TSTP Solution File: SYN471-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN471-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 23:55:42 EDT 2022
% Result : Unsatisfiable 0.79s 0.75s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN471-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.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 04:06:16 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.
% 0.79/0.75 % SZS status Unsatisfiable
% 0.79/0.75 % SZS output start Proof
% 0.79/0.75 tff(c0_1_type, type, (
% 0.79/0.75 c0_1: $i > $o)).
% 0.79/0.75 tff(a651_type, type, (
% 0.79/0.75 a651: $i)).
% 0.79/0.75 tff(a615_type, type, (
% 0.79/0.75 a615: $i)).
% 0.79/0.75 tff(hskp14_type, type, (
% 0.79/0.75 hskp14: $o)).
% 0.79/0.75 tff(hskp10_type, type, (
% 0.79/0.75 hskp10: $o)).
% 0.79/0.75 tff(c2_1_type, type, (
% 0.79/0.75 c2_1: $i > $o)).
% 0.79/0.75 tff(c3_1_type, type, (
% 0.79/0.75 c3_1: $i > $o)).
% 0.79/0.75 tff(ndr1_0_type, type, (
% 0.79/0.75 ndr1_0: $o)).
% 0.79/0.75 tff(a605_type, type, (
% 0.79/0.75 a605: $i)).
% 0.79/0.75 tff(hskp1_type, type, (
% 0.79/0.75 hskp1: $o)).
% 0.79/0.75 tff(hskp31_type, type, (
% 0.79/0.75 hskp31: $o)).
% 0.79/0.75 tff(hskp24_type, type, (
% 0.79/0.75 hskp24: $o)).
% 0.79/0.75 tff(hskp12_type, type, (
% 0.79/0.75 hskp12: $o)).
% 0.79/0.75 tff(c1_1_type, type, (
% 0.79/0.75 c1_1: $i > $o)).
% 0.79/0.75 tff(a609_type, type, (
% 0.79/0.75 a609: $i)).
% 0.79/0.75 tff(a672_type, type, (
% 0.79/0.75 a672: $i)).
% 0.79/0.75 tff(a604_type, type, (
% 0.79/0.75 a604: $i)).
% 0.79/0.75 tff(hskp9_type, type, (
% 0.79/0.75 hskp9: $o)).
% 0.79/0.75 tff(a598_type, type, (
% 0.79/0.75 a598: $i)).
% 0.79/0.75 tff(hskp4_type, type, (
% 0.79/0.75 hskp4: $o)).
% 0.79/0.75 tff(a644_type, type, (
% 0.79/0.75 a644: $i)).
% 0.79/0.75 tff(hskp22_type, type, (
% 0.79/0.75 hskp22: $o)).
% 0.79/0.75 tff(a594_type, type, (
% 0.79/0.75 a594: $i)).
% 0.79/0.75 tff(a656_type, type, (
% 0.79/0.75 a656: $i)).
% 0.79/0.75 tff(hskp25_type, type, (
% 0.79/0.75 hskp25: $o)).
% 0.79/0.75 tff(a595_type, type, (
% 0.79/0.75 a595: $i)).
% 0.79/0.75 tff(hskp28_type, type, (
% 0.79/0.75 hskp28: $o)).
% 0.79/0.75 tff(a603_type, type, (
% 0.79/0.75 a603: $i)).
% 0.79/0.75 tff(hskp8_type, type, (
% 0.79/0.75 hskp8: $o)).
% 0.79/0.75 tff(hskp21_type, type, (
% 0.79/0.75 hskp21: $o)).
% 0.79/0.75 tff(a631_type, type, (
% 0.79/0.75 a631: $i)).
% 0.79/0.75 tff(hskp11_type, type, (
% 0.79/0.75 hskp11: $o)).
% 0.79/0.75 tff(a599_type, type, (
% 0.79/0.75 a599: $i)).
% 0.79/0.75 tff(hskp5_type, type, (
% 0.79/0.75 hskp5: $o)).
% 0.79/0.75 tff(a608_type, type, (
% 0.79/0.75 a608: $i)).
% 0.79/0.75 tff(a625_type, type, (
% 0.79/0.75 a625: $i)).
% 0.79/0.75 tff(a597_type, type, (
% 0.79/0.75 a597: $i)).
% 0.79/0.75 tff(hskp3_type, type, (
% 0.79/0.75 hskp3: $o)).
% 0.79/0.75 tff(a627_type, type, (
% 0.79/0.75 a627: $i)).
% 0.79/0.75 tff(hskp19_type, type, (
% 0.79/0.75 hskp19: $o)).
% 0.79/0.75 tff(hskp7_type, type, (
% 0.79/0.75 hskp7: $o)).
% 0.79/0.75 tff(hskp18_type, type, (
% 0.79/0.75 hskp18: $o)).
% 0.79/0.75 tff(a602_type, type, (
% 0.79/0.75 a602: $i)).
% 0.79/0.75 tff(1,assumption,(~c0_1(a651)), introduced(assumption)).
% 0.79/0.75 tff(2,assumption,(~hskp14), introduced(assumption)).
% 0.79/0.75 tff(3,plain,
% 0.79/0.75 (^[U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.79/0.75 inference(bind,[status(th)],[])).
% 0.79/0.75 tff(4,plain,
% 0.79/0.75 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.75 inference(quant_intro,[status(thm)],[3])).
% 0.79/0.75 tff(5,plain,
% 0.79/0.75 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.75 inference(rewrite,[status(thm)],[])).
% 0.79/0.75 tff(6,plain,
% 0.79/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.79/0.75 inference(bind,[status(th)],[])).
% 0.79/0.75 tff(7,plain,
% 0.79/0.75 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.75 inference(quant_intro,[status(thm)],[6])).
% 0.79/0.75 tff(8,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.79/0.75 tff(9,plain,
% 0.79/0.75 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.79/0.75 tff(10,plain,
% 0.79/0.75 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.75 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.79/0.75 tff(11,plain,(
% 0.79/0.75 ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.76 inference(skolemize,[status(sab)],[10])).
% 0.79/0.76 tff(12,plain,
% 0.79/0.76 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.79/0.76 tff(13,assumption,(hskp10), introduced(assumption)).
% 0.79/0.76 tff(14,plain,
% 0.79/0.76 (((~hskp10) | (~c3_1(a605))) <=> ((~hskp10) | (~c3_1(a605)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(15,plain,
% 0.79/0.76 (((~c3_1(a605)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a605)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(16,axiom,((~c3_1(a605)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.79/0.76 tff(17,plain,
% 0.79/0.76 ((~hskp10) | (~c3_1(a605))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.79/0.76 tff(18,plain,
% 0.79/0.76 ((~hskp10) | (~c3_1(a605))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.79/0.76 tff(19,plain,
% 0.79/0.76 (~c3_1(a605)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.79/0.76 tff(20,plain,
% 0.79/0.76 (((~hskp10) | c2_1(a605)) <=> ((~hskp10) | c2_1(a605))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(21,axiom,((~hskp10) | c2_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.79/0.76 tff(22,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.79/0.76 tff(23,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.79/0.76 tff(24,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.79/0.76 tff(25,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.79/0.76 tff(26,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.79/0.76 tff(27,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.79/0.76 tff(28,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.79/0.76 tff(29,plain,
% 0.79/0.76 ((~hskp10) | c2_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.79/0.76 tff(30,plain,
% 0.79/0.76 (c2_1(a605)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[29, 13])).
% 0.79/0.76 tff(31,plain,
% 0.79/0.76 (((~hskp10) | c0_1(a605)) <=> ((~hskp10) | c0_1(a605))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(32,axiom,((~hskp10) | c0_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.79/0.76 tff(33,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.79/0.76 tff(34,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.79/0.76 tff(35,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.79/0.76 tff(36,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.79/0.76 tff(37,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.79/0.76 tff(38,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.79/0.76 tff(39,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.79/0.76 tff(40,plain,
% 0.79/0.76 ((~hskp10) | c0_1(a605)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.79/0.76 tff(41,plain,
% 0.79/0.76 (c0_1(a605)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[40, 13])).
% 0.79/0.76 tff(42,assumption,(~ndr1_0), introduced(assumption)).
% 0.79/0.76 tff(43,plain,
% 0.79/0.76 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(44,plain,
% 0.79/0.76 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(45,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.79/0.76 tff(46,plain,
% 0.79/0.76 (ndr1_0 | (~hskp1)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.79/0.76 tff(47,plain,
% 0.79/0.76 (ndr1_0 | (~hskp1)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.79/0.76 tff(48,plain,
% 0.79/0.76 (~hskp1),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[47, 42])).
% 0.79/0.76 tff(49,plain,
% 0.79/0.76 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(50,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.79/0.76 tff(51,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.79/0.76 tff(52,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.79/0.76 tff(53,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.79/0.76 tff(54,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.79/0.76 tff(55,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.79/0.76 tff(56,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[55, 49])).
% 0.79/0.76 tff(57,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.79/0.76 tff(58,plain,
% 0.79/0.76 ((~hskp31) | ndr1_0),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.79/0.76 tff(59,plain,
% 0.79/0.76 (~hskp31),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.79/0.76 tff(60,plain,
% 0.79/0.76 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(61,plain,
% 0.79/0.76 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(62,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 0.79/0.76 tff(63,plain,
% 0.79/0.76 (ndr1_0 | (~hskp24)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.79/0.76 tff(64,plain,
% 0.79/0.76 (ndr1_0 | (~hskp24)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.79/0.76 tff(65,plain,
% 0.79/0.76 (~hskp24),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[64, 42])).
% 0.79/0.76 tff(66,plain,
% 0.79/0.76 ((hskp24 | hskp31 | hskp1) <=> (hskp24 | hskp31 | hskp1)),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(67,plain,
% 0.79/0.76 (((hskp1 | hskp31) | hskp24) <=> (hskp24 | hskp31 | hskp1)),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(68,axiom,((hskp1 | hskp31) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.79/0.76 tff(69,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.79/0.76 tff(70,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.79/0.76 tff(71,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.79/0.76 tff(72,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.79/0.76 tff(73,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.79/0.76 tff(74,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.79/0.76 tff(75,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.79/0.76 tff(76,plain,
% 0.79/0.76 (hskp24 | hskp31 | hskp1),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[75, 66])).
% 0.79/0.76 tff(77,plain,
% 0.79/0.76 ($false),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[76, 65, 59, 48])).
% 0.79/0.76 tff(78,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.79/0.76 tff(79,plain,
% 0.79/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(80,plain,
% 0.79/0.76 ((hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605))) <=> (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(81,plain,
% 0.79/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605))))),
% 0.79/0.76 inference(monotonicity,[status(thm)],[80])).
% 0.79/0.76 tff(82,plain,
% 0.79/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.79/0.76 inference(transitivity,[status(thm)],[81, 79])).
% 0.79/0.76 tff(83,plain,
% 0.79/0.76 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.79/0.76 inference(quant_inst,[status(thm)],[])).
% 0.79/0.76 tff(84,plain,
% 0.79/0.76 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.79/0.76 tff(85,plain,
% 0.79/0.76 ($false),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[84, 78, 2, 41, 30, 19, 12])).
% 0.79/0.76 tff(86,plain,((~hskp10) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.79/0.76 tff(87,plain,
% 0.79/0.76 (~hskp10),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[86, 2])).
% 0.79/0.76 tff(88,assumption,(hskp12), introduced(assumption)).
% 0.79/0.76 tff(89,plain,
% 0.79/0.76 (((~hskp12) | (~c1_1(a609))) <=> ((~hskp12) | (~c1_1(a609)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(90,plain,
% 0.79/0.76 (((~c1_1(a609)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a609)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(91,axiom,((~c1_1(a609)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.79/0.76 tff(92,plain,
% 0.79/0.76 ((~hskp12) | (~c1_1(a609))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.79/0.76 tff(93,plain,
% 0.79/0.76 ((~hskp12) | (~c1_1(a609))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.79/0.76 tff(94,plain,
% 0.79/0.76 (~c1_1(a609)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.79/0.76 tff(95,plain,
% 0.79/0.76 (((~hskp12) | c2_1(a609)) <=> ((~hskp12) | c2_1(a609))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(96,axiom,((~hskp12) | c2_1(a609)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.79/0.76 tff(97,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.79/0.76 tff(98,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[97, 95])).
% 0.79/0.76 tff(99,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.79/0.76 tff(100,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.79/0.76 tff(101,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.79/0.76 tff(102,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.79/0.76 tff(103,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.79/0.76 tff(104,plain,
% 0.79/0.76 ((~hskp12) | c2_1(a609)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[103, 95])).
% 0.79/0.76 tff(105,plain,
% 0.79/0.76 (c2_1(a609)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[104, 88])).
% 0.79/0.76 tff(106,plain,
% 0.79/0.76 (((~hskp12) | (~c3_1(a609))) <=> ((~hskp12) | (~c3_1(a609)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(107,plain,
% 0.79/0.76 (((~c3_1(a609)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a609)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(108,axiom,((~c3_1(a609)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.79/0.76 tff(109,plain,
% 0.79/0.76 ((~hskp12) | (~c3_1(a609))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.79/0.76 tff(110,plain,
% 0.79/0.76 ((~hskp12) | (~c3_1(a609))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.79/0.76 tff(111,plain,
% 0.79/0.76 (~c3_1(a609)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[110, 88])).
% 0.79/0.76 tff(112,plain,
% 0.79/0.76 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(113,plain,
% 0.79/0.76 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[112])).
% 0.79/0.76 tff(114,plain,
% 0.79/0.76 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(115,plain,
% 0.79/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(116,plain,
% 0.79/0.76 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[115])).
% 0.79/0.76 tff(117,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.79/0.76 tff(118,plain,
% 0.79/0.76 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.79/0.76 tff(119,plain,
% 0.79/0.76 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.79/0.76 tff(120,plain,(
% 0.79/0.76 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(skolemize,[status(sab)],[119])).
% 0.79/0.76 tff(121,plain,
% 0.79/0.76 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.79/0.76 tff(122,plain,
% 0.79/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(123,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[122])).
% 0.79/0.76 tff(124,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(125,plain,
% 0.79/0.76 (^[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))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(126,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[125])).
% 0.79/0.76 tff(127,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.79/0.76 tff(128,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.79/0.76 tff(129,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.79/0.76 tff(130,plain,(
% 0.79/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(skolemize,[status(sab)],[129])).
% 0.79/0.76 tff(131,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.79/0.76 tff(132,assumption,(~hskp24), introduced(assumption)).
% 0.79/0.76 tff(133,plain,
% 0.79/0.76 ((hskp9 | hskp24) <=> (hskp9 | hskp24)),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(134,axiom,(hskp9 | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.79/0.76 tff(135,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.79/0.76 tff(136,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[135, 133])).
% 0.79/0.76 tff(137,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.79/0.76 tff(138,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.79/0.76 tff(139,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[138, 133])).
% 0.79/0.76 tff(140,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.79/0.76 tff(141,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.79/0.76 tff(142,plain,
% 0.79/0.76 (hskp9 | hskp24),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[141, 133])).
% 0.79/0.76 tff(143,plain,
% 0.79/0.76 (hskp9),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[142, 132])).
% 0.79/0.76 tff(144,plain,
% 0.79/0.76 (((~hskp9) | (~c0_1(a604))) <=> ((~hskp9) | (~c0_1(a604)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(145,plain,
% 0.79/0.76 (((~c0_1(a604)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a604)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(146,axiom,((~c0_1(a604)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.79/0.76 tff(147,plain,
% 0.79/0.76 ((~hskp9) | (~c0_1(a604))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.79/0.76 tff(148,plain,
% 0.79/0.76 ((~hskp9) | (~c0_1(a604))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.79/0.76 tff(149,plain,
% 0.79/0.76 (~c0_1(a604)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[148, 143])).
% 0.79/0.76 tff(150,plain,
% 0.79/0.76 (((~hskp9) | c2_1(a604)) <=> ((~hskp9) | c2_1(a604))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(151,axiom,((~hskp9) | c2_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.79/0.76 tff(152,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.79/0.76 tff(153,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[152, 150])).
% 0.79/0.76 tff(154,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.79/0.76 tff(155,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.79/0.76 tff(156,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[155, 150])).
% 0.79/0.76 tff(157,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[156, 150])).
% 0.79/0.76 tff(158,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.79/0.76 tff(159,plain,
% 0.79/0.76 ((~hskp9) | c2_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[158, 150])).
% 0.79/0.76 tff(160,plain,
% 0.79/0.76 (c2_1(a604)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[159, 143])).
% 0.79/0.76 tff(161,plain,
% 0.79/0.76 (((~hskp9) | c1_1(a604)) <=> ((~hskp9) | c1_1(a604))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(162,axiom,((~hskp9) | c1_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.79/0.76 tff(163,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.79/0.76 tff(164,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[163, 161])).
% 0.79/0.76 tff(165,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[164, 161])).
% 0.79/0.76 tff(166,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.79/0.76 tff(167,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[166, 161])).
% 0.79/0.76 tff(168,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[167, 161])).
% 0.79/0.76 tff(169,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.79/0.76 tff(170,plain,
% 0.79/0.76 ((~hskp9) | c1_1(a604)),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[169, 161])).
% 0.79/0.76 tff(171,plain,
% 0.79/0.76 (c1_1(a604)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[170, 143])).
% 0.79/0.76 tff(172,plain,
% 0.79/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(173,plain,
% 0.79/0.76 (((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(174,plain,
% 0.79/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 0.79/0.76 inference(monotonicity,[status(thm)],[173])).
% 0.79/0.76 tff(175,plain,
% 0.79/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.79/0.76 inference(transitivity,[status(thm)],[174, 172])).
% 0.79/0.76 tff(176,plain,
% 0.79/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.79/0.76 inference(quant_inst,[status(thm)],[])).
% 0.79/0.76 tff(177,plain,
% 0.79/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604))),
% 0.79/0.76 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.79/0.76 tff(178,plain,
% 0.79/0.76 (~c3_1(a604)),
% 0.79/0.76 inference(unit_resolution,[status(thm)],[177, 78, 171, 160, 149, 131])).
% 0.79/0.76 tff(179,plain,
% 0.79/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.79/0.76 inference(bind,[status(th)],[])).
% 0.79/0.76 tff(180,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.76 inference(quant_intro,[status(thm)],[179])).
% 0.79/0.76 tff(181,plain,
% 0.79/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.76 inference(rewrite,[status(thm)],[])).
% 0.79/0.76 tff(182,plain,
% 0.79/0.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(183,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[182])).
% 0.84/0.77 tff(184,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.84/0.77 tff(185,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.84/0.77 tff(186,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.84/0.77 tff(187,plain,(
% 0.84/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(skolemize,[status(sab)],[186])).
% 0.84/0.77 tff(188,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.84/0.77 tff(189,plain,
% 0.84/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(190,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[189])).
% 0.84/0.77 tff(191,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(192,plain,
% 0.84/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(193,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[192])).
% 0.84/0.77 tff(194,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.84/0.77 tff(195,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.84/0.77 tff(196,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.84/0.77 tff(197,plain,(
% 0.84/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(skolemize,[status(sab)],[196])).
% 0.84/0.77 tff(198,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.84/0.77 tff(199,assumption,(hskp1), introduced(assumption)).
% 0.84/0.77 tff(200,plain,
% 0.84/0.77 (((~hskp1) | (~c3_1(a594))) <=> ((~hskp1) | (~c3_1(a594)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(201,plain,
% 0.84/0.77 (((~c3_1(a594)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a594)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(202,axiom,((~c3_1(a594)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.84/0.77 tff(203,plain,
% 0.84/0.77 ((~hskp1) | (~c3_1(a594))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.84/0.77 tff(204,plain,
% 0.84/0.77 ((~hskp1) | (~c3_1(a594))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[203, 200])).
% 0.84/0.77 tff(205,plain,
% 0.84/0.77 (~c3_1(a594)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[204, 199])).
% 0.84/0.77 tff(206,plain,
% 0.84/0.77 (((~hskp1) | c1_1(a594)) <=> ((~hskp1) | c1_1(a594))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(207,axiom,((~hskp1) | c1_1(a594)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.84/0.77 tff(208,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.84/0.77 tff(209,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[208, 206])).
% 0.84/0.77 tff(210,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.84/0.77 tff(211,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.84/0.77 tff(212,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[211, 206])).
% 0.84/0.77 tff(213,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[212, 206])).
% 0.84/0.77 tff(214,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.84/0.77 tff(215,plain,
% 0.84/0.77 ((~hskp1) | c1_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[214, 206])).
% 0.84/0.77 tff(216,plain,
% 0.84/0.77 (c1_1(a594)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[215, 199])).
% 0.84/0.77 tff(217,plain,
% 0.84/0.77 (((~hskp1) | c0_1(a594)) <=> ((~hskp1) | c0_1(a594))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(218,axiom,((~hskp1) | c0_1(a594)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.84/0.77 tff(219,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.84/0.77 tff(220,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[219, 217])).
% 0.84/0.77 tff(221,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.84/0.77 tff(222,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.84/0.77 tff(223,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[222, 217])).
% 0.84/0.77 tff(224,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[223, 217])).
% 0.84/0.77 tff(225,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.84/0.77 tff(226,plain,
% 0.84/0.77 ((~hskp1) | c0_1(a594)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[225, 217])).
% 0.84/0.77 tff(227,plain,
% 0.84/0.77 (c0_1(a594)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[226, 199])).
% 0.84/0.77 tff(228,assumption,(~c3_1(a604)), introduced(assumption)).
% 0.84/0.77 tff(229,assumption,(~c3_1(a594)), introduced(assumption)).
% 0.84/0.77 tff(230,assumption,(~c0_1(a604)), introduced(assumption)).
% 0.84/0.77 tff(231,assumption,(c1_1(a594)), introduced(assumption)).
% 0.84/0.77 tff(232,assumption,(c0_1(a594)), introduced(assumption)).
% 0.84/0.77 tff(233,assumption,(c1_1(a604)), introduced(assumption)).
% 0.84/0.77 tff(234,assumption,(hskp4), introduced(assumption)).
% 0.84/0.77 tff(235,plain,
% 0.84/0.77 (((~hskp4) | (~c2_1(a598))) <=> ((~hskp4) | (~c2_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(236,plain,
% 0.84/0.77 (((~c2_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(237,axiom,((~c2_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.84/0.77 tff(238,plain,
% 0.84/0.77 ((~hskp4) | (~c2_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.84/0.77 tff(239,plain,
% 0.84/0.77 ((~hskp4) | (~c2_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.84/0.77 tff(240,plain,
% 0.84/0.77 (~c2_1(a598)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[239, 234])).
% 0.84/0.77 tff(241,plain,
% 0.84/0.77 (((~hskp4) | (~c0_1(a598))) <=> ((~hskp4) | (~c0_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(242,plain,
% 0.84/0.77 (((~c0_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(243,axiom,((~c0_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.84/0.77 tff(244,plain,
% 0.84/0.77 ((~hskp4) | (~c0_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.84/0.77 tff(245,plain,
% 0.84/0.77 ((~hskp4) | (~c0_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.84/0.77 tff(246,plain,
% 0.84/0.77 (~c0_1(a598)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[245, 234])).
% 0.84/0.77 tff(247,plain,
% 0.84/0.77 (((~hskp4) | (~c1_1(a598))) <=> ((~hskp4) | (~c1_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(248,plain,
% 0.84/0.77 (((~c1_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a598)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(249,axiom,((~c1_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.84/0.77 tff(250,plain,
% 0.84/0.77 ((~hskp4) | (~c1_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.84/0.77 tff(251,plain,
% 0.84/0.77 ((~hskp4) | (~c1_1(a598))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.84/0.77 tff(252,plain,
% 0.84/0.77 (~c1_1(a598)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[251, 234])).
% 0.84/0.77 tff(253,assumption,(~c0_1(a598)), introduced(assumption)).
% 0.84/0.77 tff(254,plain,
% 0.84/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(255,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[254])).
% 0.84/0.77 tff(256,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(257,plain,
% 0.84/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(258,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[257])).
% 0.84/0.77 tff(259,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.84/0.77 tff(260,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.84/0.77 tff(261,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.84/0.77 tff(262,plain,(
% 0.84/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(skolemize,[status(sab)],[261])).
% 0.84/0.77 tff(263,plain,
% 0.84/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.84/0.77 tff(264,assumption,(~c1_1(a598)), introduced(assumption)).
% 0.84/0.77 tff(265,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(266,plain,
% 0.84/0.77 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598))) <=> (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(267,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604))))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[266])).
% 0.84/0.77 tff(268,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.77 inference(transitivity,[status(thm)],[267, 265])).
% 0.84/0.77 tff(269,plain,
% 0.84/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(270,plain,
% 0.84/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.84/0.77 tff(271,plain,
% 0.84/0.77 (c0_1(a598) | (~c3_1(a598))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[270, 78, 233, 232, 231, 230, 264, 229, 263, 228])).
% 0.84/0.77 tff(272,plain,
% 0.84/0.77 (~c3_1(a598)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[271, 253])).
% 0.84/0.77 tff(273,assumption,(~c2_1(a598)), introduced(assumption)).
% 0.84/0.77 tff(274,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(275,plain,
% 0.84/0.77 (((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(276,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598)))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[275])).
% 0.84/0.77 tff(277,plain,
% 0.84/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.84/0.77 inference(transitivity,[status(thm)],[276, 274])).
% 0.84/0.77 tff(278,plain,
% 0.84/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(279,plain,
% 0.84/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.84/0.77 tff(280,plain,
% 0.84/0.77 ($false),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[279, 78, 253, 264, 273, 198, 272])).
% 0.84/0.77 tff(281,plain,(c0_1(a598) | c1_1(a598) | c2_1(a598) | (~c1_1(a604)) | (~c0_1(a594)) | (~c1_1(a594)) | c0_1(a604) | c3_1(a594) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.77 tff(282,plain,
% 0.84/0.77 ($false),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[281, 252, 246, 240, 233, 232, 231, 230, 229, 228])).
% 0.84/0.77 tff(283,plain,((~hskp4) | (~c1_1(a604)) | (~c0_1(a594)) | (~c1_1(a594)) | c0_1(a604) | c3_1(a594) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.77 tff(284,plain,
% 0.84/0.77 (~hskp4),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[283, 227, 171, 216, 149, 205, 178])).
% 0.84/0.77 tff(285,plain,
% 0.84/0.77 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(286,plain,
% 0.84/0.78 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[285])).
% 0.84/0.78 tff(287,plain,
% 0.84/0.78 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(288,plain,
% 0.84/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(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)) | 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) | (~c2_1(U)) | (~c3_1(U)) | (~c0_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)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_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)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(289,plain,
% 0.84/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[288])).
% 0.84/0.78 tff(290,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)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.84/0.78 tff(291,plain,
% 0.84/0.78 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.84/0.78 tff(292,plain,
% 0.84/0.78 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.84/0.78 tff(293,plain,(
% 0.84/0.78 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(skolemize,[status(sab)],[292])).
% 0.84/0.78 tff(294,plain,
% 0.84/0.78 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.84/0.78 tff(295,assumption,(hskp14), introduced(assumption)).
% 0.84/0.78 tff(296,plain,
% 0.84/0.78 (((~hskp14) | c2_1(a615)) <=> ((~hskp14) | c2_1(a615))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(297,axiom,((~hskp14) | c2_1(a615)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.84/0.78 tff(298,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.84/0.78 tff(299,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[298, 296])).
% 0.84/0.78 tff(300,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[299, 296])).
% 0.84/0.78 tff(301,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.84/0.78 tff(302,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[301, 296])).
% 0.84/0.78 tff(303,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[302, 296])).
% 0.84/0.78 tff(304,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.84/0.78 tff(305,plain,
% 0.84/0.78 ((~hskp14) | c2_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[304, 296])).
% 0.84/0.78 tff(306,plain,
% 0.84/0.78 (c2_1(a615)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[305, 295])).
% 0.84/0.78 tff(307,plain,
% 0.84/0.78 (((~hskp14) | c0_1(a615)) <=> ((~hskp14) | c0_1(a615))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(308,axiom,((~hskp14) | c0_1(a615)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.84/0.78 tff(309,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.84/0.78 tff(310,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[309, 307])).
% 0.84/0.78 tff(311,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[310, 307])).
% 0.84/0.78 tff(312,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.84/0.78 tff(313,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[312, 307])).
% 0.84/0.78 tff(314,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[313, 307])).
% 0.84/0.78 tff(315,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.84/0.78 tff(316,plain,
% 0.84/0.78 ((~hskp14) | c0_1(a615)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[315, 307])).
% 0.84/0.78 tff(317,plain,
% 0.84/0.78 (c0_1(a615)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[316, 295])).
% 0.84/0.78 tff(318,plain,
% 0.84/0.78 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(319,plain,
% 0.84/0.78 ((hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594))) <=> (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(320,plain,
% 0.84/0.78 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[319])).
% 0.84/0.78 tff(321,plain,
% 0.84/0.78 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(transitivity,[status(thm)],[320, 318])).
% 0.84/0.78 tff(322,plain,
% 0.84/0.78 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(323,plain,
% 0.84/0.78 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.84/0.78 tff(324,plain,
% 0.84/0.78 (~c3_1(a615)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[323, 132, 78, 317, 306, 232, 231, 229, 294])).
% 0.84/0.78 tff(325,plain,
% 0.84/0.78 (^[U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(326,plain,
% 0.84/0.78 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[325])).
% 0.84/0.78 tff(327,plain,
% 0.84/0.78 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(328,plain,
% 0.84/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(329,plain,
% 0.84/0.78 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[328])).
% 0.84/0.78 tff(330,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.84/0.78 tff(331,plain,
% 0.84/0.78 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.84/0.78 tff(332,plain,
% 0.84/0.78 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.84/0.78 tff(333,plain,(
% 0.84/0.78 ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(skolemize,[status(sab)],[332])).
% 0.84/0.78 tff(334,plain,
% 0.84/0.78 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.84/0.78 tff(335,plain,
% 0.84/0.78 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(336,plain,
% 0.84/0.78 ((hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(337,plain,
% 0.84/0.78 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[336])).
% 0.84/0.78 tff(338,plain,
% 0.84/0.78 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(transitivity,[status(thm)],[337, 335])).
% 0.84/0.78 tff(339,plain,
% 0.84/0.78 ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(340,plain,
% 0.84/0.78 ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.84/0.78 tff(341,plain,
% 0.84/0.78 (hskp25 | c3_1(a615)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[340, 78, 317, 306, 334])).
% 0.84/0.78 tff(342,plain,
% 0.84/0.78 (hskp25),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[341, 324])).
% 0.84/0.78 tff(343,plain,
% 0.84/0.78 (((~hskp25) | (~c0_1(a656))) <=> ((~hskp25) | (~c0_1(a656)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(344,plain,
% 0.84/0.78 (((~c0_1(a656)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a656)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(345,axiom,((~c0_1(a656)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.84/0.78 tff(346,plain,
% 0.84/0.78 ((~hskp25) | (~c0_1(a656))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.84/0.78 tff(347,plain,
% 0.84/0.78 ((~hskp25) | (~c0_1(a656))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.84/0.78 tff(348,plain,
% 0.84/0.78 (~c0_1(a656)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[347, 342])).
% 0.84/0.78 tff(349,plain,
% 0.84/0.78 (((~hskp25) | c3_1(a656)) <=> ((~hskp25) | c3_1(a656))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(350,axiom,((~hskp25) | c3_1(a656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.84/0.78 tff(351,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.84/0.78 tff(352,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[351, 349])).
% 0.84/0.78 tff(353,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[352, 349])).
% 0.84/0.78 tff(354,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.84/0.78 tff(355,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[354, 349])).
% 0.84/0.78 tff(356,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[355, 349])).
% 0.84/0.78 tff(357,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[356, 349])).
% 0.84/0.78 tff(358,plain,
% 0.84/0.78 ((~hskp25) | c3_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[357, 349])).
% 0.84/0.78 tff(359,plain,
% 0.84/0.78 (c3_1(a656)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[358, 342])).
% 0.84/0.78 tff(360,plain,
% 0.84/0.78 (((~hskp25) | c1_1(a656)) <=> ((~hskp25) | c1_1(a656))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(361,axiom,((~hskp25) | c1_1(a656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.84/0.78 tff(362,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.84/0.78 tff(363,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[362, 360])).
% 0.84/0.78 tff(364,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[363, 360])).
% 0.84/0.78 tff(365,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[364, 360])).
% 0.84/0.78 tff(366,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[365, 360])).
% 0.84/0.78 tff(367,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[366, 360])).
% 0.84/0.78 tff(368,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[367, 360])).
% 0.84/0.78 tff(369,plain,
% 0.84/0.78 ((~hskp25) | c1_1(a656)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[368, 360])).
% 0.84/0.78 tff(370,plain,
% 0.84/0.78 (c1_1(a656)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[369, 342])).
% 0.84/0.78 tff(371,plain,
% 0.84/0.78 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(372,plain,
% 0.84/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[371])).
% 0.84/0.78 tff(373,plain,
% 0.84/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(374,plain,
% 0.84/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> ((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(375,plain,
% 0.84/0.78 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[374])).
% 0.84/0.78 tff(376,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.84/0.78 tff(377,plain,
% 0.84/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.84/0.78 tff(378,plain,
% 0.84/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[377, 373])).
% 0.84/0.78 tff(379,plain,(
% 0.84/0.78 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(skolemize,[status(sab)],[378])).
% 0.84/0.78 tff(380,plain,
% 0.84/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[379, 372])).
% 0.84/0.78 tff(381,assumption,(~hskp4), introduced(assumption)).
% 0.84/0.78 tff(382,plain,
% 0.84/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(383,plain,
% 0.84/0.78 ((hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(384,plain,
% 0.84/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[383])).
% 0.84/0.78 tff(385,plain,
% 0.84/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.84/0.78 inference(transitivity,[status(thm)],[384, 382])).
% 0.84/0.78 tff(386,plain,
% 0.84/0.78 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(387,plain,
% 0.84/0.78 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.84/0.78 tff(388,plain,
% 0.84/0.78 (hskp28 | c3_1(a615)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[387, 78, 381, 317, 306, 380])).
% 0.84/0.78 tff(389,plain,
% 0.84/0.78 (hskp28),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[388, 324])).
% 0.84/0.78 tff(390,plain,
% 0.84/0.78 (((~hskp28) | c3_1(a595)) <=> ((~hskp28) | c3_1(a595))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(391,axiom,((~hskp28) | c3_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.84/0.78 tff(392,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.84/0.78 tff(393,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[392, 390])).
% 0.84/0.78 tff(394,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.84/0.78 tff(395,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[394, 390])).
% 0.84/0.78 tff(396,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[395, 390])).
% 0.84/0.78 tff(397,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[396, 390])).
% 0.84/0.78 tff(398,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[397, 390])).
% 0.84/0.78 tff(399,plain,
% 0.84/0.78 ((~hskp28) | c3_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[398, 390])).
% 0.84/0.78 tff(400,plain,
% 0.84/0.78 (c3_1(a595)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[399, 389])).
% 0.84/0.78 tff(401,plain,
% 0.84/0.78 (((~hskp28) | c2_1(a595)) <=> ((~hskp28) | c2_1(a595))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(402,axiom,((~hskp28) | c2_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.84/0.78 tff(403,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.84/0.78 tff(404,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[403, 401])).
% 0.84/0.78 tff(405,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[404, 401])).
% 0.84/0.78 tff(406,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.84/0.78 tff(407,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[406, 401])).
% 0.84/0.78 tff(408,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[407, 401])).
% 0.84/0.78 tff(409,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[408, 401])).
% 0.84/0.78 tff(410,plain,
% 0.84/0.78 ((~hskp28) | c2_1(a595)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[409, 401])).
% 0.84/0.78 tff(411,plain,
% 0.84/0.78 (c2_1(a595)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[410, 389])).
% 0.84/0.78 tff(412,plain,
% 0.84/0.78 (((~hskp28) | c1_1(a595)) <=> ((~hskp28) | c1_1(a595))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(413,axiom,((~hskp28) | c1_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.84/0.79 tff(414,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.84/0.79 tff(415,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[414, 412])).
% 0.84/0.79 tff(416,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[415, 412])).
% 0.84/0.79 tff(417,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[416, 412])).
% 0.84/0.79 tff(418,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[417, 412])).
% 0.84/0.79 tff(419,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[418, 412])).
% 0.84/0.79 tff(420,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[419, 412])).
% 0.84/0.79 tff(421,plain,
% 0.84/0.79 ((~hskp28) | c1_1(a595)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[420, 412])).
% 0.84/0.79 tff(422,plain,
% 0.84/0.79 (c1_1(a595)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[421, 389])).
% 0.84/0.79 tff(423,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(424,plain,
% 0.84/0.79 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(425,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[424])).
% 0.84/0.79 tff(426,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.84/0.79 inference(transitivity,[status(thm)],[425, 423])).
% 0.84/0.79 tff(427,plain,
% 0.84/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(428,plain,
% 0.84/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.84/0.79 tff(429,plain,
% 0.84/0.79 ($false),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[428, 78, 422, 411, 400, 370, 359, 171, 160, 348, 149, 131])).
% 0.84/0.79 tff(430,plain,((~hskp14) | hskp4 | hskp24 | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a594)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.79 tff(431,plain,
% 0.84/0.79 (~hskp14),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[430, 284, 132, 227, 216, 205])).
% 0.84/0.79 tff(432,plain,
% 0.84/0.79 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(433,plain,
% 0.84/0.79 ((hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594))) <=> (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(434,plain,
% 0.84/0.79 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[433])).
% 0.84/0.79 tff(435,plain,
% 0.84/0.79 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.84/0.79 inference(transitivity,[status(thm)],[434, 432])).
% 0.84/0.79 tff(436,plain,
% 0.84/0.79 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(437,plain,
% 0.84/0.79 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.84/0.79 tff(438,plain,
% 0.84/0.79 (hskp14 | (~c2_1(a594))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[437, 78, 227, 205, 12])).
% 0.84/0.79 tff(439,plain,
% 0.84/0.79 (~c2_1(a594)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[438, 431])).
% 0.84/0.79 tff(440,plain,
% 0.84/0.79 (^[U: $i] : refl((hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(441,plain,
% 0.84/0.79 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[440])).
% 0.84/0.79 tff(442,plain,
% 0.84/0.79 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(443,plain,
% 0.84/0.79 (^[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)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp22))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(444,plain,
% 0.84/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[443])).
% 0.84/0.79 tff(445,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.84/0.79 tff(446,plain,
% 0.84/0.79 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.84/0.79 tff(447,plain,
% 0.84/0.79 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[446, 442])).
% 0.84/0.79 tff(448,plain,(
% 0.84/0.79 ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(skolemize,[status(sab)],[447])).
% 0.84/0.79 tff(449,plain,
% 0.84/0.79 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[448, 441])).
% 0.84/0.79 tff(450,plain,
% 0.84/0.79 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(451,plain,
% 0.84/0.79 ((hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594))) <=> (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(452,plain,
% 0.84/0.79 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[451])).
% 0.84/0.79 tff(453,plain,
% 0.84/0.79 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(transitivity,[status(thm)],[452, 450])).
% 0.84/0.79 tff(454,plain,
% 0.84/0.79 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(455,plain,
% 0.84/0.79 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.84/0.79 tff(456,plain,
% 0.84/0.79 (hskp22 | hskp4 | c2_1(a594)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[455, 78, 227, 216, 449])).
% 0.84/0.79 tff(457,plain,
% 0.84/0.79 (hskp22),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[456, 439, 284])).
% 0.84/0.79 tff(458,plain,
% 0.84/0.79 (((~hskp22) | (~c3_1(a644))) <=> ((~hskp22) | (~c3_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(459,plain,
% 0.84/0.79 (((~c3_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(460,axiom,((~c3_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.84/0.79 tff(461,plain,
% 0.84/0.79 ((~hskp22) | (~c3_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.84/0.79 tff(462,plain,
% 0.84/0.79 ((~hskp22) | (~c3_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.84/0.79 tff(463,plain,
% 0.84/0.79 (~c3_1(a644)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[462, 457])).
% 0.84/0.79 tff(464,plain,
% 0.84/0.79 (((~hskp22) | (~c2_1(a644))) <=> ((~hskp22) | (~c2_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(465,plain,
% 0.84/0.79 (((~c2_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(466,axiom,((~c2_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.84/0.79 tff(467,plain,
% 0.84/0.79 ((~hskp22) | (~c2_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.84/0.79 tff(468,plain,
% 0.84/0.79 ((~hskp22) | (~c2_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[467, 464])).
% 0.84/0.79 tff(469,plain,
% 0.84/0.79 (~c2_1(a644)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[468, 457])).
% 0.84/0.79 tff(470,plain,
% 0.84/0.79 (((~hskp22) | (~c0_1(a644))) <=> ((~hskp22) | (~c0_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(471,plain,
% 0.84/0.79 (((~c0_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a644)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(472,axiom,((~c0_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.84/0.79 tff(473,plain,
% 0.84/0.79 ((~hskp22) | (~c0_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.84/0.79 tff(474,plain,
% 0.84/0.79 ((~hskp22) | (~c0_1(a644))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[473, 470])).
% 0.84/0.79 tff(475,plain,
% 0.84/0.79 (~c0_1(a644)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[474, 457])).
% 0.84/0.79 tff(476,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(477,plain,
% 0.84/0.79 (((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644)) <=> (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(478,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644)))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[477])).
% 0.84/0.79 tff(479,plain,
% 0.84/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.84/0.79 inference(transitivity,[status(thm)],[478, 476])).
% 0.84/0.79 tff(480,plain,
% 0.84/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(481,plain,
% 0.84/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644)),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.84/0.79 tff(482,plain,
% 0.84/0.79 (c1_1(a644)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[481, 78, 475, 469, 463, 198])).
% 0.84/0.79 tff(483,plain,
% 0.84/0.79 (^[U: $i] : refl((hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(484,plain,
% 0.84/0.79 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[483])).
% 0.84/0.79 tff(485,plain,
% 0.84/0.79 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(486,plain,
% 0.84/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp4))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp4) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(487,plain,
% 0.84/0.79 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[486])).
% 0.84/0.79 tff(488,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.84/0.79 tff(489,plain,
% 0.84/0.79 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.84/0.79 tff(490,plain,
% 0.84/0.79 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[489, 485])).
% 0.84/0.79 tff(491,plain,(
% 0.84/0.79 ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(skolemize,[status(sab)],[490])).
% 0.84/0.79 tff(492,plain,
% 0.84/0.79 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[491, 484])).
% 0.84/0.79 tff(493,plain,
% 0.84/0.79 (^[U: $i] : refl((hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(494,plain,
% 0.84/0.79 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[493])).
% 0.84/0.79 tff(495,plain,
% 0.84/0.79 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(496,plain,
% 0.84/0.79 (^[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)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(497,plain,
% 0.84/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[496])).
% 0.84/0.79 tff(498,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.84/0.79 tff(499,plain,
% 0.84/0.79 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.84/0.79 tff(500,plain,
% 0.84/0.79 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[499, 495])).
% 0.84/0.79 tff(501,plain,(
% 0.84/0.79 ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(skolemize,[status(sab)],[500])).
% 0.84/0.79 tff(502,plain,
% 0.84/0.79 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[501, 494])).
% 0.84/0.79 tff(503,plain,
% 0.84/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(504,plain,
% 0.84/0.79 ((hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594))) <=> (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(505,plain,
% 0.84/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[504])).
% 0.84/0.79 tff(506,plain,
% 0.84/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.84/0.79 inference(transitivity,[status(thm)],[505, 503])).
% 0.84/0.79 tff(507,plain,
% 0.84/0.79 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(508,plain,
% 0.84/0.79 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.84/0.79 tff(509,plain,
% 0.84/0.79 (hskp8 | hskp4 | c2_1(a594)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[508, 78, 227, 216, 502])).
% 0.84/0.79 tff(510,plain,
% 0.84/0.79 (hskp8),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[509, 439, 284])).
% 0.84/0.79 tff(511,plain,
% 0.84/0.79 (((~hskp8) | (~c2_1(a603))) <=> ((~hskp8) | (~c2_1(a603)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(512,plain,
% 0.84/0.79 (((~c2_1(a603)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a603)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(513,axiom,((~c2_1(a603)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.84/0.79 tff(514,plain,
% 0.84/0.79 ((~hskp8) | (~c2_1(a603))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.84/0.79 tff(515,plain,
% 0.84/0.79 ((~hskp8) | (~c2_1(a603))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[514, 511])).
% 0.84/0.80 tff(516,plain,
% 0.84/0.80 (~c2_1(a603)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[515, 510])).
% 0.84/0.80 tff(517,plain,
% 0.84/0.80 (((~hskp8) | (~c1_1(a603))) <=> ((~hskp8) | (~c1_1(a603)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(518,plain,
% 0.84/0.80 (((~c1_1(a603)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a603)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(519,axiom,((~c1_1(a603)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.84/0.80 tff(520,plain,
% 0.84/0.80 ((~hskp8) | (~c1_1(a603))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.84/0.80 tff(521,plain,
% 0.84/0.80 ((~hskp8) | (~c1_1(a603))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.84/0.80 tff(522,plain,
% 0.84/0.80 (~c1_1(a603)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[521, 510])).
% 0.84/0.80 tff(523,plain,
% 0.84/0.80 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(524,plain,
% 0.84/0.80 ((hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603)) <=> (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(525,plain,
% 0.84/0.80 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603)))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[524])).
% 0.84/0.80 tff(526,plain,
% 0.84/0.80 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.84/0.80 inference(transitivity,[status(thm)],[525, 523])).
% 0.84/0.80 tff(527,plain,
% 0.84/0.80 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(528,plain,
% 0.84/0.80 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.84/0.80 tff(529,plain,
% 0.84/0.80 (c3_1(a603)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[528, 78, 431, 284, 522, 516, 492])).
% 0.84/0.80 tff(530,plain,
% 0.84/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(531,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[530])).
% 0.84/0.80 tff(532,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(533,plain,
% 0.84/0.80 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(534,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[533])).
% 0.84/0.80 tff(535,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.84/0.80 tff(536,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.84/0.80 tff(537,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[536, 532])).
% 0.84/0.80 tff(538,plain,(
% 0.84/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[537])).
% 0.84/0.80 tff(539,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[538, 531])).
% 0.84/0.80 tff(540,plain,
% 0.84/0.80 (((~hskp8) | c0_1(a603)) <=> ((~hskp8) | c0_1(a603))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(541,axiom,((~hskp8) | c0_1(a603)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.84/0.80 tff(542,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.84/0.80 tff(543,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[542, 540])).
% 0.84/0.80 tff(544,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[543, 540])).
% 0.84/0.80 tff(545,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[544, 540])).
% 0.84/0.80 tff(546,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[545, 540])).
% 0.84/0.80 tff(547,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[546, 540])).
% 0.84/0.80 tff(548,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[547, 540])).
% 0.84/0.80 tff(549,plain,
% 0.84/0.80 ((~hskp8) | c0_1(a603)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[548, 540])).
% 0.84/0.80 tff(550,plain,
% 0.84/0.80 (c0_1(a603)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[549, 510])).
% 0.84/0.80 tff(551,plain,
% 0.84/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(552,plain,
% 0.84/0.80 (((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603))) <=> (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(553,plain,
% 0.84/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[552])).
% 0.84/0.80 tff(554,plain,
% 0.84/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.84/0.80 inference(transitivity,[status(thm)],[553, 551])).
% 0.84/0.80 tff(555,plain,
% 0.84/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(556,plain,
% 0.84/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.84/0.80 tff(557,plain,
% 0.84/0.80 ($false),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[556, 78, 171, 160, 550, 469, 463, 522, 539, 178, 529, 482])).
% 0.84/0.80 tff(558,plain,((~hskp1) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.84/0.80 tff(559,plain,
% 0.84/0.80 (~hskp1),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[558, 132])).
% 0.84/0.80 tff(560,plain,
% 0.84/0.80 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(561,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[560])).
% 0.84/0.80 tff(562,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(563,plain,
% 0.84/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(564,plain,
% 0.84/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[563])).
% 0.84/0.80 tff(565,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.84/0.80 tff(566,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.84/0.80 tff(567,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[566, 562])).
% 0.84/0.80 tff(568,plain,(
% 0.84/0.80 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[567])).
% 0.84/0.80 tff(569,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[568, 561])).
% 0.84/0.80 tff(570,assumption,(hskp21), introduced(assumption)).
% 0.84/0.80 tff(571,plain,
% 0.84/0.80 (((~hskp21) | (~c1_1(a631))) <=> ((~hskp21) | (~c1_1(a631)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(572,plain,
% 0.84/0.80 (((~c1_1(a631)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a631)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(573,axiom,((~c1_1(a631)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.84/0.80 tff(574,plain,
% 0.84/0.80 ((~hskp21) | (~c1_1(a631))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.84/0.80 tff(575,plain,
% 0.84/0.80 ((~hskp21) | (~c1_1(a631))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[574, 571])).
% 0.84/0.80 tff(576,plain,
% 0.84/0.80 (~c1_1(a631)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[575, 570])).
% 0.84/0.80 tff(577,plain,
% 0.84/0.80 (((~hskp21) | c3_1(a631)) <=> ((~hskp21) | c3_1(a631))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(578,axiom,((~hskp21) | c3_1(a631)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.84/0.80 tff(579,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.84/0.80 tff(580,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[579, 577])).
% 0.84/0.80 tff(581,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[580, 577])).
% 0.84/0.80 tff(582,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.84/0.80 tff(583,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[582, 577])).
% 0.84/0.80 tff(584,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[583, 577])).
% 0.84/0.80 tff(585,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[584, 577])).
% 0.84/0.80 tff(586,plain,
% 0.84/0.80 ((~hskp21) | c3_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[585, 577])).
% 0.84/0.80 tff(587,plain,
% 0.84/0.80 (c3_1(a631)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[586, 570])).
% 0.84/0.80 tff(588,plain,
% 0.84/0.80 (((~hskp21) | c0_1(a631)) <=> ((~hskp21) | c0_1(a631))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(589,axiom,((~hskp21) | c0_1(a631)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.84/0.80 tff(590,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.84/0.80 tff(591,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[590, 588])).
% 0.84/0.80 tff(592,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[591, 588])).
% 0.84/0.80 tff(593,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.84/0.80 tff(594,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[593, 588])).
% 0.84/0.80 tff(595,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[594, 588])).
% 0.84/0.80 tff(596,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[595, 588])).
% 0.84/0.80 tff(597,plain,
% 0.84/0.80 ((~hskp21) | c0_1(a631)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[596, 588])).
% 0.84/0.80 tff(598,plain,
% 0.84/0.80 (c0_1(a631)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[597, 570])).
% 0.84/0.80 tff(599,assumption,(~hskp1), introduced(assumption)).
% 0.84/0.80 tff(600,plain,
% 0.84/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(601,plain,
% 0.84/0.80 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(602,plain,
% 0.84/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[601])).
% 0.84/0.80 tff(603,plain,
% 0.84/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.84/0.80 inference(transitivity,[status(thm)],[602, 600])).
% 0.84/0.80 tff(604,plain,
% 0.84/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(605,plain,
% 0.84/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.84/0.80 tff(606,plain,
% 0.84/0.80 ($false),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[605, 78, 599, 598, 587, 233, 576, 230, 569, 228])).
% 0.84/0.80 tff(607,plain,((~hskp21) | hskp1 | (~c1_1(a604)) | c0_1(a604) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.80 tff(608,plain,
% 0.84/0.80 (~hskp21),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[607, 559, 171, 149, 178])).
% 0.84/0.80 tff(609,plain,
% 0.84/0.80 ((hskp21 | hskp4 | hskp1) <=> (hskp21 | hskp4 | hskp1)),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(610,plain,
% 0.84/0.80 (((hskp1 | hskp21) | hskp4) <=> (hskp21 | hskp4 | hskp1)),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(611,axiom,((hskp1 | hskp21) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.84/0.81 tff(612,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.84/0.81 tff(613,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[612, 609])).
% 0.84/0.81 tff(614,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[613, 609])).
% 0.84/0.81 tff(615,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[614, 609])).
% 0.84/0.81 tff(616,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[615, 609])).
% 0.84/0.81 tff(617,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.84/0.81 tff(618,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[617, 609])).
% 0.84/0.81 tff(619,plain,
% 0.84/0.81 (hskp21 | hskp4 | hskp1),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[618, 609])).
% 0.84/0.81 tff(620,plain,
% 0.84/0.81 (hskp4),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[619, 608, 559])).
% 0.84/0.81 tff(621,plain,
% 0.84/0.81 (~c2_1(a598)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[239, 620])).
% 0.84/0.81 tff(622,plain,
% 0.84/0.81 (~c1_1(a598)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[251, 620])).
% 0.84/0.81 tff(623,plain,
% 0.84/0.81 (~c0_1(a598)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[245, 620])).
% 0.84/0.81 tff(624,plain,
% 0.84/0.81 (hskp31),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[76, 559, 132])).
% 0.84/0.81 tff(625,plain,
% 0.84/0.81 (((~hskp31) | c2_1(a672)) <=> ((~hskp31) | c2_1(a672))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(626,axiom,((~hskp31) | c2_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.84/0.81 tff(627,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.84/0.81 tff(628,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[627, 625])).
% 0.84/0.81 tff(629,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.84/0.81 tff(630,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[629, 625])).
% 0.84/0.81 tff(631,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[630, 625])).
% 0.84/0.81 tff(632,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[631, 625])).
% 0.84/0.81 tff(633,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.84/0.81 tff(634,plain,
% 0.84/0.81 ((~hskp31) | c2_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[633, 625])).
% 0.84/0.81 tff(635,plain,
% 0.84/0.81 (c2_1(a672)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[634, 624])).
% 0.84/0.81 tff(636,plain,
% 0.84/0.81 (((~hskp31) | c0_1(a672)) <=> ((~hskp31) | c0_1(a672))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(637,axiom,((~hskp31) | c0_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.84/0.81 tff(638,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.84/0.81 tff(639,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[638, 636])).
% 0.84/0.81 tff(640,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[639, 636])).
% 0.84/0.81 tff(641,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[640, 636])).
% 0.84/0.81 tff(642,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[641, 636])).
% 0.84/0.81 tff(643,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[642, 636])).
% 0.84/0.81 tff(644,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[643, 636])).
% 0.84/0.81 tff(645,plain,
% 0.84/0.81 ((~hskp31) | c0_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[644, 636])).
% 0.84/0.81 tff(646,plain,
% 0.84/0.81 (c0_1(a672)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[645, 624])).
% 0.84/0.81 tff(647,plain,
% 0.84/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(648,plain,
% 0.84/0.81 (((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(649,plain,
% 0.84/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[648])).
% 0.84/0.81 tff(650,plain,
% 0.84/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(transitivity,[status(thm)],[649, 647])).
% 0.84/0.81 tff(651,plain,
% 0.84/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.84/0.81 inference(quant_inst,[status(thm)],[])).
% 0.84/0.81 tff(652,plain,
% 0.84/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.84/0.81 tff(653,plain,
% 0.84/0.81 (~c1_1(a672)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[652, 78, 646, 635, 171, 160, 623, 622, 621, 188, 178])).
% 0.84/0.81 tff(654,plain,
% 0.84/0.81 (((~hskp31) | c3_1(a672)) <=> ((~hskp31) | c3_1(a672))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(655,axiom,((~hskp31) | c3_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.84/0.81 tff(656,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.84/0.81 tff(657,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[656, 654])).
% 0.84/0.81 tff(658,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[657, 654])).
% 0.84/0.81 tff(659,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[658, 654])).
% 0.84/0.81 tff(660,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[659, 654])).
% 0.84/0.81 tff(661,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[660, 654])).
% 0.84/0.81 tff(662,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[661, 654])).
% 0.84/0.81 tff(663,plain,
% 0.84/0.81 ((~hskp31) | c3_1(a672)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[662, 654])).
% 0.84/0.81 tff(664,plain,
% 0.84/0.81 (c3_1(a672)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[663, 624])).
% 0.84/0.81 tff(665,plain,
% 0.84/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(666,plain,
% 0.84/0.81 ((hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(667,plain,
% 0.84/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[666])).
% 0.84/0.81 tff(668,plain,
% 0.84/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(transitivity,[status(thm)],[667, 665])).
% 0.84/0.81 tff(669,plain,
% 0.84/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.84/0.81 inference(quant_inst,[status(thm)],[])).
% 0.84/0.81 tff(670,plain,
% 0.84/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.84/0.81 tff(671,plain,
% 0.84/0.81 ($false),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[670, 78, 559, 646, 664, 171, 149, 569, 178, 653])).
% 0.84/0.81 tff(672,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 0.84/0.81 tff(673,plain,
% 0.84/0.81 (((~hskp24) | (~c2_1(a651))) <=> ((~hskp24) | (~c2_1(a651)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(674,plain,
% 0.84/0.81 (((~c2_1(a651)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a651)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(675,axiom,((~c2_1(a651)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.84/0.81 tff(676,plain,
% 0.84/0.81 ((~hskp24) | (~c2_1(a651))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.84/0.81 tff(677,plain,
% 0.84/0.81 ((~hskp24) | (~c2_1(a651))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[676, 673])).
% 0.84/0.81 tff(678,plain,
% 0.84/0.81 (~c2_1(a651)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[677, 672])).
% 0.84/0.81 tff(679,plain,
% 0.84/0.81 (((~hskp24) | c1_1(a651)) <=> ((~hskp24) | c1_1(a651))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(680,axiom,((~hskp24) | c1_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.84/0.81 tff(681,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.84/0.81 tff(682,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[681, 679])).
% 0.84/0.81 tff(683,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[682, 679])).
% 0.84/0.81 tff(684,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[683, 679])).
% 0.84/0.81 tff(685,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[684, 679])).
% 0.84/0.81 tff(686,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[685, 679])).
% 0.84/0.81 tff(687,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[686, 679])).
% 0.84/0.81 tff(688,plain,
% 0.84/0.81 ((~hskp24) | c1_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[687, 679])).
% 0.84/0.81 tff(689,plain,
% 0.84/0.81 (c1_1(a651)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[688, 672])).
% 0.84/0.81 tff(690,assumption,(~c3_1(a609)), introduced(assumption)).
% 0.84/0.81 tff(691,assumption,(c2_1(a609)), introduced(assumption)).
% 0.84/0.81 tff(692,plain,
% 0.84/0.81 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(693,plain,
% 0.84/0.81 ((hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609))) <=> (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(694,plain,
% 0.84/0.81 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[693])).
% 0.84/0.81 tff(695,plain,
% 0.84/0.81 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.84/0.81 inference(transitivity,[status(thm)],[694, 692])).
% 0.84/0.81 tff(696,plain,
% 0.84/0.81 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.84/0.81 inference(quant_inst,[status(thm)],[])).
% 0.84/0.81 tff(697,plain,
% 0.84/0.81 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[696, 695])).
% 0.84/0.81 tff(698,plain,
% 0.84/0.81 (~c0_1(a609)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[697, 78, 2, 691, 690, 12])).
% 0.84/0.81 tff(699,plain,
% 0.84/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(700,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[699])).
% 0.84/0.81 tff(701,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(702,plain,
% 0.84/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(703,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[702])).
% 0.84/0.81 tff(704,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.84/0.81 tff(705,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.84/0.81 tff(706,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[705, 701])).
% 0.84/0.81 tff(707,plain,(
% 0.84/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[706])).
% 0.84/0.81 tff(708,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[707, 700])).
% 0.84/0.81 tff(709,assumption,(~c1_1(a609)), introduced(assumption)).
% 0.84/0.81 tff(710,plain,
% 0.84/0.81 (^[U: $i] : refl((hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(711,plain,
% 0.84/0.81 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[710])).
% 0.84/0.81 tff(712,plain,
% 0.84/0.81 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(713,plain,
% 0.84/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp5))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(714,plain,
% 0.84/0.81 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[713])).
% 0.84/0.81 tff(715,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.84/0.81 tff(716,plain,
% 0.84/0.81 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.84/0.81 tff(717,plain,
% 0.84/0.81 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.84/0.81 tff(718,plain,(
% 0.84/0.81 ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[717])).
% 0.84/0.81 tff(719,plain,
% 0.84/0.81 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[718, 711])).
% 0.84/0.81 tff(720,plain,
% 0.84/0.81 (((~hskp24) | c3_1(a651)) <=> ((~hskp24) | c3_1(a651))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(721,axiom,((~hskp24) | c3_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.84/0.81 tff(722,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.84/0.81 tff(723,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[722, 720])).
% 0.84/0.81 tff(724,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[723, 720])).
% 0.84/0.81 tff(725,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[724, 720])).
% 0.84/0.81 tff(726,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[725, 720])).
% 0.84/0.81 tff(727,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[726, 720])).
% 0.84/0.81 tff(728,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[727, 720])).
% 0.84/0.81 tff(729,plain,
% 0.84/0.81 ((~hskp24) | c3_1(a651)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[728, 720])).
% 0.84/0.81 tff(730,plain,
% 0.84/0.81 (c3_1(a651)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[729, 672])).
% 0.84/0.81 tff(731,plain,
% 0.84/0.81 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(732,plain,
% 0.84/0.81 ((hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651))) <=> (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(733,plain,
% 0.84/0.81 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[732])).
% 0.84/0.81 tff(734,plain,
% 0.84/0.81 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.84/0.81 inference(transitivity,[status(thm)],[733, 731])).
% 0.84/0.81 tff(735,plain,
% 0.84/0.81 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.84/0.81 inference(quant_inst,[status(thm)],[])).
% 0.84/0.81 tff(736,plain,
% 0.84/0.81 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.84/0.81 tff(737,plain,
% 0.84/0.81 (hskp10 | hskp5),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[736, 78, 689, 730, 678, 719])).
% 0.84/0.81 tff(738,plain,
% 0.84/0.81 (hskp5),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[737, 87])).
% 0.84/0.81 tff(739,plain,
% 0.84/0.81 (((~hskp5) | c3_1(a599)) <=> ((~hskp5) | c3_1(a599))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(740,axiom,((~hskp5) | c3_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.84/0.81 tff(741,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.84/0.81 tff(742,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[741, 739])).
% 0.84/0.81 tff(743,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[742, 739])).
% 0.84/0.81 tff(744,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[743, 739])).
% 0.84/0.81 tff(745,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[744, 739])).
% 0.84/0.81 tff(746,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[745, 739])).
% 0.84/0.81 tff(747,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[746, 739])).
% 0.84/0.81 tff(748,plain,
% 0.84/0.81 ((~hskp5) | c3_1(a599)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[747, 739])).
% 0.84/0.81 tff(749,plain,
% 0.84/0.81 (c3_1(a599)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[748, 738])).
% 0.84/0.81 tff(750,plain,
% 0.84/0.81 (((~hskp5) | c2_1(a599)) <=> ((~hskp5) | c2_1(a599))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(751,axiom,((~hskp5) | c2_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.84/0.81 tff(752,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.84/0.82 tff(753,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[752, 750])).
% 0.84/0.82 tff(754,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[753, 750])).
% 0.84/0.82 tff(755,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[754, 750])).
% 0.84/0.82 tff(756,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[755, 750])).
% 0.84/0.82 tff(757,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[756, 750])).
% 0.84/0.82 tff(758,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[757, 750])).
% 0.84/0.82 tff(759,plain,
% 0.84/0.82 ((~hskp5) | c2_1(a599)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[758, 750])).
% 0.84/0.82 tff(760,plain,
% 0.84/0.82 (c2_1(a599)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[759, 738])).
% 0.84/0.82 tff(761,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(762,plain,
% 0.84/0.82 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(763,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651))))),
% 0.84/0.82 inference(monotonicity,[status(thm)],[762])).
% 0.84/0.82 tff(764,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(transitivity,[status(thm)],[763, 761])).
% 0.84/0.82 tff(765,plain,
% 0.84/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(766,plain,
% 0.84/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.84/0.82 tff(767,plain,
% 0.84/0.82 ((~c0_1(a599)) | c0_1(a651)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[766, 78, 689, 691, 760, 749, 678, 709, 690, 708])).
% 0.84/0.82 tff(768,plain,
% 0.84/0.82 (~c0_1(a599)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[767, 1])).
% 0.84/0.82 tff(769,plain,
% 0.84/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(770,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[769])).
% 0.84/0.82 tff(771,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(772,plain,
% 0.84/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(773,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[772])).
% 0.84/0.82 tff(774,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.84/0.82 tff(775,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.84/0.82 tff(776,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[775, 771])).
% 0.84/0.82 tff(777,plain,(
% 0.84/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(skolemize,[status(sab)],[776])).
% 0.84/0.82 tff(778,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[777, 770])).
% 0.84/0.82 tff(779,plain,
% 0.84/0.82 (((~hskp5) | (~c1_1(a599))) <=> ((~hskp5) | (~c1_1(a599)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(780,plain,
% 0.84/0.82 (((~c1_1(a599)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a599)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(781,axiom,((~c1_1(a599)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.84/0.82 tff(782,plain,
% 0.84/0.82 ((~hskp5) | (~c1_1(a599))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.84/0.82 tff(783,plain,
% 0.84/0.82 ((~hskp5) | (~c1_1(a599))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.84/0.82 tff(784,plain,
% 0.84/0.82 (~c1_1(a599)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[783, 738])).
% 0.84/0.82 tff(785,plain,
% 0.84/0.82 (^[U: $i] : refl((hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(786,plain,
% 0.84/0.82 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[785])).
% 0.84/0.82 tff(787,plain,
% 0.84/0.82 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(788,plain,
% 0.84/0.82 (^[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) | hskp8) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(789,plain,
% 0.84/0.82 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[788])).
% 0.84/0.82 tff(790,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.84/0.82 tff(791,plain,
% 0.84/0.82 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.84/0.82 tff(792,plain,
% 0.84/0.82 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[791, 787])).
% 0.84/0.82 tff(793,plain,(
% 0.84/0.82 ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(skolemize,[status(sab)],[792])).
% 0.84/0.82 tff(794,plain,
% 0.84/0.82 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[793, 786])).
% 0.84/0.82 tff(795,plain,
% 0.84/0.82 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(796,plain,
% 0.84/0.82 ((hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651))) <=> (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(797,plain,
% 0.84/0.82 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))))),
% 0.84/0.82 inference(monotonicity,[status(thm)],[796])).
% 0.84/0.82 tff(798,plain,
% 0.84/0.82 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.84/0.82 inference(transitivity,[status(thm)],[797, 795])).
% 0.84/0.82 tff(799,plain,
% 0.84/0.82 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(800,plain,
% 0.84/0.82 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.84/0.82 tff(801,plain,
% 0.84/0.82 (hskp14 | hskp8 | c0_1(a651)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[800, 78, 689, 730, 794])).
% 0.84/0.82 tff(802,plain,
% 0.84/0.82 (hskp8),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[801, 1, 2])).
% 0.84/0.82 tff(803,plain,
% 0.84/0.82 (~c2_1(a603)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[515, 802])).
% 0.84/0.82 tff(804,plain,
% 0.84/0.82 (c0_1(a603)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[549, 802])).
% 0.84/0.82 tff(805,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(806,plain,
% 0.84/0.82 (((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(807,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.84/0.82 inference(monotonicity,[status(thm)],[806])).
% 0.84/0.82 tff(808,plain,
% 0.84/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.84/0.82 inference(transitivity,[status(thm)],[807, 805])).
% 0.84/0.82 tff(809,plain,
% 0.84/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(810,plain,
% 0.84/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.84/0.82 tff(811,plain,
% 0.84/0.82 (~c3_1(a603)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[810, 78, 804, 760, 749, 803, 784, 778, 768])).
% 0.84/0.82 tff(812,plain,
% 0.84/0.82 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(813,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[812])).
% 0.84/0.82 tff(814,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(815,plain,
% 0.84/0.82 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(816,plain,
% 0.84/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[815])).
% 0.84/0.82 tff(817,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.84/0.82 tff(818,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.84/0.82 tff(819,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[818, 814])).
% 0.84/0.82 tff(820,plain,(
% 0.84/0.82 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.82 inference(skolemize,[status(sab)],[819])).
% 0.84/0.83 tff(821,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[820, 813])).
% 0.84/0.83 tff(822,plain,
% 0.84/0.83 (~c1_1(a603)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[521, 802])).
% 0.84/0.83 tff(823,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(824,plain,
% 0.84/0.83 ((hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609))) <=> (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(825,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609)))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[824])).
% 0.84/0.83 tff(826,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.84/0.83 inference(transitivity,[status(thm)],[825, 823])).
% 0.84/0.83 tff(827,plain,
% 0.84/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(828,plain,
% 0.84/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.84/0.83 tff(829,plain,
% 0.84/0.83 (hskp11),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[828, 78, 691, 804, 690, 822, 821, 811, 698])).
% 0.84/0.83 tff(830,plain,
% 0.84/0.83 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(831,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[830])).
% 0.84/0.83 tff(832,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(833,plain,
% 0.84/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(834,plain,
% 0.84/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[833])).
% 0.84/0.83 tff(835,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.84/0.83 tff(836,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.84/0.83 tff(837,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[836, 832])).
% 0.84/0.83 tff(838,plain,(
% 0.84/0.83 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(skolemize,[status(sab)],[837])).
% 0.84/0.83 tff(839,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[838, 831])).
% 0.84/0.83 tff(840,assumption,(hskp11), introduced(assumption)).
% 0.84/0.83 tff(841,plain,
% 0.84/0.83 (((~hskp11) | (~c3_1(a608))) <=> ((~hskp11) | (~c3_1(a608)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(842,plain,
% 0.84/0.83 (((~c3_1(a608)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a608)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(843,axiom,((~c3_1(a608)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.84/0.83 tff(844,plain,
% 0.84/0.83 ((~hskp11) | (~c3_1(a608))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.84/0.83 tff(845,plain,
% 0.84/0.83 ((~hskp11) | (~c3_1(a608))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[844, 841])).
% 0.84/0.83 tff(846,plain,
% 0.84/0.83 (~c3_1(a608)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[845, 840])).
% 0.90/0.83 tff(847,plain,
% 0.90/0.83 (((~hskp11) | (~c0_1(a608))) <=> ((~hskp11) | (~c0_1(a608)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(848,plain,
% 0.90/0.83 (((~c0_1(a608)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a608)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(849,axiom,((~c0_1(a608)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.90/0.83 tff(850,plain,
% 0.90/0.83 ((~hskp11) | (~c0_1(a608))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.90/0.83 tff(851,plain,
% 0.90/0.83 ((~hskp11) | (~c0_1(a608))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[850, 847])).
% 0.90/0.83 tff(852,plain,
% 0.90/0.83 (~c0_1(a608)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[851, 840])).
% 0.90/0.83 tff(853,plain,
% 0.90/0.83 (((~hskp11) | c1_1(a608)) <=> ((~hskp11) | c1_1(a608))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(854,axiom,((~hskp11) | c1_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.90/0.83 tff(855,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.90/0.83 tff(856,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[855, 853])).
% 0.90/0.83 tff(857,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[856, 853])).
% 0.90/0.83 tff(858,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[857, 853])).
% 0.90/0.83 tff(859,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[858, 853])).
% 0.90/0.83 tff(860,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[859, 853])).
% 0.90/0.83 tff(861,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[860, 853])).
% 0.90/0.83 tff(862,plain,
% 0.90/0.83 ((~hskp11) | c1_1(a608)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[861, 853])).
% 0.90/0.83 tff(863,plain,
% 0.90/0.83 (c1_1(a608)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[862, 840])).
% 0.90/0.83 tff(864,assumption,(~hskp28), introduced(assumption)).
% 0.90/0.83 tff(865,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(866,plain,
% 0.90/0.83 ((hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608))) <=> (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(867,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[866])).
% 0.90/0.83 tff(868,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[867, 865])).
% 0.90/0.83 tff(869,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(870,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.90/0.83 tff(871,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[870, 78, 864, 689, 730, 863, 678, 852, 846, 839])).
% 0.90/0.83 tff(872,plain,((~hskp11) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.90/0.83 tff(873,plain,
% 0.90/0.83 (hskp28),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[872, 829])).
% 0.90/0.83 tff(874,plain,
% 0.90/0.83 (c3_1(a595)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[399, 873])).
% 0.90/0.83 tff(875,plain,
% 0.90/0.83 (c2_1(a595)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[410, 873])).
% 0.90/0.83 tff(876,plain,
% 0.90/0.83 (c1_1(a595)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[421, 873])).
% 0.90/0.83 tff(877,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(878,plain,
% 0.90/0.83 ((hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(879,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[878])).
% 0.90/0.83 tff(880,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[879, 877])).
% 0.90/0.83 tff(881,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(882,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.90/0.83 tff(883,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[882, 78, 87, 876, 875, 874, 689, 678, 121, 1])).
% 0.90/0.83 tff(884,plain,(c0_1(a651) | (~c2_1(a609)) | c3_1(a609) | c1_1(a609) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.90/0.83 tff(885,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[884, 111, 105, 1, 94, 2])).
% 0.90/0.83 tff(886,plain,((~hskp12) | c0_1(a651) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.90/0.83 tff(887,plain,
% 0.90/0.83 (~hskp12),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[886, 2, 1])).
% 0.90/0.83 tff(888,assumption,(~hskp10), introduced(assumption)).
% 0.90/0.83 tff(889,assumption,(~hskp12), introduced(assumption)).
% 0.90/0.83 tff(890,plain,
% 0.90/0.83 ((hskp9 | hskp12 | hskp10) <=> (hskp9 | hskp12 | hskp10)),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(891,plain,
% 0.90/0.83 (((hskp10 | hskp9) | hskp12) <=> (hskp9 | hskp12 | hskp10)),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(892,axiom,((hskp10 | hskp9) | hskp12), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.90/0.83 tff(893,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.90/0.83 tff(894,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[893, 890])).
% 0.90/0.83 tff(895,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[894, 890])).
% 0.90/0.83 tff(896,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[895, 890])).
% 0.90/0.83 tff(897,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[896, 890])).
% 0.90/0.83 tff(898,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[897, 890])).
% 0.90/0.83 tff(899,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[898, 890])).
% 0.90/0.83 tff(900,plain,
% 0.90/0.83 (hskp9 | hskp12 | hskp10),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[899, 890])).
% 0.90/0.83 tff(901,plain,
% 0.90/0.83 (hskp9),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[900, 889, 888])).
% 0.90/0.83 tff(902,plain,
% 0.90/0.83 (c2_1(a604)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[159, 901])).
% 0.90/0.83 tff(903,assumption,(~c1_1(a604)), introduced(assumption)).
% 0.90/0.83 tff(904,assumption,(~c3_1(a615)), introduced(assumption)).
% 0.90/0.83 tff(905,plain,
% 0.90/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(906,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[905])).
% 0.90/0.83 tff(907,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(908,plain,
% 0.90/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(909,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[908])).
% 0.90/0.83 tff(910,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.90/0.83 tff(911,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.90/0.83 tff(912,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[911, 907])).
% 0.90/0.83 tff(913,plain,(
% 0.90/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(skolemize,[status(sab)],[912])).
% 0.90/0.83 tff(914,plain,
% 0.90/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[913, 906])).
% 0.90/0.83 tff(915,plain,
% 0.90/0.83 (~hskp9),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[170, 903])).
% 0.90/0.83 tff(916,plain,
% 0.90/0.83 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(917,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[916])).
% 0.90/0.84 tff(918,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(919,plain,
% 0.90/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(920,plain,
% 0.90/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[919])).
% 0.90/0.84 tff(921,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.90/0.84 tff(922,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.90/0.84 tff(923,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.90/0.84 tff(924,plain,(
% 0.90/0.84 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(skolemize,[status(sab)],[923])).
% 0.90/0.84 tff(925,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[924, 917])).
% 0.90/0.84 tff(926,plain,
% 0.90/0.84 (hskp21),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[619, 599, 381])).
% 0.90/0.84 tff(927,plain,
% 0.90/0.84 (~c1_1(a631)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[575, 926])).
% 0.90/0.84 tff(928,plain,
% 0.90/0.84 (c3_1(a631)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[586, 926])).
% 0.90/0.84 tff(929,plain,
% 0.90/0.84 (c0_1(a631)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[597, 926])).
% 0.90/0.84 tff(930,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(931,plain,
% 0.90/0.84 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604))) <=> (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(932,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[931])).
% 0.90/0.84 tff(933,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[932, 930])).
% 0.90/0.84 tff(934,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(935,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.90/0.84 tff(936,plain,
% 0.90/0.84 (~c2_1(a604)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[935, 78, 599, 929, 928, 903, 927, 230, 925])).
% 0.90/0.84 tff(937,plain,
% 0.90/0.84 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(938,plain,
% 0.90/0.84 ((hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604)) <=> (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(939,plain,
% 0.90/0.84 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604)))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[938])).
% 0.90/0.84 tff(940,plain,
% 0.90/0.84 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.90/0.84 inference(transitivity,[status(thm)],[939, 937])).
% 0.90/0.84 tff(941,plain,
% 0.90/0.84 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(942,plain,
% 0.90/0.84 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.90/0.84 tff(943,plain,
% 0.90/0.84 (hskp14 | hskp4 | c2_1(a604) | c3_1(a604)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[942, 78, 903, 492])).
% 0.90/0.84 tff(944,plain,
% 0.90/0.84 (c3_1(a604)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[943, 2, 381, 936])).
% 0.90/0.84 tff(945,assumption,(~hskp8), introduced(assumption)).
% 0.90/0.84 tff(946,plain,
% 0.90/0.84 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(947,plain,
% 0.90/0.84 ((hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651))) <=> (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(948,plain,
% 0.90/0.84 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[947])).
% 0.90/0.84 tff(949,plain,
% 0.90/0.84 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[948, 946])).
% 0.90/0.84 tff(950,plain,
% 0.90/0.84 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(951,plain,
% 0.90/0.84 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.90/0.84 tff(952,plain,
% 0.90/0.84 (hskp8 | hskp4 | (~c0_1(a651))),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[951, 78, 689, 678, 502])).
% 0.90/0.84 tff(953,plain,
% 0.90/0.84 (~c0_1(a651)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[952, 945, 381])).
% 0.90/0.84 tff(954,plain,
% 0.90/0.84 ($false),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[801, 953, 945, 2])).
% 0.90/0.84 tff(955,plain,(hskp8 | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.90/0.84 tff(956,plain,
% 0.90/0.84 (hskp8),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[955, 2, 381])).
% 0.90/0.84 tff(957,plain,
% 0.90/0.84 (~c2_1(a603)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[515, 956])).
% 0.90/0.84 tff(958,plain,
% 0.90/0.84 (~c1_1(a603)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[521, 956])).
% 0.90/0.84 tff(959,plain,
% 0.90/0.84 (c3_1(a603)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[528, 78, 2, 381, 958, 957, 492])).
% 0.90/0.84 tff(960,plain,
% 0.90/0.84 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(961,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[960])).
% 0.90/0.84 tff(962,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(963,plain,
% 0.90/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(964,plain,
% 0.90/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[963])).
% 0.90/0.84 tff(965,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.90/0.84 tff(966,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.90/0.84 tff(967,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[966, 962])).
% 0.90/0.84 tff(968,plain,(
% 0.90/0.84 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(skolemize,[status(sab)],[967])).
% 0.90/0.84 tff(969,plain,
% 0.90/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[968, 961])).
% 0.90/0.84 tff(970,plain,
% 0.90/0.84 (c0_1(a603)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[549, 956])).
% 0.90/0.84 tff(971,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(972,plain,
% 0.90/0.84 ((hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603))) <=> (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(973,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[972])).
% 0.90/0.84 tff(974,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[973, 971])).
% 0.90/0.84 tff(975,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(976,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.90/0.84 tff(977,plain,
% 0.90/0.84 (hskp12),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[976, 78, 970, 958, 957, 969, 959])).
% 0.90/0.84 tff(978,plain,
% 0.90/0.84 (~c3_1(a609)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[110, 977])).
% 0.90/0.84 tff(979,plain,
% 0.90/0.84 (c2_1(a609)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[104, 977])).
% 0.90/0.84 tff(980,plain,
% 0.90/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(981,plain,
% 0.90/0.84 (((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604)) <=> (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(982,plain,
% 0.90/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[981])).
% 0.90/0.84 tff(983,plain,
% 0.90/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[982, 980])).
% 0.90/0.84 tff(984,plain,
% 0.90/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(985,plain,
% 0.90/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.90/0.84 tff(986,plain,
% 0.90/0.84 (~c0_1(a609)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[985, 78, 979, 903, 936, 978, 230, 914, 944])).
% 0.90/0.84 tff(987,plain,
% 0.90/0.84 (~c1_1(a609)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[93, 977])).
% 0.90/0.84 tff(988,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(989,plain,
% 0.90/0.84 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(990,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[989])).
% 0.90/0.84 tff(991,plain,
% 0.90/0.84 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[990, 988])).
% 0.90/0.84 tff(992,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(993,plain,
% 0.90/0.84 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.90/0.85 tff(994,plain,
% 0.90/0.85 ($false),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[993, 78, 599, 929, 928, 979, 927, 987, 925, 986])).
% 0.90/0.85 tff(995,plain,(hskp14 | hskp1 | c1_1(a604) | c0_1(a604) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.90/0.85 tff(996,plain,
% 0.90/0.85 (hskp14),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[995, 599, 903, 230, 381])).
% 0.90/0.85 tff(997,plain,
% 0.90/0.85 (c0_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[316, 996])).
% 0.90/0.85 tff(998,plain,
% 0.90/0.85 (((~hskp14) | (~c1_1(a615))) <=> ((~hskp14) | (~c1_1(a615)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(999,plain,
% 0.90/0.85 (((~c1_1(a615)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a615)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1000,axiom,((~c1_1(a615)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.90/0.85 tff(1001,plain,
% 0.90/0.85 ((~hskp14) | (~c1_1(a615))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.90/0.85 tff(1002,plain,
% 0.90/0.85 ((~hskp14) | (~c1_1(a615))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1001, 998])).
% 0.90/0.85 tff(1003,plain,
% 0.90/0.85 (~c1_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1002, 996])).
% 0.90/0.85 tff(1004,plain,
% 0.90/0.85 (c2_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[305, 996])).
% 0.90/0.85 tff(1005,plain,
% 0.90/0.85 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(1006,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[1005])).
% 0.90/0.85 tff(1007,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1008,plain,
% 0.90/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(1009,plain,
% 0.90/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[1008])).
% 0.90/0.85 tff(1010,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.90/0.85 tff(1011,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.90/0.85 tff(1012,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1011, 1007])).
% 0.90/0.85 tff(1013,plain,(
% 0.90/0.85 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[1012])).
% 0.90/0.85 tff(1014,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1013, 1006])).
% 0.90/0.85 tff(1015,assumption,(c2_1(a615)), introduced(assumption)).
% 0.90/0.85 tff(1016,assumption,(c0_1(a615)), introduced(assumption)).
% 0.90/0.85 tff(1017,assumption,(~hskp9), introduced(assumption)).
% 0.90/0.85 tff(1018,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1019,plain,
% 0.90/0.85 ((hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1020,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[1019])).
% 0.90/0.85 tff(1021,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.90/0.85 tff(1022,plain,
% 0.90/0.85 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(1023,plain,
% 0.90/0.85 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.90/0.85 tff(1024,plain,
% 0.90/0.85 ((~c3_1(a615)) | c0_1(a651)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1023, 1017, 78, 689, 1016, 1015, 678, 1014])).
% 0.90/0.85 tff(1025,plain,
% 0.90/0.85 (~c3_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1024, 1])).
% 0.90/0.85 tff(1026,assumption,(~c1_1(a615)), introduced(assumption)).
% 0.90/0.85 tff(1027,plain,
% 0.90/0.85 (hskp28 | c3_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[387, 78, 381, 1016, 1015, 380])).
% 0.90/0.85 tff(1028,plain,
% 0.90/0.85 (hskp28),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1027, 1025])).
% 0.90/0.85 tff(1029,plain,
% 0.90/0.85 (c3_1(a595)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[399, 1028])).
% 0.90/0.85 tff(1030,plain,
% 0.90/0.85 (c2_1(a595)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[410, 1028])).
% 0.90/0.85 tff(1031,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1032,plain,
% 0.90/0.85 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1033,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[1032])).
% 0.90/0.85 tff(1034,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.90/0.85 tff(1035,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(1036,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.90/0.85 tff(1037,plain,
% 0.90/0.85 (~c0_1(a595)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1036, 78, 1030, 1029, 689, 1015, 678, 1026, 708, 1, 1025])).
% 0.90/0.85 tff(1038,plain,
% 0.90/0.85 (hskp25 | c3_1(a615)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[340, 78, 1016, 1015, 334])).
% 0.90/0.85 tff(1039,plain,
% 0.90/0.85 (hskp25),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1038, 1025])).
% 0.90/0.85 tff(1040,plain,
% 0.90/0.85 (~c0_1(a656)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[347, 1039])).
% 0.90/0.85 tff(1041,plain,
% 0.90/0.85 (c3_1(a656)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[358, 1039])).
% 0.90/0.85 tff(1042,plain,
% 0.90/0.85 (c1_1(a656)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[369, 1039])).
% 0.90/0.85 tff(1043,plain,
% 0.90/0.85 (c1_1(a595)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[421, 1028])).
% 0.90/0.85 tff(1044,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1045,plain,
% 0.90/0.85 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595))) <=> (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1046,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[1045])).
% 0.90/0.85 tff(1047,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[1046, 1044])).
% 0.90/0.85 tff(1048,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(1049,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.90/0.85 tff(1050,plain,
% 0.90/0.85 ($false),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1049, 78, 1043, 1030, 1029, 1042, 1041, 1040, 131, 1037])).
% 0.90/0.85 tff(1051,plain,(c0_1(a651) | (~c2_1(a615)) | c1_1(a615) | (~c0_1(a615)) | hskp4 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.90/0.85 tff(1052,plain,
% 0.90/0.85 (c0_1(a651)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1051, 1004, 1003, 997, 381, 915])).
% 0.90/0.85 tff(1053,plain,
% 0.90/0.85 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1054,plain,
% 0.90/0.85 ((hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651))) <=> (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1055,plain,
% 0.90/0.85 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[1054])).
% 0.90/0.85 tff(1056,plain,
% 0.90/0.85 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.90/0.85 tff(1057,plain,
% 0.90/0.85 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(1058,plain,
% 0.90/0.85 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.90/0.85 tff(1059,plain,
% 0.90/0.85 (hskp22 | hskp4 | (~c0_1(a651))),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1058, 78, 689, 678, 449])).
% 0.90/0.85 tff(1060,plain,
% 0.90/0.85 (hskp22),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1059, 1052, 381])).
% 0.90/0.85 tff(1061,plain,
% 0.90/0.85 (~c3_1(a644)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[462, 1060])).
% 0.90/0.85 tff(1062,plain,
% 0.90/0.85 (~c2_1(a644)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[468, 1060])).
% 0.90/0.85 tff(1063,plain,
% 0.90/0.85 (~c0_1(a644)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[474, 1060])).
% 0.90/0.85 tff(1064,plain,
% 0.90/0.85 (c1_1(a644)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[481, 78, 1063, 1062, 1061, 198])).
% 0.90/0.85 tff(1065,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1066,plain,
% 0.90/0.85 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1067,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[1066])).
% 0.90/0.85 tff(1068,plain,
% 0.90/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1067, 1065])).
% 0.90/0.86 tff(1069,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1070,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.90/0.86 tff(1071,plain,
% 0.90/0.86 ($false),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1070, 78, 599, 929, 928, 1063, 1061, 927, 569, 1064])).
% 0.90/0.86 tff(1072,plain,(hskp1 | hskp4 | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.86 tff(1073,plain,
% 0.90/0.86 (hskp1),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1072, 381, 903, 230])).
% 0.90/0.86 tff(1074,plain,
% 0.90/0.86 (~c3_1(a594)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[204, 1073])).
% 0.90/0.86 tff(1075,plain,
% 0.90/0.86 (c0_1(a594)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[226, 1073])).
% 0.90/0.86 tff(1076,plain,
% 0.90/0.86 (hskp14 | (~c2_1(a594))),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[437, 78, 1075, 1074, 12])).
% 0.90/0.86 tff(1077,plain,
% 0.90/0.86 (~c2_1(a594)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1076, 2])).
% 0.90/0.86 tff(1078,plain,
% 0.90/0.86 (c1_1(a594)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[215, 1073])).
% 0.90/0.86 tff(1079,plain,
% 0.90/0.86 (hskp22 | c2_1(a594)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[455, 78, 381, 1075, 1078, 449])).
% 0.90/0.86 tff(1080,plain,
% 0.90/0.86 (hskp22),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1079, 1077])).
% 0.90/0.86 tff(1081,plain,
% 0.90/0.86 (~c3_1(a644)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[462, 1080])).
% 0.90/0.86 tff(1082,plain,
% 0.90/0.86 (~c2_1(a644)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[468, 1080])).
% 0.90/0.86 tff(1083,plain,
% 0.90/0.86 (~c0_1(a644)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[474, 1080])).
% 0.90/0.86 tff(1084,plain,
% 0.90/0.86 (c1_1(a644)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[481, 78, 1083, 1082, 1081, 198])).
% 0.90/0.86 tff(1085,plain,
% 0.90/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1086,plain,
% 0.90/0.86 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604))) <=> (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1087,plain,
% 0.90/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1086])).
% 0.90/0.86 tff(1088,plain,
% 0.90/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1087, 1085])).
% 0.90/0.86 tff(1089,plain,
% 0.90/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1090,plain,
% 0.90/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.90/0.86 tff(1091,plain,
% 0.90/0.86 (~c3_1(a604)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1090, 78, 903, 1075, 1078, 1083, 1081, 230, 1074, 263, 1084])).
% 0.90/0.86 tff(1092,plain,
% 0.90/0.86 (c2_1(a604)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[943, 1091, 381, 2])).
% 0.90/0.86 tff(1093,plain,
% 0.90/0.86 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1094,plain,
% 0.90/0.86 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1093])).
% 0.90/0.86 tff(1095,plain,
% 0.90/0.86 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1096,plain,
% 0.90/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1097,plain,
% 0.90/0.86 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1096])).
% 0.90/0.86 tff(1098,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.90/0.86 tff(1099,plain,
% 0.90/0.86 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.90/0.86 tff(1100,plain,
% 0.90/0.86 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1099, 1095])).
% 0.90/0.86 tff(1101,plain,(
% 0.90/0.86 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(skolemize,[status(sab)],[1100])).
% 0.90/0.86 tff(1102,plain,
% 0.90/0.86 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1101, 1094])).
% 0.90/0.86 tff(1103,plain,
% 0.90/0.86 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1104,plain,
% 0.90/0.86 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1105,plain,
% 0.90/0.86 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1104])).
% 0.90/0.86 tff(1106,plain,
% 0.90/0.86 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1105, 1103])).
% 0.90/0.86 tff(1107,plain,
% 0.90/0.86 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1108,plain,
% 0.90/0.86 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.90/0.86 tff(1109,plain,
% 0.90/0.86 (hskp4 | hskp3 | c1_1(a604) | (~c2_1(a604))),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1108, 78, 230, 1102])).
% 0.90/0.86 tff(1110,plain,
% 0.90/0.86 (hskp3),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1109, 1092, 903, 381])).
% 0.90/0.86 tff(1111,plain,
% 0.90/0.86 (((~hskp3) | (~c3_1(a597))) <=> ((~hskp3) | (~c3_1(a597)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1112,plain,
% 0.90/0.86 (((~c3_1(a597)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a597)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1113,axiom,((~c3_1(a597)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.90/0.86 tff(1114,plain,
% 0.90/0.86 ((~hskp3) | (~c3_1(a597))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 0.90/0.86 tff(1115,plain,
% 0.90/0.86 ((~hskp3) | (~c3_1(a597))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 0.90/0.86 tff(1116,plain,
% 0.90/0.86 (~c3_1(a597)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1115, 1110])).
% 0.90/0.86 tff(1117,plain,
% 0.90/0.86 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1118,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1117])).
% 0.90/0.86 tff(1119,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1120,plain,
% 0.93/0.86 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1121,plain,
% 0.93/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1120])).
% 0.93/0.86 tff(1122,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.93/0.86 tff(1123,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.93/0.86 tff(1124,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1123, 1119])).
% 0.93/0.86 tff(1125,plain,(
% 0.93/0.86 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(skolemize,[status(sab)],[1124])).
% 0.93/0.86 tff(1126,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1125, 1118])).
% 0.93/0.86 tff(1127,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1128,plain,
% 0.93/0.86 ((hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603))) <=> (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1129,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1128])).
% 0.93/0.86 tff(1130,plain,
% 0.93/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.93/0.86 tff(1131,plain,
% 0.93/0.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1132,plain,
% 0.93/0.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.93/0.86 tff(1133,plain,
% 0.93/0.86 (hskp21),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1132, 78, 970, 1075, 1078, 958, 1074, 1126, 959])).
% 0.93/0.86 tff(1134,plain,
% 0.93/0.86 (~c1_1(a631)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[575, 1133])).
% 0.93/0.86 tff(1135,plain,
% 0.93/0.86 (((~hskp3) | c2_1(a597)) <=> ((~hskp3) | c2_1(a597))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1136,axiom,((~hskp3) | c2_1(a597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.93/0.86 tff(1137,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 0.93/0.86 tff(1138,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1137, 1135])).
% 0.93/0.86 tff(1139,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1138, 1135])).
% 0.93/0.86 tff(1140,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1139, 1135])).
% 0.93/0.86 tff(1141,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1140, 1135])).
% 0.93/0.86 tff(1142,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1141, 1135])).
% 0.93/0.86 tff(1143,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1142, 1135])).
% 0.93/0.86 tff(1144,plain,
% 0.93/0.86 ((~hskp3) | c2_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1143, 1135])).
% 0.93/0.86 tff(1145,plain,
% 0.93/0.86 (c2_1(a597)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1144, 1110])).
% 0.93/0.86 tff(1146,plain,
% 0.93/0.86 (((~hskp3) | c1_1(a597)) <=> ((~hskp3) | c1_1(a597))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1147,axiom,((~hskp3) | c1_1(a597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.93/0.86 tff(1148,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 0.93/0.86 tff(1149,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1148, 1146])).
% 0.93/0.86 tff(1150,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1149, 1146])).
% 0.93/0.86 tff(1151,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1150, 1146])).
% 0.93/0.86 tff(1152,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1151, 1146])).
% 0.93/0.86 tff(1153,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1152, 1146])).
% 0.93/0.86 tff(1154,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1153, 1146])).
% 0.93/0.86 tff(1155,plain,
% 0.93/0.86 ((~hskp3) | c1_1(a597)),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1154, 1146])).
% 0.93/0.86 tff(1156,plain,
% 0.93/0.86 (c1_1(a597)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1155, 1110])).
% 0.93/0.86 tff(1157,plain,
% 0.93/0.86 (c3_1(a631)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[586, 1133])).
% 0.93/0.86 tff(1158,plain,
% 0.93/0.86 (c0_1(a631)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[597, 1133])).
% 0.93/0.86 tff(1159,plain,
% 0.93/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1160,plain,
% 0.93/0.86 (((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631))) <=> (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1161,plain,
% 0.93/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))))),
% 0.93/0.86 inference(monotonicity,[status(thm)],[1160])).
% 0.93/0.86 tff(1162,plain,
% 0.93/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.93/0.86 inference(transitivity,[status(thm)],[1161, 1159])).
% 0.93/0.86 tff(1163,plain,
% 0.93/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.93/0.86 inference(quant_inst,[status(thm)],[])).
% 0.93/0.86 tff(1164,plain,
% 0.93/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))),
% 0.93/0.86 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 0.93/0.86 tff(1165,plain,
% 0.93/0.86 ($false),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1164, 78, 1158, 1157, 1156, 1145, 1082, 1081, 1134, 1116, 539, 1084])).
% 0.93/0.86 tff(1166,plain,(hskp14 | c1_1(a604) | hskp4 | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.86 tff(1167,plain,
% 0.93/0.86 (hskp14),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1166, 381, 903, 230])).
% 0.93/0.86 tff(1168,plain,
% 0.93/0.86 (c0_1(a615)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[316, 1167])).
% 0.93/0.86 tff(1169,plain,
% 0.93/0.86 (~c1_1(a615)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1002, 1167])).
% 0.93/0.86 tff(1170,plain,
% 0.93/0.86 (c2_1(a615)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[305, 1167])).
% 0.93/0.86 tff(1171,plain,
% 0.93/0.86 (c0_1(a651)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1051, 1170, 1169, 1168, 381, 915])).
% 0.93/0.86 tff(1172,plain,
% 0.93/0.86 (hskp22),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[1059, 1171, 381])).
% 0.93/0.86 tff(1173,plain,
% 0.93/0.86 (~c3_1(a644)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[462, 1172])).
% 0.93/0.86 tff(1174,plain,
% 0.93/0.86 (~c2_1(a644)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[468, 1172])).
% 0.93/0.86 tff(1175,plain,
% 0.93/0.86 (~c0_1(a644)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[474, 1172])).
% 0.93/0.86 tff(1176,plain,
% 0.93/0.86 (c1_1(a644)),
% 0.93/0.86 inference(unit_resolution,[status(thm)],[481, 78, 1175, 1174, 1173, 198])).
% 0.93/0.86 tff(1177,plain,
% 0.93/0.86 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.93/0.86 inference(bind,[status(th)],[])).
% 0.93/0.86 tff(1178,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.86 inference(quant_intro,[status(thm)],[1177])).
% 0.93/0.86 tff(1179,plain,
% 0.93/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.86 inference(rewrite,[status(thm)],[])).
% 0.93/0.86 tff(1180,plain,
% 0.93/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(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) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1181,plain,
% 0.93/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1180])).
% 0.93/0.87 tff(1182,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.93/0.87 tff(1183,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.93/0.87 tff(1184,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1183, 1179])).
% 0.93/0.87 tff(1185,plain,(
% 0.93/0.87 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.87 inference(skolemize,[status(sab)],[1184])).
% 0.93/0.87 tff(1186,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1185, 1178])).
% 0.93/0.87 tff(1187,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1188,plain,
% 0.93/0.87 ((hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644)) <=> (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1189,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1188])).
% 0.93/0.87 tff(1190,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1189, 1187])).
% 0.93/0.87 tff(1191,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1192,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.93/0.87 tff(1193,plain,
% 0.93/0.87 (hskp5),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1192, 78, 1175, 1174, 1173, 1186, 1176])).
% 0.93/0.87 tff(1194,plain,
% 0.93/0.87 (~c1_1(a599)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[783, 1193])).
% 0.93/0.87 tff(1195,plain,
% 0.93/0.87 (c3_1(a599)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[748, 1193])).
% 0.93/0.87 tff(1196,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1197,plain,
% 0.93/0.87 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1198,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1197])).
% 0.93/0.87 tff(1199,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1198, 1196])).
% 0.93/0.87 tff(1200,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1201,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.93/0.87 tff(1202,plain,
% 0.93/0.87 (c0_1(a599)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1201, 78, 1195, 1075, 1078, 1175, 1173, 1194, 1074, 263, 1176])).
% 0.93/0.87 tff(1203,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1204,plain,
% 0.93/0.87 ((hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1205,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1204])).
% 0.93/0.87 tff(1206,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.93/0.87 tff(1207,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1208,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.93/0.87 tff(1209,plain,
% 0.93/0.87 ((~c3_1(a615)) | (~c1_1(a644))),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1208, 915, 78, 1168, 1170, 1175, 1174, 1014])).
% 0.93/0.87 tff(1210,plain,
% 0.93/0.87 (~c3_1(a615)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1209, 1176])).
% 0.93/0.87 tff(1211,plain,
% 0.93/0.87 (c2_1(a599)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[759, 1193])).
% 0.93/0.87 tff(1212,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1213,plain,
% 0.93/0.87 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1214,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1213])).
% 0.93/0.87 tff(1215,plain,
% 0.93/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1214, 1212])).
% 0.93/0.87 tff(1216,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1217,plain,
% 0.93/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.93/0.87 tff(1218,plain,
% 0.93/0.87 ($false),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1217, 78, 1170, 1211, 1195, 1175, 1174, 1169, 708, 1210, 1176, 1202])).
% 0.93/0.87 tff(1219,plain,(hskp4 | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.87 tff(1220,plain,
% 0.93/0.87 (hskp4),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1219, 903, 230])).
% 0.93/0.87 tff(1221,plain,
% 0.93/0.87 (~c2_1(a598)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[239, 1220])).
% 0.93/0.87 tff(1222,plain,
% 0.93/0.87 (~c1_1(a598)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[251, 1220])).
% 0.93/0.87 tff(1223,plain,
% 0.93/0.87 (~c0_1(a598)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[245, 1220])).
% 0.93/0.87 tff(1224,plain,
% 0.93/0.87 (hskp12),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[900, 87, 1017])).
% 0.93/0.87 tff(1225,plain,
% 0.93/0.87 (~c1_1(a609)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[93, 1224])).
% 0.93/0.87 tff(1226,plain,
% 0.93/0.87 (~c3_1(a609)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[110, 1224])).
% 0.93/0.87 tff(1227,plain,
% 0.93/0.87 (c2_1(a609)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[104, 1224])).
% 0.93/0.87 tff(1228,plain,
% 0.93/0.87 (c0_1(a651)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[884, 1227, 1226, 1225, 2])).
% 0.93/0.87 tff(1229,plain,
% 0.93/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1230,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1229])).
% 0.93/0.87 tff(1231,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1232,plain,
% 0.93/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1233,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | 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)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1232])).
% 0.93/0.87 tff(1234,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.93/0.87 tff(1235,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.93/0.87 tff(1236,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1235, 1231])).
% 0.93/0.87 tff(1237,plain,(
% 0.93/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(skolemize,[status(sab)],[1236])).
% 0.93/0.87 tff(1238,plain,
% 0.93/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1237, 1230])).
% 0.93/0.87 tff(1239,plain,
% 0.93/0.87 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1240,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1239])).
% 0.93/0.87 tff(1241,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1242,plain,
% 0.93/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.93/0.87 inference(bind,[status(th)],[])).
% 0.93/0.87 tff(1243,plain,
% 0.93/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(quant_intro,[status(thm)],[1242])).
% 0.93/0.87 tff(1244,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)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.93/0.87 tff(1245,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.93/0.87 tff(1246,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1245, 1241])).
% 0.93/0.87 tff(1247,plain,(
% 0.93/0.87 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(skolemize,[status(sab)],[1246])).
% 0.93/0.87 tff(1248,plain,
% 0.93/0.87 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1247, 1240])).
% 0.93/0.87 tff(1249,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1250,plain,
% 0.93/0.87 ((hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1251,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[1250])).
% 0.93/0.87 tff(1252,plain,
% 0.93/0.87 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[1251, 1249])).
% 0.93/0.87 tff(1253,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(1254,plain,
% 0.93/0.87 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 0.93/0.87 tff(1255,plain,
% 0.93/0.87 (hskp18 | (~c0_1(a651))),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1254, 78, 689, 730, 1227, 1225, 1226, 1248])).
% 0.93/0.87 tff(1256,plain,
% 0.93/0.87 (hskp18),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1255, 1228])).
% 0.93/0.87 tff(1257,plain,
% 0.93/0.87 (((~hskp18) | c3_1(a625)) <=> ((~hskp18) | c3_1(a625))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1258,axiom,((~hskp18) | c3_1(a625)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.93/0.87 tff(1259,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.93/0.87 tff(1260,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1259, 1257])).
% 0.93/0.87 tff(1261,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1260, 1257])).
% 0.93/0.87 tff(1262,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1261, 1257])).
% 0.93/0.87 tff(1263,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1262, 1257])).
% 0.93/0.87 tff(1264,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1263, 1257])).
% 0.93/0.87 tff(1265,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1264, 1257])).
% 0.93/0.87 tff(1266,plain,
% 0.93/0.87 ((~hskp18) | c3_1(a625)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1265, 1257])).
% 0.93/0.87 tff(1267,plain,
% 0.93/0.87 (c3_1(a625)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1266, 1256])).
% 0.93/0.87 tff(1268,plain,
% 0.93/0.87 (((~hskp18) | (~c1_1(a625))) <=> ((~hskp18) | (~c1_1(a625)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1269,plain,
% 0.93/0.87 (((~c1_1(a625)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a625)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1270,axiom,((~c1_1(a625)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.93/0.87 tff(1271,plain,
% 0.93/0.87 ((~hskp18) | (~c1_1(a625))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 0.93/0.87 tff(1272,plain,
% 0.93/0.87 ((~hskp18) | (~c1_1(a625))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 0.93/0.87 tff(1273,plain,
% 0.93/0.87 (~c1_1(a625)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1272, 1256])).
% 0.93/0.87 tff(1274,plain,
% 0.93/0.87 (((~hskp18) | (~c0_1(a625))) <=> ((~hskp18) | (~c0_1(a625)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1275,plain,
% 0.93/0.87 (((~c0_1(a625)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a625)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1276,axiom,((~c0_1(a625)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.93/0.87 tff(1277,plain,
% 0.93/0.87 ((~hskp18) | (~c0_1(a625))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 0.93/0.87 tff(1278,plain,
% 0.93/0.87 ((~hskp18) | (~c0_1(a625))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1277, 1274])).
% 0.93/0.87 tff(1279,plain,
% 0.93/0.87 (~c0_1(a625)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1278, 1256])).
% 0.93/0.87 tff(1280,assumption,(c0_1(a651)), introduced(assumption)).
% 0.93/0.87 tff(1281,assumption,(hskp7), introduced(assumption)).
% 0.93/0.87 tff(1282,plain,
% 0.93/0.87 (((~hskp7) | (~c0_1(a602))) <=> ((~hskp7) | (~c0_1(a602)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1283,plain,
% 0.93/0.87 (((~c0_1(a602)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a602)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1284,axiom,((~c0_1(a602)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.93/0.87 tff(1285,plain,
% 0.93/0.87 ((~hskp7) | (~c0_1(a602))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.93/0.87 tff(1286,plain,
% 0.93/0.87 ((~hskp7) | (~c0_1(a602))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1285, 1282])).
% 0.93/0.87 tff(1287,plain,
% 0.93/0.87 (~c0_1(a602)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[1286, 1281])).
% 0.93/0.87 tff(1288,assumption,(~c1_1(a625)), introduced(assumption)).
% 0.93/0.87 tff(1289,assumption,(~c0_1(a625)), introduced(assumption)).
% 0.93/0.87 tff(1290,plain,
% 0.93/0.87 (((~hskp7) | c3_1(a602)) <=> ((~hskp7) | c3_1(a602))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(1291,axiom,((~hskp7) | c3_1(a602)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.93/0.87 tff(1292,plain,
% 0.93/0.87 ((~hskp7) | c3_1(a602)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.93/0.87 tff(1293,plain,
% 0.93/0.87 ((~hskp7) | c3_1(a602)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1292, 1290])).
% 0.93/0.87 tff(1294,plain,
% 0.93/0.87 ((~hskp7) | c3_1(a602)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1293, 1290])).
% 0.93/0.87 tff(1295,plain,
% 0.93/0.87 ((~hskp7) | c3_1(a602)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1294, 1290])).
% 0.93/0.87 tff(1296,plain,
% 0.93/0.87 ((~hskp7) | c3_1(a602)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[1295, 1290])).
% 0.93/0.88 tff(1297,plain,
% 0.93/0.88 ((~hskp7) | c3_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1296, 1290])).
% 0.93/0.88 tff(1298,plain,
% 0.93/0.88 ((~hskp7) | c3_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1297, 1290])).
% 0.93/0.88 tff(1299,plain,
% 0.93/0.88 ((~hskp7) | c3_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1298, 1290])).
% 0.93/0.88 tff(1300,plain,
% 0.93/0.88 (c3_1(a602)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1299, 1281])).
% 0.93/0.88 tff(1301,plain,
% 0.93/0.88 (((~hskp7) | c2_1(a602)) <=> ((~hskp7) | c2_1(a602))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1302,axiom,((~hskp7) | c2_1(a602)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.93/0.88 tff(1303,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.93/0.88 tff(1304,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1303, 1301])).
% 0.93/0.88 tff(1305,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1304, 1301])).
% 0.93/0.88 tff(1306,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1305, 1301])).
% 0.93/0.88 tff(1307,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1306, 1301])).
% 0.93/0.88 tff(1308,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1307, 1301])).
% 0.93/0.88 tff(1309,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1308, 1301])).
% 0.93/0.88 tff(1310,plain,
% 0.93/0.88 ((~hskp7) | c2_1(a602)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1309, 1301])).
% 0.93/0.88 tff(1311,plain,
% 0.93/0.88 (c2_1(a602)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1310, 1281])).
% 0.93/0.88 tff(1312,assumption,(c3_1(a625)), introduced(assumption)).
% 0.93/0.88 tff(1313,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1314,plain,
% 0.93/0.88 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1315,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1314])).
% 0.93/0.88 tff(1316,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1315, 1313])).
% 0.93/0.88 tff(1317,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1318,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 0.93/0.88 tff(1319,plain,
% 0.93/0.88 ($false),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1318, 78, 730, 1312, 1311, 1300, 678, 1289, 1288, 1287, 778, 1280])).
% 0.93/0.88 tff(1320,plain,((~hskp7) | (~c3_1(a625)) | c0_1(a625) | c1_1(a625) | (~c0_1(a651))), inference(lemma,lemma(discharge,[]))).
% 0.93/0.88 tff(1321,plain,
% 0.93/0.88 (~hskp7),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1320, 1279, 1228, 1273, 1267])).
% 0.93/0.88 tff(1322,plain,
% 0.93/0.88 (^[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))))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(1323,plain,
% 0.93/0.88 (![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)))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[1322])).
% 0.93/0.88 tff(1324,plain,
% 0.93/0.88 (![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)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1325,plain,
% 0.93/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(1326,plain,
% 0.93/0.88 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[1325])).
% 0.93/0.88 tff(1327,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.93/0.88 tff(1328,plain,
% 0.93/0.88 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.93/0.88 tff(1329,plain,
% 0.93/0.88 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1328, 1324])).
% 0.93/0.88 tff(1330,plain,(
% 0.93/0.88 ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.93/0.88 inference(skolemize,[status(sab)],[1329])).
% 0.93/0.88 tff(1331,plain,
% 0.93/0.88 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1330, 1323])).
% 0.93/0.88 tff(1332,plain,
% 0.93/0.88 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1333,plain,
% 0.93/0.88 ((hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1334,plain,
% 0.93/0.88 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1333])).
% 0.93/0.88 tff(1335,plain,
% 0.93/0.88 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1334, 1332])).
% 0.93/0.88 tff(1336,plain,
% 0.93/0.88 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1337,plain,
% 0.93/0.88 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.93/0.88 tff(1338,plain,
% 0.93/0.88 (hskp19 | hskp7),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1337, 78, 1227, 1225, 1226, 1331])).
% 0.93/0.88 tff(1339,plain,
% 0.93/0.88 (hskp19),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1338, 1321])).
% 0.93/0.88 tff(1340,plain,
% 0.93/0.88 (((~hskp19) | (~c3_1(a627))) <=> ((~hskp19) | (~c3_1(a627)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1341,plain,
% 0.93/0.88 (((~c3_1(a627)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a627)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1342,axiom,((~c3_1(a627)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.93/0.88 tff(1343,plain,
% 0.93/0.88 ((~hskp19) | (~c3_1(a627))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.93/0.88 tff(1344,plain,
% 0.93/0.88 ((~hskp19) | (~c3_1(a627))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.93/0.88 tff(1345,plain,
% 0.93/0.88 (~c3_1(a627)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1344, 1339])).
% 0.93/0.88 tff(1346,plain,
% 0.93/0.88 (((~hskp19) | (~c2_1(a627))) <=> ((~hskp19) | (~c2_1(a627)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1347,plain,
% 0.93/0.88 (((~c2_1(a627)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a627)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1348,axiom,((~c2_1(a627)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.93/0.88 tff(1349,plain,
% 0.93/0.88 ((~hskp19) | (~c2_1(a627))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 0.93/0.88 tff(1350,plain,
% 0.93/0.88 ((~hskp19) | (~c2_1(a627))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1349, 1346])).
% 0.93/0.88 tff(1351,plain,
% 0.93/0.88 (~c2_1(a627)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1350, 1339])).
% 0.93/0.88 tff(1352,plain,
% 0.93/0.88 (((~hskp19) | c0_1(a627)) <=> ((~hskp19) | c0_1(a627))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1353,axiom,((~hskp19) | c0_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.93/0.88 tff(1354,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 0.93/0.88 tff(1355,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1354, 1352])).
% 0.93/0.88 tff(1356,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1355, 1352])).
% 0.93/0.88 tff(1357,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 0.93/0.88 tff(1358,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1357, 1352])).
% 0.93/0.88 tff(1359,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1358, 1352])).
% 0.93/0.88 tff(1360,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1359, 1352])).
% 0.93/0.88 tff(1361,plain,
% 0.93/0.88 ((~hskp19) | c0_1(a627)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1360, 1352])).
% 0.93/0.88 tff(1362,plain,
% 0.93/0.88 (c0_1(a627)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1361, 1339])).
% 0.93/0.88 tff(1363,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1364,plain,
% 0.93/0.88 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1365,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1364])).
% 0.93/0.88 tff(1366,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1365, 1363])).
% 0.93/0.88 tff(1367,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1368,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.93/0.88 tff(1369,plain,
% 0.93/0.88 ($false),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1368, 78, 730, 1362, 678, 1351, 1345, 253, 264, 273, 1238, 1228])).
% 0.93/0.88 tff(1370,plain,(hskp14 | c0_1(a598) | c1_1(a598) | c2_1(a598) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.93/0.88 tff(1371,plain,
% 0.93/0.88 (hskp14),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1370, 1223, 1222, 1221, 915])).
% 0.93/0.88 tff(1372,plain,
% 0.93/0.88 (c2_1(a615)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[305, 1371])).
% 0.93/0.88 tff(1373,plain,
% 0.93/0.88 (c0_1(a615)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[316, 1371])).
% 0.93/0.88 tff(1374,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1375,plain,
% 0.93/0.88 (((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1376,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1375])).
% 0.93/0.88 tff(1377,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.93/0.88 tff(1378,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1379,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.93/0.88 tff(1380,plain,
% 0.93/0.88 (~c3_1(a598)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1379, 78, 1373, 1372, 1223, 1222, 1221, 914, 904])).
% 0.93/0.88 tff(1381,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1382,plain,
% 0.93/0.88 (((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1383,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1382])).
% 0.93/0.88 tff(1384,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.93/0.88 tff(1385,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1386,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.93/0.88 tff(1387,plain,
% 0.93/0.88 (~c3_1(a604)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1386, 78, 1373, 1372, 903, 230, 1223, 1222, 1221, 914, 904])).
% 0.93/0.88 tff(1388,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1389,plain,
% 0.93/0.88 (((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1390,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604)))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[1389])).
% 0.93/0.88 tff(1391,plain,
% 0.93/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.93/0.88 inference(transitivity,[status(thm)],[1390, 1388])).
% 0.93/0.88 tff(1392,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(1393,plain,
% 0.93/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.93/0.88 tff(1394,plain,
% 0.93/0.88 ($false),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1393, 78, 903, 230, 1223, 1222, 1221, 198, 1387, 1380])).
% 0.93/0.88 tff(1395,plain,(c3_1(a615) | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.88 tff(1396,plain,
% 0.93/0.88 (c3_1(a615)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1395, 903, 230])).
% 0.93/0.88 tff(1397,plain,
% 0.93/0.88 ((~c3_1(a615)) | c0_1(a651)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1023, 915, 78, 689, 1373, 1372, 678, 1014])).
% 0.93/0.88 tff(1398,plain,
% 0.93/0.88 (c0_1(a651)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[1397, 1396])).
% 0.93/0.88 tff(1399,plain,
% 0.93/0.88 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(1400,plain,
% 0.93/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[1399])).
% 0.93/0.88 tff(1401,plain,
% 0.93/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(1402,plain,
% 0.93/0.88 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~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(V))) <=> ((~ndr1_0) | (~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(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~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(V))) | c2_1(U)) <=> ((~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(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.93/0.89 inference(bind,[status(th)],[])).
% 0.93/0.89 tff(1403,plain,
% 0.93/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.89 inference(quant_intro,[status(thm)],[1402])).
% 0.93/0.89 tff(1404,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.93/0.89 tff(1405,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.93/0.89 tff(1406,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1405, 1401])).
% 0.93/0.89 tff(1407,plain,(
% 0.93/0.89 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.89 inference(skolemize,[status(sab)],[1406])).
% 0.93/0.89 tff(1408,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1407, 1400])).
% 0.93/0.89 tff(1409,plain,
% 0.93/0.89 (~c1_1(a615)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1002, 1371])).
% 0.93/0.89 tff(1410,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1411,plain,
% 0.93/0.89 ((hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1412,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1411])).
% 0.93/0.89 tff(1413,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1412, 1410])).
% 0.93/0.89 tff(1414,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1415,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 0.93/0.89 tff(1416,plain,
% 0.93/0.89 (hskp12 | (~c0_1(a651))),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1415, 78, 689, 1373, 1372, 678, 1409, 1408])).
% 0.93/0.89 tff(1417,plain,
% 0.93/0.89 (hskp12),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1416, 1398])).
% 0.93/0.89 tff(1418,plain,
% 0.93/0.89 (~c3_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[110, 1417])).
% 0.93/0.89 tff(1419,plain,
% 0.93/0.89 (~c1_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[93, 1417])).
% 0.93/0.89 tff(1420,plain,
% 0.93/0.89 (c2_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[104, 1417])).
% 0.93/0.89 tff(1421,plain,
% 0.93/0.89 (hskp18),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1254, 78, 689, 730, 1420, 1419, 1418, 1248, 1398])).
% 0.93/0.89 tff(1422,plain,
% 0.93/0.89 (c3_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1266, 1421])).
% 0.93/0.89 tff(1423,plain,
% 0.93/0.89 (~c1_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1272, 1421])).
% 0.93/0.89 tff(1424,plain,
% 0.93/0.89 (~c0_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1278, 1421])).
% 0.93/0.89 tff(1425,plain,
% 0.93/0.89 (~hskp7),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1320, 1424, 1398, 1423, 1422])).
% 0.93/0.89 tff(1426,plain,
% 0.93/0.89 (hskp19 | hskp7),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1337, 78, 1420, 1419, 1418, 1331])).
% 0.93/0.89 tff(1427,plain,
% 0.93/0.89 (hskp19),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1426, 1425])).
% 0.93/0.89 tff(1428,plain,
% 0.93/0.89 (~c3_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1344, 1427])).
% 0.93/0.89 tff(1429,plain,
% 0.93/0.89 (~c2_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1350, 1427])).
% 0.93/0.89 tff(1430,plain,
% 0.93/0.89 (c0_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1361, 1427])).
% 0.93/0.89 tff(1431,plain,
% 0.93/0.89 ($false),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1368, 78, 730, 1430, 678, 1429, 1428, 1223, 1222, 1221, 1238, 1398])).
% 0.93/0.89 tff(1432,plain,(c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(1433,plain,
% 0.93/0.89 (c1_1(a604)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1432, 230])).
% 0.93/0.89 tff(1434,plain,
% 0.93/0.89 (~c3_1(a604)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[177, 78, 1433, 902, 230, 131])).
% 0.93/0.89 tff(1435,plain,
% 0.93/0.89 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.93/0.89 inference(bind,[status(th)],[])).
% 0.93/0.89 tff(1436,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(quant_intro,[status(thm)],[1435])).
% 0.93/0.89 tff(1437,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1438,plain,
% 0.93/0.89 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.93/0.89 inference(bind,[status(th)],[])).
% 0.93/0.89 tff(1439,plain,
% 0.93/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(quant_intro,[status(thm)],[1438])).
% 0.93/0.89 tff(1440,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.93/0.89 tff(1441,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.93/0.89 tff(1442,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1441, 1437])).
% 0.93/0.89 tff(1443,plain,(
% 0.93/0.89 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(skolemize,[status(sab)],[1442])).
% 0.93/0.89 tff(1444,plain,
% 0.93/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1443, 1436])).
% 0.93/0.89 tff(1445,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1446,plain,
% 0.93/0.89 ((hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1447,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1446])).
% 0.93/0.89 tff(1448,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1447, 1445])).
% 0.93/0.89 tff(1449,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1450,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.93/0.89 tff(1451,plain,
% 0.93/0.89 ($false),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1450, 78, 889, 689, 730, 902, 678, 230, 1444, 1434])).
% 0.93/0.89 tff(1452,plain,(hskp12 | c0_1(a604) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(1453,plain,
% 0.93/0.89 (hskp12),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1452, 87, 230])).
% 0.93/0.89 tff(1454,plain,
% 0.93/0.89 (c0_1(a651)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[886, 1453, 2])).
% 0.93/0.89 tff(1455,plain,
% 0.93/0.89 (~c3_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[110, 1453])).
% 0.93/0.89 tff(1456,plain,
% 0.93/0.89 (~c1_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[93, 1453])).
% 0.93/0.89 tff(1457,plain,
% 0.93/0.89 (c2_1(a609)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[104, 1453])).
% 0.93/0.89 tff(1458,plain,
% 0.93/0.89 (hskp18),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1254, 78, 689, 730, 1457, 1456, 1455, 1248, 1454])).
% 0.93/0.89 tff(1459,plain,
% 0.93/0.89 (~c1_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1272, 1458])).
% 0.93/0.89 tff(1460,plain,
% 0.93/0.89 (~c0_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1278, 1458])).
% 0.93/0.89 tff(1461,plain,
% 0.93/0.89 (c3_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1266, 1458])).
% 0.93/0.89 tff(1462,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1463,plain,
% 0.93/0.89 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1464,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1463])).
% 0.93/0.89 tff(1465,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1464, 1462])).
% 0.93/0.89 tff(1466,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1467,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 0.93/0.89 tff(1468,plain,
% 0.93/0.89 (~c2_1(a625)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1467, 78, 730, 1461, 678, 1460, 1459, 778, 1454])).
% 0.93/0.89 tff(1469,plain,
% 0.93/0.89 (~hskp7),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1320, 1460, 1454, 1459, 1461])).
% 0.93/0.89 tff(1470,plain,
% 0.93/0.89 (hskp19 | hskp7),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1337, 78, 1457, 1456, 1455, 1331])).
% 0.93/0.89 tff(1471,plain,
% 0.93/0.89 (hskp19),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1470, 1469])).
% 0.93/0.89 tff(1472,plain,
% 0.93/0.89 (~c3_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1344, 1471])).
% 0.93/0.89 tff(1473,plain,
% 0.93/0.89 (~c2_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1350, 1471])).
% 0.93/0.89 tff(1474,plain,
% 0.93/0.89 (c0_1(a627)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1361, 1471])).
% 0.93/0.89 tff(1475,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1476,plain,
% 0.93/0.89 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1477,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1476])).
% 0.93/0.89 tff(1478,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1477, 1475])).
% 0.93/0.89 tff(1479,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1480,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 0.93/0.89 tff(1481,plain,
% 0.93/0.89 ($false),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1480, 78, 730, 1474, 678, 1473, 1472, 1460, 1459, 1238, 1454, 1468])).
% 0.93/0.89 tff(1482,plain,(hskp14 | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(1483,plain,
% 0.93/0.89 (hskp14),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1482, 230])).
% 0.93/0.89 tff(1484,plain,
% 0.93/0.89 (c0_1(a615)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[316, 1483])).
% 0.93/0.89 tff(1485,plain,
% 0.93/0.89 (~c1_1(a615)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1002, 1483])).
% 0.93/0.89 tff(1486,plain,
% 0.93/0.89 (c2_1(a615)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[305, 1483])).
% 0.93/0.89 tff(1487,plain,
% 0.93/0.89 (hskp9 | (~c3_1(a615)) | c0_1(a651)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1023, 78, 689, 1016, 1015, 678, 1014])).
% 0.93/0.89 tff(1488,plain,
% 0.93/0.89 (~c3_1(a615)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1487, 1017, 1])).
% 0.93/0.89 tff(1489,plain,
% 0.93/0.89 (hskp4),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1051, 1017, 1015, 1016, 1026, 1])).
% 0.93/0.89 tff(1490,plain,
% 0.93/0.89 (~c2_1(a598)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[239, 1489])).
% 0.93/0.89 tff(1491,plain,
% 0.93/0.89 (~c1_1(a598)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[251, 1489])).
% 0.93/0.89 tff(1492,plain,
% 0.93/0.89 (~c0_1(a598)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[245, 1489])).
% 0.93/0.89 tff(1493,plain,
% 0.93/0.89 (~c3_1(a598)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1379, 78, 1016, 1015, 1492, 1491, 1490, 914, 1488])).
% 0.93/0.89 tff(1494,plain,
% 0.93/0.89 ($false),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[279, 78, 1492, 1491, 1490, 198, 1493])).
% 0.93/0.89 tff(1495,plain,(hskp9 | (~c0_1(a615)) | (~c2_1(a615)) | c1_1(a615) | c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(1496,plain,
% 0.93/0.89 (hskp9),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1495, 1, 1486, 1485, 1484])).
% 0.93/0.89 tff(1497,plain,
% 0.93/0.89 (c2_1(a604)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[159, 1496])).
% 0.93/0.89 tff(1498,plain,
% 0.93/0.89 (~c3_1(a604)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[177, 78, 1433, 1497, 230, 131])).
% 0.93/0.89 tff(1499,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1500,plain,
% 0.93/0.89 ((hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1501,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1500])).
% 0.93/0.89 tff(1502,plain,
% 0.93/0.89 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1501, 1499])).
% 0.93/0.89 tff(1503,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1504,plain,
% 0.93/0.89 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 0.93/0.89 tff(1505,plain,
% 0.93/0.89 (hskp28),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[1504, 78, 689, 730, 1433, 678, 230, 839, 1498])).
% 0.93/0.89 tff(1506,plain,
% 0.93/0.89 (c3_1(a595)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[399, 1505])).
% 0.93/0.89 tff(1507,plain,
% 0.93/0.89 (c2_1(a595)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[410, 1505])).
% 0.93/0.89 tff(1508,plain,
% 0.93/0.89 (c1_1(a595)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[421, 1505])).
% 0.93/0.89 tff(1509,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1510,plain,
% 0.93/0.89 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(1511,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[1510])).
% 0.93/0.89 tff(1512,plain,
% 0.93/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.93/0.89 tff(1513,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(1514,plain,
% 0.93/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))),
% 0.93/0.90 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.93/0.90 tff(1515,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1514, 78, 1508, 1507, 1506, 689, 730, 1433, 1497, 230, 131, 1])).
% 0.93/0.90 tff(1516,plain,(c0_1(a651) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(1517,plain,
% 0.93/0.90 (c0_1(a651)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1516, 230])).
% 0.93/0.90 tff(1518,plain,
% 0.93/0.90 (hskp12 | (~c0_1(a651))),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1415, 78, 689, 1484, 1486, 678, 1485, 1408])).
% 0.93/0.90 tff(1519,plain,
% 0.93/0.90 (hskp12),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1518, 1517])).
% 0.93/0.90 tff(1520,plain,
% 0.93/0.90 (~c3_1(a609)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[110, 1519])).
% 0.93/0.90 tff(1521,plain,
% 0.93/0.90 (~c1_1(a609)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[93, 1519])).
% 0.93/0.90 tff(1522,plain,
% 0.93/0.90 (c2_1(a609)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[104, 1519])).
% 0.93/0.90 tff(1523,plain,
% 0.93/0.90 (hskp18),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1254, 78, 689, 730, 1522, 1521, 1520, 1248, 1517])).
% 0.93/0.90 tff(1524,plain,
% 0.93/0.90 (~c1_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1272, 1523])).
% 0.93/0.90 tff(1525,plain,
% 0.93/0.90 (~c0_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1278, 1523])).
% 0.93/0.90 tff(1526,plain,
% 0.93/0.90 (c3_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1266, 1523])).
% 0.93/0.90 tff(1527,plain,
% 0.93/0.90 (~c2_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1467, 78, 730, 1526, 678, 1525, 1524, 778, 1517])).
% 0.93/0.90 tff(1528,plain,
% 0.93/0.90 (~hskp7),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1320, 1525, 1517, 1524, 1526])).
% 0.93/0.90 tff(1529,plain,
% 0.93/0.90 (hskp19 | hskp7),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1337, 78, 1522, 1521, 1520, 1331])).
% 0.93/0.90 tff(1530,plain,
% 0.93/0.90 (hskp19),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1529, 1528])).
% 0.93/0.90 tff(1531,plain,
% 0.93/0.90 (~c3_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1344, 1530])).
% 0.93/0.90 tff(1532,plain,
% 0.93/0.90 (~c2_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1350, 1530])).
% 0.93/0.90 tff(1533,plain,
% 0.93/0.90 (c0_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1361, 1530])).
% 0.93/0.90 tff(1534,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1480, 78, 730, 1533, 678, 1532, 1531, 1525, 1524, 1238, 1517, 1527])).
% 0.93/0.90 tff(1535,plain,(c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(1536,plain,
% 0.93/0.90 (~hskp9),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[148, 1535])).
% 0.93/0.90 tff(1537,plain,
% 0.93/0.90 (hskp12 | hskp10),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[900, 1536])).
% 0.93/0.90 tff(1538,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1537, 887, 87])).
% 0.93/0.90 tff(1539,plain,(hskp14 | c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(1540,plain,
% 0.93/0.90 (hskp14),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1539, 1])).
% 0.93/0.90 tff(1541,plain,
% 0.93/0.90 (c0_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[316, 1540])).
% 0.93/0.90 tff(1542,plain,
% 0.93/0.90 (c2_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[305, 1540])).
% 0.93/0.90 tff(1543,plain,
% 0.93/0.90 (~c1_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1002, 1540])).
% 0.93/0.90 tff(1544,plain,
% 0.93/0.90 ((~c0_1(a615)) | (~c2_1(a615)) | c1_1(a615) | c0_1(a651)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1495, 1536])).
% 0.93/0.90 tff(1545,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1544, 1543, 1542, 1, 1541])).
% 0.93/0.90 tff(1546,plain,(c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(1547,plain,
% 0.93/0.90 (hskp18),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1254, 78, 689, 730, 105, 94, 111, 1248, 1546])).
% 0.93/0.90 tff(1548,plain,
% 0.93/0.90 (~c1_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1272, 1547])).
% 0.93/0.90 tff(1549,plain,
% 0.93/0.90 (~c0_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1278, 1547])).
% 0.93/0.90 tff(1550,plain,
% 0.93/0.90 (c3_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1266, 1547])).
% 0.93/0.90 tff(1551,plain,
% 0.93/0.90 (~c2_1(a625)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1467, 78, 730, 1550, 678, 1549, 1548, 778, 1546])).
% 0.93/0.90 tff(1552,plain,
% 0.93/0.90 (~hskp7),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1320, 1549, 1546, 1548, 1550])).
% 0.93/0.90 tff(1553,plain,
% 0.93/0.90 (hskp19 | hskp7),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1337, 78, 105, 94, 111, 1331])).
% 0.93/0.90 tff(1554,plain,
% 0.93/0.90 (hskp19),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1553, 1552])).
% 0.93/0.90 tff(1555,plain,
% 0.93/0.90 (~c3_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1344, 1554])).
% 0.93/0.90 tff(1556,plain,
% 0.93/0.90 (~c2_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1350, 1554])).
% 0.93/0.90 tff(1557,plain,
% 0.93/0.90 (c0_1(a627)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1361, 1554])).
% 0.93/0.90 tff(1558,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1480, 78, 730, 1557, 678, 1556, 1555, 1549, 1548, 1238, 1546, 1551])).
% 0.93/0.90 tff(1559,plain,(~hskp12), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(1560,plain,
% 0.93/0.90 (hskp10),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1537, 1559])).
% 0.93/0.90 tff(1561,plain,
% 0.93/0.90 (hskp14),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[86, 1560])).
% 0.93/0.90 tff(1562,plain,
% 0.93/0.90 (~c1_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1002, 1561])).
% 0.93/0.90 tff(1563,plain,
% 0.93/0.90 (c2_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[305, 1561])).
% 0.93/0.90 tff(1564,plain,
% 0.93/0.90 (c0_1(a615)),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[316, 1561])).
% 0.93/0.90 tff(1565,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[1415, 78, 1559, 689, 1564, 1563, 678, 1562, 1408, 1546])).
% 0.93/0.90 % SZS output end Proof
%------------------------------------------------------------------------------