,
% 1.44/1.27 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342))) <=> (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3382,plain,
% 1.44/1.27 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3381])).
% 1.44/1.27 tff(3383,plain,
% 1.44/1.27 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.44/1.27 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.44/1.27 tff(3384,plain,
% 1.44/1.27 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))),
% 1.44/1.27 inference(quant_inst,[status(thm)],[])).
% 1.44/1.27 tff(3385,plain,
% 1.44/1.27 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.44/1.27 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.44/1.27 tff(3386,plain,
% 1.44/1.27 ($false),
% 1.44/1.27 inference(unit_resolution,[status(thm)],[3385, 181, 3379, 3366, 39, 28, 17, 10])).
% 1.44/1.27 tff(3387,plain,(~hskp25), inference(lemma,lemma(discharge,[]))).
% 1.44/1.27 tff(3388,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3389,plain,
% 1.44/1.27 ((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.44/1.27 inference(rewrite,[status(thm)],[])).
% 1.44/1.27 tff(3390,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278))))),
% 1.44/1.27 inference(monotonicity,[status(thm)],[3389])).
% 1.44/1.27 tff(3391,plain,
% 1.44/1.27 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.44/1.28 inference(transitivity,[status(thm)],[3390, 3388])).
% 1.44/1.28 tff(3392,plain,
% 1.44/1.28 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))),
% 1.44/1.28 inference(quant_inst,[status(thm)],[])).
% 1.44/1.28 tff(3393,plain,
% 1.44/1.28 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278))),
% 1.44/1.28 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 1.44/1.28 tff(3394,plain,
% 1.44/1.28 (hskp25 | hskp23),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3393, 181, 3362, 3364, 2030, 3365])).
% 1.44/1.28 tff(3395,plain,
% 1.44/1.28 (hskp23),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3394, 3387])).
% 1.44/1.28 tff(3396,plain,
% 1.44/1.28 ((~hskp23) | c1_1(a2282)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[1186, 3360])).
% 1.44/1.28 tff(3397,plain,
% 1.44/1.28 (c1_1(a2282)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3396, 3395])).
% 1.44/1.28 tff(3398,plain,
% 1.44/1.28 (hskp4),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[1005, 3360])).
% 1.44/1.28 tff(3399,plain,
% 1.44/1.28 (~c0_1(a2282)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[199, 3398])).
% 1.44/1.28 tff(3400,plain,
% 1.44/1.28 (c2_1(a2282)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[247, 3398])).
% 1.44/1.28 tff(3401,plain,
% 1.44/1.28 (hskp18 | (~c1_1(a2282))),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3221, 181, 3363, 3364, 3400, 3399, 2632, 3365])).
% 1.44/1.28 tff(3402,plain,
% 1.44/1.28 (hskp18),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3401, 3397])).
% 1.44/1.28 tff(3403,plain,
% 1.44/1.28 (~c1_1(a2308)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[2650, 3402])).
% 1.44/1.28 tff(3404,plain,
% 1.44/1.28 (c3_1(a2308)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[2668, 3402])).
% 1.44/1.28 tff(3405,plain,
% 1.44/1.28 (~c2_1(a2308)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[2644, 3402])).
% 1.44/1.28 tff(3406,plain,
% 1.44/1.28 (hskp17 | (~c3_1(a2308)) | c2_1(a2308) | c1_1(a2308)),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3250, 3360, 3363, 3362, 3364])).
% 1.44/1.28 tff(3407,plain,
% 1.44/1.28 ($false),
% 1.44/1.28 inference(unit_resolution,[status(thm)],[3406, 3405, 3404, 3369, 3403])).
% 1.44/1.28 % SZS output end Proof
%------------------------------------------------------------------------------